wOrcaFlex Manual Version 9.8a Orcina Ltd. Daltongate Ulverston Cumbria LA12 7AJ UK Telephone: E-mail: Web Site: +44 (0) 1229 584742
[email protected] www.orcina.com 1 w Contents CONTENTS 1 INTRODUCTION 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 11 Installing OrcaFlex Running OrcaFlex Parallel Processing Distributed OrcaFlex Orcina Licence Monitor Demonstration Version OrcaFlex Examples Validation and QA Orcina References and Links 11 13 14 15 15 15 15 15 15 16 2 TUTORIAL 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 21 Getting Started Building a Simple System Adding a Line Adjusting the View Static Analysis Dynamic Analysis Multiple Views Looking at Results Getting Output Input Data 21 21 21 22 22 23 23 23 24 24 3 USER INTERFACE 3.1 3.2 3.3 25 Introduction 25 3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 25 25 25 27 28 28 Program Windows The Model Model States Toolbar Status Bar Mouse and Keyboard Actions OrcaFlex Model Files 31 3.2.1 3.2.2 3.2.3 3.2.4 31 32 38 39 Data Files Text Data Files Simulation Files Relative Paths Model Browser 39 3.3.1 3.3.2 41 42 Model Browser Views Move Selected Objects Wizard 3 w Contents 3.4 3.5 Libraries 43 3.4.1 3.4.2 43 46 Menus 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.5.6 3.5.7 3.5.8 3.5.9 3.5.10 3.5.11 3.5.12 3.6 3.7 3.8 3.9 Using Libraries Building a Library 46 File Menu Edit Menu Model Menu Calculation Menu View Menu Replay Menu Graph Menu Results Menu Tools Menu Workspace Menu Window Menu Help Menu 46 48 48 49 50 51 51 51 52 52 53 53 3D Views 53 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 3.6.7 3.6.8 3.6.9 3.6.10 54 56 56 57 58 60 60 60 60 61 View Parameters View Control Navigating in 3D Views Shaded Graphics How Objects are Drawn Selecting Objects Creating and Destroying Objects Dragging Objects Connecting Objects Printing, Copying and Exporting Views Replays 61 3.7.1 3.7.2 3.7.3 3.7.4 62 62 63 63 Replay Parameters Replay Control Custom Replays Custom Replay Wizard Data Forms 65 3.8.1 3.8.2 65 66 Data Fields Data Form Editing Results 3.9.1 3.9.2 3.9.3 3.9.4 3.9.5 3.9.6 3.9.7 3.9.8 3.9.9 3.9.10 3.9.11 3.9.12 67 Producing Results Selecting Variables Summary and Full Results Statistics Linked Statistics Offset Tables Line Clashing Report Time History and XY Graphs Range Graphs Offset Graphs Spectral Response Graphs Extreme Value Statistics Results 4 67 68 69 69 69 70 70 71 72 73 73 73 w 3.9.13 Contents Presenting OrcaFlex Results 76 3.10 Graphs 3.10.1 3.11 3.12 3.13 3.14 3.15 76 Modifying Graphs 78 Spreadsheets Text Windows Workspaces Comparing Data Preferences 78 78 79 79 80 4 AUTOMATION 4.1 4.2 4.3 Introduction Batch Processing 83 83 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.2.8 83 84 85 85 88 94 95 95 Introduction Script Files Script Syntax Script Commands Examples of setting data Handling Script Errors Obtaining Data Names Automating Script Generation Text Data Files 4.3.1 4.3.2 4.4 83 97 Examples of setting data Automating Generation 97 103 Post-processing 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.4.7 4.4.8 4.4.9 4.4.10 105 Introduction OrcaFlex Spreadsheet Instruction Format Pre-defined commands Basic commands Time History and related commands Range Graph commands Data commands Instructions Wizard Duplicate Instructions 5 THEORY 5.1 5.2 5.3 5.4 5.5 5.6 119 Coordinate Systems Direction Conventions Object Connections Interpolation Methods Static Analysis 5.5.1 5.5.2 5.5.3 105 105 108 110 110 111 112 112 113 116 119 120 121 121 123 Line Statics Buoy and Vessel Statics Vessel Multiple Statics 123 126 127 Dynamic Analysis 127 5 w Contents 5.6.1 5.6.2 5.7 5.8 5.9 5.10 Calculation Method Ramping 128 130 Friction Theory Spectral Response Analysis Extreme Value Statistics Theory Environment Theory 130 133 134 136 5.10.1 5.10.2 5.10.3 5.10.4 5.10.5 5.10.6 Buoyancy Variation with Depth Current Theory Seabed Theory Seabed Non-Linear Soil Model Theory Morison's Equation Waves 5.11 Vessel Theory 5.11.1 5.11.2 5.11.3 5.11.4 5.11.5 5.11.6 5.11.7 5.11.8 5.11.9 5.11.10 136 137 137 138 143 144 151 Vessel Rotations RAOs and Phases RAO Quality Checks Wave Drift and Sum Frequency Loads Sea State Disturbance Stiffness, Added Mass and Damping Impulse Response and Convolution Manoeuvring Load Other Damping Current and Wind Loads 151 152 154 155 160 161 164 165 166 166 5.12 Line Theory 168 5.12.1 5.12.2 5.12.3 5.12.4 5.12.5 5.12.6 5.12.7 5.12.8 5.12.9 5.12.10 5.12.11 5.12.12 5.12.13 5.12.14 5.12.15 5.12.16 5.12.17 5.12.18 5.12.19 5.12.20 5.12.21 168 170 171 171 172 175 175 176 176 177 177 177 179 180 181 182 184 186 186 187 187 Overview Structural Model Details Calculation Stages Calculation Stage 1 Tension Forces Calculation Stage 2 Bend Moments Calculation Stage 3 Shear Forces Calculation Stage 4 Torsion Moments Calculation Stage 5 Total Load Line End Orientation Line Local Orientation Treatment of Compression Contents Flow Effects Line Pressure Effects Pipe Stress Calculation Pipe Stress Matrix Hydrodynamic and Aerodynamic Loads Drag Chains Line End Conditions Interaction with the Sea Surface Interaction with Seabed and Shapes Clashing 5.13 6D Buoy Theory 5.13.1 5.13.2 189 Overview Lumped Buoy Added Mass, Damping and Drag 6 189 191 w 5.13.3 5.13.4 5.13.5 5.13.6 Contents Spar Buoy and Towed Fish Added Mass and Damping Spar Buoy and Towed Fish Drag Slam Force Contact Forces 5.14 3D Buoy Theory 5.15 Winch Theory 5.16 Shape Theory 202 203 204 6 SYSTEM MODELLING: DATA AND RESULTS 6.1 6.2 6.3 Modelling Introduction Data in Time History Files Variable Data 6.3.1 6.4 6.5 External Functions 211 212 Statics Dynamics Integration & Time Steps Explicit Integration Implicit Integration Numerical Damping Response Calculation Results Post Calculation Actions Drawing Properties Report 213 214 215 215 217 217 218 218 218 223 223 Environment 6.5.1 6.5.2 6.5.3 6.5.4 6.5.5 6.5.6 6.5.7 6.5.8 6.5.9 6.5.10 6.5.11 6.5.12 6.5.13 6.5.14 6.5.15 6.5.16 6.5.17 6.5.18 6.5.19 6.5.20 6.5.21 207 207 208 210 General Data 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.4.6 6.4.7 6.4.8 6.4.9 6.4.10 6.4.11 192 195 197 201 223 Sea Data Sea Density Data Seabed Data Wave Data Data for Regular Waves Data for Random Waves Data for JONSWAP and ISSC Spectra Data for Ochi-Hubble Spectrum Data for Torsethaugen Spectrum Data for Gaussian Swell Spectrum Data for User Defined Spectrum Data for Time History Waves Data for User Specified Components Data for Response Calculation Wave Calculation Waves Preview Modelling Design Waves Setting up a Random Sea Current Data Wind Data Drawing Data 7 224 225 225 229 230 230 231 232 233 233 233 233 235 235 235 237 238 239 241 243 244 w Contents 6.5.22 6.5.23 6.5.24 6.6 6.7 249 251 Vessel Modelling Overview Vessel Data Vessel Types Importing Hydrodynamic Data Supports Modelling Vessel Slow Drift Vessel Response Reports Vessel Results 252 253 261 287 296 305 307 308 Lines 6.8.1 6.8.2 6.8.3 6.8.4 6.8.5 6.8.6 6.8.7 6.8.8 6.8.9 6.8.10 6.8.11 6.8.12 6.8.13 6.8.14 6.8.15 6.8.16 6.8.17 6.8.18 6.8.19 6.8.20 6.8.21 6.8.22 6.9 245 245 246 Solid Friction Coefficients Data Vessels 6.7.1 6.7.2 6.7.3 6.7.4 6.7.5 6.7.6 6.7.7 6.7.8 6.8 External Functions Results Wave Scatter Conversion 312 Line Data Line Types Attachments Rayleigh Damping P-y Models Code Checks Line Contact Line Results Drag Chain Results Flex Joint Results Line Setup Wizard Line Type Wizard Chain Rope/Wire Line with Floats Homogeneous Pipe Hoses and Umbilicals Modelling Stress Joints Modelling Bend Restrictors Modelling non-linear homogeneous pipes Line Ends Modelling Compression in Flexibles 6D Buoys 6.9.1 6.9.2 6.9.3 6.9.4 6.9.5 6.9.6 6.9.7 6.9.8 6.9.9 6.9.10 6.9.11 6.9.12 314 329 340 343 346 348 359 369 380 380 380 382 383 386 389 393 394 396 398 400 402 404 405 Wings Common Data Applied Loads Wing Data Wing Type Data Lumped Buoy Properties Lumped Buoy Drawing Data Spar Buoy and Towed Fish Properties Spar Buoy and Towed Fish Drag & Slam Spar Buoy and Towed Fish Added Mass and Damping Spar Buoy and Towed Fish Drawing Shaded Drawing 8 406 407 409 409 410 412 413 414 416 417 418 419 w 6.9.13 6.9.14 6.9.15 6.9.16 6.9.17 6.9.18 6.9.19 Contents Other uses External Functions Properties Report Results Buoy Hydrodynamics Hydrodynamic Properties of a Rectangular Box Modelling a Surface-Piercing Buoy 6.10 3D Buoys 6.10.1 6.10.2 6.10.3 431 Data Properties Report Results 431 432 432 6.11 Winches 6.11.1 6.11.2 6.11.3 6.11.4 6.11.5 6.11.6 6.11.7 6.11.8 433 Data Wire Properties Control Control by Stage Control by Whole Simulation Drive Unit External Functions Results 434 435 435 435 436 436 437 437 6.12 Links 6.12.1 6.12.2 438 Data Results 438 439 6.13 Shapes 6.13.1 6.13.2 6.13.3 6.13.4 6.13.5 6.13.6 6.13.7 440 Data Blocks Cylinders Curved Plates Planes Drawing Results 441 442 442 443 444 444 445 6.14 All Objects Data Form 445 7 MODAL ANALYSIS 7.1 7.2 449 Data and Results Theory 449 451 8 FATIGUE ANALYSIS 8.1 8.2 8.3 8.4 8.5 8.6 8.7 421 421 421 422 425 426 428 455 Introduction Commands Data Load Cases Data for Regular Analysis Load Cases Data for Rainflow Analysis Load Cases Data for Spectral Analysis Load Cases Data for SHEAR7 9 455 456 457 458 458 459 461 9 8.2 9.1.2.2 9.2.2 469 469 SHEAR7 VIVA 469 476 Time Domain Models 479 9.1.2.12 8.14 8.11 8.8 8.1 9.1 Frequency Domain Models 9.3 Wake Oscillator Models Vortex Tracking Models VIV Drawing 482 485 490 10 .15 Components Data Analysis Data S-N and T-N Curves Integration Parameters Results Automation Fatigue Points How Damage is Calculated 461 461 462 463 463 464 465 465 9 VIV ANALYSIS 9.10 8.1 9.13 8.w Contents 8. If you are new to OrcaFlex then please see the tutorial and examples. floating lines. However. This is the most important factor since OrcaFlex is a computation-intensive program and simulation run times can be long for complex models. Both 32 bit and 64 bit versions of Excel are supported although we strongly recommend the 64 bit version to avoid the severe constraints on memory usage of the 32 bit version. As much disk space as you require to store simulation files. A screen resolution of 1280×1024 or greater with 32 bit colour. OrcaFlex is also used for applications in the Defence. At least 4GB of memory.8a). If you have a multi-core system with a 64 bit version of Windows then you may benefit from fitting even more memory. 1. 11 . Results output includes animated replay plus full graphical and numerical presentation. For further details of OrcaFlex and our other software. A powerful processor with fast floating point and memory performance. A DirectX 9 compatible graphics card with at least 256MB memory for the most effective use of the shaded graphics facility. moorings. including all types of marine risers (rigid and flexible). etc. If installing from disc. A lumped mass element is used which greatly simplifies the mathematical formulation and allows quick and efficient development of the program to include additional force terms and constraints on the system in response to new engineering requirements. Installation To install OrcaFlex: You will need to install from an account with administrator privileges. especially on multi-core systems. installation and towed systems. Simulation files vary in size. Windows 7 or Windows 8. please contact Orcina or your Orcina agent. A multi-core system to take advantage of OrcaFlex's multi-threading capabilities. Copyright notice Copyright Orcina Ltd. a marine dynamics program developed by Orcina for static and dynamic analysis of a wide range of offshore systems. global analysis. 1987-2014. but can be hundreds of megabytes each for complex models. OrcaFlex is a powerful package and to get the best results we would recommend: A 64 bit edition of Windows 7 or later.w 1 Introduction.1 INSTALLING ORCAFLEX Hardware Requirements OrcaFlex can be installed and run on any computer that has: Windows Vista. modal analysis can be performed for either the whole system or for individual lines. All rights reserved. This is less important than processor performance but some aspects of OrcaFlex do perform better when more memory is available. Inputs include ship motions. The program can be operated in batch mode for routine analysis work and there are also special facilities for post-processing your results including fully integrated fatigue analysis capabilities. OrcaFlex makes extensive use of graphics to assist understanding. Both 32 bit and 64 bit versions of Windows are supported. OrcaFlex is a fully 3D non-linear time domain finite element program capable of dealing with arbitrarily large deflections of the flexible from the initial configuration. If you are using small fonts (96dpi) the screen resolution must be at least 1024×768. OrcaFlex can handle multi-line systems.exe program on the disc (on many machines this program will run automatically when you insert the disc). OrcaFlex provides fast and accurate analysis of catenary systems such as flexible risers and umbilical cables under wave and current loads and externally imposed motions. If you are using large fonts (120dpi) the screen resolution must be at least 1280×1024. In addition to the time domain features. regular and random waves. Then click on 'Install OrcaFlex'. insert the OrcaFlex installation disc and run the Autorun. Microsoft Excel (Excel 2010. RAOs can be calculated for any results variable using the Spectral Response Analysis feature. line dynamics after release. or later) in order to use the OrcaFlex automation facilities. Installing OrcaFlex INTRODUCTION Welcome to OrcaFlex (version 9. Oceanography and Renewable energy sectors. Then run the extracted file Setup. If you are using a local dongle. and save the licence files to the same folder.exe. It is. For details see the OrcaDongle help file.lic).com/Support/Dongle. If the driver is not present. Dongles labelled 'Nxxx' can be used in the same way as 'Hxxx' dongles. 'N' dongles can hold up to 10 OrcaFlex licences for use over a network. Does the dongle you are using have an OrcaFlex licence on it? Again. alternatively. Orcina Shell Extension When you install OrcaFlex the Orcina Shell Extension is also installed.lic (where xxx is the dongle number) and will be in the OrcaFlex installation folder. If OrcaFlex cannot find the dongle then this program may be used to check that the dongle is working correctly and has the expected number of licences. click on Read Me on the Autorun menu or open the file Installation Guide. with the error that it can't obtain a licence. You can then open an OrcaFlex file by simply double-clicking the filename in Explorer. allowing the program to be shared by multiple users. But we can only supply a new dongle in the case where the old dongle is returned to us. Dongle Troubleshooting We supply. This application monitors the OrcaFlex licences claimed on a network at any time and reports which machines and users are claiming licences for the various Orcina programs. The shell extension also provides file properties information. This integrates with Windows Explorer. what you have purchased or leased. then you should be able to copy the required file(s) from the root level of the OrcaFlex installation disc into the installation folder.pdf on the disc.sim) with OrcaFlex. is it plugged into your machine? If so. you can follow the link on our website to download the latest driver software from the dongle manufacturer. Warning: Orcina can normally resupply disks or manuals (a charge being made to cover costs) if they are lost or damaged. The OrcaDongle program is included on the OrcaFlex installation disc. you will need to wait until a licence becomes free before you can run OrcaFlex. It is also available for download from www. you can check this with OrcaDongle. If not. You will also need to install the OrcaFlex dongle supplied by Orcina. but they can also be used over a network. If they are. Windows will often do this installation automatically for you when you plug in the dongle. Users of network dongles may find the Orcina Licence Monitor to be useful. a dongle utility program called OrcaDongle. and possibly a number of licence files (. are all the licences in use? The Orcina Licence Monitor may be of use in determining this. Dongles are usually supplied as USB devices.orcina. instructions can be found in the Dongle directory on the OrcaFlex installation disc. See below for details. then please check the following. Dongles labelled 'Hxxx' (where xxx is the dongle number) must be plugged into the machine on which OrcaFlex is run. we can supply dongles with larger capacities on request. Do you have a licence file for the dongle you wish to access? This file will be named Nxxx. If you have any difficulty installing OrcaFlex please contact Orcina or your Orcina agent. in essence. is the dongle device driver installed? You can check this by running OrcaDongle. including information on network and silent installation. If you are using a network dongle. 12 . Extract the files from the zip file to some temporary location. Note: The dongle is effectively your licence to run one copy (or more. In the latter case the dongle should be installed by your network administrator. and you may choose to install it from the Autorun menu in the same way as OrcaFlex. and it should be treated with appropriate care and security. Diagnostics If OrcaFlex fails to start. but parallel port dongles are still available if required. For further details. a small hardware device that must be attached to the machine or to the network to which the machine is attached. you can choose to install the device driver when you install OrcaFlex. The dongle requires a device driver to be installed on any machine to which it is attached. Installing OrcaFlex If you have received OrcaFlex by e-mail or from the web you will have a zip file. if the dongle is enabled for more copies) of OrcaFlex. such as which version of OrcaFlex wrote the file and the Comments text for the model in the file.w Introduction. By default.lic or Hxxx.dat and . and associates the data and simulation file types (. If you lose your dongle you cannot run OrcaFlex. Dongles OrcaFlex is supplied with a dongle. with OrcaFlex. the hyphen character '-' can be used as an alternative to the '/' character.w Introduction.exe Filename Option1 Option2 … etc.e.yml) or simulation file (. Command Line Parameters OrcaFlex can accept various parameters on the command line to modify the way it starts up. Ideally. /NetworkDongle Only search for licences on a network dongle. Batch Calculation switches These switches allow you to instruct OrcaFlex to start a batch calculation as soon as the program has loaded. After starting up OrcaFlex will automatically open that file. This helps you share the licences with other users of that network dongle. select Start menu | Run… (or Windows key and 'R') and enter the text between the quotes (including the % characters). This is sometimes useful when using a network dongle since it allows you to leave full licences free for other users when you only need a statics-only licence. You can suppress this dialog using the following switch. are optional parameters that allow you configure the start-up behaviour. The program behaves the same as if the user clicks OK on that dialog without changing any module choices. please also email to us the diagnostics file named OrcLog. Filename is optional.txt which OrcaFlex will have written on failing to find a licence. The syntax is: OrcaFlex. If OrcaFlex finds a network dongle and there is a choice of which licences to claim from it. depending on your version of Windows). A full OrcaFlex licence is needed for dynamic analysis. if that is all you need. see below. one in local mode and connected to the local machine) and if none is found then it looks for a licence on a network dongle (i. To open this folder. Option2 etc.sim).2 RUNNING ORCAFLEX A shortcut to run OrcaFlex is set up on the Start menu when you install OrcaFlex (see Start\Programs\Orcina Software\ or the All Apps screen. The following switches allow you to modify this default behaviour.dat or . it first looks for a licence on a local dongle (i. "Orcina Software" group. This shortcut passes no parameters to OrcaFlex so it gives the default start-up behaviour. so that the full licence is left free for others to use when you do not need it yourself. For the first character of an option switch. 1. /LocalDongle Only search for licences on a local dongle. Module Choice switch This switch is only relevant if the dongle found is a network dongle and there is a choice of licences to claim from that dongle. You can specify your choice using the following command line switch: /DisableDynamics Choose the statics-only basic licence. Option1. This default behaviour can be changed by command-line parameters. The following switches are available: 13 . /DisableInteractiveStartup Do not display the Choose Modules dialog.e. For example if the network dongle contains both a full licence and a statics-only licence then you can choose to use the statics-only licence. This file can be found in the folder "%appdata%\Orcina\OrcaFlex". The Choose Modules dialog can be suppressed using command-line parameters. This can be useful if you have a local dongle but want to use a network dongle that has licences for more modules. If you do not specify all the choices then the program displays the Choose Modules dialog to ask for your remaining choices. Default Start-up OrcaFlex has two basic modules: full OrcaFlex and statics-only OrcaFlex. Running OrcaFlex If none of these help. then OrcaFlex displays a Choose Modules dialog to ask you which modules you want to claim. When you run OrcaFlex it looks for an Orcina dongle from which it can claim an OrcaFlex licence (either a full licence or a statics-only licence). then please contact us at Orcina with a description of the problem. Dongle Search switches By default the program searches first for a licence on a local dongle and then for a licence on a network dongle. By default. They can be any of the following switches. one in network mode and accessed via a licence manager over the network). for example by setting up your own shortcuts with particular parameter settings. If present it should be the name of an OrcaFlex data file (. If this is not suitable you can configure the start-up behaviour using command-line parameters. Any local dongle will be ignored. No search will be made for network dongles. interactively at least.exe. For example using the switch /ThickLines=5 forces OrcaFlex to draw all lines at a thickness of at least 5. The command line can contain more than one file list. The different versions of the DLL are both named OrcFxAPI.6 also installed OrcFxAPI. .exe and the 64 bit executable is named OrcaFlex64. is available in both 32 and 64 bit versions. The OrcaFlex DLL. Batch processing. /CloseAfterBatch Instructs the program to close once the batch is complete. Versions of OrcaFlex prior to 9. /BatchAnalysisStatics. If these parameters are missing then the program defaults to dynamic analysis. the 64 bit executable will not run on a 32 bit system. For up to date information on hardware choice for OrcaFlex please refer to www. All OrcaFlex automation capabilities are fully supported for both 32 and 64 bit. 14 . OrcaFlex can make good use of the additional processing capacity afforded by such machines. /LowPriority. The batch calculation will contain all the files specified on the command line (you can have more than one) in the order in which they are specified. ThickLines switch The /ThickLines switch allows you to specify a minimum thickness for lines drawn on OrcaFlex 3D View windows. Conversely. for models with more than one Line performance is significantly improved. The number of these threads (the thread count) defaults to the number of logical processors available on your machine. using all available processing resources. Text files within the file list will be treated as batch script files.dll to the Windows system directory. the main benefit of 64 bits is that this version can access more memory than the 32 bit version.e. fatigue analysis and OrcaFlex spreadsheet post-processing tasks process jobs and load cases concurrently. On a 64 bit system. For example /ThreadCount=1 forces OrcaFlex to use a single execution thread which has the effect of disabling parallel processing. You can use relative paths which will be relative to the working directory. The 32 bit executable is named OrcaFlex. Should you wish to change it you can use the Tools | Set Thread Count menu item. Thread count OrcaFlex manages a number of execution threads to perform the parallel calculations. the shortcuts and file associations are configured to execute the 64 bit version. performance is only improved for models with more than one Line object.dll. /NormalPriority. This means that. On a 32 bit system. 1. This is especially significant for machines with a very large number of processors. The installation program installs binary files (. This switch has been added to make OrcaFlex 3D Views clearer when projected onto a large screen.orcina. 32 and 64 bit OrcaFlex The installation package copies both 32 and 64 bit versions of the executables. /BatchAnalysisDynamics specify what type of analysis to perform to the specified files.dll. We recommend that automation of analysis be carried out using Distributed OrcaFlex or one of the programming interfaces.dll. /HighPriority. This default will work well for most cases. If no value is specified (i. OrcFxAPI. Parallel Processing /Batch Start a batch calculation as soon as the program has loaded. the shortcuts and file associations are configured to execute the 32 bit version.com/Support/Benchmark. even on a 32 bit system. /FileList instructs the program that any text files specified on the command line contain a list of files to include in the batch calculation. The available switches are /RealtimePriority. the switch is /ThickLines) then the minimum thickness is taken to be 2. However. The 64 bit version runs slightly quicker than the 32 bit version.lib) to <InstallationDir>\OrcFxAPI\Win32 and <InstallationDir>\OrcFxAPI\Win64 respectively.3 PARALLEL PROCESSING Machines with multiple processors or processors with multiple cores are becoming increasingly common. you will need to set it up yourself – the installation program does not do so. /AboveNormalPriority. /BelowNormalPriority. OrcaFlex performs the calculations of the model's Line objects in parallel. The thread count can also be controlled by a command line switch. ThreadCount switch The /ThreadCount switch allows you to set the number of execution threads used by OrcaFlex for parallel processing. Process Priority switches These switches determine the processing priority of OrcaFlex. However. If you wish to create a shortcut to the 32 bit version on a 64 bit system. this is no longer the case.w Introduction. Please refer to the OrcFxAPI help file for details of how to link to OrcFxAPI. as reported by the operating system. Note that the batch calculation switches are provided for backwards compatibility. 1.orcina.com/SoftwareProducts/OrcaFlex/Validation. print. Licence information: the dongle name.com/Support/DistributedOrcaFlex. export or copy to the clipboard.orcina. These examples can also be found at www. see the Introduction topic and the tutorial. 1. Other programs that use the OrcaFlex programming interface (OrcFxAPI) such as Distributed OrcaFlex and the OrcaFlex spreadsheet are also monitored. You can obtain information on each licence claimed that includes: Network information: the computer name.9 ORCINA Orcina is a creative engineering software and consultancy company staffed by mechanical engineers. Usually this is the OrcaFlex executable. As well as developing engineering software. Program information: which modules are being used.com/Support/OrcinaLicenceMonitor. so it allows you to see exactly how the program works. fluid mechanics and mathematical modelling. hydrodynamics. and the location of the program which has claimed the licence.4 DISTRIBUTED ORCAFLEX Distributed OrcaFlex is a suite of programs that enables a collection of networked. These example files are also available from www. marine and nuclear industries. Contact Details Orcina Ltd. the dongle type (network or local) and the time the licence was claimed. There are numerous example files provided on the demonstration disc.com/SoftwareProducts/OrcaFlex/Examples.orcina. OrcaFlex licensed computers to run OrcaFlex jobs. Daltongate Ulverston Cumbria LA12 7AJ UK 15 .7 ORCAFLEX EXAMPLES OrcaFlex is supplied with an examples disc containing a comprehensive collection of example files. and you cannot save files. transparently. In particular the demonstration version allows you to open any prepared OrcaFlex data or simulation file. naval architects. using spare processor time. but it can also be.orcina. for example.orcina.w Introduction. give them the demonstration version and copies of your OrcaFlex simulation files. To do this.com/SoftwareProducts/OrcaFlex/Examples. 1. network address and the user name. we offer a wide range of analysis and design services with particular strength in dynamics.8 VALIDATION AND QA The OrcaFlex validation documents are available from www. OrcaFlex can also make use of machines with multiple processors using parallel processing technology. If you open a simulation file then you can then examine the results.com/SoftwareProducts/OrcaFlex/Demo.orcina.5 ORCINA LICENCE MONITOR The Orcina Licence Monitor (OLM) is a service that monitors the current number of OrcaFlex licences claimed on a network in real time. 1.6 DEMONSTRATION VERSION For an overview of OrcaFlex. OLM can be downloaded from www. the version. The demonstration version of OrcaFlex has some facilities disabled – you cannot calculate statics or run simulation. mathematicians and software engineers with long experience in such demanding environments as the offshore. For more information about Distributed OrcaFlex please refer to www. Distributed OrcaFlex can be downloaded from this address. If you have the full version of OrcaFlex then you can use the demonstration version to show your customers your OrcaFlex models and results for their system. Otherwise the demonstration version is just like the full version. The demonstration version can be downloaded from www. 1. see replays of the motion etc. Distributed OrcaFlex 1. Excel when the licence is claimed by the OrcaFlex spreadsheet. 4561-4572. 39-45. Environmental Conditions and Environmental Loads. Fluid Mech.htm). 17-33. Prediction of Wave height and Period for a Constant Wind Velocity Using the JONSWAP Results. PhD Thesis University of Warwick. API. American Petroleum Institute. Recommended Practice for Planning. Offshore Technology Research Center (Texas A&M University) Final Project Report (http://www. Design. Chapman D A. Recommended Practice for Planning. API RP 2A-WSD. Submarine Pipeline Systems. 1991. 1962. 3rd Edition. Dynamic Risers. Position Mooring. Bellanger M. API RP 2SK. 70. 2001. Operation. Floating structures: A guide for design and analysis. OMAE.10 REFERENCES AND LINKS References API. American Petroleum Institute.gov/tarprojects/510. API RP 2RD. API. Aranha J A P. Bridge C. DNV-OS-F101. 9. API RP 2A-WSD. API Bulletin. Classification of Mooring Systems for Permanent Offshore Units. Cyclic Tests of Model Pipe in Kaolin. Ocean Engineering. ASME Journal of Applied Mechanics. ESDU 71016 ESDU International. British Standards. American Petroleum Institute. J. October 2010. Springer. Bureau Veritas.. API RP 1111.orcina. 1984. Digital Processing of Signals. No. Coles S. OTC 19494. 2009. 1970. Construction. 1998. 275. Dean R G. no. Dynamics of fixed marine structures.com/ContactOrcina. Casarella M J and Parsons M. No. 147-155. 60. PD 8010. Blevins R D. Chung J and Hulbert G M. For details please refer to www. Geophys. 1982. NR 493 R02 E. Fluid forces. DNV-RP-C205. API. 1. October 2010. 1989. 16 . August 2012. Aubeny C.com Web Site: www. American Petroleum Institute. Schiffstechnik. Laver K. 4. pressures and moments on rectangular blocks. 2000. Stream function representation of non-linear ocean waves. OTC 16628. The impulse response function and ship motions. 371-375.orcina. 2008. Centre for Marine and Petroleum Technology publication 101/98. Edited by Barltrop N D P. 2005. Wiley. 2006. Dirlik T. Application of computers in Fatigue Analysis. BSI. Code of practice for pipelines. A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method. An Introduction to Statistical Modelling of Extreme Values. 11. Design of Risers for Floating Production Systems and Tension-Leg Platforms. Cable Systems Under Hydrodynamic Loading.mms. Steel Catenary Riser Touchdown Point Vertical Interaction Models. A formula for wave drift damping in the drift of a floating body. DNV-OS-E301. 2002. DNV-OS-F201. 127. Biscontin G and Zhang J. Designing and Constructing Fixed Offshore Platforms – Working Stress Design. Res. 2005. 1985. Designing and Constructing Fixed Offshore Platforms – Working Stress Design. Forces on and Stability of a Cylinder in a Wake. Design and Analysis of Stationkeeping Systems for Floating Structures. API. Evans T. Cummins W E. Carter D J T. Modelling and Analysis of Marine Operations. API. 1. References and Links Telephone: +44 (0) 1229 584742 E-mail: orcina@orcina. 2004. American Petroleum Institute. Aubeny C. Oilfield Publications Limited. ESDU 71016. Part 2: Subsea pipelines. 1993. Marine Technology Society Journal 4. 1993. Seafloor interaction with steel catenary risers. Butterworth Heinemann for MTD. Towed Cable Behaviour During Ship Turning Manoeuvres. 1965. Clukey E. Ocean Engineering. 4. 2J. 2004. London. April 2011. 101-109. 2008. October 2010. Comparison of Analyses of Marine Drilling Risers. J. 1994. Barltrop N D P and Adams A J. CMPT. and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design). 27-44. DNV-RP-H103. 2004.w Introduction. J.com Orcina Agents We have agents in many parts of the world. Gaudin C and Randolph M. 9. 1998. Model Basin Testing of Flexible Marine Risers. Ocean Waves: The Stochastic Approach. Ship Research. 1977. Witherby & Co. 1981. slowly-varying forces on vessels in irregular waves. 1985. 1974. Kotik J and Mangulis V. ESDU 80025 ESDU International. Mechanical Engineering Science. Morison J R. 1995. Fatigue strength of welded structures. Applied Ocean Research. J. Coastal & Ocean Eng. OMAE Houston. Proc. On Prediction of Extreme Values. No 4. Port.389. Lamb H. No. 12. 1987. Second-order hydrodynamics applied to moored structures. and Schaaf S A. Oil Companies International Marine Forum. 1990. 15. Journal of Sound and Vibration. 3rd International Symposium on Cable Dynamics. Gregory R W and Paidoussis M P. ASCE. 111. Cambridge University Press. A high-order cnoidal wave theory. Proc Int Symp Dynamics of Marine Vehicles and Structures in Waves. O'Brien M D. 1970. Fenton J D. 581-586. OTC 7237. Ed. 293 Series A. 59-84. 1996. Johnson J W. No. References and Links ESDU 80025. 1998. 79. 1979. Proc 15th Coastal Engineering Conference. 1994. 1999. Interaction in Deep-Sea Riser Arrays. Published by the author at Hoerner Fluid Dynamics. 1995. Hydrodynamic forces and moments of streamlined bodies of revolution at large incidence. edited by B. Huse E. 1. ISBN 1 85573 013 8. 17 . 1993. 3-25. 1983. Chapter in "The Sea – Volume 9: Ocean Engineering Science". London. Schiffstechnik. Prediction of Wind and Current Loads on VLCCs. 291-301. Mechanical Engineering Science. 94. Personal communication – pre-print of chapter in forthcoming book on cnoidal wave theory. pressures and flow field velocities for circular cylindrical structures: Single cylinder with two-dimensional flow. M. Applied Ocean Research. Woodhead Publishing Ltd. Soc. Unstable oscillation of tubular cantilevers conveying fluid: Part 1:Theory. The force exerted by surface waves on piles. Hydrodynamics. 41. 97. 1950. Ochi M K and Hubble E N. Mean forces. Larsen C M. Norway. 85-103. Ochi M K. Malenica S et al. A state-of-the-art survey. A fifth-order Stokes theory for steady waves. Fluid Dynamic Drag. 216-234. 1994. Ochi M K. Mech Eng Publications Ltd. Newman J N. 1987. Sea loads on ships and offshore structures.Cambridge University Press. 9. J. On the joint distribution of wave periods and amplitudes in a random wave field. 17. A Model for Vortex Induced Oscillation of Structures. J. Petrol Trans AIME. 1973. Fossati F and Resta F. 301-328. R. Maddox S J. Trondheim. 361-368. Series A. Journal of Applied Mechanics. On the Kramers-Kronig relations for ship motions. 17.w Introduction. 2 nd edition. Falco M. Bishop RED and Price WG. Non-linear wave theories. Wave and current forces on a vertical cylinder free to surge and sway. Wiley: New York. NJ 08723. 12. MIT Press. J. 1968. 189. Fenton J D. 512-527. Articulated models of cantilevers conveying fluid: The study of a paradox. Marine Structures. Newman J N. Fenton J D. Fluid Mech. 9. 1998. 1932. Mathematical and Physical Sciences. 99-104. 1970. Shipbuilding Progress. Hartnup G C. Isherwood R M. J. No 2. 288-300. Second-order. 1976. London. 6th Edition. Faltinsen O M. Regulations relating to loadbearing structures in the petroleum activities. Hoerner S F 1965. 129-161. 1995. Ship Technology Research. Int. Fenton J D. No. 241-258. Waterway. 1993. NDP. Norwegian Petroleum Directorate. Iwan W D and Blevins R D. On the vortex induced vibration of submarine cables: Design optimization of wrapped cables for controlling vibrations. Dynamics of tubular cantilevers conveying fluid. Le MeHaute and D. Longuet-Higgins M S. Proceedings Royal Society London.. Flexible Riser Analysis – Comparison of Results from Computer Programs. Airey R G and Fraser J M. 1974. Marine Hydrodynamics. 79-90. Mueller H F. Paidoussis M P. Molin B. 1990. 1 (January). 29-37. USA. 47-50. The vortex-induced oscillation of non-uniform structural systems. Six-parameter wave spectra. Iwan W D. London. September 1974. 1991. Hanes. Cambridge University Press. 1962. Paidoussis M P and Deksnis E B. A Revised Parameterisation of the JONSWAP Spectrum. Elsevier Applied Science. Basic Ship Theory 3rd ed. OMAE paper 29315. Torsethaugen K and Haver S. ISOPE-2008-MWU10. 184-196. J. A discrete-vortex analysis of flow about stationary and transversely oscillating circular cylinders. 46-54. Houston. 1980. Article No. 811. Oxford. NPS-69SL79011. no. Energy Resources Technology. Saint-Marcoux J-F. 2007. 1951. Proc. J. Incompressible Aerodynamics. 2009 (www.orcina. van Nostrand. 1979. 1960.orcina. Canada. TN No N-1688.com/Resources/Papers/ISOPE2008-MWU-10. AIAA Journal. pressure and weight on pipe and riser deformations and stresses. Sarpkaya T. 1979. 1965. California. Quiggin P P. LowFrequency Damping and Response. Pode L. Randolph M and Quiggin P. J. Skjelbreia L. Revised edition. Wichers J E W. Applied Ocean Research. Editions Technip. Le comportement mecanique des risers influence des principaux parametres. Dynamics of Timoshenko beams conveying fluid. 1976. Time domain simulation of the 3D bending hysteresis behaviour of an unbonded flexible riser. 1981. Simplified double peak spectral model for ocean waves.pdf) Young A D.17. Rawson and Tupper. Tan Z. 11. No 4. A new definition of the rainflow cycle counting method. 1984. Coastal & Ocean Eng. Vibration Problems in Engineering. A Simulation Model for a Single Point Moored Tanker. Brendling WJ. 1984. 1987. BSP Professional Books. The influence of tension. Petroleum Technology. Rychlik I. Int.orcina. Paper No. Fatigue 9. ISOPE 2004 Touson. Sparks C P. 482. Lateral buckling of axially constrained pipes. Principles of Naval Architecture. Tucker M J. (www. DTMB Report. 2004-JSC-193. 399-401. Issue 1. 2008. Sarpkaya T. Recent Developments in the Analysis of Wave Drift Forces. Naval Postgraduate School. Blevins R D. Damping of moored floating structures. Standing RG. J. Non-linear hysteretic seabed model for catenary pipeline contact. no. 2009. (Chichester). Sobey R J. Wichers J E W. 2: Ship Dynamics and Design. 1961. 215224. 1987. 87-91. France. Mechanical Engineering Science.1955. Rienecker M M and Fenton J D. 1987. 1991. 1988. Roark R J. 6. Hendrickson J. Tables for Computing the Equilibrium Configuration of a Flexible Cable in a Uniform Stream. OMAE paper 79259. The Use of Anchors in Offshore Petroleum Operations. 1989. 1979. 18. 1967. edited by J P Comstock. 35. OTC 7489. Triantafyllou M S. 210-220. Taylor R and Valent P. Coastal Eng. Waves in Ocean Engineering. J. No 2. New York. Wilson D. Slowly oscillating mooring forces in single point mooring systems. ASCE 113. Society of Naval Architects and Marine Engineers. Fifth order gravity wave theory. 104. Quiggin P. 2007 (www.w Introduction. Shoaff R L. Port. Thwaites.com/Resources/Papers/OMAE2007-29315. Tucker et al. Sheldrake T. Goodwin P. Ellis Horwood Ltd. No 2. Naval Civil Engineering Laboratory (USA). 1984. Monterey. Thieke R J and Westberg R J. 1994. 1984. 5. Paper No. Yue D K P and Tein D Y S. OTC paper 5456. A Fourier approximation method for steady water waves. Inviscid Model of Two-Dimensional Vortex Shedding by a Circular Cylinder. Wave theories. Revue de l'Institut Francais du Petrol. 18 . Timoshenko S. 1987. Waterway. BOSS79 (Second International Conference on Behaviour of Offshore Structures). Palmer A C and Baldry J A S. Sparks C P. 2004. References and Links Paidoussis M P and Lathier B E. Puech A.pdf). 1193-1200. 565-587. 1984. Fluid Mech. 1283-1284. Shoaff R L. 79-0281R. Boundary Layers. Delft University Thesis. 687. Design Guide for Drag Embedment Anchors. 4th edition McGraw-Hill. Report no.com/Resources/Papers/OMAE2009-79259. Formulas for Stress and Strain. ISOPE Conference 2008. Vancouver. 106. Wu M. Nov 1974. J. Longman Scientific & Technical (Harlow). 119-137. 7th Conf. 119-121. 1974.pdf). Marcollo Tel: +1 713 255 0020 Email: shear7@amogconsulting. References and Links Suppliers of frequency domain VIV software SHEAR7 AMOG Consulting Inc.com VIVA JD Marine 11777 Katy Freeway.com 19 . 770 South Post Oak Lane.w Introduction. TX 77056 USA Attention: Dr. Suite 434 South Houston. Suite 505 Houston. TX 77079 USA Tel: +1 281 531 0888 Email: info@jdmarineus. H. . etc. For the moment we will leave the line properties (length. Figure: The OrcaFlex main window 2. you are presented with a 3D view showing just a blue line representing the sea surface and a brown line representing the seabed. to avoid confusion. The crosshair cursor reappears – move the mouse to a point just to the right of the vessel and click. select the vessel with the mouse. or other details. Using the mouse. As usual in Windows software. Do this as follows: 21 . Getting Started TUTORIAL 2. press and hold down the mouse button and move the mouse around. At the top of the screen are menus. At this point.2 BUILDING A SIMPLE SYSTEM To start with. The end of the line moves around following the mouse. we will build a simple system consisting of one line and one vessel only. On completion of the tutorial we suggest that you also look through the pre-run examples – see Example Files.) at their default values. click on the new vessel button on the toolbar. Place the cursor anywhere on the screen and click the mouse button. Move the mouse to a point close to the left-hand end of the line. Now press and hold down the mouse button and move the mouse around.1 GETTING STARTED This short tutorial gives you a very quick run through the model building and results presentation features of OrcaFlex. Release the mouse button. move to the right-hand end. click on the new line button .) 2. (To alter vessel vertical position. positioned at the sea surface. the line has a default set of properties and both ends are at fixed positions relative to the Global origin. nearly all actions can be done in several ways: here. and the cursor reverts to the pointer shape. mass. On starting up OrcaFlex.3 ADDING A LINE Now add a line. To select the vessel. (Final positioning to exact locations has to be done by typing in the appropriate numbers – select the line with the mouse and double click to bring up the line data form. The line appears as a catenary loop at the mouse position. but we will connect the left-hand end to the ship. and the line is redrawn at each position. This time the right-hand end of the line is dragged around. then double click to open the Vessel data window. we will usually only refer to one way of doing the action we want. the right-hand end lies above the water and the line hangs down into the water. move the cursor close to the vessel and click the mouse button – the message box (near the top of the 3D view) will confirm when the vessel has been selected. In this way. generally using the mouse.w 2 Tutorial. The cursor changes from the usual pointer to a crosshair cursor to show that you have now selected a new object and OrcaFlex is waiting for you to decide where to place it. click and drag. Using the mouse. you can put the ends of the lines roughly where you want them. a tool bar and a status bar arranged in the manner common to most Windows software. but remains at the sea surface.) Move the line ends until the left-hand end of the line is close to the bow of the ship. The vessel follows the mouse horizontally. A "ship" shape appears on screen. Leave the vessel positioned roughly as before with the line in a slack catenary. make sure you have selected the line. right or left.5 STATIC ANALYSIS Note: If you are running the demonstration version of OrcaFlex then this facility is not available. There are three shortcut keys which are particularly useful for controlling the view. Now select the vessel again and drag it around with the mouse. it is not always apparent that this has occurred. When this has happened. Edit the view parameters if you wish by positioning the cursor in the appropriate box and editing as required. Click on the line near the left-hand end. and the Static Analysis button changes to light grey to indicate that this command is no longer available. The message box at the left-hand end of the status bar tells you what is currently selected. You are offered the following choices: 22 . 2. 2. This also resets back to the default view. Warning: OrcaFlex will allow you to look up at the model from underneath. By judicious use of the buttons and scroll bars you should be able to find any view you like. You can move your view point up. not the vessel or the sea. If you have selected the wrong thing. the elevation angle is shown as negative in the title bar. (Note that you don't have to click at the end of the line in order to select it – anywhere in the left-hand half of the line will select the left-hand end. down. effectively from under the seabed! Because the view is isometric and all lines are visible. A rectangle on screen shows the area which will be zoomed to fill the window when the mouse button is released. you can alter the view with the mouse. to select that end of the line. Hold down the ALT key and left mouse button and drag. SHIFT+ALT+left mouse button zooms out – the existing view shrinks to fit in the rectangle. The SHIFT key reverses the action of the button. Close the 3D View and add a new one (use the Window|Add 3D View menu item).4 ADJUSTING THE VIEW The default view of the system is an elevation of the global X-Z plane – you are looking horizontally along the positive Y axis. The new window will have the default view centre and view size. and you can zoom in or out. Alternatively. Press the Reset button on the Edit View Parameters form. As a rule. Release the mouse and move it to the vessel. to indicate the connection.) 2. use the scroll bars at the bottom and right edges of the window. Adjusting the View 1. CTRL+E gives an elevation. Click on each of the top 3 buttons in turn: then click again with the SHIFT key held down. When editing the model. The appearance of the line will have changed a little. (CTRL+P and CTRL+E leave the view azimuth unchanged. CTRL+Q rotates the view through 90° about the vertical axis. The message box reports which line is being analysed and how many iterations have occurred. hold down the CTRL key and click. For example CTRL+P gives a plan view from above. using the view control buttons near the top left corner of the window. The view direction (the direction you are looking) is shown in the Window Title bar in azimuth/elevation form (azimuth=270. (See Static Analysis for more details). This opens a Results . click on the calculate statics button . try again.w Tutorial. Zoom out repeatedly until the model reappears. The message box will confirm the connection and. When the analysis is finished (almost instantly for this simple system) the Program State message in the centre of the Status Bar changes to read "Statics Complete". it is better to choose a point well away from any other object when selecting something with the mouse. elevation=0). or moving the view centre too far) there are a number of ways of retrieving it: Press CTRL+T or right click in the view window and select Reset to Default View. OrcaFlex uses a quick approximation to a catenary shape for general guidance only. The left-hand end of the line now moves with the vessel. To run a static analysis of the system. the triangle at the end of the line will now be the same colour as the vessel. This gives a more precise way of controlling the view and is particularly useful if you want to arrange exactly the same view of 2 different models – say 2 alternative configurations for a particular riser system. We can now examine the results of the static analysis by clicking on the Results button Selection window. If you want to move the view centre without rotating.) Now click the button on the 3D View to bring up the Edit View Parameters form. and this shape is replaced with the true catenary shape when static analysis has been carried out. If you should accidentally lose the model completely from view (perhaps by zooming in too close. To make all views replay together. Click the Start Replay button . To rearrange the screen and make best use of the space. Ignore the graph options for the moment. Alternatively. Dynamic Analysis Results in numerical and graphical form. The graph appears in a new window.5s and click OK. click Window and choose Tile Vertical (F4) or Tile Horizontal (SHIFT+F4). then click Table. then select Effective Tension at End A and click the Graph button. These 23 . To view more static analysis results repeat this process: click on the Results button and select as before. An animated replay of the simulation is shown in the 3D view window. 2. To remove an unwanted view simply close its view window. Results for all objects or one selected object.w Tutorial.8 LOOKING AT RESULTS Now click on the Results button . so OrcaFlex lets you "zoom" in and out in time. Now click again on Replay Parameters. Click again to add a third view. These are standard Windows operations which may be useful if you want to tidy up the screen without having to close a window down completely. with various further choices which determine what the table or graph will contain. the wave building and with it the motions of the system. Simulation time is shown in the Status bar. You are offered the following choices: Results as Tables or Graphs. Results for all objects or one selected object.7 MULTIPLE VIEWS You can add another view of the system if you wish by clicking on the View button . you can also call up Range Graphs of effective tension. If you are running the demonstration version of OrcaFlex then you cannot do this. As the simulation progresses. To exit from replay mode click on the Stop Replay button . top left. You can call up time histories of a wide range of parameters for most objects. click on Replay Parameters and adjust the speed. At the end of the simulation the replay begins again. and the 3D view shows the motions of the system as the wave passes through. set Replay Period to Latest Wave and click on the Continuous box to deselect. select Summary Results and All Objects. bend moment and many other variables. The animated replay is now much jerkier than before because fewer frames are being shown. Select Time History for any line. but instead you can load up the results of a pre-run simulation – see Examples. click on Replay Control and check the All Views box. you can minimise windows so that they appear as small icons on the background. Results for different objects are presented in different sheets. then begins again. You can then restart the animation by clicking on 'Start Replay' as before. 2. edit Interval to 0. A summary of the static analysis results is then displayed in spreadsheet form. etc. Just as you can "zoom" in and out in space for a closer view. Click on the Replay Parameters button . Each view can be manipulated independently to give. Use the view control keys and mouse as before to change the view. At the end of the wave period the replay pauses. Click the Run Dynamic Simulation button . Clicking repeatedly on this button steps through the replay one frame at a time – a very useful facility for examining a particular part of the motion in detail. Negative time means the wave is still building up from still water to full amplitude. Now click on the Replay Step button to pause the replay. Alternatively use the shortcuts CTRL+F and SHIFT+CTRL+F to make the replay faster or slower respectively. To slow down or speed up the replay. with various further choices which determine what the table or graph will contain. the status bar reports current simulation time and expected (real) time to finish the analysis. This opens a Results Selection window. For lines. or you can re-size them or move them around manually with the mouse. The replay consists of a series of "frames" at equal intervals of time. Click with the SHIFT key held down to step backwards. 2. curvature. simultaneous plan and elevation views. This means that you see the simulation start from still water. The replay period shown is at the end of the simulation and has duration of a single wave period. The default Replay Period is Whole Simulation. say.6 DYNAMIC ANALYSIS We are now ready to run the simulation. results tables. 2. Getting Output show maximum. To familiarise yourself with OrcaFlex. Finally. The manual also includes a range of examples which expand on particular points of interest or difficulty. or by clicking Print on the popup menu. This displays the data structure in tree form in the Model Browser. 24 . Detailed numerical results are available by selecting Summary Results.10 INPUT DATA Take a look through the input data forms. End of Tutorial We hope you have found this tutorial useful. This returns OrcaFlex to the reset state. Full Results. Alternatively use the question mark Help icon in the top right corner of the form. Statistics and Linked Statistics. Note: Printing and export facilities are not available in the demonstration version of OrcaFlex. in which you can edit the data freely. For details of a data item. either using copy and paste via the clipboard or else by exporting to a file. such as the colours used for drawing.) Now click on the Model Browser button . select the item with the mouse and press the F1 key. Many of the data items are self explanatory. again using the popup menu.w Tutorial. The results can be exported as Excel compatible spreadsheets for further processing as required.9 GETTING OUTPUT You can get printed copies of data. Results Post-Processing Extra post-processing facilities are available through Excel spreadsheets. Further numerical results are available in tabular form by selecting Summary Results. Statistics and Linked Statistics. Have a look around all the object data forms available to get an idea of the capabilities of OrcaFlex. Full Results. Time history and range graph results are also available in numerical form – select the variable you want and press the Values button. Start by resetting the program: click on the Reset button . system views and results graphs by means of the File | Print menu. (While a simulation is active you can only edit certain non-critical items. try building and running models of a number of different systems. 2. please remember that we at Orcina are on call to handle your questions if you are stuck. mean and minimum values of the variable plotted against position along the line. Output can also be transferred into other applications. Select an item and double click with the mouse to bring up the data form. other than the capacity of your computer. Spreadsheet and Text Windows may be tiled so that they sit side-by-side. any number of child windows can be placed which may be: 3D View Windows showing 3D pictorial views of the model Graph Windows showing results in graphical form Spreadsheet Windows showing results in numerical form Text Windows reporting status Additional temporary windows are popped up. you can save your model to a data file. Object names are not case-sensitive.1. buoys. a Status Bar and usually at least one 3D view. The model always has two standard objects: General contains general data. Each object has a name. a Tool Bar. Environment represents the sea.g. lines etc. such as Data Forms for each object in the model (allowing data to be viewed and modified) and dialog windows (used to specify details for program actions such as loading and saving files). The window caption shows the program version and the file name for the current model. Arranging Windows 3D View.1. For more details see Modelling and Analysis. Figure: The OrcaFlex main window Within this main window. such as Lines. At any time. The actions that you can perform at any time depend on the current Model State.3 Model States OrcaFlex builds and analyses a mathematical model of the system being analysed. such as title. units etc. Introduction USER INTERFACE 3. so Riser.1 INTRODUCTION 3. This behaviour is the same as for Windows file names. vessels. Graph. Vessels and Buoys. You can then use the Model Browser or the toolbar to add other objects to represent the parts of your system. the model being built up from a series of interconnected objects. 3. which can be any length.1. waves. seabed. 3.1 Program Windows OrcaFlex is based upon a main window that contains the Menus. current etc. to the number of objects you can add to the model. 25 .w 3 User Interface. While one of these temporary windows is present you can only work inside that window – you must dismiss the temporary window before you can use other windows. the menus or toolbar. but they must remain within the bounds of the main window. There is no limit. This model consists of a number of objects that represent the parts of the system – e.2 The Model OrcaFlex works by building a mathematical computer model of your system. The program rearranges the windows every time a new window is created. riser and RISER would all refer to the same object. by CLICKING on the Reset button. You cannot store the simulation to a file while simulating – you must pause the simulation first. Simulation Complete The simulation is complete. Calculating Statics OrcaFlex is calculating the statics position of the model. You can also store the part-run simulation to a file. the current state being shown on the status bar. You can use the Extend Dynamic Simulation facility if you wish to simulate for a further period of time. Introduction OrcaFlex works on the model by moving through a sequence of states. Simulating The dynamic simulation is running. You can abort the calculation by CLICKING the Reset button.g. The simulation results are available and you can store the results to a simulation file for later examination. No results are available. but it is paused. results etc. colours used).w User Interface. but only make minor changes (e. The results of the simulation so far are available and you can examine the model data. The results so far are available and you can examine the model data. available in each state. In Reset state you can freely change the model and edit the data. Simulation Paused There is a simulation active. 26 . Statics Complete The statics calculation is complete and the static position results are available. You are allowed to make changes to the model when in this state but if you make any changes (except for very minor changes like colours used) then the model will be automatically reset and the statics results will be lost. RESET Calculate Static Position Reset Calculating Statics Edit or Reset STATICS COMPLETE Reset Run Pause SIMULATION UNSTABLE Simulating SIMULATION Reset PAUSED Run Extend Simulation SIMULATION COMPLETE Figure: Reset Model States The states used are as follows: Reset The state in which OrcaFlex starts. The following diagram shows the sequence of states used and the actions. before significant changes to the model can be made. You must reset the model. 4. In Reset state. Button Action Equivalent Menu Item Open File | Open Save File | Save Model Browser Model | Model Browser New Vessel Model | New Vessel New Line Model | New Line New 6D Buoy Model | New 6D Buoy New 3D Buoy Model | New 3D Buoy New Winch Model | New Winch New Link Model | New Link New Shape Model | New Shape Calculate Statics Calculation | Single Statics Run Simulation Calculation | Run Dynamic Simulation Pause Simulation Calculation | Pause Dynamic Simulation Reset Calculation | Reset Start Replay Replay | Start Replay Stop Replay Replay | Stop Replay Step Replay Forwards Replay | Step Replay Forwards 27 .w User Interface. Typical model state flow To illustrate how model states work. Finalise the model. You may also want to examine the results up until the point at which the simulation became unstable. Steps (2) to (5) are repeated as required. please treat these results with caution – because the simulation eventually went unstable this indicates that the dynamic simulation may not have converged at earlier simulation times. 2. Run a final complete simulation (to reach Simulation Complete state) and generate reports using the results. here is an example of a typical working pattern: 1. Run a simulation and monitor the results during the simulation (in Simulating state). 6. If further changes to the model are needed then Reset the model and edit the model accordingly. open a new model from a data file or use the current model as the starting point for a new model. by CLICKING on the Reset button. You must reset the model. add or remove objects and edit the model data as required for the new model. This allows you to try and understand why the simulation has become unstable. 5. Steps (2) and (3) are repeated as required. Make any corrections to the model that are needed – this will automatically reset the model. Introduction Simulation Unstable The simulation has become unstable. 3. However. The selection of buttons available varies with the current Program State. Run a static analysis (to get to Statics Complete state) and examine the static position results. It is generally best to use a very simple model in the early stages of design and only add more features when the simple model is satisfactory.4 Toolbar The toolbar holds a variety of buttons that provide quick access to the most frequently used menu items. 3. In Reset state. perhaps improving the discretisation (for example by reducing the time step sizes or increasing the number of segments used for Lines). The simulation results are available and you can store the results to a simulation file for later examination.1. before significant changes to the model can be made. 5 Status Bar The Status Bar is divided into three fields: The Message Box This is at the left-hand end. When a statics calculation is done messages showing the progress of the calculation are shown in the message box.6 Mouse and Keyboard Actions As well as the standard Windows mouse operations such as selection and dragging OrcaFlex uses some specialised actions. The Program State Indicator In the centre and shows which state the program is in (see Model States). such as Copy. or ALT then F then X A number of frequently used menu items may also be accessed by shortcut keys. Keys on Main Window New model CTRL+N Open file CTRL+O Save file CTRL+S Open data SHIFT+CTRL+O Save data SHIFT+CTRL+S Help F1 Print F7 Show / hide Model Browser F6 Switch to Model Browser SHIFT+F6 Calculate static position F9 Run dynamic simulation F10 Pause dynamic simulation F11 Reset F12 28 . Error messages are also shown here. drag a box over the region you want to view.1.w User Interface. Export etc. or the current iteration number or simulation time. Graph or Text Window displays a popup menu of frequently used actions. To see all the messages from the statics calculation CLICK on the message box – the Statics Progress Window will then be opened.1. Example: To exit from the program (menu: File | Exit) press ALT+F then X. See the tables below. Clicking the right mouse button over a 3D View. 3. including: The global coordinates of the position of the cursor. in the current view plane. Distances when using the measuring tape tool. The shortcut keys are also displayed on the OrcaFlex menus. For wire frame 3D Views and Graph Windows the mouse can be used for zooming. such as CTRL+R to start a replay. The Information Box This is on the right. such as the name of the currently selected object. Simply hold the ALT key down and using the left mouse button. Paste. It shows additional information. We suggest that as you become more familiar with the operation of OrcaFlex that you memorise some of the shortcut keys for actions that you use frequently. All of the menu items can be selected from the keyboard by pressing ALT followed by the underlined letters. It shows information about the progress of the current action. Introduction Button Action Equivalent Menu Item Edit Replay Parameters Replay | Edit Replay Parameters Add New 3D View Window | Add 3D View Examine Results Results | Select Results Help Contents and Index Help | OrcaFlex Help 3. w User Interface. Introduction Open results selection form F5 Go to next window CTRL+F6 Go to previous window SHIFT+CTRL+F6 Tile windows vertically F4 Tile windows horizontally SHIFT+F4 Close selected window CTRL+F4 Close program ALT+F4 Keys on Model Browser View by Groups CTRL+ALT+G Edit data ENTER Move selected objects CTRL+M Rename object F2 Locate F3 Compare F8 Lock / Unlock objects CTRL+L Hide/Show CTRL+H Properties ALT+ENTER Cut CTRL+X Copy CTRL+C Paste CTRL+V Delete DELETE Switch to Main Window SHIFT+F6 Close browser F6 Keys on Data Forms Help F1 Go to next data form F6 Go to previous data form SHIFT+F6 Display data names for currently selected data item or table. F7 Display Properties Report ALT+ENTER Show connections report F8 Copy form F9 Export form F10 Open calculator F12 Data Selection Keys Go to next data item or table TAB Go to previous data item or table SHIFT+TAB Go to data item or table labelled with underlined letter ALT+LETTER Move around within a table ←→↑↓ Select multiple cells in table SHIFT + ← → ↑ ↓ SHIFT+HOME SHIFT+END Go to first or last column in table HOME END 29 . CTRL+wheel Pan SHIFT+drag 3D View Control Keys Elevation view CTRL+E Plan view CTRL+P Rotate viewpoint up (increment view elevation angle) CTRL+ALT+↑ Rotate viewpoint down (decrement view elevation angle) CTRL+ALT+↓ Rotate viewpoint right (increment view azimuth angle) CTRL+ALT+→ Rotate viewpoint left (decrement view azimuth angle) CTRL+ALT+← Rotate viewpoint +90° CTRL+Q Rotate viewpoint -90° SHIFT+CTRL+Q Zoom In CTRL+I. ALT+drag Zoom Out SHIFT+CTRL+I. SHIFT+ALT+drag Move view centre – mouse panning SHIFT+drag Move view centre – fine adjustment ←→↑↓ Move view centre – coarse adjustment CTRL + ← → ↑ ↓ Edit view parameters for current 3D view CTRL+W Reset to default view CTRL+T Set as default view SHIFT+CTRL+T Show entire model CTRL+ALT+T 3D View Control Keys (for wire frame graphics only) CTRL+Y Show / Hide local axes 30 . Introduction PGUP PGDN Go up or down table several rows at a time Data Editing Keys Enter new value for selected cell Type new value Edit current value of selected cell F2 Open drop-down list ALT + ↑ ↓ Move around within new data value being entered ← → HOME END Accept edit ENTER Accept edit and go to adjacent cell in table ↑↓ Cancel edit ESC Copy selected cell(s) to clipboard CTRL+C Paste from clipboard CTRL+V Fill selection from top (copy top cell down) CTRL+D Fill selection from left (copy leftmost cell to right) CTRL+R Fill selection from bottom (copy bottom cell up) CTRL+U SHIFT+CTRL+D Fill selection from right (copy rightmost cell to left) CTRL+L SHIFT+CTRL+R Insert new rows in table INSERT Delete selected rows from table DELETE Graph Control Keys Use default ranges CTRL+T Zoom ALT+drag. CTRL+wheel. CTRL+wheel.w User Interface. Text data file program version compatibility As mentioned above.yml). The program is not able to be as helpful and informative when working with text data files across program versions. binary data files contain all data whether or not it is active. or view if none selected. Text data files can be created without the use of OrcaFlex simply by entering text into a text editor. Text data files.w User Interface. as written by OrcaFlex. we cannot achieve the same level of compatibility as that for binary data files. The conversion process takes as input a text data file written with version A. The procedure is as follows: 31 . may not be compatible with other versions of the program. Binary data files have strong version compatibility features. Text data files are highly readable and self-documenting which makes them ideal for QA and archival purposes. text data files written by one version of the program. OrcaFlex Model Files Show / Hide node axes CTRL+ALT+Y Undo most recent drag CTRL+Z Lock/Unlock selected object CTRL+L Place new object SPACE or ENTER Edit selected object CTRL+F2 Cut selected object to clipboard CTRL+X Copy selected object. in general. On the other hand. The fact that the binary data file contains inactive data can be very useful and so. when OrcaFlex attempts to open a binary data file written by a later version of the program it is able to report informative compatibility warnings. Another application well suited to the use of text data files is automation. In general we would not advocate this approach to model building. For very simple systems it may be a practical approach but more complex models are usually much easier to build and inspect using the full capabilities and visualisation strengths of OrcaFlex. For example.2. say.dat) or text data files (. to clipboard CTRL+C Paste object from clipboard (followed by mouse click or ENTER to position the new object) CTRL+V Delete selected object DELETE Measuring tape tool SHIFT+CTRL+drag Replay Control Keys Start / Stop replay CTRL+R Replay faster CTRL+F Replay slower SHIFT+CTRL+F Step forwards one frame in the replay and pause CTRL+A Step backwards one frame in the replay and pause CTRL+B Edit replay parameters CTRL+D 3.1 Data Files OrcaFlex models are saved to either binary data files (. text data files can be very effective when making minor changes to existing models. there is a conversion utility available from the Tools menu. On the other hand. This is the main reason why we recommend using the binary data file for your model data and to use text data files principally for automation tasks.2 ORCAFLEX MODEL FILES 3. version B say. The output is a text data file compatible with the version that performs the conversion. if implicit time integration is selected in the model then all data relating to explicit time integration is excluded from the text data file. Using text data files for such minor variations of existing models makes it much easier to monitor just what has been changed. we would recommend that model building and development is performed using the binary data file. for example by using standard text differencing programs. For example. Whilst we strive to achieve as much compatibility as possible for text data files across program versions. In case you do need to open text data files prepared with a different version of the program. The conversion process makes use of the high levels of compatibility afforded by the binary data file. contain only data that is active in the model. 32 . Then a Line is created and named "Line1".w User Interface. Finally the section data are specified: three sections are created with varying section lengths and segment lengths. Version A saves the resulting model to a temporary file. press the Convert button. OrcaFlex Model Files A backup of the original text data file is saved to a directory named _textdatafilebackups.[120. Text data files can be opened and saved by OrcaFlex. Version B opens the temporary file.0. you provide the path to the OrcFxAPI DLL for version A. version A is specified to be OrcaFlex 9. Default values are used for all data which are not specified. Version A opens the text data file. A very simple example is shown below: General: StageDuration: . replacing the original version.[40. So. 2. To specify version A.50. version B is implicitly taken to be the version of the program that performs the conversion. Version B saves the resulting model in text data file format.0] . in binary data file format.[60.0 Lines: .2. in the example below. When you are reading to perform the conversion. Do not convert text data files that use the IncludeFile or BaseFile identifiers.10. 3. TargetSegmentLength: .0] . If you do convert such files. Figure: Text data file conversion tool The input text data files are added to the Files list.6. 5. As mentioned above.0 .2 Text Data Files Text data files are used to define and represent OrcaFlex models in a human readable and easily editable format. either using the Add Files button.0.0. the IncludeFile or BaseFile identifiers will be processed and lost. 10. Warning: You should only convert text data files that specify base case models.Name: Line1 Length.0] This example first defines a 10s build-up stage followed by stage 1 with 50s duration. or by drag and drop. TargetSegmentLength: . form a single block.Name: Umbilical. then a SPACE. We have found Notepad++ to be a very effective editor for YAML files. followed by a colon (:).net/ – Notepad++. However.8 . A second block follows Environment: containing a single name/value pair which defines the water depth. 10] 33 .yaml. Elements of a text data file The most basic element of a text data file is the name/value pair: UnitsSystem: SI The name (UnitsSystem) is written first. 60.0 Outline indentation is used to delimit blocks in a YAML file. New items in a list are introduced by a dash (-) followed by a SPACE. Note: YAML files must be saved with the UTF-8 character encoding. http://notepad-plus. YAML files are plain text files and so can be edited in any text editor. 40. http://www. YAML file format Text data files use a standard file format called YAML and should be saved with the . OrcaFlex itself uses indentation of two spaces when it writes YAML files. Indentation must be made with SPACE characters rather than TAB characters.[Line Type2. Names and values in YAML files can contain spaces and other punctuation: Lines: . and then the value (SI).) in the examples here has been added to aid readability. http://www. 2] .[Line Type1. bold.>.org/ – Official YAML homepage. It does not matter how many spaces are used so long as the indentation is consistent within each block. The names used in text data files are the same as used to identify data items in batch script files.[Line Type1.yaml.yml file extension.sourceforge.org/wiki/YAML – YAML page on Wikipedia.Name: Line1 LineType. Lists are commonly used to represent tables of data: Lines: .Name: Umbilical TopEnd: End A ContentsDensity: 0. More details on the YAML format and Notepad++ can be obtained from the following web sites: http://en. Notepad++ has a tabbed interface for easy editing of multiple files and has code folding and syntax highlighting facilities that work well with YAML files./?.w Note: User Interface. This block is ended by Environment: because it is not indented. To understand this better consider the following example: General: UnitsSystem: SI SimulationIntegrationMethod: Implicit Environment: WaterDepth: 80 The two lines immediately following General: which are indented by two spaces. 120.wikipedia.Name: 12" Riser . This concept.Name: Riser TopEnd: End B ContentsDensity: 0.<\| This example also contains a list. Length. upper . known as significant indentation. Items in a list can span more than a single line: Lines: . italic etc.Name: £"!$%^&*(){}[]=+-_#~'@:.org/spec/ – Complete technical specification of YAML. The YAML file format was chosen because it is extremely easy to read and write. is perhaps a little unusual as most data formats and programming languages use symbols to indicate the beginnings and ends of blocks. 5] . it is good practice to use the same indentation throughout a file. and is not a feature or requirement of text data files themselves. OrcaFlex Model Files The formatting (colour. Z components and we adopt the convention that these components appear in that order when grouped.8 .Name: Line1 Length.[Line Type1.Name: 3D Buoy1 InitialX: 0 InitialY: 0 InitialZ: 10 DragAreaX: 100 DragAreaY: 100 DragAreaZ: 30 PenWidth: 4 PenStyle: Solid PenColour: Yellow The majority of grouped data are X. Length and TargetSegmentLength which are interpreted in that order.) character is used as a separator. TargetSegmentLength. Code folding editors can help somewhat. 5. The IncludeFile identifier allows you to move data into a separate file which is then included in the main file: # File: C:\Desktop\main. LineType: .16 TargetLogSampleInterval: 0. 40] . YAML files may contain comments which are introduced by a hash (#) character followed by a SPACE. Line Type1] . Yellow] Without grouping the file would be significantly longer: 3DBuoys: .[40. 30] Pen: [4.[120. TargetSegmentLength indicates three columns of data. All subsequent text on the same line is comment and is ignored when OrcaFlex reads a text data file.Y. particularly if it contains vessel hydrodynamic data. 120] Some data are closely related to each other and can naturally be grouped in a text data file: 3DBuoys: . Comments are not preserved by OrcaFlex and any user comments in a manually edited YAML file opened with OrcaFlex will be lost if the file is saved.[Line Type2.Name: 3D Buoy1 InitialPosition: [0. but even so such files can be awkward to work with. 2.1 A text data file can be rather large.[60. 60] . Line Type1] . OrcaFlex Model Files The name LineType. Length: . in which case default values will be used: Lines: . if you wish. Length. 10] DragArea: [100. omit columns.Name: Line1 LineType. LineType. 0. Solid.[Line Type1.1 # Integration SimulationIntegrationMethod: Implicit ImplicitConstantTimeStep: 0. Note that you do not have to present the data in the same order as it appears in OrcaFlex.Name: FPSO 34 . Line Type2] You can.yml VesselTypes: . The comma (. The following example is equivalent to the previous example: Lines: . 10. 100. Comments are formatted in green in the following example: General: # Statics BuoysIncludedInStatics: Individually Specified # Dynamics StageDuration: .w User Interface. .. Everything else is in fact optional and can be omitted. Any references (e.g. The rest of the header contains a number of comments detailing the version of OrcaFlex which created the file. Similarly Vessels and 3D/6D Buoys appear before Lines.8 . Winches and Shapes so that any connection references (e.. a Line connected to a Vessel) can be ordered correctly. lines is the main body of the file and is known in YAML terminology as a document... these comments can be omitted. remainder of large file omitted . The YAML directive can be omitted.1) is known as the YAML directive and specifies which version of YAML the file adheres to. OrcaFlex Model Files IncludeFile: FPSO.g..yml in the same directory as the main text data file. A text data file saved by OrcaFlex contains some extra information: %YAML 1.1 # Integration SimulationIntegrationMethod: Implicit ImplicitConstantTimeStep: 0.. Lines referring to Line Types) must be ordered so that the referenced object appears before any references to it.Name: Vessel1 VesselType: FPSO The included file contains just the data for the vessel type: # File: C:\Desktop\FPSO. the file name etc.yml Created: 12:35 on 21/07/2009 User: jamie Machine: holly --- General: # Statics BuoysIncludedInStatics: Individually Specified # Dynamics StageDuration: . Again. In this example we have used a relative path and so the program will look for FPSO. using this approach can offer significant QA benefits.1 # # # # # Program: OrcaFlex 9.yml Vessels: . The section between the --.4 RefCurrentDirection: 180 . A YAML file can contain multiple documents. As well as making the main file shorter and more readable.3a File: C:\Desktop\untitled. OrcaFlex processes the file line by line in the order in which it appears in the file.lines but OrcaFlex has no special treatment for such multi-document files and all data are read into a single OrcaFlex model.yml Length: 240 RAOResponseUnits: degrees RAOWaveUnit: amplitude WavesReferredToBy: period (s) # . So Line Types appear before Lines in the file. The first line (%YAML 1. separated by --.and . Links.w User Interface.1 Environment: # Seabed SeabedType: Flat WaterDepth: 100 SeabedModel: Linear SeabedNormalStiffness: 100 # Current RefCurrentSpeed: 0.16 TargetLogSampleInterval: 0. 35 .. Ordering issues The order in which the data appear in a text data file is very important. For example. Perl.). This means that the text data file format. The common automation task of making systematic variations to a base case requires the ability to specify an existing object for which data modifications are to be made. as illustrated in the following example: BaseFile: base. This rule has implications for the order in which data are presented in the text data file. The way such data are handled can make certain automation tasks difficult. data relating to the explicit solver are inactive when the implicit solver is selected.8 Length[1]: 180 Delete: Connector When this text data file is loaded in OrcaFlex the program does the following: 1. Ruby etc. The BaseFile identifier differs from IncludeFile in that it is able to load either binary or text data files (IncludeFile only works with text data files).yml: # base.dat.dat Riser: ContentsDensity: 0. Opens the OrcaFlex binary data file named base. Standard text data files typically specify the entire model. See the Automation topic Text Data Files: Examples of setting data for examples of setting various model data items. starting from whatever state the model is in when the IncludeFile identifier is encountered. Consider the following example: General: InnerTimeStep: 0. On the other hand.yml and rotation. 4. OrcaFlex Model Files The other ordering issue relates to inactive data. Python. Inactive data cannot be specified in a text data file. facility for automating the production of text data files. combined with a text processing script language (e. 3.w User Interface. can form a very effective automation tool.Name: Vessel1 Lines: . Some specialist features have been included in the text data file to aid with automation tasks. Deletes the object named "Connector". In addition BaseFile clears all existing data in the model before loading the contents of the specified file. Data which are not currently available are known as inactive data. The OrcaFlex Spreadsheet provides a simple.Name: Line1 EndAConnection: Vessel1 36 . This is done using the object's name – in the example above the Riser: line performs this step. Sets the length of the first section of "Riser" to 180. base. The indexing syntax (Length[1] in the example) performs this task. located in the same directory as the text data file. Automation Text data files can easily be modified and/or generated by computer programs/scripts. In a similar vein it is a common requirement to modify data for certain items in a list or table without specifying the entire table. Note that as for batch script files the indices are always 1-based. Updating issues Some data items are interpreted with respect to the values of other data in the model – for example connection data. Sets the contents density for the OrcaFlex Line called "Riser" to 0. 2. Consider the following simple example consisting of two YAML input files.yml Vessels: .8. IncludeFile acts incrementally. The solution is to set the integration method before setting the time step: General: SimulationIntegrationMethod: Explicit InnerTimeStep: 0.g.01 This principle applies in general – you should set as soon as possible all data which influences whether other data are active.01 SimulationIntegrationMethod: Explicit Since the default integration method is the implicit solver the attempt to set the explicit time step (InnerTimeStep) will fail because it is inactive data. yet effective. as illustrated below: # rotation. carried out interactively in the GUI behave as expected. General: StageDuration: . but a few other data items in the program also suffer from this problem. that it was in before the rotation. because updates to the position and connection are postponed until the entire file loading process has been completed. In addition.yml BaseFile: base. it makes sense to use this feature as a matter of course for text data file automation. This can be achieved by setting a special attribute of the General object named UpdateModelWhilstReadingFile.yml General: UpdateModelWhilstReadingFile: True Line1: EndAConnection: Fixed Vessel1: InitialHeading: 45 Line1: EndAConnection: Vessel1 This setting is disabled by default because it does affect load performance. So the previous file could also be written as follows: Variables: BuildUp: 7 Stage1: =5*BuildUp General: StageDuration: . Expression evaluator OrcaFlex can understand mathematical expressions in text data files. These operators will invariably be used with the conditional function if(X. So for a very large YAML file it is not desirable to enable this.=4+3 .* / The exponentiation operator: ^ The comparison operators: < <= > >= <> = The comparison operators evaluate to 1 if the condition is satisfied. We have illustrated the point with connection data. with respect to global axes. In addition you can define named variables. The pre-defined constant pi can be used to express the value π. but leave the line in the exact same position.=Stage1 The expression evaluator supports the following operators: The basic arithmetic operators: + . The solution is to force the program to update the model fully after each item has been read from the YAML file.w User Interface. otherwise to 0. Z). This can be very counterintuitive since the same actions.yml BaseFile: base.yml Line1: EndAConnection: Fixed Vessel1: InitialHeading: 45 Line1: EndAConnection: Vessel1 The idea here is to rotate the vessel. the impact is negligible. OrcaFlex Model Files EndAX: 45 EndBX: 90 # rotation. However. a number of pre-defined functions are supported: Function Description 37 . Unfortunately the above files do not achieve this.=BuildUp . So.=5*(4+3) This file specifies a model with two stages of duration 7 and 35. for a small YAML variation file. Y. An expression is indicated by the presence of a prefixed equals sign. However. loads etc. This section is essentially a binary data file. discarding the lines once processed. Consequently the save process is not the inverse of the load process and any manual modifications to the input file will be overwritten when the file is saved by OrcaFlex. When saving a file OrcaFlex exports each object. The latest calculated state (positions. sinh(X) The hyperbolic sine of X cosh(X) The hyperbolic cosine of X tanh(X) The hyperbolic tangent of X asinh(X) The inverse hyperbolic sine of X acosh(X) The inverse hyperbolic cosine of X atanh(X) The inverse hyperbolic tangent of X Manually edited text data files Saving a text data file. This section is not present for static state simulation files. OrcaFlex Model Files Function Description abs(X) The magnitude or absolute value of X sgn(X) The sign of X. These are binary files containing the following sections: The model data. 3. OrcaFlex reads and interprets a text data file line by line to build the model incrementally. eX ln(X) The natural logarithm. Y. Simulation files can be generated in a number of different ways: 38 . This section allows static state results to be retrieved and also enables partially-run dynamic simulations to be continued. if the model created when this file is loaded is saved. The log file which contains results for a dynamic simulation. the text data file would contain data for all the objects imported by the BaseFile command. +1 if X>0. evaluates to X*180/π rad(X) Converts from degrees to radians.2. evaluates to Y if X≠0. In the short automation example above. or to discover data names and data structure for an object. the full data for the line Riser and other default data not specified in the input file. evaluates to X*π/180 sin(X) The sine of X cos(X) The cosine of X tan(X) The tangent of X asin(X) The inverse sine of X acos(X) The inverse cosine of X atan(X) The inverse tangent of X atan2(Y. including any default values. X) The two argument version of the inverse tangent. Y) XY. Z if X=0 round(X) The nearest integer to X floor(X) The largest integer not greater than X ceil(X) The smallest integer not less than X pow(X. log10 deg(X) Converts from radians to degrees.sim).) of the model. then editing it is a good way to create a base file for automation. Z) The conditional operator. 0 if X=0 rand A random number between 0 and 1 if(X. equivalent to the exponentiation operator X^Y sqrt(X) The square root of X exp(X) The exponential function. please be aware that this is a one way process. loge log10(X) Logarithm to base 10.w User Interface.3 Simulation Files Results from OrcaFlex calculations (statics or dynamics) are saved to simulation files (. evaluates to -1 if X<0. the parent file is the text data file.3 MODEL BROWSER At any time you can use the Model Browser to see what objects you have in your model.4 Relative Paths Relative paths are file names that do not specify the drive and directory.dat' or 'Project1\Temp.dat. 3. results can be post-processed from simulation files in a number of different ways: Interactively from the results form. From the batch processing form. . From the OrcaFlex programming interface. the parent file is the batch script file. OrcaFlex takes it to be either relative to the directory containing the 'parent file' or else relative to the Windows working directory when OrcaFlex was started. For file names in batch script files. From the OrcaFlex programming interface (OrcFxAPI). For file names in a text data file. or the Model | Model Browser menu item or use the keyboard shortcuts 39 . then using relative paths means that the script file will still work if you rename the directory or copy it to somewhere else. For example if all the files referred to in a batch script file are placed in (or below) the same directory as that script file. the parent file is the spreadsheet file.ftg file that you have opened or saved to.sim) that you have opened or saved to. For file names in OrcaFlex spreadsheets. 'Temp. For load case file names in a fatigue analysis. use the model browser button (F6 to open the model browser). To display the model browser.dat'). e. as follows. if there is no such file (because it is a new model or fatigue analysis that has not yet been saved) then there is no parent file so OrcaFlex uses the working directory. In all other cases OrcaFlex uses the working directory. Model Browser Interactively from the main OrcaFlex window. SHEAR7 file names. external function file names.dat' or 'c:\My Documents\Project1\Temp. For functional load case file names in an OrcaFlex model. 3. the parent file is the custom replay file. When you specify a relative path. Relative paths are usually more convenient. Similarly. Using post calculation actions. Which of these is used depends on the context.g. After a calculation (statics or dynamics) has performed then a simulation can be saved using the File | Save or File | Save As menu items.yml or . the parent file is the latest file (.2. For file names used by the Custom Replay Wizard. In the last two cases. For time history file names. From Distributed OrcaFlex. VIVA file names and imported 3D models for shaded graphics.dat' (as opposed to full pathnames such as 'c:\My Documents\Temp. the parent file is the OrcaFlex model file. From the OrcaFlex spreadsheet. post calculation action scripts. the parent file is the latest .w User Interface. Use double click to view or edit the object's data. show. Locked. Add Add a new object to the model. to show their contents. Several symbols are used in the list of objects: Categories can be opened. 40 . You can also import using drag and drop with the mouse. You can navigate the list and select the object required by clicking with the mouse. You can then Import objects from that second file into the current model. Model Browser Figure: Model Browser The Model Browser consists of a list of all the objects in the model. and its popup menu. To select more than one object you use the standard Windows key presses CTRL+CLICK to add to a selection and SHIFT+CLICK to extend a selection. or using the arrow keys and return. These objects cannot be dragged by the mouse in the 3D View. provide the following model management facilities. copy. Objects. Library The Library menu facilities allow you to open a second data file. to simplify viewing a complex model. locate) on many objects at once. Note: More than one object can be selected in the model browser. This allows you to perform the same action (e. or closed.g. hide. delete. arranged into categories according to object type. Model Browser Facilities The model browser menus.w User Interface. If the list is longer than the window then you can either enlarge the window or use the scroll bar. Groups View This view allows you to customise how the objects are arranged in the model browser. floating. Lock/Unlock Lock or unlock the selected object. Expand All/Collapse All Expands or collapses all top level containers in the current browser view. Lines etc. Hide/Hide All/Show/Show All Control whether the objects are drawn on 3D views. The browser has a number of folders containing objects of the same type.3. For example all the lines are contained in a folder called "Lines". Vessels. or by selecting it and pressing ENTER. Delete Delete the selected object from the model. You can add any number of browser groups to the browser. Dock Left. This is useful if you are working on the static position of one particular line – you can drag it up to the top of the list of lines. Objects can be reordered within a folder but they cannot be moved to a different folder. Groups can contain any number of objects or other groups.) or browser groups. Cut/Copy Cut or Copy the selected object to the clipboard. Dock Right Determines whether the Model Browser is a separate. or though the popup menu. This is useful in complex models where many objects are on the 3D view. Types View This is the traditional model browser view. The Compare Data configuration is used to perform the comparison. Compare Compares data for the two selected objects. Properties Shows the object properties form for the selected object. The objects can be simple OrcaFlex objects (e. You can switch between views by clicking on the model browser View | View by Groups menu item.1 Model Browser Views There are 2 ways of viewing objects in the model browser: by Types or by Groups.w User Interface. These groups are simply folders in the browser tree. This action can also be invoked by double-clicking an item. A corresponding command on the main form's Window menu switches focus back. top-level window or is docked inside the main OrcaFlex window. Rename Rename the selected object. Switch to Main Window The browser's Window menu enables you to switch focus to the main form without closing the browser window. Reorder You can use drag and drop with the mouse to reorder objects in the model. 3. Model Browser Edit Open the object's data form. Paste Paste an object from the clipboard into the model.g. so that it will be tackled first when OrcaFlex does the static analysis. The highlighting method is determined by the Locate Object Method preference. Move Selected Objects Opens the Move Selected Objects Wizard. Floating. 41 . In this way a hierarchical structure for the model can be created. Locate Finds and highlights the object in any open 3D view windows. g. This multiple selection is performed using the standard Windows key presses CTRL+CLICK to add to a selection and SHIFT+CLICK to extend a selection. the Groups View allows you to perform the same action (e. Groups can be renamed in the same way as other objects. Points The wizard shows a list of the points associated with each selected object.e. The wizard is most useful when you select multiple objects. Note: If your selection includes an item which contains other objects (e.g. As well as allowing you the freedom to structure your model however you like.2 Move Selected Objects Wizard This wizard allows you to move and rotate a number of objects en masse. hide. Select the entire model. links and winches with multiple connection points the list shows each connection point for that object. This works when the model browser is in Groups View mode. Objects can be added to a group by dragging the objects onto the group. If you wish to move 2 groups then select both of them (using CTRL+CLICK) and open the wizard. New Position Here you give a reference point and its new position. Groups can be dragged into other groups and so a hierarchical structure for the model can be created. You can do this in the model browser using CTRL+CLICK to add to a selection and SHIFT+CLICK to extend a selection. Here you specify a direction and distance which determine a position change. This is applied to all the points included in the move operation. Displacement For this method you specify a position change (i. For example select the Lines folder if you wish to move all the lines in a model. a displacement) which will be applied to all the points included in the move operation. Polar Displacement This method is similar to the Displacement method. Select this item if you wish to move all objects in the model. copy. The grouping structure is also used when cycling through data forms – clicking the Next button takes you to the next object in the groups view. For objects like lines. This allows you to move all objects in that group. Select a group. Then click Move Selected Objects on the browser's edit menu (also available from the popup menu). Selecting objects Before using the wizard you must select (in the model browser) the objects which you wish to move. This might be useful if you wanted to move only the End A line connection points and leave the End B connection points unchanged. Select an object type folder. There are a variety of ways in which you can do this. The list also shows the global coordinates of each point. We list a few of the more useful methods below: Select a single object.3.w User Interface. delete. show. 3. Select multiple objects. a group or an object type folder) then all objects contained by that item will be moved by the wizard. For each point you have the option of including or excluding it in the move operation. The first item in the model browser is titled "Model". To use the wizard you must first open the Model Browser and select the objects which you wish to move. This works when the model browser is in Types View mode. locate) on all objects in a group. vessels and shapes a single point is shown. Model Browser To add groups you select the Edit | Add Group menu item or use the popup menu. Move specified by There are 4 methods of specifying how the objects are moved. The same displacement is applied to all other points included in the move. 42 . This is easiest to do when the model browser is in Groups View mode. for example. Any number of objects can be added to a group in one operation by first selecting the objects and then dragging them. There is no limitation to the type of selections you can make. a group or a number of groups or even the entire model. For objects like buoys. buoys etc. You specify an angle of rotation and a central point about which the rotation is performed. Once such a library file has been built you can quickly build new models using the library – this gives faster model building and can make QA procedures safer. This is done by clicking the Move button. seabed direction etc. To do this click the open button file. To do this run OrcaFlex and open the model browser by clicking the model browser button F2. use the Library menu on the Model Browser. Now the model browser will look like: 43 on the model browser and select your data . Moving the objects Once you have decided which objects to include in the move and how the move is specified you are ready to actually move the objects. and this makes it easy to use the model browser to copy objects from one model to another. wave and current directions. For example.) is not included in the rotation. Note that any OrcaFlex data file can be opened as a library file.) stored in an ordinary OrcaFlex data file.1 Using Libraries Libraries allow you to easily import objects from one OrcaFlex model to another. lines.g.4. 3. or pressing Now you open your file as a library. Libraries Rotation This method rotates the included points in the horizontal plane. a library may contain all the standard Line Types that you use regularly. The model browser should look like: or the Model | Model Browser menu item. 3. Note that the environment data (e. To open a library file.4 LIBRARIES An OrcaFlex Library is a collection of OrcaFlex objects (line types.w User Interface. To do so select the required line types and click the import button . Note that you can select a number of objects and import them all in one go.w User Interface. You do this by using the standard Windows key presses CTRL+CLICK to add to a selection and SHIFT+CLICK to extend a selection. As an alternative to the import button the objects can be dragged from the right-hand pane to the left-hand pane or the Library | Import menu item can be used. If you do this the library will look like: 44 . Libraries We are now going to copy some objects from the right-hand pane to the left-hand pane. w User Interface. Now the model browser looks like: Some other points related to library files: 45 . Libraries Once you have imported the required objects you can close the library by selecting the Library | Close menu item on the model browser. When an object is imported from a library. but not edit. 3. This allows you to import objects from one OrcaFlex data file to another. Then you should close the model browser and save the data file by clicking the button on the main OrcaFlex form. Then you import the required objects as described in Using Libraries. You can also control the relative sizes of its two panes. To do this you would open the model browser and load your project data file as a library using the open button on the model browser. The Model menu gives access to the model building facilities. however. Starting with a blank model you can add objects in the usual way and set their data.5. The Workspace menu allows you to save and restore collections of view. you would want to reuse objects that had previously been created and used for a project. The Graph menu gives you access to facilities related to the currently active graph window. which can act as a title for the library. The Edit menu has data and object editing facilities. Variable Data Sources etc. You can set up as many library files as you wish. by dragging the right border of the left pane. In practice it is most convenient to put your commonly used OrcaFlex objects into files designated as OrcaFlex library files. and allows you to adjust the layout of your windows.5 MENUS OrcaFlex has the following menus: The File menu has the file opening and saving commands. Notes: Because they are OrcaFlex models. by double clicking it in the Model Browser or by selecting it and using the popup menu. You can view. The Window menu gives access to the various windows that are available. The Help menu leads to the various help documentation that is available.4. The Tools menu allows you adjust preferences and to lock or unlock objects. the current model may already have an object of that name. except perhaps for the General data Comment field. Attachment Types. For example you might have separate libraries for Line Types. You can re-size the model browser by dragging its border. The Results menu leads to the results facilities. You build a library file in the same way as you build a standard OrcaFlex data file. The View menu provides view control. The Replay menu provides replay control. 46 . Because the library file is just an ordinary OrcaFlex data file.1 File Menu New Deletes all objects from the model and resets data to default values.. 3. This data file can now be used as a library. In this case OrcaFlex automatically gives the object a new name based on the old name. This procedure can be repeated with a number of different data files until you have all the objects you wish to keep in the library.w User Interface. but these would not usually be used. including batch processing.2 Building a Library A library file is simply an OrcaFlex data file – you can use any OrcaFlex data file as a library. you can temporarily treat any OrcaFlex data file as a library. The Calculation menu provides commands for starting and stopping analyses. Menus Because library files are simply ordinary OrcaFlex data files. 3. Typically. The model browser's Library menu contains a list of the most recently used libraries. libraries contain General and Environment data. This allows you to edit the data of the objects in the library. the data for a library object. it can also be opened using File | Open. or you may choose to use just one library for everything. plus commands for printing or exporting data or results and managing libraries. graph and spreadsheet windows. Vessel Types. For this option to be available. Properties Displays the system file properties dialog for the current file. You can choose either the binary file format (. Spreadsheets or Text Windows. Most Recent Files List of the most recently used files. If a simulation file is specified then OrcaFlex reads just the data from it. Selected Printer Allows you to change the selected printer. Otherwise a data file will be saved.dat or .sim) – to the currently selected file name. If a file of that name already exists then you are asked whether to overwrite the file. You can also open an OrcaFlex file by dragging and dropping it onto the OrcaFlex window. For example if you have Windows Explorer running in one window and OrcaFlex running in another then you can ask OrcaFlex to open a file by simply dragging it from Explorer and dropping it over the OrcaFlex window. If you open a data file then OrcaFlex reads in the data. 47 . If a file of that name already exists then it is overwritten. If a file of that name already exists then you are asked whether to overwrite the file. either the Distributed OrcaFlex Viewer or Client must also be installed on the machine. Open Data Read the data from an existing data file or simulation file. Graphs. using extension .sim). replacing the existing model. Printer Setup Opens the Windows Printer Setup dialog.dat) or the text file format (. Compare Data Compares the data of two OrcaFlex models. Save Save an OrcaFlex file – either a data file (.yml) from the Save as type drop down list. allowing you to print 3D Views. To read just the data from a simulation file.yml.yml) or a simulation file (. you can use the Open Data menu item.yml) or a simulation file (. This is mainly intended to make it easier to find the full path for files with long names. Menus Open Open an OrcaFlex file – either a data file (. Print Display the Print form dialog. When saving data you can choose either the binary file format (. If calculation results (either statics or dynamics) are available then a simulation file will be saved.dat or .dat or . Save Data Save the data to the currently selected file name. Exit Close OrcaFlex. See Comparing Data for details.w User Interface. ignoring the simulation results in the file. Save As This is the same as Save but allows you to specify the file name to save to. whereas if you select a simulation file then OrcaFlex reads in both the data and the simulation results. Selecting an item on the list causes the file to be opened. Note: You cannot save a dynamic simulation while it is running – you must pause the simulation first. If a file of that name already exists then it is overwritten. Submit to Distributed OrcaFlex Submit the current file for processing by Distributed OrcaFlex. Save Data As This is the same as Save Data but allows you to specify the file name to save to.yml) from the Save as type drop down list.dat) or the text file format (. 3. the object is inserted at the next mouse CLICK position in a 3D view. from where it can be pasted into a word processor document. After selecting Paste. Select All Selects all the cells in a Spreadsheet. This can be used to duplicate an object several times within the model. you will probably need to put the text into a fixed space font since most of the data are in tables. graph or spreadsheet is copied to the clipboard. any connected objects are disconnected. Delete If the active window is a 3D View then the currently selected object is deleted. A three dimensional position is generated by finding the point where the mouse CLICK position falls on a plane normal to the view direction and passing through the View Centre. Show Connections Report Displays a spreadsheet containing information about all object connections in the model. The object is placed at the position of the next mouse CLICK within a 3D View. Cut Copies the current selection to the clipboard and then deletes it. 48 . If there is no currently selected object then the currently selected 3D view.5. You can then use Edit | Paste to create duplicate copies of the object.w User Interface. then that object is copied to the clipboard. Menus 3. and any graphs associated with the object are closed.2 Edit Menu Undo Drag Undo the most recent drag. Paste Insert object from clipboard. The data for the object is copied to the clipboard in text form. This is useful if you accidentally drag an object. The mouse cursor changes to the New Object symbol . text window. Copy If there is a currently selected object (see Selecting Objects). New Vessel New Line New 6D Buoy New 3D Buoy New Winch New Link New Shape Create new objects.3 Model Menu Model Browser Toggles the visibility of the Model Browser. Vessels are always placed initially at the sea surface. If the active window is a Spreadsheet then the selected cells are cleared. Before the object is deleted.5. If the current window is a Spreadsheet then the contents of the clipboard are pasted into the spreadsheet. Note: After pasting into a word processor. to the orientations found in the static analysis. The User Specified Starting Shape data are set to the calculated node positions.4 Calculation Menu Single Statics Start the single statics calculation (see Static Analysis). You can then set the end connection stiffness to their actual values. If the model is in the statics complete state then clicking the menu item sets the initial positions of buoys. During the simulation. This is sometimes useful to simplify a data file. vessels and free line ends it modifies data for all Lines in the following way: 1. which is shown as a minimised window icon.w User Interface. or to find out which types are in use. If the model is in the simulation paused or stopped state. For any line end with zero bend connection stiffness. 49 . Use Static Line End Orientations This menu item is only available after a successful static analysis. This is done as follows. OrcaFlex will automatically do a statics calculation first.g. In such cases you can use dynamics with no wave motion to find the static equilibrium position and then click Use Calculated Positions. 2. Delete Unused Variable Data Sources Deletes any variable data sources that are not in use. If necessary. or to find out which variable data sources are in use. Line Types. the end azimuth and end declination will be set to the azimuth and declination of the end node. vessels and free line ends to be the calculated static positions. as found by the static analysis. Progress and any error messages that occur are reported in the Statics Progress Window. This is useful when OrcaFlex statics fails to find an equilibrium configuration.5. then run the static analysis and then click the Use Static Line End Orientations menu item. This can be desirable when setting up a model. The Step 1 Statics Method is set to User Specified. Menus Delete Unused Types Deletes any types (e. the Status Bar shows the current simulation time and an estimate of the time that the simulation will take. and all 3D View windows and Graphs are updated at regular intervals. This action can be useful if you want to set the line end orientation to that which gives zero end moments when the line is in its static position. Run Dynamic Simulation Start a dynamic simulation (see Dynamic Analysis). Clicking the menu item sets the line end orientation data. 3. If the line includes torsion and the line end connection twist stiffness is zero. for all line ends in the model that have zero connection stiffness. Use Specified Starting Shape for Lines This menu item is an extension of Use Calculated Positions. This is sometimes useful to simplify a data file. As well as setting the initial positions of buoys. To do this first set the end connection stiffness values to zero. then clicking the menu item sets the initial positions of buoys and free line ends to be the latest positions in the simulation. since the positions found are likely to be good estimates for the next statics calculation. as found by the static analysis. Multiple Statics Starts the multiple offset statics calculation (see Multiple Statics).) that are not in use. then the end gamma will be set to the gamma of the end node. The statics calculation can be interrupted by CLICKING the Reset button. If a replay is active then clicking the menu item sets the initial positions of buoys and free line ends to be the positions at the latest replay time. Use Calculated Positions This menu item is available after a successful static iteration or when the simulation is finished or paused. Progress and any error messages that occur are reported in the Statics Progress Window. which is shown as a minimised window icon. Clump Types etc. The statics calculation can be interrupted by CLICKING the Reset button. As described above these positions are either the results of a static calculation or the results of a dynamic simulation. The simulation can be restarted by CLICKING the Run button. This feature is particularly useful for simulations run in batch mode or by Distributed OrcaFlex. Rotate Up / Down / Left / Right Change the view direction. for the active 3D view.5 View Menu Change Graphics Mode Toggles the graphics mode between wire frame and shaded. Toggle Shaded Fill Mode Toggles the shaded graphics fill mode between solid and mesh modes. by the view rotation increment. Reset to Default View Set the view parameters for the active 3D View to be the default view of the model. Zoom In / Zoom Out Click the zoom button to zoom in (decrease view size) or SHIFT+CLICK it to zoom out (increase view size). Note that data for the new stage. View Warnings Displays a window allowing you to review all warnings displayed by OrcaFlex during a calculation (statics or dynamics). Extend Dynamic Simulation This facility is only available when the current simulation is either paused or completed. the data for the new stage can be edited because the new stage has not yet started. e. 3. Reset Reset the model. Batch Processing Run a batch of analyses automatically while the program is unattended. This is particularly useful if you have a simulation that has not been run for long enough. individual) waves. without having to restart it from scratch.g. The model can then be edited or a new model loaded. are initially set to be the same as for the previous stage. Menus Pause Dynamic Simulation Pause the simulation. Plan Set the active 3D View to a plan view (Elevation = 90°).e. for the active 3D View. You are asked to specify the length of the new stage. However. Elevation Set the active 3D view to an elevation view (Elevation = 0°). You can then continue the simulation. discarding any existing results. for winch control and vessel prescribed motion. Rotate 90 / Rotate -90 Increase (or decrease) the view azimuth by 90°. Wave Scatter Conversion Opens the Wave Scatter Conversion form. It adds another stage to the current simulation.w User Interface.5. Edit View Parameters Adjust the View Parameters for the active 3D View. This facility converts a scatter table of sea states to a scatter table of regular (i. The wizard is only available when the current simulation is in Reset state. To save the results of a part-run simulation you need to pause it first. In these circumstances warnings are not displayed since to do so would require user intervention. 50 . without having to reset. Line Setup Wizard Opens the Line Setup Wizard. See Batch Processing for details. thus allowing you to watch the variables during a simulation. Graphs such as Time Histories. Show Entire Model Set the view parameters for the active 3D View so that the entire model will be displayed. Properties Opens the graph properties form (which can also be opened by double clicking the graph).5. See Replays for more details. 51 . the replay speed etc.5.8 Results Menu Select Results Display the results form which allows you to choose from the currently available selection of graphs and results tables. Step Replay Backwards Step the replay forwards or backwards one frame at a time. Export Video Exports the replay as either an AVI file or a PDF file. the time interval between frames. Replay Faster / Slower Increase or decrease the replay frame rate (replay speed). Start / Stop Replay Starts or stops the replay. Axes This submenu gives you control of the 3D View Axes Preferences.w User Interface. 3. Extreme Value Statistics (only available for time history graphs) Opens a new Extreme Value Statistics form. Click the button to step forwards. For more information see Replays. XY Graphs and Range Graphs may be created before a simulation has been run. Rainflow half-cycle Empirical Cumulative Distribution (only available for time history graphs) Opens a new rainflow half-cycle empirical cumulative distribution graph. such as the period of simulation to replay. Step Replay Forwards.6 Replay Menu Edit Replay Parameters Adjust the Replay Parameters. CLICK with SHIFT held down to step backwards. 3. 3. Empirical Cumulative Distribution (only available for time history graphs) Opens a new empirical cumulative distribution graph. Menus Set as Default View Set the default view of the model to be the view parameters of the active 3D View. Spectral Density (only available for time history graphs) Opens a new spectral density graph.7 Graph Menu Use Default Ranges Sets the graph axes to their original ranges Values Displays a spreadsheet containing the numerical values on which the graph is based.5. Fatigue Analysis Opens the Fatigue Analysis form. Modal Analysis Opens the Modal Analysis form. Most Recent Files List of the most recently saved workspaces in the directory which contains the current model. Set Thread Count Allows you to change the number of execution threads used by OrcaFlex for parallel processing. Menus Report Vessel Response Opens the Vessel Response form.10 Workspace Menu Open Workspace Opens a previously saved workspace file and restores the window layout described in that workspace file. Save Workspace Save the current window layout to a workspace file. Use folder default Applies the default workspace to the current model. Use file default. See Preferences.5. then the default for the file is used. Make default for this folder Makes the current window layout the default workspace for the current simulation file or for the current folder. it will be switched off. 52 . default axes ranges are chosen based on the extent of the curves shown in the graph. The Speed Index is also reported by Distributed OrcaFlex. It is always preferable. The default workspace for a simulation file will be restored whenever you open that file. Selecting an item on the list causes the workspace to be loaded. If a default workspace exists for a both a file and the folder containing the file. The Speed Index is calculated by performing a series of floating point calculations that are representative of the calculations performed by OrcaFlex itself. Lock / Unlock All Objects Locks or unlocks all objects in the model. Larger values correspond to faster machines. When the workspace is subsequently opened. 3.9 Tools Menu Lock / Unlock Selected Object Locking an object prevents it from being accidentally dragged or connected using the mouse on 3D views. 3. When the workspace is subsequently opened. Lock / Unlock Selected Object toggles the lock on the currently selected object.w User Interface. then it will be switched on. to compare actual OrcaFlex simulation run times for models representative of your typical use. The status of the object locks is shown by symbols in the Model Browser. If this option is not checked then graph axes ranges are not written to the workspace file. Preserve axes ranges If this option is checked then graph axes ranges will be written to the workspace file. This is useful if you have changed the window layout and wish to restore the default workspace layout without re-loading the model. Calculate Speed Index The Speed Index is an approximate measure of how quickly a machine can perform OrcaFlex simulations. respectively. Preferences Allows you to control various program settings so that you can customise the program to the way you prefer to work. Make default for this file. The default workspace for a folder will be restored whenever you open any simulation file in that folder.5. Convert Text Data Files This tool allows you to convert multiple text data files to be compatible with the current version of the program. If the lock is off. The value reported is meant only to give an estimate of the relative performance of similar machines. Locked Objects may still have their positions edited in the data Edit Forms. those axes ranges will be restored. if possible. Remove file default. Remove folder default Deletes the default workspace. If the lock is on. for example if you nudge the mouse slightly while trying to DOUBLE CLICK. shaded draws the model as solid objects with lighting. Orcina Home Page Opens the Orcina homepage (www. Tutorial Opens the help file at the start of the OrcaFlex tutorial. Having multiple views on screen allows you to watch different parts of the system simultaneously. About Displays a window giving the program version. enable you to switch focus between the main form and the model browser window. 53 . 3. API Documentation Opens the online documentation for the OrcaFlex programming interface. details about Orcina Ltd and various other miscellaneous information. What's New Gives a list of recent improvements and alterations to OrcaFlex.com). If a window is hidden under others it can be selected easily from this list. Updates for version 9. Keyboard Shortcuts Lists the keyboard shortcuts used by OrcaFlex. Two distinct types of 3D View are available: wire frame shows an isometric projection of the model. Examples Opens the help file at the introduction to the OrcaFlex Examples topics. Window List This is a list of all currently open windows. The program automatically tiles windows every time a new window is created or deleted. graph or spreadsheet) so that they fill the main window area and fit side by side without overlapping. 3D Views 3. Tile Horizontal Arranges all the windows (3D View. Statics Progress Displays the Statics Progress Window.5. shading.6 3D VIEWS 3D Views are windows showing a spatial representation of the model. Any available updates can be downloaded from this page. and the corresponding command on the model browser's Window menu.5.orcina. Tile Vertical. External Function Output Displays a window containing the diagnostics text produced by external functions. or to see different views at the same time (for example a plan and an elevation).w User Interface. perspective and hidden line removal.12 Help Menu OrcaFlex Help Opens the OrcaFlex on-line help system. 3. Switch to Model Browser This command.8a Opens the Orcina website at the support page for this version of the program.11 Window Menu Add 3D View Add another 3D View Window. for details. Note that this is the distance in the plane of the 3D view. the picture may be exported to a file or the windows clipboard. 54 . so that you can examine or edit its data. zoomed and panned to allow any aspect of the system to be viewed.6. or loading a simulation file. drag them around in the view and make connections between objects. For this reason. Also. 3D Views may be printed by selecting the view desired and using the print menu. Finally. Replays may be played in just one 3D View window. 3D Views Figure: A wire frame 3D View (left) alongside a shaded 3D View (right) 3D View windows may be rotated. The view is controlled by a number of View parameters – see View Parameters – and the caption of a 3D View window shows the current View Azimuth and View Elevation values.w User Interface. The objects in a 3D view are "live" in the sense that you can use the mouse pointer to select objects.1 View Parameters The view shown in a 3D view window is determined by the following parameters. which can be adjusted using the view control buttons or the Edit View Parameters item on the View menu. 3. Windows may be arranged by dragging their borders or using the Window | Tile Vertical/Horizontal menu items. where horizontal is taken to mean horizontal on the screen. Measuring Tape Tool (only available in wire frame mode) You can measure distance on a 3D view using the measuring tape tool. Note: When using the shaded view objects cannot be selected. Multiple view windows may be placed side-by-side so that you can view different parts of the system simultaneously or view from different angles (for example a plan and elevation view). Hold down the SHIFT and CTRL keys and then drag a line between any two points – the distance between them is displayed on the status bar. the wire frame view is most useful when building your model. If you DOUBLE CLICK on an object then the data form for that object appears. The angle to the horizontal is also displayed. Dragging Objects. 3D Views may be closed by CLICKING the cross at the top right-hand corner. dragged etc. irrespective of the view orientation. Further 3D View windows are added by using the Window | Add 3D View menu item or by CLICKING on the Add 3D View button on the tool bar. This allows you to build nonin-plane models on screen with the mouse. or in all of them simultaneously – see Preferences. Creating and Destroying Objects. a dynamic replay (animation) can be shown in one or more 3D View windows. while a scale bar in the view indicates the current View Size. After running a simulation. A replay shows a sequence of snapshots of the model taken at specified intervals throughout part or all of the simulation. See Selecting Objects. Object Connections. ) Mesh: the mesh triangles are transparent. Example: View Elevation +90° means looking in plan view from above. the same grid then being used to compute the disturbance at all other points on the sea surface. (You can specify some translucency for sea surface drawing. perspective and hidden line removal. The view shown is that seen when looking from this direction. This is only used if the sea state RAOs are being interpolated on direction and period only.w User Interface. by a viewer who is in that direction from the view centre.e. Relative to Global gives the view from a fixed camera position. Example: If the window on screen is wider than it is high. The elevation angle is then measured upwards (downwards for negative elevation angles) from there. 55 . where you want a view that tracks along with the overall movement of the model. Elevation and Gamma These determine the direction (from the view centre) from which the model is being viewed and the rotation about this direction. i. Shaded: the model is represented as a collection of solid objects with lighting. Window Size You can adjust the size of a 3D view window either by dragging the window border. View Azimuth = 270° (or -90°) means a standard elevation view. This parameter must be greater than zero. with only their edges visible. the control will be hidden otherwise. If None is selected then the sea surface will be drawn as if there were no disturbance. The default setting is Solid. seabed drawing and plane shapes. The latter is sometimes useful when exporting a view or exporting a replay video. if no vessels specify sea state disturbance then the list of disturbance vessels will be hidden. Graphics Mode Can be either of the following options: Wire frame: the model is represented using an isometric wire frame projection.0 then an object 100 units high would just fill the height of the window. or by setting its window size on the view parameters form. Only those vessels that specify sea state disturbance RAOs will be available for selection. since it gives you the ability to look inside and through objects that otherwise are solid. Disturbance Position Specifies the position on the sea surface at which the disturbance due to a vessel will be computed. shading. The Mesh option may sometimes be useful for complex models. 6D Buoy or Shape object in the model. The azimuth angle is measured from the x direction towards the y direction of the object we are relative to. since it makes it easier to export multiple files and produce videos with identical dimensions. Centre Defines the coordinates of the point that is shown at the centre of the window. looking along the Y axis. 3D Views Relative To The view parameters can be specified relative to Global or relative to any Vessel. The reason that the position is needed is that interpolation on direction and period only requires an initial position from which to construct its direction and period interpolation grid. Can be either of the following options: Solid: the mesh triangles used to represent the model are opaque. and View Size = 100. Disturbance Vessel Specifies that the sea surface will be drawn as if disturbed by the presence of this vessel. and View Elevation = 0°. Azimuth. This may be in global or relative coordinates. Fill Mode Available only for the shaded graphics mode. Relative to an object gives the view from a camera that moves with that object. giving the effect of solid objects. This can be useful when modelling systems such as towed cases. Size The diameter of the view area. The Gamma angle rotates about this view direction. It equals the distance represented by the smaller of the 2 sides of the view window. it starts with this default view. For more precise control you can set the view parameters explicitly using the View Parameters form. Rotating Rotating in 3D Views can be achieved by a variety of means: Drag the 3D View with the CTRL key held down. Use these cursor keys with the CTRL key held down to effect larger shifts. 3. CTRL+E. For shaded views only you can rotate about the viewer position (as opposed to rotating about the view centre) by holding down the ALT key (as well as the CTRL key) whilst dragging. Elevation. Rotate Left or Rotate Right menu items or shortcut keys CTRL+ALT+ ↑ ↓ ← →. first set up a 3D View to the default view that you want and then use the Set as Default View command (on the view menu or popup menu). Move up and down with the PGUP and PGDN keys. 56 . You can set an existing 3D view to the default view by using the Reset to Default View command (on the view menu or popup menu). Turn the wheel to scroll the 3D view up and down. Whenever a new 3D view is created. Edit the View Centre in the View Parameters form. Rotate 90 or Rotate -90 menu items or shortcut keys CTRL+P. CTRL+Q and SHIFT+CTRL+Q. 3D Views Default View Each model has its own default view parameters that are saved with the model data. Turn it with the CTRL key held down to zoom in or out on the location at which the mouse is currently pointing. To set the default view parameters. Edit the View Azimuth and View Elevation in the view parameters form. As an alternative you can use the calculated based on the model extent option which results in a default view that is sized so that the entire model will be displayed. We call this direct manipulation of the view centre panning. Finally.3 Navigating in 3D Views Moving Moving in 3D Views can be achieved by a variety of means: Drag the 3D View with the SHIFT key held down. Use the rotate buttons . 3D views can also be controlled using the View menu and various shortcut keys – see Mouse and Keyboard Actions and Navigating in 3D Views. Use the cursor keys ↑ ↓ ← →.6.w User Interface.2 View Control You can adjust the view in a 3D view window using the view control buttons: Button + SHIFT + SHIFT + SHIFT Menu Item Shortcut Action View | Rotate Up CTRL+ALT+↑ Increase view elevation View | Rotate Down CTRL+ALT+↓ Decrease view elevation View | Rotate Right CTRL+ALT+→ Increase view azimuth View | Rotate Left CTRL+ALT+← Decrease view azimuth View | Zoom In CTRL+I Zoom in View | Zoom Out SHIFT+CTRL+I Zoom out View | Change Graphics Mode CTRL+G Changes graphics mode View | Edit View Parameters CTRL+W Edit View Parameters You can also use the mouse wheel button to change view. 3. Use the Plan. Use the scroll bars on the 3D View. Pressing these with the SHIFT key held reverses the rotation. Use the Rotate Up.6. Rotate Down. If there are objects on the other side of these surfaces then they can be obscured. These surfaces are drawn with a user-specified amount of translucency which allows you to compensate for this. Figure: Shaded graphics Using the Shaded Graphics mode To a large extent there is no extra work required to build a model for the shaded graphics mode. When you release. You are able to build a model or take an existing model designed using the wire frame mode and simply change to the shaded graphics mode to see a high quality shaded rendering of your model. hold the ALT key down. You can also zoom in and out by a fixed amount. 3D Views Zooming You can zoom into and out of 3D Views by using the zoom button . place the mouse in one corner of the desired rectangle and press down the left mouse button while dragging the mouse to the opposite corner. repeat the operation holding down the SHIFT and ALT keys – the region shown in the window will shrink to fit into the rectangle drawn.w User Interface. keeping the same view centre. In addition. Translucency The Sea Surface and Seabed are drawn as textured surfaces. shading. To do this. Also you can zoom in on a particular region of interest in a 3D view by defining a rectangle around it on screen using the mouse. you can zoom in or out using the mouse wheel button with the CTRL key held down. To zoom out. by using ALT+CLICK and ALT+SHIFT+CLICK. the zoom menu items and the shortcut keys CTRL+I and SHIFT+CTRL+I. the region selected will be expanded to fill the window. 3.6.4 Shaded Graphics The shaded graphics mode renders the model as solid objects with lighting. There are a number of things you can do to improve your experience with the shaded graphics mode as described below. 57 . perspective and hidden line removal. The following methods of zooming are only available in wire frame 3D Views. To change the pen colour. For information on generating and importing 3D models specific to your project please refer to www.) defined in the drawing data for that object. You can change the pen colours etc. used at any time by editing the drawing data for that object. if you installed XVID from an older installation package. It is also important to make sure that your computer's graphics settings specify a colour mode of 16 bits (65536 colours) or better. Should you wish to use a different codec you can select this from the Preferences form. a turret moored FPSO. The Move Selected Objects facility can help you do this.com/Support/ShadedGraphics. The isometric wire frame view has no such requirement. To suppress drawing either set the line style to null (the blank style at the bottom of the drop down list) or else hide the object. e.5 How Objects are Drawn Each object in the model is drawn as a series of lines using the Pen Colour. On some machines the display driver cannot draw the dashed or dotted pen styles and instead draws nothing. Hardware Requirements The shaded graphics mode does require the presence of a DirectX 9 compatible graphics card. Wings and Shapes as well as for Vessels. We would recommend using a card with 256MB or more. then you may only have the 32 bit version of the codec installed. In our experience the most important factor to consider when choosing a card to work with shaded graphics is the amount of memory. The latest versions of the XVID codec install both 32 and 64 bit versions.5 from the view centre.orcina. 3. Video export Just as for wire frame views OrcaFlex can export video files of a replays in shaded views. Notes: If your machine's graphics capabilities are insufficient then the shaded graphics mode may fail to function properly or indeed fail to function at all.6. The software that performs this compression is called a codec. a semisub and a subsea template. In our experience the freely available XVID codec performs very well. When producing videos it is very important to use compression.g. You can import 3D models for 6D Buoys.w User Interface. Notes: In Windows. OrcaFlex by default will draw a solid. While this can be sufficient you may prefer something less simplistic. Objects like Vessels present more difficulties. a line width of zero does not mean "don't draw" – it means draw with the minimum line width. Line Width and Style (solid. We have provided a very basic selection of generic models which you are free to use. you must have the 64 bit version of the codec installed. an installation vessel. This problem can also manifest itself by failure to draw the sky which appears plain white. 3D Views Importing 3D models Objects like Lines are straightforward to draw. For wire frame replays OrcaFlex uses a built-in codec called run-length encoding.orcina. blocky images usually indicate a graphics card with insufficient memory. the turret moored FPSO above. In order to export videos from 64 bit OrcaFlex using the XVID codec. Alternatively you may import a more detailed 3D model. This codec is not suitable for shaded replays and in fact there is no suitable built-in codec in Windows. by opening the model browser. 58 . We would recommend using an MPEG-4 codec of which many are available. For best results you should centre your model close to the global origin. For example. dashed etc. You can also exclude (or include) individual objects from the 3D view. select and CLICK the colour button on the data form and then CLICK on the new colour wanted. There are models of an FPSO. So on such machines only the solid and blank pen styles work. OrcaFlex defines the viewer position to be in a line in the view direction (defined by the view azimuth and view elevation) at a distance of view size * 1. otherwise the video file size becomes unreasonably large. It is possible to rotate the view around both the view centre and around the viewer position.com/Support/ShadedGraphics. OrcaFlex uses the Line Type contact diameter to determine the thickness of each segment of the Line. Installing the latest version will resolve the problem. A link to the XVID codec can be found at www. filled-in shape based on the wire frame data you have specified. However. Viewer Position Because the shaded graphics mode uses perspective it requires the concept of the viewer position as well as the viewer centre. selecting the object and then using the Hide (or Show) command on the browser's Edit or popup menu. low quality. This line or grid is drawn using the sea surface pen. current and wind directions can be drawn as arrows in the top right-hand corner of 3D views. The wave. Link or Winch is which. Wings are drawn as rectangles in either the 6D Buoy pen or the Wing Type pen as determined in the Wing Type data. Links and Winches and Shapes are special slave objects that can be connected to other master objects – see Connecting Objects. Lines are drawn as a series of straight lines. For Spar Buoys and Towed Fish the vertices and edges are automatically generated by OrcaFlex to represent the stack of cylinders that make up the buoy. Separate pens are used for the segments and nodes. a choice of which pen to use to draw the segments. on the Line Data form.w User Interface. then it is drawn in the colour of the master object to which it is connected. The other joints are drawn as small squares. If the Surface Type is set to Single Line then one line is drawn. Flex Joints are drawn as a circular blob using the colour and line style specified on the attachment types form. current and wind directions can be drawn as arrows in the top right-hand corner of 3D views. Lines. As an option Spar Buoys and Towed Fish can be drawn as a stack of circular cylinders – this is the default setting. The drag chain drawing therefore directly reflects the way in which the chain is modelled. then it is drawn in the colour of the Line. Cylinders and Curved Plates) or as a grid (Planes). The Seabed is drawn as a grid using the seabed pen. If the joint is Free. aligned in the wave direction. directly beneath the node. If the Surface Type is set to Grid then a grid of lines is drawn. each slave object has a joint at each end that you can connect to a master object or else leave Free. Vessels are drawn as a solid. 6D Buoys are drawn as a wire frame of edges and vertices. 59 . 3D Buoys are drawn as a single vertical line of length equal to the height of the buoy. The wave. Clumps are drawn as a thin vertical bar. For Lumped Buoys. joining points drawn at each node. To allow these connections to be made. width and style. When the program is in Reset or Statics Complete state these joints are drawn as follows: The joint at End A of a line or end 1 of a Link or Winch is drawn as a small triangle. Shapes are drawn either as wire frames (Blocks. The supported part of the chain (if any is supported) is separately drawn as a blob at the seabed. The Sea Surface and Seabed are drawn as textured surfaces using their respective pen colours. Optionally the support cylinder ends can be drawn as circles with the support type diameter. of length equal to the hanging length and at the angle calculated using the above theory. You can control both what is drawn (see 3D View Drawing Preferences) and the drawing data used. The hanging part of the chain is drawn as a line. Shapes are drawn as solid objects and Planes allow for user-specified levels of translucency. There is also. one for each segment. Support cylinders are drawn as a straight line. for shapes you can also control the number of lines used to draw the shape. This is controlled by the user's choice of Surface Type as specified on the drawing page on the Environment data form. for example. Shaded Drawing For shaded views the various objects are drawn as follows: View axes and global axes are drawn as small triplets of lines showing their origin and the orientation of their axes. Alternatively Vessels can be represented by an imported 3D model. The Sea Surface is drawn as a grid or as a single line. Links and Winches are drawn as a straight line segments joining the connection points. Vessels are drawn as a wire frame of edges and vertices defined by the user on the Vessel and Vessel Types data forms. Drag Chains are drawn using the colour and line style specified on the attachment types form. This distinguishes which end of a Line. Link or Winch to which it belongs. so you can. As well as controlling the pen colour. increase the pen width used for the nodes to make them more visible. filled-in shape based on the wire frame data. You can control both what is drawn (see 3D View Drawing Preferences) and the drawing data used. The cylinder length is defined by the support type. If the joint is connected to a master object. Alternatively Shapes can be represented by an imported 3D model. Both surfaces can be drawn with user-specified levels of translucency. the vertices and edges are defined by the user on the buoy data form. 3D Views Wire Frame Drawing For wire frame views the various objects are drawn as follows: The various coordinate systems can be drawn as small triplets of lines showing their origin and the orientation of their axes. 3. Flex Joints are drawn as cylinders with radius 2R and length 4R where R is the radius of the node to which the flex joint is attached. etc. A new object of that type is created at the position of the next CLICK on a 3D View. Dragging is only available in Reset or Statics Complete states. Lines are drawn as a series of cylinders.6.9 Connecting Objects Unlocked slave objects (e. and when the object is not locked. To do this select the object and press CTRL+C to take a copy of it. Lumped 6D Buoys are drawn as a solid. Alternatively they can be represented by an imported 3D model. 3. 60 . The current coordinates of the object are shown in the Status Bar during the drag operation. Wings are drawn as plates using their specified span and chord. Links and Winches are drawn as a series of cylinders joining the connection points. to disconnect it – select it and then CTRL+CLICK on the sea surface.w User Interface.7 Creating and Destroying Objects When the model is in Reset or Statics Complete state then you can create and destroy objects using the mouse. Alternatively 6D Buoys can be represented by an imported 3D model. CLICK on an object to open its data form. Objects may be locked to prevent unintended drag operations moving them (see Locking an object).) can be connected to master objects using the mouse in a 3D View (see Object Connections). Spar Buoys and Towed Fish are drawn as solid objects using the specified cylinder geometry. The connection is indicated in the Status Bar and the joint connected is drawn in the colour of the master object to show the connection. The mouse cursor changes to show this. Their coordinates may still be edited on their data form. When the mouse button is released. Support cylinders are drawn as cylinders with length and diameter defined by the support type. CLICK on the appropriate new object button on the tool bar or select the Model | New Object menu item.e.6.6. To create a new object. Drag Chains are drawn as a chain with bar diameter derived from the drag chain's effective diameter. To connect a joint to a Fixed Point. There is also. If several objects have overlapping hot zones at the mouse position.8 Dragging Objects An unlocked object may be dragged to relocate it by pressing the mouse button down and holding it down while moving the mouse. You will be asked to confirm the action. You can also create a new object by copying an existing one. on the Line Data form. To deselect the object (without selecting another object) CLICK on the 3D view away from all objects. one for each segment using the contact diameter as specified on the Line Type form. The currently selected object is indicated in the Status bar. Lines. simply select it and then press the DELETE key. select it and then CTRL+CLICK on the global axes.6 Selecting Objects A single CLICK on or near an object in a 3D View selects it ready for further operations. Other objects are moved in the global coordinate frame. The diameter of the cylinders can be specified on the object's data form.6. filled-in shape based on the wire frame data. All objects have a hot zone around them. Links. To Free a joint – i. 3. they will be selected in turn at subsequent CLICKS. First select the end of the slave that you want to connect by CLICKING on or near its end joint. 3. You can now press CTRL+V (more than once if you want more than one copy) – again the mouse cursor changes and the copy object is pasted at the position of the next mouse CLICK in a 3D view. Note: Objects must be dragged a certain minimum distance (as specified in the Preferences form) before the drag operation is started. Then hold down the CTRL key while CLICKING on the master object – the two will then be connected together. This method of creating a new object is particularly useful if you want an almost identical object – you can create a copy of it and then just change the data that you want to differ. This prevents accidental movement of objects when DOUBLE CLICKING etc. Note: Slave objects that are connected are moved relative to their master's local origin. This operation is only permitted for master-slave object pairs. a choice of which pen to use to draw the segments.g. for example connecting a line to a vessel. To destroy an object. 3D Views 3D Buoys and Clumps are drawn as an ellipsoid with the specified volume and height. then the object will be positioned at the new location. 3. Replays To connect an object to an Anchor (a fixed point with a coordinate relative to the seabed). select it and then CTRL+CLICK on the seabed grid. you are not restricted to regularly spaced times. A replay is therefore like a short length of film. Snapshots: The times are specified explicitly in a list. rotating and zooming effects. This allows an object to be placed exactly on the seabed. This means that.w User Interface. Custom Replays are replays where you have complete control over frames which make up the replay. you can include frames showing the static configuration of a model. After a 3D view has been transferred to another application you should be careful not to change its aspect ratio. In Word you can maintain aspect ratio by dragging the corners of the picture. simulation time) written in the top left-hand corner of the frame. If the add program/file details to output preference is enabled. for example.g. There are various controls and parameters that allow you to control a replay. In order to play the AVI file you will need to ensure that the codec used to generate the video file has been installed on the target playback machine. If you require an anchor coordinate close to. connect it to the seabed at a distance and then drag it nearer or edit the coordinate in the Data Form. the facility is very powerful and you are certainly not restricted to this application. If you have a time history graph window open when the replay is run. resizing video clips (after pasting into your presentation) will introduce aliasing (digitisation errors). First select the view and adjust the viewpoint as desired. So whilst the AVI container format is well known and understood. with each frame of the film being a snapshot of a model as it was at a given time. See Custom Replays for details. If needed. you can have frames from different simulation files in the same replay. so the file can then be imported into other applications. but not on the seabed. This type of replay is therefore only available when a simulation is active and can only cover the period that has already been simulated. then the replay time is indicated on the graph. Note: AVI files can be very large if the window size is large or there are a lot of frames in the replay. Note however. whereas if you drag the centres of the sides then the aspect ratio is changed.6. Custom replays were originally introduced to help visualise series of static snapshots. However. for example during a lowering operation. the video stream inside the container is compressed using a codec. If the object is close to the seabed then the program snaps it onto the seabed. using the Export Video button on the replay parameters form. Then to copy to the clipboard press CTRL+C. so that the pictures may be used in other applications such as word processors and graphics packages. The generated file uses the view parameters of the most recently selected 3D view window. Active Simulation Replay Times There are two options for specifying the times used for an active simulation replay: Regularly spaced: The times used for the replay are at regular spaced intervals and cover a range determined by the period specified on the replay form. or select Copy from the popup menu. The popup menu also has commands to print or export the 3D view. for example to be shown in a presentation. copied to the windows clipboard. that AVI is what is known as a container format. AVI is a standard video format. view angles and view centre to achieve panning. you are able to vary the view size. since this will produce unequal scaling in the vertical and horizontal directions and invalidate the scale bar. Also. The codec used for the generating the video file can be set on the Preferences form. 61 . then each frame in the video has details of that frame (e. Different AVI files can use different codecs and so it is possible for a machine to be able to play some AVI files and not others.7 REPLAYS A Replay is a sequence of 3D views shown one after another to give an animation. Copying and Exporting Views 3D Views may be printed. depending on which codecs are installed on the machine. Replay Type Active Simulation Replays show the model as it was at specified times during the currently active simulation. so it is often best to set the 3D View window size to the required size before you export the video. or exported to a windows graphics metafile. Export Video Replays can be exported as either AVI files or as PDF files. When you export a video clip you will be asked to select a file name for the video using the standard Save File window. 3. you can first adjust the printer setup using the Printer Setup command on the popup menu or on the File menu.10 Printing. before it starts again at the beginning. some replay settings can only be modified on the Replay Parameters form. Frame interval in real time (Snapshot times only) For regular spaced time replays.5 seconds causes the replay to show 16 frames. and so on. 9. Show Trails If this is selected. by using toolbar buttons or with shortcut keys. 15. The toolbar has a section dedicated to replay control: Figure: Replay toolbar controls The replay control buttons.5. However. in order to make the replay speed setting meaningful we introduce an artificial frame interval for snapshot replays. These can be set to '~' which is interpreted as simulation start time and simulation finish time respectively. then the frame rate is 2/T. …. 8. the smallest possible interval.2 Replay Control The replay can be controlled from the Replay menu. All Views If this is selected. for example. In addition.0.7. Replay Period (Regular spaced times only) The part of the simulation that the replay covers. 3. selecting stage 2 and a replay time step of 0. So. just one simulation stage (an asterisk * denotes an incomplete stage). the latest wave period or else a user specified period. You can select to replay the whole simulation. then when each frame of the replay is drawn the previous frame is first overdrawn in grey – this results in grey trails showing the path of each object. if the replay speed is set to 100%. So.7. Example: For a simulation with stages of 8 seconds each. there is a well-defined relationship between replay frame rate and real time. for snapshot replays. this is more suitable for non-cyclic motion. It is specified as a percentage of real time.0.1 Replay Parameters The replay can be controlled by the following parameters that can be set in the Replay Parameters form. accessed using the Replay Parameters button.5.e. allowing motion to be viewed from several different viewpoints. 200% means twice as fast etc. i. The value '~' is interpreted as the actual sample interval. so 100% means at real time. then the replay frame rate is equal to 1/T where T is the specified frame interval. If you select User Specified then you can enter your own Start and End Times for the replay period. automatically cycling back to the first frame after the last frame has been shown. there is no such relationship. then the replay is shown in all 3D Views simultaneously. If the replay speed is set to 200%. Non-continuous means that there will be a pause at the end of the replay. Interval (Regular spaced times only) The simulation time step size between frames of the replay. this is suitable for replays of whole cycles of regular cyclic motion. Otherwise the replay is played in the currently selected view window only. Replays 3. menu items are listed in the table below: Button + SHIFT Menu Item Shortcut Action Replay | Start Replay CTRL+R Start replay Replay | Stop Replay CTRL+R Stop replay Replay | Step Replay Forwards CTRL+A Step to next frame and pause Replay | Step Replay Backwards CTRL+B Step to previous frame and pause 62 . Speed Determines how fast the replay is played.w User Interface. corresponding to times 8. Using shorter intervals means that you see a smoother animation (though the extra drawing required may slow the animation). Continuous Continuous means replaying like an endless film loop. In addition you are able to vary the view size. We recommend that you save your custom replay file before you start setting up the replay sections.3 Custom Replays Custom replays allow you to piece together arbitrary frames from one or more OrcaFlex files. Replays Menu Item Shortcut Action Replay | Replay Faster CTRL+F Speed up replay Replay | Replay Slower SHIFT+CTRL+F Slow down replay Replay | Replay Parameters CTRL+D Edit replay parameters Replay Time Control Next to the Step Replay button is a drop-down button which allows you to enter directly a replay time. Replay Specification This is the file containing the custom replay specification – that is the file that is saved by the Custom Replay Wizard.4 Custom Replay Wizard The Custom Replay Wizard allows you to define a series of replay sections. Continuous. 3. if you wish. vary the time intervals between frames. rotate and zoom the 3D View using the normal buttons and shortcuts.w Button User Interface. In this mode of operation you will be able manually to pan. 63 . To use the custom replay feature you must first set the Replay Type data item on the Replay Parameters form to Custom Replay. The replay time is displayed on and can be controlled from Time History graphs. view angles and view centre to achieve panning. 3. Custom Replay Data Custom replay specifies view parameters (size. position. This is because once you have saved the custom replay file you will be able to use relative paths for the OrcaFlex file names. This allows direct control of the replay time. Custom Replay Files When you have built your custom replay you must save it using the File menu or save button on the toolbar. A series of regularly spaced snapshots from a simulation file. Using frames from dynamic simulation files allows you to create replays where the frames are from one or more simulations. an animation of an installation procedure. Each frame of the replay can be either the static configuration. for example.7. Custom replay files can be opened in a similar way. and. CTRL+A and CTRL+B. rotating and zooming effects. Replay Slider Control The final part of the replay toolbar is the replay slider. or a snapshot of a specified time in a dynamic simulation file. Using frames of static configurations you can string together a series of static snapshots giving. 2. Different files can be used for different replay sections. For fine grained adjustment of replay time you can use the Replay | Step Replay Forwards and Replay | Step Replay Backwards actions or alternatively their shortcuts.7. The static configuration of a model specified by either a data file or a simulation file. Each replay section can show either: 1. These parameters are Target Speed. Next you must build the custom replay which is most easily done using the Custom Replay Wizard. This can be particularly useful for long simulations for which the slider control does not provide sufficient resolution. angles and graphics mode) If this data item is not checked then the replay will use the view parameters of whichever 3D View window it appears in. This can be used for precise control of the replay time. which can be opened by clicking the Custom Replay Wizard button. Custom Replay Parameters Custom replays also make use of some of the parameters needed for standard simulation replays. All Views and Show Trails. Drag the slider to the left to move to an earlier part of the replay and to the right to move to a later part. Frames of both static and dynamic configurations can be included in the same custom replay. Specifies either the Solid or Mesh fill mode for the replay section. and so on. 64 . view azimuth and view elevation for the first and last frames of the replay section. rotating and zooming effects This item is only available if the "Custom replay specifies view parameters" option is enabled. For each replay section you must also specify the following: Replay Section Name This is a descriptive name for the replay section. then the interval between frames will be half this value.yml) or a simulation file (. These are OrcaFlex simulation times for the specified simulation file of this replay section. Dynamics This setting determines whether the replay section defines snapshots from a dynamic simulation or a static configuration. in real time. Use smoothed panning. If the target replay speed is. This may be useful while developing the custom replay because it allows you to concentrate on particular replay sections. rotating and zooming during replay sections then the transition from one section to another sometimes appears to be disjointed. assuming a target replay speed of 100%. If this option is checked then the transition between sections is smoothed. The custom replay displays static configurations for a data file by loading the file and then performing the static calculation. Replays If this data item is checked then you will be required to specify the view parameters (view size. When the replay is running OrcaFlex displays a description of the current frame in the message box on the status bar – this includes the replay section name. rotating and zooming effects in your replay. using the given disturbance position. These view parameters are varied between these values for the other frames in the replay section.dat or . view elevation and graphics mode) for each replay section. Disturbance Vessel and Disturbance Position Specifies whether or not the sea surface will be drawn as if disturbed by the presence of a particular vessel. From View Parameters. Number of Frames This is the total number of frames in the replay section. Frame interval in real time OrcaFlex needs to know how fast to play the replay. This can be time consuming – static state simulation files can be used instead to avoid the overhead of performing statics each time the replay is shown. To View Parameters The view size. If you are panning. between each replay frame. If the file is a data file then the replay section will show the static configuration and so this data item cannot be edited. view azimuth. Included in Replay This allows you to exclude certain sections from the replay. Simulation Time From. While learning how custom replays work we recommend that you do not check this data item.sim). Graphics Mode Specifies either the Wire frame or Shaded graphics mode for the replay section. This description can also be included in exported videos. View Parameter data The following data items are only available when the specifies view parameters option is checked. view centre. Hint: These values can be copied from OrcaFlex's View Parameters form using the clipboard.w User Interface. view centre. say 200%. This data item specifies the interval. Replay Sections You can specify any number of replay sections. This allows you to include panning. Simulation Time To This specifies the period of the dynamic simulation covered by the replay section. If your custom replay is a series of static snapshots then you would usually set this value to 1. Shaded Graphics Fill Mode Available only for shaded graphics mode. If the replay section is a static snapshot then these data items are not editable. OrcaFlex File Name The model to be used for this section – either a data file (. including: The data form can be printed. used for example for titles and comments. Clump Types and Drag Chain Types. It can be opened from the popup menu or alternatively by pressing F12. Popup Menu The popup menu on a data form provides various facilities.8 DATA FORMS Each object in the model has data items that define its properties. Next Accepts the data changes made and then displays the next form in sequence. Line Types. which you can edit. The data names for the currently-selected block of data items. copied to the clipboard or exported to a file. weight in water etc. 6D Buoys. displacement.1 Data Fields Data items on each Data Form are displayed in Fields. These reports are currently available for General Data. The following types of fields are used: Text A general string of text. Holding the SHIFT key down while CLICKING the Next button accepts the changes and then displays the previous data form in sequence. which can be accessed by various methods: use the Model Browser DOUBLE CLICK the object in a 3D view RIGHT CLICK the object in a 3D view and use the popup menu. If a simulation is active then most data items cannot be changed since they affect the calculation. You can select a field with the mouse. or use the keyboard to navigate around the form. It can be opened from the popup menu or alternatively by pressing Alt+Enter. Vessels. Name Each object is given a name. 3. Data forms for 3D Buoys. The data are examined and edited in the object's Data Form. This is a spreadsheet listing information about other objects connected to it. and the arrow keys move across the fields in a group. Vessels and Lines provide a Connections Report. can be displayed using the Model | Show Connections Report menu item. Object names must be unique – you cannot have two objects with the same name. Data Forms 3.w User Interface. but for all objects in the model. Cancel Cancels the data changes made and then closes the form. 6D Buoys. Access to the next and previous data form and to the Variable Data form. The calculator can also be closed by pressing F12 – if you do this then the value in the calculator is transferred to the active edit cell. Calculator A simple calculator is available from any OrcaFlex data form. 3D Buoys. but you can change things like the object's colour. Numbers can be transferred to and from it with standard Windows copy ( CTRL+C) and paste (CTRL+V). a report of the properties of that object. generally with related fields organised into Groups or Tables. 65 . Lines.8. The data for the whole model may be printed using the File | Print menu item. Note that the same information. The report displays properties like weight in air. Object properties reports On data forms of some objects. Control Buttons OK Accepts the data changes made and then closes the form. You can also use the keyboard shortcuts F6 for next and SHIFT+F6 for previous. TAB moves from group to group. 8.0. viewing additional properties Group Movement TAB Next Group SHIFT+TAB Previous Group ALT+… Move to the group with this letter underlined in its heading Field Movement ←↑↓→ Go to adjacent row or column HOME Go to leftmost column END Go to rightmost column PAGE UP Go to top row PAGE DOWN Go to bottom row Table Editing INSERT. Editing mode is entered by DOUBLE CLICKING a cell with the mouse. Colour Selection These show as a block of colour. Data Forms Numeric Numbers can be entered in a number of formats such as 3. For some numeric data items the values ~ and/or Infinity are permitted. SHIFT+CLICK Select a block of fields DOUBLE CLICK Start Edit Mode in this field (please also see Data Fields) SECONDARY BUTTON CLICK Context sensitive popup menu for copying. pressing F2. List Boxes These allow you to choose from a list of pre-determined values.w User Interface. If the value has been truncated for display. or by starting to type alphanumeric characters. Input can also be from the Windows clipboard.2 Data Form Editing The TAB. for example an object's mass must always be greater than zero. and the new value takes effect. Check Boxes These show a tick. The characters that have been typed can be edited by using the arrow keys to move around (now within the field) and the BACKSPACE and DELETE keys. Editing mode is ended. which are entered into the field as they are typed. exporting and printing the form and. DELETE Insert or delete rows Start Editing F2 Edit 66 .0E6. meaning not selected. Spin Buttons These are small buttons with up and down arrows. It is possible to enter more digits than are displayed. or are blank.3 or 3. The meaning is data item specific. used for incrementing and decrementing the associated field (such as the number of entries in a table). Many numeric fields have limits on the range of values that can be entered. when you press ENTER or select another field or button on the form.3. If you edit a colour field a colour selection dialog is opened. Warnings are given if invalid values are typed. Mouse Actions CLICK Select Field CLICK+DRAG. even if the program truncates the value for the purpose of display. CTRL+C copies the selected field or block of fields to the clipboard whilst CTRL+V pastes from the clipboard into the selected field. . HOME. END and ARROW keys and the mouse can be used to navigate around the Edit Form. 0.0e6 or 3. 3. SHIFT+TAB. for some objects. You are only permitted to use the values that are included in the drop-down list 3. To end editing mode but reject the edit (and so keep the old value) press ESC. meaning selected. The exact value that you enter is used in calculations. then you can hover the mouse over the value and view the full precision value in the popup hint. Results are available as text tables (summary results. For 6D Buoys that have wings attached.w User Interface.Z coordinates of the Position for which you want results. The types of results available depend on the current model state.1 Producing Results You can access results by either CLICKING on the Results button on the toolbar or by using the Select Results menu item. If the values of a graph are required in text form then CLICK the Values button – this give the values in a Spreadsheet window. 67 . velocity and acceleration results are reported at a user specified Position on the object. The Select Results form allows you to select the results you want by specifying: Result Type This option allows you to select which of the various types of results output you require.9 RESULTS 3. For lines you must specify the arc length along the line – see Line Results. There is a Keep Open switch on the form's popup menu. or alternatively stays open (and on top) until you explicitly close it. XY graphs. the Select Results form then appears. Graphs and Tables can be sent straight to the printer by CLICKING the Print button. Period For time histories. XY graphs and range graphs you must specify the period of the simulation to be included. velocity and acceleration results there is also an option to specify that the results should be affected by the presence of a disturbance vessel. The Whole Simulation. A…Z Edit (replace) During Editing ← →. offset tables. full results. For 6D Buoys and Vessels the translational position. results for the buoy and for each wing are available separately. This can be: One of the numbered stages of the simulation. For sea surface elevation. The coordinates of this Position are specified in object local coordinates. A Specified Period.9. These time values can be set to '~' which is interpreted as simulation start time and simulation finish time respectively. which allows you to choose whether the form automatically closes when you select a result. linked statistics. Object The object for which you want results. END Move within field End Editing ESC Cancel edit ↑↓ Accept edit and move to previous/next row ENTER Accept edit Copy / Paste CTRL+C Copy selected field/block to clipboard CTRL+V Paste from clipboard into selected field CTRL+D Fill selection from top (copy top cell down) CTRL+R Fill selection from left (copy leftmost cell to right) CTRL+U SHIFT+CTRL+D Fill selection from bottom (copy bottom cell up) CTRL+L SHIFT+CTRL+R Fill selection from right (copy rightmost cell to left) 3. defined by a start and end time. Results Mouse Actions 0…9. extreme value statistics or line clashing reports) or as graphs (time histories.Y. offset graphs or spectral response graphs). range graphs. HOME. statistics. For the Environment you must specify the global X. Inadequate segmentation warning If any lines have. during the simulation. Direct Tensile Strain. Results The Latest Wave (only available for regular wave simulations) which is defined to be the wave period immediately preceding the latest simulation time. as follows: Select the spreadsheet window to which you want to append. However. von Mises Stress. Worst ZZ Strain. Normalised Tension.9. Then open the Select Results form and select the variables that you want to append. by clicking on it. End Force results and Vortex Force results. Direct Tensile Stress. General Results OrcaFlex spike logs Implicit solver iteration count and Implicit solver time step. Clash Force. Max von Mises Stress and ZZ Stress. However. This allows you to see. Such variables include Wall Tension. For the currently selected object. This is normally the latest simulated time. how a results variable evolves over a simulation. ZZ Strain. Variable The desired variable(s). The Instantaneous Value period is available when a simulation has been run. Definitions of the results variables can be obtained by selecting them in the Variable list box and then pressing F1. Torque. and the Graph button will give a separate Graph Window for each variable. gone into greater compression than their segment Euler load then a warning note is added to the Results form. All the other results are derived from the simulation log file which OrcaFlex creates automatically when a simulation is run. Offset warning If any of the multiple statics calculations have failed then a warning note is added to the Results form. Line Results OrcaFlex spike logs Effective Tension. statistics and range graphs are derived from the simulation log file. If multiple variables are selected. This must be done before the simulation is started. Spike Logging A special algorithm is used for logging results that tend to vary rapidly to ensure that any spikes that may occur between samples are recorded. We refer to this algorithm as spike logging.w User Interface. For Range Graphs the period can also be Static State or Instantaneous Value: The Static State period is only available after a statics calculation and the graph shows a curve of the values in the static configuration. Link and Winch Results OrcaFlex spike logs Tension and Velocity. Usually this means that finer segmentation is needed in some sections of these lines in order to model compression adequately. for an entire line. OrcaFlex samples the variables for each object at regular intervals and stores the sampled values in the log file. In addition other results which are derived from these quantities are effectively spike logged by association. Solid Contact Force. New columns can be appended to existing time history spreadsheet windows. 68 .2 Selecting Variables Each object has associated with it a list of currently selected results variables. Solid Results OrcaFlex spike logs contact force magnitude. its selected variables are shown in a list on the results form – you can of course modify this list. then the Values button will give a single Spreadsheet Window with a column for each selected variable. All time histories. For some result types the list can contain multiple selected variables. You can control the time resolution of the results by setting the Target Sample Interval data item on the general data form. if a replay is active then the graph shows a curve of values at the active replay time. It shows a curve of the values at the instantaneous simulation time. Such lines are marked with the symbol § in the Object list. 3. because more samples are taken this will also increase the size of the simulation file that is created. Decreasing the sample interval will improve the time resolution of the results (and increase the number of samples taken). As the simulation progresses. Logging for results The summary and full results are taken directly from the current state of the model. Clash Energy. 9. These can be used to determine suitable explicit integration time steps. since these results are already minima – the shortest distance to any other line and to any point on the seabed. estimated as the average time between successive local maxima. The summary results are simply an abbreviated form of the full results. To obtain one of these results tables: Select Summary Results or Full Results on the Results form. m2 second spectral moment. Explicit integration time steps When the model is in Statics Complete state the summary and full results include estimates of the shortest natural periods of objects or of the whole model. m4 fourth spectral moment estimated as m2/Tc2.e. 3. then they show the positions of objects at the latest time calculated. Select the object and the variables of interest (see Selecting Variables).9. 3. If Statistics by Wave Period is selected then these periods are successive wave periods. estimated as σ2.4 Statistics The Statistics report provides. m0 zeroth spectral moment. OrcaFlex finds the minimum and maximum of each variable and reports these extreme values. To obtain a Statistics report: Select Statistics. estimated as m0/Tz2. Provided that the selected spreadsheet window is a time history values table and that the time periods for both sets of histories match. estimated as (1-Tc2/Tz2)½. otherwise they are the stages of the simulation. For example. estimated as the average time between successive up-crossings of the mean value μ.9. The report also includes: μ mean. 69 . σ standard deviation. Tc mean crest period. This allows you to have a single window containing results from different objects. the root mean square about the mean). These statistics are reported for each of a number of periods of the simulation. for each statistics variable: The minimum and maximum values and the simulation times when they occurred. Select the object required. If a simulation is active.5 Linked Statistics The Linked Statistics table relates a group of variables for a given object. Results Then hold the CTRL button down and click the Values button. not all of the intermediate nodes. For a specified group of variables and a specified period of simulation. For example. 3. Note: Be careful when interpreting statistics of Line Clearance and Seabed Clearance. The mean and standard deviation (i. then the new time histories will be appended to the active window.w User Interface. ε spectral bandwidth parameter. in Statics Complete state the full results tables show the positions of objects in their static position.3 Summary and Full Results These spreadsheet windows give the current state of an object or of the whole model. The simulation inner time step should normally be no more than 1/10th of the shortest natural period of the model – this is given at the top of the summary results or full results report for All Objects. Click the Table button. The report is presented in a spreadsheet. Tz mean up-crossing period. CLICK the Table button. the times they occurred and the values that all the other variables took at those times. the maximum of Line Contact Clearance will be the maximum value that the smallest clearance took during the period. in which the results for lines only include the end nodes. In addition the full results table for a line contains detailed reports of the shortest natural periods. Each event is given a number to identify it. Summary table The summary table lists all clash events for segments on the selected line. End Time and Duration The simulation time of the start and end of the clash event together with its duration.6 Offset Tables These Text Windows are available only after multiple statics calculations and only for vessels. e. The report is presented in a spreadsheet. the maximum of Line Contact Clearance will be the maximum value that the smallest clearance took during the period. Select the required object and period. Note: Be careful when interpreting statistics of Line Clearance and Seabed Clearance. since these results are already minima – the shortest distance to any other line and to any point on the seabed. 3. For example. This is counted as a single clash event from the perspective of S1. Results To obtain a Linked Statistics report: Select Linked Statistics. CLICK the Table button.9. 3. Select the period required. Start Time. To obtain a Line Clashing Report: Select Line Clashing Report on the Results form. Select the offset vessel. if the clash is a sliding contact. For a given offset direction they report the total load on the vessel and show how it varies with offset distance. Select a line. The clash event ends when S1 is no longer in contact with any other line segments. CLICK the Table button.g. The report is presented in a spreadsheet. Segment number and segment arc length This identifies the segment S1 on the selected line.7 Line Clashing Report The Line Clashing Report produces a detailed tabular report about the line clashing events during a simulation. Note: During the course of a clash event the segment S1 may be in contact with a number of different line segments from other lines. Contents of the Line Clashing Report The report lists a summary table followed by a detailed table as described below.w User Interface. Total Impulse The total impulse of the clash event. The worst tension in any segment of any line connected to the vessel is also reported for each offset. CLICK the OK button. The report is presented in a spreadsheet. 70 .9. Select the offset direction required. We shall refer to the selected line as L1 and to the particular segment on this line as S1. For each clash event the following results are reported: Event number A number of clash events may occur during the simulation. To obtain an Offset Table: Select Offset Table on the Results form. A clash event is deemed to start when a segment from the selected line first comes into contact with another line segment. This is useful when relating the summary results of a clash event to the detailed results. Select the variables of interest (see Selecting Variables). This is the normal component of relative velocity of the two contact points at the start of the time step during which the clash event started.. So in this example it adds 360° to the -179° value and hence reports: . Graphs are automatically deleted if the object that they refer to is removed. 3. i.w User Interface. If the vessel's heading passes through 180° then without range jump suppression the time history would be: . Select the variable required (see Selecting Variables).9. Max Penetration At each time step we calculate the depth of penetration between the outer surfaces of segment S 1 and all other segments. Select the object required. Let the radii of the two segments be r1 and r2 (as defined by the line type contact diameter). For example consider vessel heading. 3. You can therefore set up one or more graph windows at the start of a simulation and watch the graphs develop as the simulation progresses. 180°. The clash force vector is monitored during each clash event and the greatest magnitude of this vector is reported. Contact velocity The detailed table also includes the contact velocity for each individual contact.e. between the centrelines of the two segments. If during the course of a clash event segment S1 is in contact with a number of segments on other lines then the start time.e. 179°. 71 . Peak Clash Energy A scalar value reporting the greatest value of clash energy achieved during the clash event. CLICK the Graph button. Select the period required. obtained using the Fourier Transform. 179°. The penetration of these two segments is defined to be (r1 + r2) – d. The period of simulation covered by the graph is chosen from a list. 180°. For XY graphs the steps 2 and 3 need to be done for both axes. . If you reset the simulation then the curves will be removed but the graphs will remain. To avoid this jump OrcaFlex adds or subtracts multiples of 360° to give the best continuation of the previous value. 2. XY graphs are of one time dependent variable against another. Range Jump Suppression For time histories of angles OrcaFlex chooses the angle's range so that the time history is continuous. More than one variable can be selected for time histories. Results Peak Clash Force A scalar value reporting the greatest value of clash force achieved during the clash event. This addition is valid since 181° and -179° are of course identical headings. To obtain a Time History or XY Graph: 1. for example by loading a new model. OrcaFlex calculates the shortest separation distance. Spectral Density From any time history graph you can use the popup menu to obtain the spectral density graph for that time history. and then repeating steps 2 and 3. they are regularly updated during the simulation... Note that this means that angle time history results can go outside the range -360° to +360°. 181°. d. Do this by CLICKING on one of the options labelled Xaxis or Y-axis.8 Time History and XY Graphs Time History graphs are of a single variable against time. Select Time History or XY Graph on the Results form.. The value reported as Max Penetration is the maximum value of penetration between segment S1 and any other segment over the duration of the clash event. end time and duration of each of those individual contacts is reported. The curve shown on the graph is the one-sided power spectral density (PSD) per unit time of the sampled time history. which is normally reported in the range -180° to +180°. Time history and XY graphs are displayed in Graph Windows and they are "live" – i. so you can adjust the model and re-run the simulation and the graphs will then be redrawn.. Let S2 be a segment on another line.. The fundamental frequency is specified on the General data form. -179°. . with a 360° jump. Detailed table The detailed table reports information about each individual contact between segment S1 and another segment. which are located at the bottom of the results form. Select the variable required (see Selecting Variables). CLICK the Graph button. Bend Moment range graphs have an extra curve showing the maximum permitted bend moment (EI / Minimum Bend Radius specified on the Line Types data form). Select the arc lengths required. 72 . Stress range graphs show the Allowable Stress (as specified on the Line Types data form). a selected arc length range. The PSDs are calculated for each period and then averaged to give the reported PSD which has the effect of smoothing the resulting PSD. The empirical cumulative distribution of these half-cycles is then plotted. Range graphs for code check results have an extra curve showing the maximum allowable value. or a selected line section.9 Range Graphs Range graphs are only available for a selection of variables and they are only available for Lines. This can be the entire line. Gaussian) distribution. In particular: Range graphs show the minimum. at Mean ± xσ. Select the period required. Effective tension range graphs have extra curves showing the segment Euler load and the Allowable Tension value (as specified on the Line Types data form). The curve on this graph is produced in the following way: 1. To obtain a Range Graph: Select Range Graph on the Results form. Select the object required. Rainflow half-cycle Empirical Cumulative Distribution From any time history graph you can use the popup menu to obtain the rainflow half-cycle empirical cumulative distribution graph for that time history.w User Interface.e. The standard deviation is calculated from all the samples that lie in the simulation period chosen for the graph. For details of this algorithm see the paper by Rychlik. This smoothing technique is only applied if there is more than 200s of data in the time history. where x is a user chosen value and σ is the standard deviation. Two curves are then drawn. Empirical Cumulative Distribution From any time history graph you can use the popup menu to obtain the empirical cumulative distribution graph for that time history. 3. Bend radius range graphs have an extra curve showing the Minimum Bend Radius specified on the Line Types data form. They have what is called 'serial correlation'. Curvature range graphs have an extra curve showing the maximum permitted curvature (the reciprocal of the Minimum Bend Radius specified on the Line Types data form). They show the values the variable took.9. Warning: Be careful not to assume that 95% of the data lie in the interval Mean ± 2σ. Results Notes: Using the Fourier Transform to estimate the PSD inevitably introduces 'noise' or 'leakage' to the spectrum. This graph shows what proportion of the samples in the time history are less than or equal to a given value. during a specified part of the simulation. as a function of arc length along the Line. To reduce the leakage the time history is partitioned into a number of overlapping periods. A Standard Deviation curve can also be added to a range graph – to do this edit the graph's properties (by double clicking on the graph) and set the Standard Deviation curve's visible property (by default the curves are not visible). This common guideline is based on the assumption that the data are sampled from a Normal (i. which often affects the accuracy of statistical results based on them. The time history is analysed using the rainflow cycle-counting algorithm. 2. These graphs are sometimes referred to as Exceedence Plots since they can sometimes be used to estimate the probability that the variable will exceed a given value. mean and maximum values that the variable took during the specified part of the simulation with the exception that the Line Clearance range graphs only show the minimum value. Warning: The samples in a time history are not independent. The rainflow algorithm produces a list of half-cycles associated with the time history. OrcaFlex uses the fitted distribution to estimate and report the required extreme statistic (e. More than one variable can be selected. You may. The statistical theory for this estimation is well-established and is described in the theory section. Note that this force is not necessarily in the offset direction. 73 . Select the offset direction required. perform a mooring analysis in an irregular sea-state and then estimate the maximum mooring line tension for a 3-hour storm. To obtain a Spectral Response Graph: Select Spectral Response Graph on the Results form. The following variables are plotted against offset distance: Restoring Force The magnitude of the horizontal component of the total force applied to the vessel by the attached Lines or other objects. The graph plots the calculated RAO for the selected variable on the Y axis and wave frequency on the X axis.11 Spectral Response Graphs These graphs are available only if you have run a response calculation wave. Such values are needed when using standards such as DNV-OS-F201 and API RP 2SK. for example by loading a new model. You can therefore set up one or more graph windows at the start of a simulation and watch the graphs develop as the simulation progresses. The graph is only available once the simulation has been completed. Results Range graphs are displayed in Graph Windows and they are "live" – i. Select the object required. OrcaFlex can estimate extreme values for any given result variable by analysing the simulated time history of the variable using extreme value statistical methods. Vertical Force The vertically downwards component of the total force applied to the vessel by the attached Lines or other objects. return level). Select the variable required. The procedure is essentially this: You select the statistical distribution to be used to model the distribution of extremes. for example to determine the likelihood of a load exceeding a critical value that may lead to failure. 3. about the vertical. applied to the vessel by the attached Lines or other objects. OrcaFlex provides diagnostic graphs that you should use to judge the reliability of the results. See Results below. for a specified period of exposure. The Extreme Value Statistics Results form is designed to lead you through this process. they are regularly updated during the simulation. CLICK the Graph button.12 Extreme Value Statistics Results There is often a requirement to predict the extreme responses of a system. OrcaFlex applies range jump suppression for range graphs of angles.10 Offset Graphs These graphs are available only after a multiple statics calculation has been done and only for the offset vessel.w User Interface.9. CLICK the Graph button. If you reset the simulation then the curves will be removed but the graphs will remain. Select the offset vessel.9. OrcaFlex estimates the distribution model parameters that best fit the simulation time history of the variable.9. 3. Range Jump Suppression Just as it does for Time History and XY Graphs. To obtain an Offset Graph: Select Offset Graph on the Results form. so you can adjust the model and re-run the simulation and the graphs will then be redrawn. Select the variable required (see Selecting Variables). Worst Tension The largest tension in any segment of any Line connected to the vessel.g. See Data below. Yaw Moment The moment. for instance. Graphs are automatically deleted if the object that they refer to is removed. 3.e. In this case OrcaFlex will break the sequence of time history values into clusters of successive values that stay above the threshold. This helps with setting the threshold and decluster period. Results When you open the Extreme Value Statistics Results form. Threshold and Decluster Period These data are only required when using the Weibull and GPD distributions. for lower tail) the estimated extreme value. The decluster period controls the declustering. These distributions are both fitted using the maximum likelihood method. Moving then to either of the other pages (Results or Diagnostic Graphs) will cause OrcaFlex to carry out the estimation part of the procedure. Results The following data items. The number of data points that will be included in the analysis (after the threshold and declustering have been done) is also displayed. and are as follows. e. The Diagnostic Graphs assist in testing the model. which are fitted to extremes of the time history and those extremes are selected using the peaks-over-threshold method with (optional) declustering. particularly in deep water. Extremes to analyse Specifies whether maxima (upper tail) or minima (lower tail) are to be analysed. but the Generalised Pareto is preferred by the extreme value statistics community because of its sound mathematical foundations. relative to this duration. The threshold is drawn on the time history graph. Historically.e. A positive value. do not affect the fitting of the statistical model. '~'. Data For convenience. but ignoring any that do not exceed the threshold. to help visualise its value relative to the extremes of the data. The most extreme value of each such cluster will then be included in the analysis. the estimation uncertainty inherent in that value etc.w User Interface. It can be set to one of the following: Zero. and all values above the specified threshold will be included. for many other variables of interest. For example. they are applied to the fitted model to obtain the reported results. The data required for the fitting of the model are entered on this page. For details see the Extreme Value Statistics Theory section. the Gaussian assumption is invalid and leads to poor estimates of extreme values. the Weibull distribution has often been used for marine systems. you will come first to the Data page. the time history result graph is reproduced on the Data page. will determine the accuracy of the estimate for the return level. The length of the simulation.01 (i. in which case no declustering will be done. for a selected results variable. The most extreme value of each of the resulting merged clusters will then be included in the analysis. Risk factor is the probability of exceeding (or falling below. and for responses which are approximately linear with respect to wave height. Rather. The threshold controls the peaks-over-threshold method. This helps avoid or reduce any statistical dependence between the extreme data values used in the analysis. This special value may be used to tell OrcaFlex to take the clusters to be the groups of values between successive up-crossings of the mean value (or down-crossings if analysing lower tail). Rayleigh distribution. Weibull and Generalised Pareto (GPD) distributions. Rayleigh Storm duration is the return period for which the return level is reported. found on the Results page. However. where you will select the distribution. 74 . but may give very wide confidence intervals if there are too few such extremes in the data).g. the return value for the specified period. This allows you to control the extent to which the analysis is based on only the extreme values in the data (the tail of the distribution). a risk factor of 1%). This is perhaps a reasonable assumption for waves. This method assumes that the variable is a stationary Gaussian process. This is generally not recommended since the values are unlikely to be independent. Distributions These fall into two groups. according to the statistical method with which they are applied. The Results page reports the estimated statistics. It will then decluster by merging successive clusters that are separated by periods (during which the variable is less than the threshold) that last no longer than the specified decluster period. and a too-extreme value (which will fit to only the more relevant extreme data points. you may ask for the 3-hour extreme value that is exceeded with a probability of 0. The best value for the threshold is one that strikes a balance between a not-extreme-enough value (which will increase the number of data points fitted but may give biased fitting by allowing less extreme values to influence the fitting too much). based upon the data. drawn through each point. for example an obvious trend away from the diagonal) indicates poor model fit. If.e. The fitted values of the model parameters and corresponding standard errors are also reported. OrcaFlex reports this estimated confidence interval in addition to the estimated return level. or even in their not appearing at all. The Return Level Plot shows return level against return period (i. and the pair of outer lines the corresponding pointwise 95% confidence limits. a number of the vertical lines fail to reach the diagonal. and again these are then denoted by 'N/A'. then you should reconsider the entries on the data page: 75 . The Quantile Plot displays quantiles of the empirical data plotted against model quantiles. then that may raise concerns about the validity of the fitted model. Note: For some values of storm duration (usually small values) it might not be possible to calculate the return level. Diagnostic Graphs The diagnostic graphs will help you to assess the goodness-of-fit of the model. and should lie between the confidence limits if the model fits the data well. As with the quantile plot. Results Weibull and GPD Storm duration is defined as for the Rayleigh distribution. are pointwise 95% tolerance intervals and may be used as a guide to deciding whether any departure from the diagonal is significant. If the model is a good fit. The vertical lines. If all the vertical lines intersect the diagonal line. then the points should lie close to the superimposed 45° diagonal line. as follows. An example of diagnostics graphs indicating a good model fit is shown below: Figure: Diagnostics graphs for a good model fit If either of these graphs indicates a poor model fit. a significant number of points contravening these limits indicates poor model fit. They should be interpreted together. and how appropriate or not the fitted distribution is. however. The reported return level is defined to be the level whose expected number of exceedences in the specified storm duration is one. with the latter on a logarithmic scale to highlight the effect of extrapolation. The points are the empirical return levels. OrcaFlex may sometimes be unable to determine the confidence limits for some return periods – this may result in gaps in the confidence limit lines. for a specified confidence level. storm duration). The maximum likelihood fitting procedure used for these distributions allows the estimation of a confidence interval for the return level. and any significant departure from this (especially a systematic one. the calculation may fail to determine the confidence limits.w User Interface. This is indicated by the value 'N/A' (meaning 'not available'). then the modelled values are probably sufficiently close to the empirical value not to be of concern. Similarly. The central line on the graph is the return level for the fitted model. not in isolation. Again. for some combinations of storm duration and confidence level. Note: Resizing video clips (after pasting into your presentation) will introduce aliasing (re-digitisation errors) so it is best to set the OrcaFlex 3D View window to the required size before you export the video. The distribution may be inappropriate – the data may simply not conform to the selected distribution. To adjust a graph's properties (range of axes. Replays Replays can be transferred by exporting to an AVI file and then importing that video clip file into the presentation program. To avoid these problems. The Weibull and GPD distributions are not available in the current version due to the complexity of threshold selection. This can be done in two ways: 1. 3.10 GRAPHS When you request results in graphical form. That is. Graphs Graphs can be transferred from OrcaFlex to presentation programs by simple copy + paste. Use Default Ranges. they are presented in Graph Windows.9. or too short (so successive data points might not be independent). colours. Note: In PowerPoint. or too high. OrcaFlex spreadsheet The OrcaFlex spreadsheet post-processing facility supports analysis using the Rayleigh distribution via the Rayleigh Extremes command. An XVID encoded AVI file (and possibly other codecs) added to Microsoft PowerPoint slides as a Movie Object may not play correctly (displaying a blank screen on replay. from where you can paste it into other applications. The full analysis capability is available via the programming interface. and tile them on the screen together with 3D Views and text results windows. Delphi. this displays the video player window and menus.w User Interface. showing different results. etc.) see Modifying Graphs. analysis using the Weibull and GPD distributions is available. in contrast to the OrcaFlex spreadsheet. The Video Clip Object links to the AVI file (it is not embedded within PowerPoint) so the file location needs to be accessible when running the presentation. Here are some tips on how this can be done. This gives better resolution than the default Paste action. Decluster period. Threshold. To set options such as auto repeat. right-click on the image in the slide. Copy copies the graph to the clipboard. This may be too long (so too few data points). From the PowerPoint menu. an XVID AVI file needs to be inserted as a Video Clip Object. hence including too many points which are not in the tail of the distribution. OrcaFlex programming interface The C/C++. 3. choose Insert | Object. You can open several simultaneous graph windows. As with all other functionality. or 2. the Python and MATLAB interfaces are the easiest to use. Values. Python and MATLAB programming interfaces to OrcaFlex all support automation of extreme value statistics. Graphs Distribution. Automation The extreme value statistics capabilities can be automated in a number of different ways. The threshold may be too low. then select Video Clip Object | Open. or the video only appearing in full screen mode). it is better to use Paste Special and then select the Enhanced Metafile format. instead of using Paste. Graphs have a popup menu that provides the following facilities. 76 . The computer running the presentation must also have the XVID codec installed. resulting in too few data points for the analysis and consequent large variation in the results. Drag and Drop the AVI file onto the PowerPoint slide. Select 'Create from file' and Browse to your file (do not select the 'Link' option).13 Presenting OrcaFlex Results OrcaFlex users often wish to show their OrcaFlex results in a slide presentation prepared using a presentation program such as Microsoft PowerPoint. From the clipboard you can then paste it into another application. Graphs can also be exported using the popup menu. The replay time indicator on a Time History graph can be directly manipulated using the mouse. When a replay is in progress the replay time is indicated on both Time History and XY graphs. Extreme Value Statistics (for time history graphs). so once you have set up a set of interesting graphs you can edit the model and re-run the simulation to see the effect of changing the model. Graphs Spectral Density. Empirical Cumulative Distribution. with the CTRL key pressed you can click and then drag the indicator. Export enables you to export the graph to a metafile or bitmap file. use the File | Print menu item. however. Print facilities. Rainflow half-cycle Empirical Cumulative Distribution. since updating them can significantly slow down the simulation. prior to running a simulation – the graph will be empty initially and will grow as the simulation progresses.w User Interface. Note that we do not recommend this for graphs of line clearance. Figure: Replay time indicator on a Time History Graph (vertical line at Time=16s) and on an XY Graph (grey cross in bottom right of the graph). Properties. Similarly. With the CTRL key pressed you simply click on a Time History graph and the indicator moves to where you have clicked. Also. 77 . for instance into a word processor document. The workspace feature provides a very powerful way of managing collections of related graphs. Copy and Paste with graphs You can also copy a graph to the clipboard – simply select the graph window by CLICKING on it and then using the Edit | Copy menu item. This direct manipulation of the replay time indicator is designed to help understand and visualise how your model is behaving at key moments of the simulation. You can also set up results graphs when in reset state. Graphs of simulation results are updated automatically as the simulation progresses. Any open 3D Views are updated to show the new replay time. they are kept even if you reset the simulation. Printing Graphs To print a graph. xls). then the graph window should be made large on screen (e. 3. For example.csv) or as tab delimited text (.g. It only appears on graphs that have multiple curves. 78 . 3. maximised). Note that the legend includes all the curves. use the File | Print menu. you can export the text to a file using the window's File menu or the popup menu. comma separated values (. Labels You can alter the text and fonts of the axis and tick labels. Save As Default Changes to a graph's properties normally only apply to that graph. Mouse shortcuts can also be used: CTRL+wheel to zoom. You can also easily transfer the results to other applications by either: Copy and paste via the Windows clipboard. Select the block to be transferred and press CTRL+C. the tick spacing and the number of small ticks. If you want to reverse this process then right click the mouse and choose Use Default Ranges from the popup menu. This is useful if you want to set the range to a specific value and want the tick spacing to be set automatically. But for general settings (fonts etc. and you can control their position and style.11 SPREADSHEETS Some numerical results (e. The Use Default Tick Spacing button sets the tick spacing and the number of small ticks to sensible default values based on the range. Legend The legend is a key showing which curve is which. even if some of them may not be visible at the time.txt). 3. Curves You can control the line properties and visibility for each curve on the graph. Choose Export from the popup menu to save as Excel format (. You can add more intercepts. If you wish to modify or extend it you must first save it as described below. You can control whether the legend is shown and if so where and using what font.g. e. In fact the X and Y axes themselves are considered to be intercepts. You can also copy text to the clipboard – simply select a region of text and then use the Edit | Copy menu item (or press CTRL+C).g. if you are copying a graph to a Word Processor and want the graph to be full page size. Spreadsheets Note: When copying a graph to the clipboard. From the clipboard you can then paste it into another application. If you want a number of graphs on one page of a document then the graph should be smaller on screen – try tiling or cascading the windows (see the Window menu). obtained with the Values button on the Results form) appear in an Excel compatible spreadsheet. Copying and Exporting Spreadsheets To print the spreadsheet right click and select Print. Alternatively. for example to mark things like stage start times.) you can also click the Save As Default button. like the axes. Intercepts Intercepts are lines. that go right across the graph. but remember that OrcaFlex time histories are normally quite long and will therefore produce many pages. SHIFT+drag to pan. If necessary. To print a text window. Saving to file. A form is then shown which allows you to change various aspects of the graph.w User Interface. range graphs.12 TEXT WINDOWS Simple text windows are used for some reports – see below. Printing. You can also change the appearance of a graph by double clicking on the graph or by selecting Properties from the graph's popup menu.10. the size of the graph window you copy from has an effect on how the text label fonts appear when the graph is pasted into another application. OrcaFlex then remembers the current settings for use with future graphs. By experimenting with various differently sized graphs it should be possible to arrange for the fonts to appear as you wish. as follows: Axes You can set the range.1 Modifying Graphs You can zoom into a graph by holding down the ALT key and dragging a box around the area that you want the graph to display. The spreadsheet is read-only. you can first adjust the printer setup using File | Printer Setup. When you release the mouse button the region selected will be expanded to fill the graph. This creates a text file with the . graph or spreadsheet) open within OrcaFlex. graph or spreadsheet windows can be saved using the Workspace | Save Workspace menu item.wrk file extension containing a specification of the current window layout.13 WORKSPACES It is common to have many windows (3D View. so when you first use this facility you need to configure OrcaFlex to tell it which compare program that you want to use. or by selecting the Window | Statics Progress menu item if you wish to watch the process more closely. You can then compare files as follows: On the Files page. If you define a default workspace for a directory then the workspace is restored whenever you open any simulation file in that directory. These can be data or simulation files. Workspaces Statics Progress Window During a Statics Calculation. This means that you can look at the same collection of results for any number of simulation files. This can be particularly valuable when sending files to someone who is not an experienced OrcaFlex user. As an alternative to comparing two data files on disk you can optionally choose to compare the currently loaded model with a single file on disk. The comparison is done using a user-provided compare program. OrcaFlex then saves the data from the two files to temporary text files and then runs the user-specified compare program to compare those text files. suppose you saved a workspace containing a graph of Effective Tension of a Line called Riser. This can even be useful when sending files to Orcina for software support because they contain a precise specification of the results you are interested in. the progress of the calculation is shown in the message box on the status bar. as described above. just a logical description of the window. 3.14 COMPARING DATA The Compare Data menu item opens the Compare Data form. and how to use it. 3. Configuration On the Configuration page you need to tell OrcaFlex the text file compare program that you want to use. Default workspaces As an alternative to loading a workspace by using the Workspace menu items you can associate default workspaces with either individual simulation files or with entire directories. If you then loaded a different simulation file and open that workspace then you would see the Effective Tension of the Line called Riser in the new simulation file and not the simulation filed open when the workspace was saved. If you define a default workspace for a simulation file then the workspace is restored whenever you open that same simulation file. 79 . Getting the most out of workspaces We recommend that you save your workspace files in the same directory as the OrcaFlex files. Like other text windows it may be printed. Click the Compare button. This window may be viewed by clicking on the message box during statics. see Configuration below. By including a workspace file with the results of interest you can be sure that they will view the correct information. However the messages are also sent to a text window that is normally minimised. If you do so then the workspace file will appear in the Most Recent Files list on the Workspace menu. Workspace files are not limited to simulation files – static results and multiple statics results can also be saved. The workspace can be restored at any time with the Workspace | Open Workspace menu item. copied or exported. specify the two files that you wish to compare. Workspace files can be very useful if you are sending simulation files to another person.w User Interface. we at Orcina have a preference for WinMerge. The workspace facility is designed to help manage these windows. The compare program must be a program that can compare text files passed to it through the command line. which allows you to find differences between the data in two OrcaFlex files. Many such programs are available on the web. Workspace files A collection of view. Note that the contents of the windows are not saved to the workspace file. This can give significant time savings if you wish to look at a number of different results windows for a large number of OrcaFlex models. For example. 3D View Axes View Axes The view axes show the same directions as the global axes. Different refresh intervals can be used for static and dynamic calculations. A value of zero means that OrcaFlex will never timeout the wire frame drawing. OrcaFlex also replaces special strings %name1 and %name2 with readable names describing the two files or objects that are being compared. Can also be set from the View menu. The majority of settings can be adjusted in the Preferences form. drag away and then back again. rather than at the global origin. 3D View Minimum Mouse Drag Distance Object positions are not updated until the mouse has been dragged at least this distance (in pixels). Preferences Compare Program This is the compare program's executable file name. Refresh Interval During a calculation all 3D View and Graph windows are updated at the rate specified. but are drawn in the top right-hand corner of 3D views. To make a small movement. if the model you are searching for is obscured by other objects then this method may not help you to locate the object. Normally the default setting of Flash object is sufficient to locate objects.15 PREFERENCES OrcaFlex has a number of settings that can be customised to suit the way that you work. For most compare programs the default setting of %1 %2 will be sufficient. If no program is specified OrcaFlex uses a very basic. If the drawing procedure exceeds the permitted time then the sea surface will not be displayed. like a blinking cursor. When the Flash object preference is set then the Locate action repeatedly draws and hides the object on the 3D View. compare facility. Not all compare programs have the capability of assigning readable names and just use the file name. Locate Object Method Can be either Flash object or Hide other objects. View Rotation Increment Each CLICK on a Rotate View button increments or decrements View Azimuth or Elevation by this amount. In this case you should use the Hide other objects preference. When the Hide other objects preference is set then the Locate action temporarily hides all other objects. Background Colour This sets the background colour of all 3D View windows.w User Interface. OrcaFlex replaces the special strings %1 and %2 with the file names of the temporary text files. built-in. It determines what method the Locate action in the model browser uses. or just the file name if the executable file resides in a directory which is on your system path. so the use of this facility is optional. Can also be set from the View menu. However. Wire Frame Drawing Timeout This sets the maximum amount of time that OrcaFlex will allow for the drawing of the sea surface in wire frame 3D views. 3D views with a Disturbance Vessel may be more prone to timing out due to the extra computational effort required to calculate the shape of the disturbed sea surface. If you are using WinMerge then we recommend using the following: /e /x /s /dl %name1 /dr %name2 %1 %2 3. You can specify either the full path. or edit the coordinate directly in the object's Edit Form. Command Line Parameters This defines the command line parameters that are passed to the compare program. This prevents accidental changes to object positions. Otherwise you will need to consult the documentation of your compare program. This limit will commonly only affect models with a high sea surface grid density and/or number of wave components. which is accessed by using the Tools | Preferences menu item. 80 . Scale Bar Determines whether a scale bar is drawn in 3D views. current and wind directions are drawn in the 3D view. The force is drawn as a line. This means that the AVI file produced can be extremely large. Can also be set from the View menu.0. if you are unsure of what value to use then we recommend trying 32 bit or 16 bit colour depth. 81 . buoys and line ends are shown. Out of Balance Forces If selected.w Note: User Interface. If you choose Uncompressed then each frame of the video is stored as an uncompressed bitmap. Node Axes Determines whether axes for line nodes are shown. whereas the other wave trains' directions are drawn in the secondary wave direction pen. When multiple wave trains are present the first wave train is taken to be the dominant one and is drawn using sea surface pen. This preference can also be set from the View menu. starting at the force's effective point of application. When OrcaFlex exports the video it ensures that the frame sizes are a multiple of this number. Can also be set from the View menu. For example XVID requires frame sizes to be multiples of 8. Environment Axes Determines whether the wave. and whose length represents the size of the force. In our experience the freely available (licensed under the GPL) XVID codec performs very well. Local Axes Determines whether the local axes for vessels. since it enables you to see how far a buoy or vessel is from being in equilibrium. This preference is sometimes useful for static analysis. Because the different graphics modes produce very different images they require different types of codec. Again. 4 characters long. Note: Out of Balance Forces are not drawn for shaded graphics views. the 3ivx codec (character code 3IV2). Shaded Graphics Codec The run-length encoding which works well for wire frame graphics is not suitable for shaded replays and in fact there is no suitable built-in codec in Windows. Padding: MPEG-4 codecs commonly require round number frame sizes (width and height in pixels). The AVI files produced using this codec can be played on most Windows PCs. Lines up to ViewSize/2 long mean forces up to 10 force units and lines from ViewSize/2 to ViewSize mean forces from 10 to 1000 force units. Global Axes Determines whether the global axes are drawn. The scaling is piecewise linear and based on the View Size of the 3D view. then in the static analysis (not during the simulation) there are extra lines drawn on the 3D view. Wire Frame Graphics Codec Run-length encoding is the default setting and is usually the best choice. Colour depth: Some MPEG-4 codecs require a specific colour depth. You can choose to use other codecs that are installed on your machine. Video The video preferences allow you to control the compression algorithm used for exported video. Should you do so then you must also specify the following information: Codec 4 character code: Codecs are identified by unique codes. This preference can also be set from the View menu. Good alternatives to XVID include DIVX. We would recommend using an MPEG-4 codec of which many are available. Drawing the local axes on the 3D view helps you check the orientations of these objects. at the model's global origin (0. Note: Local Axes are not drawn for shaded graphics views. representing the out of balance force acting on each vessel and buoy. The software which performs this compression is called a codec. Preferences The Scale Bar is not drawn for shaded graphics views because it would be meaningless due to perspective. This preference can also be set from the View menu.0). The Shaded Graphics topic has more information about the XVID codec. If you are unsure of what number to use for your codec then we recommend trying 8 which usually works. This codec offers good compression rates for OrcaFlex wire frame video. For example. Batch Auto Save If this is enabled then simulations run in batch mode are automatically stored to simulation files at the specified regular Auto Save Interval. file name. Add program/file details to output If this is checked then external output includes text with details of the program version.e. When you save a file. Once a message has been disabled.w User Interface. This is useful if your computer is prone to failure (for example because of overnight power failures) since the part-run simulation file can be loaded and continued. you can select which format to use with the Save as type drop-down on the standard file dialog. Messages A number of OrcaFlex warning messages can be disabled by checking Don't show this message again on the warning message form. but less compression (i. Higher values have better visual quality. since then the program will then waste a lot of time repeatedly storing away the results. spreadsheets can be output in Excel. Lower values have worse visual quality. but greater compression (i. The Auto Save Interval should be neither too short. larger file size). Miscellaneous Show Splash Screen Determines whether OrcaFlex displays its splash screen when the program starts. Default File Types OrcaFlex outputs files of a wide variety of formats. These messages can be re-enabled by checking the appropriate box on this page. nor too long. comma separated or tab delimited formats. The default file types preferences allow you to control which file format is first selected when a file dialog opens. Preferences Output JPEG Compression Quality A value between 0 and 100 that determines the quality of exported JPEG files.e. file modified time etc. it will not be shown again. since then a lot of simulation work will be lost if a failure occurs. smaller file size). 82 . rather than having to re-run the whole simulation from scratch. by using the Calculation | Batch Processing menu item. This is useful if your computer is prone to failure (for example because of overnight power failures) since the part-run simulation file can be loaded and continued. The list can include any number and mixture of the following types of job: 1. Note: If you wish to use Excel for any reason while OrcaFlex is processing spreadsheets within a batch it is important that you open Excel first. 4. 6. An OrcaFlex Spreadsheet (.xlsx).1 Introduction Simulations. This choice is made from the Add Files file dialog window. but with a . script files.1 INTRODUCTION OrcaFlex provides several important facilities for automating and post-processing work: OrcaFlex is supplied with a special Excel spreadsheet which enables you to automate the extraction of simulation results into your own spreadsheet.dat or . if you have a quadcore machine then 4 simulation files can be run concurrently. For example you can write programs to automate post-processing or that use OrcaFlex as a statics calculation engine.2. So.2 BATCH PROCESSING 4. OrcaFlex opens the simulation file. then open the file you wish to work on. runs the dynamic simulation and then saves the results in a simulation file with the same name as the data file. moorings etc. 4. OrcFxAPI is a Windows dynamic link library (DLL) that is installed when you install OrcaFlex. finishes the dynamic simulation and then saves the completed simulation. See the OrcFxAPI help file for details. Static analysis of pre-prepared OrcaFlex data files (. or from the popup menu. performs the static analysis and then saves the results in a simulation file with the same name as the data file.yml). and which provides facilities for setting data. resulting in unpredictable failures. OrcaFlex opens the data file. OrcaFlex includes a well-documented programming interface called OrcFxAPI (short for OrcaFlex Application Program Interface).sim extension. A batch script file (. 5. Multi-threading The batch processing functionality can make use of multiple processor cores. OrcaFlex performs the fatigue analysis and saves the results to a binary . for example as an overnight job. The most common use of script files is to perform a series of systematic variations on a base data file.sim). Note that if the spreadsheet's "Contains Dependencies" options is checked then the workbook will be processes as a single job using a single thread. Dynamic analysis of pre-prepared OrcaFlex data files (. performs the static analysis.ftg file. You can then use the normal Excel calculation facilities to do your own customised post-processing and graphing. A fatigue analysis file (.dat or .yml). The simulations can either be of pre-prepared data files. post-processing spreadsheets and fatigue analyses can all be run in unattended mode. If it isn’t checked. OrcaFlex opens the script file and obeys the commands in turn. calculating static positions and extracting results from those calculations or from pre-run simulation files.yml). OrcaFlex will process all post-processing sheets in the Excel workbook.xls spreadsheet. Partially-run OrcaFlex simulation files (. 2. but with a . When adding data files (. OrcaFlex opens the data file. please contact Orcina. Introduction AUTOMATION 4. The reason for this is that when you double click an Excel file. For further information or to discuss possible applications of OrcFxAPI. Windows will try to use the copy of Excel OrcaFlex has claimed.ftg or . This command opens a form that allows you to set up a list of jobs that are to be run.dat or .txt). OrcaFlex can auto-save partial completed dynamic simulations to file at regular intervals during the batch job. This is a text file which contains OrcaFlex script commands.xls or . One important example application of this is for real-time monitoring of pipes. The Batch Processing facility enables you to run a set of simulations in unattended mode. 83 . The OrcaFlex Spreadsheet mentioned above also has facilities for automating the production of batch script files and text data files. overwriting the original file.yml) you need to specify whether static or dynamic analysis is to be performed. In addition the results tables are saved to an . or else can be specified by a batch script file that specifies the simulation as variations on a base data file. 3. rather than having to re-run the whole simulation from scratch. for example. Models can define post calculation actions which are executed after batch analyses.sim extension.w 4 Automation. then each instructions sheet will be broken down into multiple load cases which are individually added to the batch and may be processed simultaneously. Batch Processing Since some batch tasks can depend on the output of other tasks OrcaFlex processes tasks in a very particular order. Any errors are reported once all jobs have been processed. as follows: The batch script files are all processed first. This feature is intended principally for users with networked licences. Consequently any simulations that are processed with RunDynamics commands cannot be performed in parallel.2 Script Files OrcaFlex provides special facilities for running a series of variations on a base data file. Once again. This contains a sequence of commands to read a data file. Because of this it is advisable to use the SaveData command rather than the RunDynamics command when creating batch scripts. Script files can be written using any text editor. Such a script would create a number of OrcaFlex data files which you could then process in the batch form using all available processor cores. checks that they contain valid OrcaFlex data or script commands and reports any errors. The file can also include comments. Stop Batch Terminate processing of batch jobs. Close program when Batch completes If checked then OrcaFlex will close once the processing of jobs completes. Batch Form User Interface Close Dismisses the batch form. The syntax for the instructions is described in the next topic. The commands in batch script files are processed sequentially. it is quite unusual to do this because there are very productive facilities in the OrcaFlex spreadsheet for automatically generating script files for regular sets of cases. 84 .2. the OrcaFlex spreadsheet offers a facility to generate these text data files. 4. using a script file. Because it is common to write scripts that output data files it is important to complete all batch scripts before processing the data files. Files can be added whilst a batch is running. That is if you are browsing your file system then you can highlight files and drag them onto the jobs list. make modifications to it.w Automation. Any data or simulation files are processed next. When checking OrcaFlex spreadsheet or fatigue files it simply confirms the file exists. This can be useful if you temporarily want another process on your machine to have the processor resource that OrcaFlex is using. Files can also be added by drag and drop. It allows you to release your claim on an OrcaFlex licence as soon as the batch of jobs is complete. These warnings are suppressed when you are operating in batch mode and this button allows you to review them once the simulation has completed. Finally any OrcaFlex spreadsheet files or load cases are processed. Remove Files Removes any files highlighted in the jobs list. and run the modified file. These also cannot be started until all data or simulation files have been processed. Warnings Displays a window allowing you to review all warnings generated by OrcaFlex during a calculation. Fatigue files are processed next. These can be used to specify load case variations. Add Files Adds jobs to the list. Note that this feature has the limitation that all pre-existing jobs must be run to completion before the program starts processing the files added whilst the batch was active. If a job fails then it is abandoned but other jobs are still attempted. storing the results for later processing. However. Run Batch Processes the list of jobs. Pause Batch Pauses the currently running batch jobs. Check Files OrcaFlex opens each file in the jobs list. A more recently introduced alternative to script files are text data files. These use simulation files as input and so should not be started until all data or simulation files have been processed. You need to put quotes round file names or other parameters that include spaces or non-alphanumeric characters.dat where load is the directive and c:\temp\test. Some of the commands have different interpretations. The active model can change due to a Load/LoadData command. For example '6" pipe' and "200' riser" are valid. 2. or following a NewModel/NewFatigue command. Saves tabular results to an Excel workbook with the same name.2.ftg extension. variables or values containing spaces or non-alphanumeric characters must be enclosed in single or double quotes and they must not contain the same quote character as is used to enclose them. but an . those processors will not be fully utilised. Lines etc. Load <FileName> Opens the OrcaFlex file named <FileName>. and object names are all case independent. Note that: Directives.w Automation. 4.3 Script Syntax An OrcaFlex batch script is made up of commands.2. Note: We no longer recommend that you use the RunStatics and RunDynamics commands. The recommended approach is to use the batch script to generate OrcaFlex data files and then add those to the batch job list. LoadData <FileName> Opens the data from the OrcaFlex data file named <FileName>. RunDynamics <FileName> Run dynamics for the current model and save the resulting simulation to <FileName>. File names. so needs to be enclosed in double quotes instead of single. The commands in a batch script are executed sequentially. which are ignored. so needs to be enclosed in single quotes. Batch Processing 4. optionally separated by white space (one or more spaces or tabs). This means that if your machine has multiple processors. or a Fatigue Analysis. RunStatics <FileName> Perform statics for the current model and save the resulting simulation to <FileName>. but the following are not valid: 6 inch pipe – contains spaces. This can be either an OrcaFlex model containing Vessels. Run <FileName> (Fatigue active) This command: 1. The file can be a data file. at the start of script execution to being an OrcaFlex model. a simulation file or a fatigue analysis file. again with optional white space separators. 3.4 Script Commands The script commands are executed in the context of an active model. The following batch script commands are currently available. A command can be: 1. variable names. and comments. 85 . as described below.. 6"pipe – contains a double quote. For example: Length = 55. A directive followed by one or more arguments.xls extension. This will result in the most effective use of processor resources.dat is the argument. which are obeyed sequentially. 2. depending on what type of model is active. '6' pipe' – contains a single quote. so needs to be enclosed in quotes. Performs the fatigue analysis. A comment is a line that is either blank or on which the first non-blank characters are "//".0. After the file is saved the model is reset. arguments. Saves the results to <FileName> which should have the . For example: load c:\temp\test. After the file is saved the model is reset. An assignment of the form VariableName=value. If your script includes a relative file name then it is taken to be relative to the directory from which the script was loaded. The active model defaults. Run <FileName> (OrcaFlex model active) This command is identical to RunDynamics. Note: In the Load/LoadData. NewFatigue This command makes the active model a Fatigue Analysis and then resets data to default values. When saving data. for example: Select Environment Select WaveTrain Primary WaveDirection = 30.yml then a text data file will be saved. deletes all objects from the model and then resets data to default values.0 Similarly. if the file extension is . This command is equivalent to the File | New menu item. If the optional <ObjectName> parameter is included then the new object will be given that name. if the Environment has been selected and there is more than one current data set. Select Edit | Add from the Model Browser menu to see a list of possible values for this parameter. SaveData <FileName> Save the data from the current model to <FileName>. Save/SaveData and RunStatics/RunDynamics/Run commands. Save <FileName> (Fatigue active) Saves the fatigue model to <FileName> which should have the . The <ObjectType> parameter can be "Line Type". NewModel This command makes the active model an OrcaFlex model. This list of possible variable data source object types can be found in the Data Source Type tree on the variable data form. Alternatively variable data sources can be created by setting the <ObjectType> parameter to "Bending Stiffness". Otherwise a data file will be saved. <ObjectName> must then be either the name of an object that exists in the current model or one of the reserved names 'General' (for the General data form) or 'Environment' (for the Environment data form). meaning select the named object. "Vessel Type". otherwise a binary data file will be saved. and by default is 'object'. then before you can specify any wave train data you must give another select command to select the wave train. otherwise a binary data file will be saved. You would normally follow this command with a Save command. "Drag Coefficient" etc. The <ObjectType> parameter is optional. Create <ObjectType> [<ObjectName>] Creates a new object of type <ObjectType>. If calculation results (either statics or dynamics) are available then a simulation file will be saved. then you must select one of them before specifying any current data. Other <ObjectType> values only need to be specified in the following special cases. ExtendSimulation <StageDuration> Adds a new stage of length <StageDuration>. Reset Resets the current model. "Line". Delete <ObjectName> Deletes the object called <ObjectName>. If the Environment has been selected and there is more than one wave train. This command is equivalent to the Calculation | Reset menu item. Some examples of the select and assignment commands are given in Examples of setting data. "Winch" etc. If the file extension is .ftg extension. This second select command has the form: Select WaveTrain <WaveTrainName> So. This command is equivalent to the Fatigue Analysis File | New menu item. Batch Processing Save <FileName> (OrcaFlex model active) Save the current model to <FileName>.yml then a text data file will be saved. The new object is automatically selected which means that subsequent assignment commands apply to this new object. This command is equivalent to the Calculation | Extend Dynamic Simulation menu item. Select [<Object Type>] <ObjectName> Specify the object to which subsequent assignment commands will apply. For example: 86 .w Automation. if <FileName> is a relative path then it is taken to be relative to the directory from which the script file was loaded. but in this case the first row of the table is stage 0 (the build-up stage) so this command (slightly confusingly) sets the velocity for stage 1. WaveLoad or QTF. before specifying vessel type data for a given wave direction you must give another select command to select that direction. and is always 1-based. For example: Select SNcurve "S-N Curve1" SNDataA = 23. but makes scripts more readable. then before specifying any draught-dependent data you must give another select command that selects the draught.16 When the a Fatigue Analysis is active. For example: Select Environment CurrentRamp = Yes If VariableName is the name of a variable that appears in a table in OrcaFlex.0 Note that this is not the same as setting the Active Current.8 Note: Indentation with spaces or tabs is optional.w Automation. numeric or text) and it must be given in the same units as used in the current model. Batch Processing Select Environment Select Current Current2 RefCurrentDirection = 270. 87 . for example: Select "Vessel Type1" Select Draught Transit Select RAOs Displacement RAOOriginX = 10 RAOOriginY = 0 RAOOriginZ = 2 Select Direction 45 RAOSurgeAmplitude[2] = 0. More examples of the select and assignment commands are given in Examples of setting data.8 sets the velocity in the 2nd row of the table. then its row number must be given. you should avoid setting up multiple current data in batch scripts if possible: this is best done interactively on the Environment form.0 Select TNcurve "T-N Curve1" TNcurvem = 2.e. Assignment Assignment commands take the form VariableName = Value The VariableName on the left-hand side must be one of the recognised variable names and the named variable must exist in the currently selected object. Note that this sometimes requires care. If a vessel type has been selected and it has more than one draught. This second select command has the form: Select Draught <DraughtName> Before specifying data for RAOs you need to specify the type of RAOs – this can be either Displacement. [1] is the first row of the table. This takes the form: Select Direction <Direction> So. The row number is given as an index enclosed by either square or round brackets (don't mix them on the same line). since in OrcaFlex the table might not be 1-based. For example: Select Vessel1 Length = 110 Draught = "Operating draught" If VariableName is the name of a variable that appears in a check box in OrcaFlex then the Value should be Yes or No.1 Select Direction 90 RAOSurgeAmplitude[2] = 0. The Value on the right-hand side must be in the appropriate form for that variable (i. you need to select S-N and T-N curves before assigning their data. This is done with a command of the form: Select RAOs <RAO type> Similarly. the command PrescribedMotionVelocity[2] = 4. For example.e. In fact. i. when setting the prescribed motion for a vessel. The object name is most easily found on the Model Browser. SHEAR7MdsFile <LineName> <FileName> [<FirstMode> <LastMode>] Exports to <FileName> a SHEAR7 Mds file for the line named <LineName>. The input data for the Wizard should first be set using data assignment commands. Batch Processing InvokeWizard Sets the data for the selected object using either the Line Type Wizard or the Plasticity Wizard.5 Examples of setting data The Select command is probably the most difficult script command to use. If these parameters are omitted then all modes are exported. 2.txt) or a comma separated file (.csv). Only the Transverse and Mostly Transverse modes are included in the exported file. SHEAR7OutputFile <LineName> <FileName> Exports to <FileName> the SHEAR7 output file for the line named <LineName>.csv). The file can be an Excel spreadsheet (. If you have specified first and last modes to export then these mode numbers refer to the transverse and mostly transverse modes. a tab delimited file (. Some examples of this procedure follow: Select Link1 UnstretchedLength = 50 Select "3D Buoy1" Mass = 4 Volume = 8 88 . 3. The file extension that you specify (e. Set the data using one or more commands of the form VariableName = Value.xls). . then that vessel will be used.xls). If no vessel is specified. Sort the modes into order of decreasing period / increasing frequency.w Automation.2. selecting the required data item and pressing F7. This command is only available if the SHEAR7 interface is in use. DisplacementRAOsReport <FileName> [<VesselName>] SpectralResponseReport <FileName> [<VesselName>] Exports the vessel response report spreadsheets to the specified file for the specified vessel. SHEAR7DataFile <LineName> <FileName> Exports to <FileName> a SHEAR7 data file for the line named <LineName>. If they are specified then mode numbers in the range <FirstMode> to <LastMode> inclusive are exported. The decision is taken based on the file extension that you specify. 4. Select the object using the command Select <ObjectName>. and there is only one vessel in the model. An example of how to use this command is given in Examples of setting data. The program takes the following steps: 1. The <FirstMode> and <LastMode> parameters are optional. . The decision is taken based on the file extension that you specify.g. The input data for the Wizard should first be set using data assignment commands. Remove all modes which are not Transverse or Mostly Transverse.plt etc. To help understand how it works we present some examples of its use below: Simple examples For many objects the script commands for setting data take the form: 1. WaveSearch <FileName> Exports the wave search spreadsheet to the specified file. The file can be an Excel spreadsheet (. An example of how to use this command is given in Examples of setting data. 4. Export the modes in the range <FirstMode> to <LastMode> inclusive. The selected object must be either a line type or a bend stiffness variable data source. The variable name is found by opening the relevant data form. The input data for the response reports should first be set using data assignment commands. a tab delimited file (. The input data for the wave search should first be set using data assignment commands. Calculate all modes. InvokeLineSetupWizard Invokes the Line Setup Wizard calculation. 2.) is used to determine which output file is exported.out.txt) or a comma separated file (. Drag Chain Type and Wing Type data These data are also set by first selecting the type by name and then assigning the data.01 OuterTimeStep = 0. This makes use of the alternative syntax for Select which is Select <Object Type> <ObjectName>. This is not essential but makes reading the script easier.1 Data found on the Environment data form Data found on the Environment data form can be set as follows: Select Environment SeaBedStiffness = 3000 SeaBedDamping = 80 For data specific to a particular wave train you must first select the Environment and then select the particular wave train.5 Select Line1 IncludeTorsion = Yes Note: The name "3D Buoy" needs to be enclosed in quotes because it contains a space. When viewing for all Line Types at once.28 InnerDiameter = 0. You cannot set Line Type using index notation. For a wave 89 . Similar rules apply to Clump Type data and to Flex Joint Type data. we immediately break it in the section below! Line Type. the data appear in tables with one row per Line Type.21 On the Line Types data form there is an option to view the data for all Line Types at once or to view by individual Line Type. Data which appear in tables are always set using the indexed notation used above. Having stated this rule.2 Drag[2] = 0. The following example sets the number of sections of the line to be 2 and then sets data for both sections in turn. Clump Type and Flex Joint Type data These data are set by first selecting the type by name and then assigning the data as illustrated below: Select "Line Type1" OuterDiameter = 0.15 Moment[2] = 0.w Automation. If the name contains a double quote and spaces then it should be enclosed with single quotes. For example: Select "Drag Chain Type1" Length = 12 Select "Wing Type1" NumberOfAngles = 12 Angle[2] = -80 Lift[2] = 0. Data in tables and indices Some data in OrcaFlex appear in tables.5 Data found on the General data form Data found on the General data form can be set as follows: Select General InnerTimeStep = 0. Batch Processing Height = 7. However. For example consider the Structure page of the Line data form which specifies how a Line is made up of a number of sections. Each section is specified by its Line Type. Select Line1 NumberOfSections = 2 LineType[1] = Riser Length[1] = 75 TargetSegmentLength[1] = 4 LineType[2] = Rope Length[2] = 200 TargetSegmentLength[2] = 20 Note that we use blank lines to lay out the script. the data must be set by first selecting the type by name and then assigning the data. length etc. For example: Select Environment Select WaveTrain "Swell from SW" WaveDirection = 135 WaveType = "Dean Stream" WaveHeight = 2. Again this requires the alternative syntax for Select as shown below: Select Environment MultipleCurrentDataCanBeDefined = Yes NumberOfCurrentDataSets = 2 CurrentName[1] = "120deg" CurrentName[2] = "150deg" Select Current "120deg" RefCurrentDirection = 120 Select Current "150deg" RefCurrentDirection = 150 ActiveCurrent = "150deg" Vessel Type data Some Vessel Type data are set in a straightforward manner as follows: Select "Vessel Type1" Length = 120 PenWidth = 3 Symmetry = "XZ plane" However.5 WavePeriod = 18 Select WaveTrain "Local Wind Sea" WaveDirection = 40 WaveType = JONSWAP WaveHs = 5. wave load RAOs. Batch Processing train you replace <ObjectType> with WaveTrain and replace <ObjectName> with the name of the wave train as defined on the Environment data form. wave drift QTFs and sum frequency QTFs you must also specify to which type of RAO the data apply.w Automation.7 WaveTz = 9 Data for Current data sets Multiple Current data sets can be defined. the majority of Vessel Type data require that you also specify to which draught the data apply. For example: Select "Vessel Type1" Select Draught "Survival Draught" Select RAOs Displacement RAOOriginX = 10 RAOOriginY = 0 RAOOriginZ = 2 Select RAOs WaveLoad RAOOriginX = 0 RAOOriginY = 0 RAOOriginZ = 0 Select RAOs WaveDrift RAOOriginX = -3 RAOOriginY = 0 RAOOriginZ = 4 Select RAOs SumFrequencyQTF RAOOriginX = -3 RAOOriginY = 0 RAOOriginZ = 4 90 . For example: Select "Vessel Type1" Select Draught "Transit Draught" CurrentCoeffSurgeArea = 1200 CurrentCoeffSwayArea = 1100 CurrentCoeffYawAreaMoment = 120E3 To set data for displacement RAOs. 0 SelectedDepthBelowSeabedFrom = 10.0 ModelType = "API RP 2A Soft Clay" EffectiveUnitSoilDensity = 1. wave load RAOs and wave drift QTFs) you must specify to which direction the data apply.5 RAOYawAmplitude[2] = 0. P-y Model data P-y Model data is complicated because each depth must be selected before the model data can be accessed. Draught1" DisplacedVolume = 85e3 To set the added mass and damping data you must select the period and the row/column body: Select "Multibody Group1" NumberOfAddedMassAndDampingPeriodsOrFrequencies = 2 AddedMassAndDampingPeriodOrFrequency[1] = 11.18 However.0 C3 = 15. Batch Processing Note that the variable names are the same but different data are set depending on which type of RAOs has been selected. Draught1" AddedMassX[1] = 42.0 The fact that it is possible to set this data through batch script does not necessarily make it a good idea to do so.0 ModelType = "API RP 2A Sand" EffectiveUnitSoilDensity = 1.6 UndrainedShearStrength = 6.0 SelectedDepthBelowSeabedFrom = 0. Draught1" SelectedAddedMassAndDampingColumnBody = "Vessel Type2.0 SelectedAddedMassAndDampingRowBody = "Vessel Type1.0 SelectedAddedMassAndDampingPeriodOrFrequency = 11. In addition.0 91 . it is worth pointing out that situations where you would wish to specify RAO table data in a batch script are rare.0 k = 42.0 DampingX[1] = 35.13 Select Direction 45 RAOYawAmplitude[2] = 0. Select "P-y Model1" NumberOfDepths = 3 DepthBelowSeabedFrom[1] = 0.0 AddedMassAndDampingPeriodOrFrequency[2] = 13.3 C1 = 1.5 Epsilonc = 4.0 DepthBelowSeabedFrom[2] = 10. For example: Select "Vessel Type1" Select Draught "Survival Draught" Select RAOs Displacement Select Direction 22. when setting RAO table data (for displacement RAOs.w Automation.0 ModelType = "P-y Table" NumberOfEntries = 2 Deflection[1] = 0. It is much more likely that you would import these data into OrcaFlex from some external source and then save it as part of the base case data file.0 SelectedDepthBelowSeabedFrom = 20.0 J = 0. Multibody group data Some multibody group data are set in a straightforward manner as follows: Select "Multibody Group1" NumberOfBodies = 2 VesselType[1] = "Vessel Type1" VesselType[2] = "Vessel Type2" To set the stiffness data you must first select the body: Select "Multibody Group1" SelectedStiffnessBody = "Vessel Type2. it might be prudent to look for a more elegant solution to your problem.0 DepthBelowSeabedFrom[3] = 20. Should you find yourself doing so. This data is exceedingly unwieldy to manipulate in batch script.1 C2 = 2. 15 The SHEAR7 Hydrodynamic and Structural Section data apply to a line section.001 APIRP2RDSMYS = 380e3 Variable Data sources Data for Variable Data sources can be set from the batch script.2 Resistance[2] = 11.85 Code Checks data Code Checks data ownership is divided between the Code Checks object and Line Type objects. Batch Processing Resistance[1] = 0. The procedure for setting variable data sources is illustrated below: Select Stiffness1 NumberOfRows = 3 IndependentValue[1] = 0 DependentValue[1] = 0 IndependentValue[2] = 0.7 SHEAR7 Whole Line data and Stress Concentration Factors are accessed through a line object: Select Line1 SHEAR7CurrentProfileDiscretisation = "Regular spacing" SHEAR7CurrentProfileTargetSpacing = 10 SHEAR7LocalSCFArcLength[1] = 32. Model wide data items are owned by the Code Checks object: Select "Code Checks" APIRP2RDDesignCaseFactor = 1 The per line type code check data are just like any other line type data: Select "Line Type1" APIRP2RDCorrosionThickness = 0.0 SHEAR7LocalSCF[1] = 1.5 PenetratorContactArea[2] = 0.4 DependentValue[3] = 5000 92 . the penetrator locations data set must first be selected: Select "Line Contact Data" Select PenetratorLocationsDataSet Locations1 Penetratorx[2] = 13. so the index of the section is required: Select Line1 SHEAR7StrouhalType[1] = "Rough Cylinder" SHEAR7LiftFactor[1] = 0. The SHEAR7 file version.w Automation.6 Penetratory[2] = -2.0 Deflection[2] = 0. although once again we feel it is unlikely that you would need to do this often.9 SHEAR7SectionSNCurve[2] = Curve1 Line Contact data To edit penetrator data. output file options and S-N curve data are owned by the SHEAR7 object: Select "SHEAR7 data" SHEAR7FileVersion = 4.2 DependentValue[2] = 1000 IndependentValue[3] = 0.0 SHEAR7 data SHEAR7 data ownership is divided between the SHEAR7 object and Line objects.6 SHEAR7OutputDmg = Yes To access the S-N Curve table requires that the curve is selected first: Select "SHEAR7 data" Select SHEAR7SNCurve Curve2 SHEAR7SNCurveNumberOfPoints = 3 SHEAR7SNCurveS[3] = 10E5 SHEAR7SNCurveN[3] = 10E4 SHEAR7SNCurveEnduranceLimit = 750. calculation mode and convergence parameters) are owned by the General object. These data are owned by a variety of different objects.0 PolarR[2] = 340. the data still belong to each individual object and the appearance of a table of data is purely presentational.0 Select Line2 LineSetupIncluded = No InvokeLineSetupWizard Polar Coordinates data on the All Objects form The All Objects data form allows end connection data to be specified as polar coordinates and these polar coordinates data are only accessible from this form. The input data should be set before invoking.0e3 InvokeWizard Line Setup Wizard The Line Setup Wizard can be used from batch script using the InvokeLineSetupWizard command. Once this is complete the Wizard is invoked using the InvokeWizard command as illustrated below: Select Stiffness1 StressOD = 0. Batch Processing Note that IndependentValue and DependentValue are the variable names for the X and Y columns of the variable data source. However. Line Type Wizard The Line Type Wizard can be used from batch script.082 PipeWallThickness = 0.0 PolarTheta[2] = 45. Once this is complete the Wizard is invoked using the InvokeWizard command as illustrated below: Select "Line Type1" WizardCalculation = "Homogeneous Pipe" PipeMaterial = Steel PipeOuterDiameter = 0. First of all you must select the Line Type and set its Wizard data.0 Select Line2 PolarR[1] = 20.5 InvokeWizard Plasticity Wizard The Plasticity Wizard can be used from batch script. The following script illustrates this: Select General LineSetupCalculationMode = "Calculate Line Lengths" LineSetupMaxDamping = 20 Select Line1 LineSetupTargetVariable = "Tension" LineSetupLineEnd = "End A" LineSetupArclength = 0.0 PolarTheta[1] = 45.2 FloatPitch = 5. The model-wide data (e.80 FloatLength = 1. This means that to set the data you must first select the individual Line. First of all you must select the Bend Stiffness variable data source and set its Wizard data. Link or Winch and then set the data.g.0e6 RefStress = 385.005 InvokeWizard Select "Line Type2" WizardCalculation = "Line with Floats" FloatBaseLineType = "Line Type3" FloatDiameter = 0. as illustrated below: Select Line1 PolarR[1] = 20. The data appear in a table containing all Line. The line-specific data are owned by each individual line.w Automation.27 Type = "Ramberg-Osgood curve" E = 230.0 LineSetupTargetValue = 830. Winch and Link connections.30 StressID = 0. That is if you are setting data for a bending stiffness data source then IndependentValue denotes curvature and DependentValue denotes bend moment.0 93 . 0 PolarTheta[3] = 90. Navy.2. 94 . Each pair of hex digits controls the amount of red. To check for errors in your scripts. Teal. If you want more control over the colour then you can specify an RGB value as an integer. use the "Check Files" button on the OrcaFlex batch form. The only complication is that you must select S-N and T-N curves before assigning their data. Fatigue Analysis data Fatigue analysis data are quite simple in the script.0 PolarTheta[2] = 90.0 PolarR[2] = 340. Aqua. A value of $C0C0C0 gives a light grey and $808080 produces a darker grey.5 SNcurveCount = 2 SNcurveName[2] = ProjectSteel Select SNcurve ProjectSteel SNDataEnduranceLimit = 0. Gray. For winches the index identifies the winch connection point. Instead a neat trick is to specify the colour as a hexadecimal value by prefixing it with a $ sign as follows: Select "Line Type1" PenColour = $0000FF Select "Line Type2" PenColour = $00FF00 Select "Line Type3" PenColour = $FF0000 This sets the colours to red. The following example has the same effect as the previous one: Select "Line Type1" PenColour = 255 Select "Line Type2" PenColour = 65280 Using decimal values for RGB value is impractical.0 4.6 Handling Script Errors As with other computer programs. OrcaFlex batch script files can easily contain errors. Green. Blue.0 For lines and links an index of 1 means End A and an index of 2 means End B.0 PolarR[4] = 10. MedGray and White. Batch Processing PolarTheta[1] = 90. Lime. Maroon. Cream. SkyBlue.0 ToArclength[1] = 30. Olive.0 Select Winch1 PolarR[3] = 0. NewFatigue DamageCalculation = "Homogeneous pipe stress" AnalysisType = Rainflow ArclengthIntervalsCount = 1 FromArclength[1] = 0.0 SCF[0] = 1. Red. Fuchsia. This will read and obey all the commands in the script files except those that perform calculations or write files. The simplest is to use the pre-defined colours as follows: Select "Line Type1" PenColour = Red Select "Line Type2" PenColour = Green The full list of pre-defined colours is: Black. You can then correct the problem before running the script. It will then report any errors it finds.0 PolarTheta[4] = 90. Silver. including the line number on which the error occurs. green and blue. So white is $FFFFFF and black is $000000. Yellow. green and blue respectively. Purple. Colour data Drawing colour data items can be set through batch script in a variety of ways. It is therefore wise to check your script file for errors before running it as a batch job.w Automation. MoneyGreen. then select the Script Table cell and then click the Create Batch Scripts command which can be found on the OrcaFlex menu in Excel. and then down to the next row.8 and line lengths of 100 and 120. If the data item is in a table (or group) of data items then the Data Names form displays the names of all the data items in the table. But if you incorrectly specify a variable name which is nevertheless valid then OrcaFlex cannot detect the error. with the cell's value appended to the last header row command. To do this you must use the keyword Script Table Row. The different columns in the table each have their own names. open the appropriate data form. The names of the data items are based on the corresponding labels used on the data form. The cells in this section are processed from left to right on each row. The cases (and the whole table) end at the next row that has a blank cell in the table's first column. The other columns are ignored.dat".7 Obtaining Data Names Each OrcaFlex data item has its own name that is used to specify it in a script file.2. one row for each case. So you need to be very careful that you use the correct variable names for the data items that you want to change. The batch script filename is specified in the cell next to the Script Table cell. and then open (e. starting with "//") in the first column. It is relative to the directory containing this spreadsheet.e. Note that you can add extra columns to the table or indeed remove columns from the table. The title rows end at the first row with a blank cell in the table's first column. so if you don't specify the folder name then it will be created in the folder containing this spreadsheet. The table can be arranged with rows and columns transposed. 4. To find out the name of a data item. But if the cell is not empty then all the (non-empty) script commands in the header rows in that column are written to the script. The title rows can therefore contain any comments or other script commands that you want to appear at the start of the script. select the data item.g. Finally there are a series of rows. and the contents of those cells are simply copied to the script. and a blank value leaves the data item as it was in the previous case.w Warning: Automation. This allows different columns to set data values for the various cases. If the cell is empty then no script commands are generated. 4. and each cell generates script commands as follows. consisting of 3 sections: First is one or more title rows (shown with a green background in the example below). An example of this alternative approach can be found in the default OrcaFlex spreadsheet template.8 Automating Script Generation The OrcaFlex Spreadsheet has facilities for automating the generation of a script file for a regular set of cases. Next is a series of header rows for the cases (shown with a blue background in the example below). Because no path is specified then this file is located in the same directory as the spreadsheet. Below the Script Table cell is a table defining the script. Batch Processing If you misspell a variable name in an assignment statement then "Check Files" will report an error. by right click) the popup menu and select the Data Names command (or press F7). Four cases are produced based on this data file with current values of 0. This displays the name of the selected data item which you can select and copy directly into your batch script. 95 . An example is shown below: Figure: Example table for automatic batch script generation The script generated by this table loads a base case from a file called "Base Case. Only the first table column is used in these rows.5 and 0.2. The last header row is deemed to be the next row with a comment command (i. you then need to add an index to specify which row you want. To use this facility select the Pre-processing worksheet. Note: The Save. This is because the file name contains a space. The generated script adheres to the formatting specified in the Excel cells. the corresponding value in the script will also have 1 decimal place. First select the cell containing the text Script Table. Save and Run button Saves the script file and then processes it. say. it cannot be used if the script contains any Run commands. 1 decimal place. Otherwise the script is processed from within Excel – progress is reported on the Excel status bar. Run and Submit button is only available if Distributed OrcaFlex is installed on your machine. Should you wish to. Save button Saves the script file.w Automation. Then drop down the OrcaFlex menu contained in the main Excel menu and click Create Batch Scripts. you can modify the script file name at this point. So. 96 . Each data file saved by the script is then submitted to Distributed OrcaFlex which runs and saves the simulation file. the quotes are not needed for the file names in the last column because they do not contain spaces. You should check that the automatically generated script is as intended. However. The script is generated as follows. Batch Processing Notes: The cell containing the base case data file name has the file name surrounded by quotes. In addition. When you do this you are presented with the following window: Figure: Automatically generated batch script The script file has not been saved yet. If the script has any Run commands then OrcaFlex is loaded and the script is processed by the standard OrcaFlex batch form. Run and Submit button Saves the script file and then processes it within Excel. Save. if a cell is formatted to have. If there is a problem with the script you can click the Close button and correct the script table. Data in tables and indices Table data are set using an index in square brackets [i] after the data name. 3D Buoy1 and Line1 are modified: BaseFile: BaseCase.yml Link1: UnstretchedLength: 25 3D Buoy1: Mass: 4 Volume: 8 Height: 7. CurrentRotation: 97 . where i is the index of the table row starting at 1.0 # Define the current profile table CurrentDepth. Every table has an associated row count data item.2 RefCurrentDirection: 36. the object must be first selected by name. This results in a much more compact Text Data file that can be easily generated using a scripting language or by the OrcaFlex spreadsheet. Building an entire OrcaFlex model through the Text Data file is possible but not to be recommended. 4. increasing the count will add new rows to the end of the table containing default data. for example setting a new current profile: Environment: # Single Current CurrentMethod: Interpolated RefCurrentSpeed: 1.1 Examples of setting data This topic gives some examples of setting model data using the OrcaFlex Text Data file.w Automation.3. The normal approach is to modify an existing model imported using the BaseFile identifier and apply incremental changes. The OrcaFlex Text Data file format is described in the Text Data Files topic and this should be read before tackling this topic.3 TEXT DATA FILES 4. CurrentFactor. The easiest way to see how data for a particular model item is represented is to create the item in OrcaFlex and then save the data file as a Text Data file.5 Line1: IncludeTorsion: Yes Note that in subsequent examples we omit the BaseFile directive for brevity.yml. To create all the batch scripts in one operation select all the script tables and then click Create Batch Scripts in the OrcaFlex menu. Setting simple data To set data on an object existing in the base file BaseCase. although there are some exceptions that require specific selection identifiers and examples of these are given below. The OrcaFlex Text Data file format is not a scripting language so some Batch script command operations are not possible – for example the InvokeWizard command. here objects named Link1. it is only required if we are changing the size of the table. reducing the count will delete rows from the end of the table. Existing objects normally need to be selected by name before modifying their data. The following example sets some data in the first two sections of Line1: Line1: NumberOfSections: 2 LineType[1]: Riser Length[1]: 75 TargetSegmentLength[1]: 4 LineType[2]: Rope Length[2]: 200 TargetSegmentLength[2]: 20 The NumberOfSections identifier specifies the number of rows in the sections table. We could replace the table entirely and use a YAML list to repopulate the data. Text Data Files Multiple tables You can have multiple script tables within a workbook. 5 Creating new objects New objects can be added to the model using the type name as the identifier. Line Type1: OuterDiameter: 0. Text Data Files .7.28 InnerDiameter: 0.21 Clump Type1: Mass: 0. and clears any existing objects from the list.[50. 1.w Automation. 07.[10.0.20 Line1: LineType[2]: Variant Line Type3 And some new attachment types: ClumpType: Name: Clump 5 DragArea: [0. 0. So a new line type must be created in the data file before a line can be later modified to refer to it. Data found on the General and Environment data forms Data on these forms can be set by referencing the General or Environment objects as follows (the following example assumes that the base file model has 2 simulation stages): General: ImplicitUseVariableTimeStep: Yes ImplicitVariableMaxTimeStep: 0. Drag Chain and Wing These objects also need to be referenced by name. Flex Joint. 0. the object will be created with default data that can be then modified. In the Text Data file the plural of the type name (eg LineTypes ) introduces a new list of the type. 0] Type data: Line. 0. To add a new line type to the line types list: LineType: Name: Variant Line Type3 OuterDiameter: 0.0 Environment: SeaBedStiffness: 3000 SeaBedDamping: 80 98 . 0] .5.8. 0] .7 Drag Chain Type1: Length: 12 Wing Type1: Angle[2]: -80 Lift[2]: 0.29 InnerDiameter: 0.15 Moment[2]: 0.1 Volume: 0.2 Drag[2]: 0.[90. Clump. they cannot be selected with index notation.1] DragChainType: Name: Short Chain 2 Length: 12 Note: Objects must created before they are referred to later in the file. Stiffener.2 Height: 4 DragAreaX: 0.2 # Add another simulation stage NumberOfStages: 3 StageDuration[3]: 12. 3 WavePeriod: 7.97] To set data for displacement RAOs.w Automation. -1. The example assumes a base file model with only one wave train and adds a new wave train and names it AiryWave (after being added the wave train is automatically selected).2 WavePeriod: 12. and selects one to be the active current using the ActiveCurrent identifier: Environment: # Multiple current set MultipleCurrentDataCanBeDefined: Yes NumberOfCurrentDataSets: 2 CurrentName[1]: Ebb CurrentName[2]: Flow # To modify the Ebb current.2 CurrentSpeedAtSeabed: 0.2 RefCurrentDirection: 36. 0. Text Data Files RefCurrentSpeed: 1.2 CurrentSpeedAtSeabed: 0.53. wave load RAOs and wave drift QTFs you must also specify which type of RAO the data applies to: 99 .0 Wave train data requires that the target wave train is selected by name first.0 # Set the active current ActiveCurrent: Ebb Vessel Type data Simple vessel type data are set as for other type data mentioned above. by referencing the vessel type by name first: Vessel Type1: Length: 120 PenWidth: 3 Symmetry: XZ plane Much vessel data applies to a draught which must also then be referenced by name: Vessel Type1: Draught1: Mass: 7600 CentreOfGravity: [2.8 RefCurrentDirection: 0.8 RefCurrentDirection: 180.0 # Now select the other current SelectedCurrent: Flow CurrentMethod: Power Law CurrentSpeedAtSurface: 1. Then the first wave train is modified after being selected with the SelectedWave identifier: Environment: # Add a wave train NumberOfWaveTrains: 2 WaveName[2]: AiryWave # AiryWave is now the selected wave WaveType: Airy WaveDirection: 180 WaveHeight: 3.8 Data for Multiple Current data sets The example below creates two Currents in a multiple current set.5 # Change selected wave to Wave1 SelectedWave: Wave1 WaveDirection: 100 WaveHeight: 4. we must select it first SelectedCurrent: Ebb CurrentMethod: Power Law CurrentSpeedAtSurface: 1. Draught1 DisplacedVolume: 85e3 To set the added mass and damping data you must select the period and the row/column body: Multibody Group1: NumberOfAddedMassAndDampingPeriodsOrFrequencies: 2 AddedMassAndDampingPeriodOrFrequency[1]: 11. however the Vessel.2 The RAO data are per direction. -1.18 To modify data in the frequency dependent added mass and damping matrices.0 SelectedAddedMassAndDampingRowBody: Vessel Type1.5 RAOYawAmp[2]: 0.97] LoadRAOs: RAOOriginY: -1.5 AddedMassMatrixX[1]: 255 AddedMassMatrixY[2]: 249 AddedMassMatrixZ[1]: 136 DampingY[2]: 0. 0.w Automation. Data in the tables is accessed using index notation: Vessel Type1: Draught1: SelectedAddedMassAndDampingPeriodOrFrequency: 5. each depth needs to be selected before the model data can be accessed: # Create a new P-y model P-yModel: 100 . Draught1 AddedMassX[1]: 42. the frequency or period needs to be selected first.4 It is unlikely that you will want to change individual values in the RAO tables.53.yml Multibody group data Some multibody group data are set in a straightforward manner as follows: Multibody Group1: NumberOfBodies: 2 VesselType[1]: Vessel Type1 VesselType[2]: Vessel Type2 To set the stiffness data you must first select the body: Multibody Group1: SelectedStiffnessBody: Vessel Type2. This example sets the Yaw amplitude in the second row in the Period table for directions 22.0 DampingX[1]: 35. Draught1 SelectedAddedMassAndDampingColumnBody: Vessel Type2.0 SelectedAddedMassAndDampingPeriodOrFrequency: 11. using the SelectedAddedMassAndDampingPeriodOrFrequency identifier. Text Data Files Vessel Type1: Draught1: DisplacementRAOs: RAOOrigin: [2. so the direction also needs to be selected using the SelectedRAODirectionValue YAML identifier.5 and 45 degree of the Wave drift RAOs: Vessel Type1: Draught1: WaveDrift: SelectedRAODirectionValue: 22.0 AddedMassAndDampingPeriodOrFrequency[2]: 13.13 SelectedRAODirectionValue: 45 RAOYawAmp[2]: 0. to access the relevant tables. Draught and RAO sections of the Text Data File are ideal candidates for using the IncludeFile identifier: Vessel Type1: Draught1: DisplacementRAOs: IncludeFile: RAOs\UnladenRAOs.0 P-y Model data With P-y Model data. 0 DepthBelowSeabedFrom[2]: 10.0 SHEAR7LocalSCF[1]: 1.2.6 UndrainedShearStrength: 6 J: 0.[0. 11] Note: The above example creates a new P-y Table with two rows. To modify rows in an existing table. SHEAR7 data SHEAR7 data ownership is divided between the SHEAR7 object and Line objects. use indexing.5 Epsilonc: 4 SelectedDepthBelowSeabedFrom: 10 ModelType: API RP 2A Sand EffectiveUnitSoilDensity: 0 C1: 0 C2: 2 C3: 15 k: 42 SelectedDepthBelowSeabedFrom: 20 ModelType: P-y Table Deflection.0 # Modify existing P-y model P-yModel1: SelectedDepthBelowSeabedFrom: 0 ModelType: API RP 2A Soft Clay EffectiveUnitSoilDensity: 1. so the index of the section is required: Line1: SHEAR7StrouhalType[1]: Rough Cylinder SHEAR7LiftFactor[1]: 0. Text Data Files Name: P-yModel1 NumberOfDepths: 3 DepthBelowSeabedFrom[1]: 0.2.7 SHEAR7 Whole Line data and Stress Concentration Factors are accessed through a line object: Line1: SHEAR7CurrentProfileDiscretisation: Regular spacing SHEAR7CurrentProfileTargetSpacing: 10 SHEAR7LocalSCFArclength[1]: 32.[0.6 SHEAR7OutputDmg: Yes To access the data in the S-N Curve table requires that the curve is first selected with the SelectedSHEAR7SNCurve identifier: SHEAR7Data: SelectedSHEAR7SNCurve: Curve2 SHEAR7SNCurveNumberOfPoints: 3 SHEAR7SNCurveS[3]: 10E5 SHEAR7SNCurveN[3]: 10E4 SHEAR7SNCurveEnduranceLimit: 750.0 DepthBelowSeabedFrom[3]: 20. eg: Deflection[2]: 0.9 SHEAR7SectionSNCurve[2]: Curve1 Line Contact data To edit penetrator data. The SHEAR7 file version. output file options and S-N curve data are owned by the SHEAR7 object: SHEAR7Data: SHEAR7FileVersion: 4. Resistance: .w Automation. 0] .15 The SHEAR7 Hydrodynamic and Structural Section data applies to a line section. the penetrator locations SelectedPenetratorLocationsDataSet identifier: 101 data set must first be selected using the . [10. they are still accessed by referencing the relevant object: Line1: PolarR[1]: 20. Text Data Files LineContactData: SelectedPenetratorLocationsDataSet: Locations1 Penetratorx[2]: 13.0 PolarTheta[3]: 90. 0] .2. 9.[10.0 PolarTheta[2]: 90. If you wish to add another variable data item and retain existing data items in the list then use the following YAML format: VariableData: FluidTemperature: Name: fluidTempB IndependentValue.6 Penetratory[2]: -2. DependentValue: .0 PolarTheta[1]: 90. 1000] .0 Line2: PolarR[1]: 20. If any existing variable data items are referenced by other objects then an error will be raised.[0.5] Existing variable data sources can be referenced by name as with other objects. 5000] Polar Coordinates data on the All Objects form End connection data can be expressed using polar coordinates as presented on the All objects data form.001 APIRP2RDSMYS: 380e3 Variable Data sources New variable data sources can be created in two ways.w Automation. 17] .[100. the first example creates a new Fluid Temperature data item with 2 table rows: VariableData: FluidTemperature: .0 PolarTheta[1]: 45.[0. Model wide data items are owned by the Code Checks object: CodeChecks: APIRP2RDDesignCaseFactor: 1 The per line type code check data are just like any other line type data: Line Type1: APIRP2RDCorrosionThickness: 0.85 Code Checks data Code Checks data ownership is divided between the Code Checks object and Line Type objects.[100. 11] The above YAML also clears the Fluid Temperature data source list before adding fluidTempA.0 PolarR[2]: 3400.4.5 PenetratorContactArea[2]: 0.[0. The following example resets the table values for a Bending Stiffness variable data item: Stiffness1: IndependentValue. 15] .0 102 .0 PolarR[2]: 20.0 PolarTheta[2]: 345. DependentValue: .0 Winch1: PolarR[3]: 0. Although these data are displayed in table form.Name: fluidtempA IndependentValue. DependentValue: . yml . 0. substituting file names for the BaseFile and IncludeFile files from a collection of initial cases and variation sets.[0.97] PhaseOrigin: [~. RAOHeaveAmp.yml IncludeFile: Variation set z. End A has an index of 1 and End B an index of 2. ~. The basic idea is very similar to the facility for automating generation of batch script files. Colour data Colour data can be set using pre-defined colours or RGB values as described for Batch scripts: Line Type1: PenColour: Red Line Type1: PenColour: 255 Line Type1: PenColour: $00FF00 Importing Text Data File sections Sections of an OrcaFlex Text Data file can be imported using the IncludeFile directive. RAOSurgeAmp. 0. then select the Text Data Files cell and then click the Create Text Data Files command which can be found on the OrcaFlex menu in Excel.. RAOPitchPhase.yml The data in the included file must continue from where the original file left off but there is no need to repeat the YAML header. To use this facility select the Pre-processing worksheet. RAOSurgePhase. 0.53. 0.. An example table is shown below: 103 . -1. 0. 0. or start at the same indentation level. RAOSwayAmp. The imported segment cannot refer to objects that do not yet exist in the main data file. 0] # etc. RAOYawAmp. A very simple OrcaFlex Text Data file my comprise just the following: %YAML 1. 0. This specifies another YAML file containing a section of an OrcaFlex Text Data file that will be processed as if the data were part of the original file. 0. RAOYawPhase: .0 For lines and links. RAOPitchAmp. for example Vessel ROAs: Vessel Type1: Draught1: DisplacementRAOs: IncludeFile: MyVesselRAOs. For winches the index identifies the winch connection point.yml RAOOrigin: [2.3. RAORollPhase.1 --- # This File: C:\Desktop\Case x.yml BaseFile: BaseCase y. 360.2 Automating Generation The OrcaFlex Spreadsheet has facilities for automating the generation of text data files for a regular set of cases. 360.. RAOSwayPhase. RAORollAmp. The above file is easy to create using a script. 0. 0.0 PolarTheta[4]: 90.RAODirection: 0 RAOPeriodOrFreq. ~] RAOs: . although relative indentation in the include file is still required: # File: C:\Desktop\MyVesselRAOs. 4. Using IncludeFile is a useful way of adding or modifying complex data from a library of common object data. RAOHeavePhase. Text Data Files PolarR[4]: 10. The IncludeFile identifier can be used more than once in the same OrcaFlex Text Data file and the included files can also contain the IncludeFile identifier themselves.w Automation. Multiple tables You can have multiple tables within a workbook. So. We have adopted a convention that the variable names begin with a percentage sign (%). is known as the anchor cell. if a cell is formatted to have.dat Environment: WaveDirection: 0 WaveHeight: 8 Line1: Length[1]: 100 Note: The generated text data files adhere to the formatting specified in the Excel cells. Each row defines a single text data file. In the example given above. Relative paths can be used for the template file name and the output file names. This first of these looks like this: BaseFile: Base Case. Such ambiguities seldom arise. However.dat Environment: WaveDirection: %direction WaveHeight: %height Line1: Length[1]: %length The row immediately below the anchor cell. To process all the tables in one operation. named Case01. by the value specified in the table.yml.yml. but if you are affected then you can extend the naming convention to include a trailing % sign. When occurrences of %x1 in the template file are replaced by their actual values. The text data files are generated based on the template file specified the in cell immediately to the right of the anchor cell. In this example the template file might look like this: BaseFile: Base Case. 104 . etc. the first 3 characters of any occurrences of %x10 will also be detected. highlighted in blue. The rows beneath the variable names row are known as the value rows. The text data file is generated by starting from the template file and then replacing each variable name. in turn. For example. Text Data Files Figure: Example table for automatic text data file generation The cell containing "Text Data Files". You are free to choose these names as you please. Although you do not need to follow this convention. The %filename variable name is compulsory. 1 decimal place. The example above produces 8 text data files as its output. the variable names become %x1% and %x10% and clearly the problem does not arise.w Automation. that is it must be included as one of the variable names. Case02. doing so will have the benefit of making the variable names stand out. say. the corresponding value in the text data file will also have 1 decimal place. contains variable names. So the variable names row ends at the first empty cell. Likewise the value rows end at the first empty cell in the column beneath the anchor cell. highlighted in yellow. Choosing variable names It is clearly important that you choose unique variable names. The extent of the table is determined by the presence of empty cells. It specifies the name of the generated text data file. select all the tables and then click the Create Text Data Files command. consider the variable names %x1 and %x10. there is a further subtlety which can arise when one variable name is a sub-string of another. You can then specify the names of those files in the spreadsheet using relative paths. It is usually most convenient to save it to the directory containing the OrcaFlex files from which you want to extract results. This is a relatively minor advantage but it does reduce the likelihood of mistakenly forgetting to carry out step 2 when using batch script files. 105 . Run the batch script (or scripts) that generate all the load case data files. Modify the single base model. You can then use the normal spreadsheet facilities to calculate other post-processed results from those OrcaFlex results. However. go to All Apps and the Orcina Software group) and then select New OrcaFlex Spreadsheet. This can be done manually by transferring the results from OrcaFlex into the spreadsheet using copy + paste. Before you try to use the new spreadsheet you need to save it. In addition. more complex analyses can lead to your load cases being defined by multiple script files which have to be executed in a particular order. plus other worksheets to receive the OrcaFlex results and for any derived results. The spreadsheet also provides tools to help build the list of instructions. This shortcut creates a new spreadsheet based on the template. This automation is done using an Excel spreadsheet that has facilities for automatic extraction of specified results from one or more OrcaFlex files into nominated cells in the spreadsheet. then step 2 is not required. Note: The OrcaFlex spreadsheet works with Excel 2000 or later and requires OrcaFlex to be installed on the machine.4. Consider the following typical sequence of actions when using batch script where we assume that the basic model and scripts are already in place: 1. This is because the load case text data files contain a reference to the base model rather than containing a copy as is the case when using batch script. 3. You should base your own OrcaFlex spreadsheets on this template. Run the simulations for all load case data files. depending on your version of Windows. If you are already familiar with batch script and not yet familiar with text data files then it may prove easier to continue using batch script. so we have developed special facilities to automate the process. this is laborious and error prone if a lot of results need transferring. The choice of which to use is largely one of personal preference. Creating OrcaFlex Spreadsheets You can create OrcaFlex spreadsheets from an Excel template that is supplied with OrcaFlex. These tools are the Instructions Wizard and the Duplicate Instructions form. Using the text data file approach means that this complexity is dealt with just once when setting up the text data files. 4. open the Windows Start menu and select Programs | Orcina Software (or. Using relative paths makes it easier to rename the directory or move the spreadsheet and OrcaFlex files to some other directory.w Automation. 4. OrcaFlex spreadsheets also provide facilities for automating the production of batch script files and text data files. as described above. Post-processing Benefits over script tables The text data file approach to load case file generation described above is very similar to the approach using batch script files. as opposed to every time a modification to the base model is made.4 POST-PROCESSING 4. There is one significant advantage of using text data files which is that it avoids duplication of the OrcaFlex model data. an OrcaFlex Spreadsheet contains one or more instructions worksheets. For results post-processing. which is installed in the OrcaFlex installation directory when you install OrcaFlex on your machine. represented by an OrcaFlex data file.4. If text data files are used.1 Introduction OrcaFlex users often use spreadsheets to post-process their OrcaFlex results. To create your own OrcaFlex spreadsheet.2 OrcaFlex Spreadsheet The OrcaFlex Spreadsheet enables you to automate the extraction of results and data from OrcaFlex files into Excel. 2. label and command columns. so do not insert or delete rows above this. The entry in column A (titled Sheet Name) specifies the name of the Excel worksheet on which any output is produced. This label is output on the worksheet specified in column A and in the cell specified in column B. italic. Likewise. range graphs. 2. Hence you cannot have an instruction row that has no label and no command.w Automation. colour etc. The text of the label is specified in column C. In particular. since these are used to identify it as such. you cannot have a blank row in the middle of the instruction table. The instruction can be thought of as 3 separate sections: 1. 106 . Warning: Do not change rows 3 and 4 of an instructions table. hidden rows in the instructions table are ignored allowing you to disable certain instructions which can useful when developing and building the table. That is you can have an instruction that has a blank command cell and so only writes a label. data values etc. or one that has a blank label cell and so only writes results. Processing the Instructions When you are working with the OrcaFlex Spreadsheet an OrcaFlex menu is added to the Excel menu bar. The entries in columns B and C (titled Label Cell and Label respectively) specify a label. the spreadsheet assumes that the first instruction is row 5 of the worksheet. Either of sections 2 and 3 are optional. 3. The other columns (D to I) specify some results or data which are output on the sheet specified in column A and in the cell specified in column D. Also. to make the worksheets easy to read. This menu contains various commands to process the results instructions. The end of the table is indicated by the first row that has blank label cell. Any formatting is ignored and so you can use bold. Post-processing Instructions Table Figure: Empty instructions table Each row in the instructions table is a separate instruction. These columns can specify output of time histories. then you have the option to allow errors to be reported during the processing or Ignore Errors until the sheet is completed. which ensures an unattended spreadsheet will continue to process remaining instructions even if an error occurs. then you will be asked to select which instructions sheet you wish to process. You can do so like this: 107 . Post-processing The OrcaFlex menu within Excel Excel 2007 and later replace the menus with Microsoft's ribbon interface. Automating post-processing from VBA Sometimes it is convenient to be able to invoke the post-processing actions from VBA. The Thread Count can be set to reduce the impact processing spreadsheets will have on the responsiveness of your computer. Spreadsheet Processing Options The Processing Options menu item allows you to change the way an instructions sheet is processed. but if you are using a ribbon based version of Excel then you should interpret this as referring to the corresponding ribbon button. one of the cells in the row is a reference to the output of an earlier instruction. If this box is not checked. The Process Selected Instructions menu item tells the spreadsheet to process only the instructions in the currently selected cell or block of cells. If Ignore Errors is checked then all error messages are collated and reported on completion. By default the spreadsheet will utilise all the available processing cores.w Figure: Automation. It is only available if Contains Dependencies is not checked. The OrcaFlex Spreadsheet integrates with the ribbon as shown below: Figure: The OrcaFlex ribbon within Excel 2007 and later Throughout the documentation we refer to menu items. The Process All Instructions menu item runs all the instructions in the table. Errors are always ignored until processing completes and the number of threads used is controlled by OrcaFlex. then the Contains Dependencies box must be checked to ensure that the whole sheet is processed line by line from top to bottom using a single thread. i. If an instruction depends upon the result of a previous instruction.e. then the order in which instructions are processed is not defined and multiple lines may be processed simultaneously by multiple threads. If the currently selected sheet is not an instructions sheet and the workbook contains more than one instructions sheet. Note: When a spreadsheet is processed in an OrcaFlex Batch all the option settings are ignored apart from "Contains Dependencies". If this box is checked. Select the Add-ins page.Object module. a reboot is also required for the change to take effect.4. Select COM Add-ins in the Manage drop-down list. 5. If the above actions do not resolve the problem. 6. Open the Excel Options dialog.3 Instruction Format The easiest way to learn about the instruction format is by using the Instructions Wizard which allows you to create instructions in an interactive manner. 3. 5. Label Cell Specifies the cell.ContainsDependencies = True module. a reboot is also required for the change to take effect. Click the Go button which brings up the Disabled Items dialog. Restart Excel. 4. Click Disabled Items which brings up the Disabled Items dialog. Select the OrcaFlex spreadsheet and click Enable. 2. 4. In some cases.COMAddIns. 4.IgnoreErrors = False module. Click the Go button which brings up the COM Add-ins dialog. 7.ThreadCount = 4 Re-enabling the spreadsheet add-in The OrcaFlex spreadsheet is implemented as an Excel add-in. Post-processing Dim module as Object Set module = Application. in the specified worksheet. Select Disabled Items in the Manage drop-down list. 6. 5. 3. In the OrcaFlex Spreadsheet. Open the Excel Options dialog. This cell can be left empty. for example after an Excel crash. 4.Item("PostProcessing. Select the Add-ins page. Restart Excel. click About Microsoft Office Excel. 2. Excel 2003 1. to which the label (if not empty) will be written. Sometimes. but other cells will be left unchanged. Select the OrcaFlex spreadsheet in the Disabled Items dialog and click Enable.ProcessAll This is equivalent to pressing the Process All button. then it is possible that the add-in has been soft disabled instead – the instructions for re-enabling are as follow: Excel 2007 or greater 1.ProcessSelected Finally. On the Excel Help menu. Sheet Name Specifies the name of the worksheet in which cells are to be written. Excel 2007 or greater 1. the processing options are can also be controlled by means of the following properties: module. The above instructions refer to what Microsoft term hard disabling. To invoke the Process Selected button programmatically you use the ProcessSelected method: module. the addin can become disabled and needs to be re-enabled. Check the box next to the OrcaFlex spreadsheet and click OK.OrcaFlexSpreadSheet"). 108 . The method for achieving this differs depending on the version of Excel. If no sheet of that name exists then one will be created.w Automation. Restart Excel. in which case the label cell is ignored. Label Specifies the label string to be written to the label cell. In some cases. 2. 3. each instruction consists of the following cells. If a worksheet with this name already exists then the specified label and output cells will be overwritten. e.0". The touchdown position can be specified.0".g.g.0) will be assumed.g. "0. Theta -45. "SupportIndex=3" and "SupportIndex=4.' character. Outer.w Automation. Theta 270.y.' character or leave blank to use the vessel origin.0.g. "Inner".g. For the Rayleigh Extremes instruction you can specify the parameters for the extreme value statistics analysis. There are a variety of ways in which this can be specified: The position can be specified by arc length. For 6D Buoy objects you must specify the Wing Name if you are requesting a wing results variable or a point in local x.g. "Arclength 35") then clearances will be reported from this line to all other lines. "Node 7. Hose" etc.' character or leave blank to use the buoy origin. For Winch objects you may need to specify the winch connection number. Note: You must specify an arc length together with both R and Theta separated by the '. SupportedLineName=Line1".g.z coordinates of the point for which you want results – the coordinates must be separated by the '.Theta values. The node number can be specified.0. You can also use ranges such as "<35" or ">60" to specify all arc lengths less than a point or all arc lengths greater than a point. One of the line ends can be specified.g. e. e. For Supports results offered by Vessel and 6D Buoy objects you need to specify the support index and maybe also a supported line name. You can specify this other line by adding its name after the position. For the Environment object you need to specify the global X. 109 . For stress results you must also specify the position of the point within the cross section through the specified arc length. "End B" or more concisely "A" or "B". "20 to 50".0". For the Range Graph and Range Graph Summary commands you can specify a range of arc lengths. For the Duplicate Sheet instruction. If the command cell is empty then the output cell is ignored and just the label is output. e. to which results or data should be written. Riser". but can also be specified indirectly using standard Excel formulae. "Node 4. In this case the output cell specifies the top left cell of the block of cells to be written. The results are given for the nearest appropriate result point.g.g. If the value in this column is left empty then the entire sheet is cleared.0. this is specified after the coordinates. DisturbanceVesselName=Vessel1". e. If no point is specified then (0. "Arclength 35. "Arclength 25. "Node 4". Outer. Post-processing Output Cell Specifies the cell. For example "LINE" and "line" and "LiNe" are all regarded as different objects in OrcaFlex. e.g. "End A". You do this by specifying R. "Outer". e.' character. For Line objects you must specify the position on the line for which results are wanted. in the specified worksheet. Clearance results can be reported either as clearances from this line to all other lines or from this line to a specified other line. Different objects in OrcaFlex can have identical names except for case.g.Z coordinates of the point for which you want results – the coordinates must be separated by the '. the source worksheet is specified in this column. Theta 17. e. Some commands specify multiple-value output – for example a time history consists of a column of results.0. Line2". e. see Line Results for details.0". "Theta 270.z buoy coordinates for some results variables – the coordinates must be separated by the '. Additional Data This column is used when outputting results for certain types of OrcaFlex object. If you do not specify another line (e. If the result requires a disturbance vessel. Note: The output cell (or label cell) can be specified directly. Note: This name is case sensitive. Inner.8" etc. e. "Arclength 20. e. "Touchdown". Object Name The name of the OrcaFlex object whose results or data are output. Command This should be one of the pre-defined commands or else empty.Y. For the Clear instruction. "End B. "End A.y. For Vessel objects some results require the local x. B7. the range to be cleared is specified in this column. OrcFxAPI version. Standard Deviation. RAO direction or QTF direction to be selected. for example: Load c:\Project100\Case1. Note: This specified period format can be used to extract results at a single time point.sim or else use a relative path (relative to the directory containing the spreadsheet). Static Result. Warnings.4. Min.5 to +35.g. Empirical Distribution. 4.). Build up or a stage number (0 for the build-up.sim is in the same directory as the spreadsheet then you can use the command: Load Case1. Rainflow Half Cycle Count. Surge. Spectral Density. Rainflow Half Cycles. It can also be a specified period of simulation.dat or . Latest Wave. Post-processing Simulation Period The period of simulation for which results are wanted. If the command is Select then this is the wave train. Linked Statistics. Range Graph and Range Graph Summary commands. Range Graph Min. Curvature.sim and this has the advantage that there is no need to alter the spreadsheet if the directory is renamed or the files are moved to a different directory. Subsequent results extraction commands then apply to that file.4 to 27. Min etc. If the command is Get Data then this is the data name of the data item. You can either specify the full path of the file. Mean. Spectral Response Graph. the Command Cell can contain one of the following commands: Load. etc. Duplicate Sheet. For example if the file Case1. Static State. Time History.w Automation. Max. for example the period "27. For example Effective Tension. Range Graph. If the command is a results command (e. Time History. Range Graph Summary. draught. Range Graph. Clear. Variable The name of the output variable.4.5 Basic commands Load <file name> This command tells the spreadsheet to open the specified file.7". 1 for stage 1 etc. This can be Whole Simulation. This cell should be left empty for the data output commands Select and Get Data and when outputting static results using the Static Result. 110 .4 Pre-defined commands In the OrcaFlex Spreadsheet. Range Graph Max. Note: If you use the Static State period then a single value will be reported – the value of the variable at the very beginning of the simulation.4" will give the results at the nearest log sample to time 27. Sample Times. given in the form "t 1 to t2" where t1 and t2 are numeric time values that are in the simulation and Simulation Start Time ≤ t1 ≤ t2 ≤ Simulation End Time. Rayleigh Extremes.4. For example "20 to 30" or "12. Subsequent results extraction gives results for the static configuration. Linked Statistics. Get Data.) this should be set to the same name as is used for the results variable in OrcaFlex. The latter is often more convenient.yml) then the file is loaded and the OrcaFlex statics calculation is performed. If you specify a data file (. Working Directory. Select. 4. F:F Columns A. if the Additional Data column is not empty. 111 .sim) containing either static state results or dynamic simulation results can be loaded. If you are using relative paths then it can be useful to keep track of the base path for QA purposes. C. This command allows you to check whether any such warnings were generated. as with the Sample Times command. then the time values for those log samples will be written to cells G5…G504. All charts. Time History Returns the time history values of the specified variable. Simulations run in batch mode or by Distributed OrcaFlex do not display such warnings since to do so would require user intervention. and 8 A:A. Working Directory This outputs the directory where the spreadsheet is stored. All cell formatting is preserved. The following table illustrates some typical A1 style references: Reference Meaning A1 Cell A1 A1:B5 Cells A1 through B5 C5:D9. So if the output cell is set to G5 and there are 500 log samples in the simulation period.3:3. This is not necessarily the version of the program which performed the calculations (for example if you load a simulation file which was generated by a different version of OrcaFlex). 4. OrcFxAPI version This outputs the version of the OrcFxAPI DLL which is being used by the spreadsheet.C:C. This command returns a column of N numbers.G9:H16 A multiple-area selection A:A Column A 1:1 Row 1 A:C Columns A through C 1:5 Rows 1 through 5 1:1. 3. Otherwise. If the Additional Data column is empty then the entire sheet is cleared.8:8 Rows 1. The range is specified using Excel's A1 reference style. This command returns a column of N numbers. formulae.w Automation. where N is the number of OrcaFlex log samples that are in the specified simulation period. Results extraction spreadsheets are typically run repeatedly. then its value is taken to mean a range of cells to be cleared. Post-processing Simulation files (. and F Duplicate Sheet This command copies the entire contents of the worksheet named in the Additional Data column to the specified output sheet. This should generally be the first command in the instructions sheet or the first command following a Load command depending on whether the results are being output to a single or multiple sheets. The purpose of this command is to ensure that previously extracted results are removed and so cannot get mixed up with the latest results. If the calculation time is excessively long then we recommend that you use the Use Calculated Positions command when building your model. that exist in the source worksheet are copied.6 Time History and related commands Sample Times Returns the time values that apply to the time history results. formatting etc. Note: The statics calculation may take a significant length of time. Clear This command clears the contents of cells in the specified output sheet. Warnings This outputs the text from any warnings reported during the OrcaFlex calculations (static or dynamic). This command is the equivalent of the Calculation | View Warnings menu item.4. the period of simulation for which you want results. ExtremesToAnalyse=Upper tail The storm duration is given in hours and the risk factor is a percentage. RiskFactor=1. Otherwise. For example: StormDuration=3. in the Simulation Period column of the instruction. equalling the minimum value of the specified time history variable during the specified simulation period. you should leave this column blank and the results for the static configuration are reported. upper limit. if you have loaded a data file. two are label cells and the other two contain the overall minimum (or maximum) value that occurred at any point on the line during the specified simulation period. Range Graph Min. and lower limit. Standard Deviation Min return a single number. separated by semi-colons. You can also use ranges such as "<35" or ">60" to specify all arc lengths less than a point or all arc lengths greater than a point.8 Data commands Get Data. Range Graph Max These commands output. Empirical Distribution. and the arc length at which it occurred. Alternatively. The Range Graph command gives a table having 7 columns. The command outputs a table of statistics for those variables. minimum.4. Mean and Standard Deviation (which can be abbreviated to Std Dev). maximum. Max. If they are omitted then default values of 3 and Upper tail are used. Rayleigh Extremes Outputs the results of a Rayleigh distribution Extreme Value Statistics analysis: MPM and Extreme Value with Risk Factor. Post-processing Min. tables containing range graph results. Static Result Returns the value of the specified variable. separated by commas. If the Additional Data column in the instruction is left blank then the results will apply to the whole line. Spectral Density. 112 . for the specified variable of a line.w Automation. This command reports the value in the static configuration.g. The length units used must be the same as those used in the OrcaFlex simulation file. You can specify that only a subset of the columns are to be output.7 Range Graph commands Range Graph. For each point on the line a row is generated in the table containing the statistics of the values that occurred at that point during the specified simulation period. The table will then only include results for points whose arc length is within the specified range. If the RiskFactor parameter is omitted then the Extreme Value with Risk Factor result is not output. The first column is frequency and the second is the RAO. If you have loaded a simulation file then you must specify. one for the overall minimum and one for the overall maximum. Each row has 4 cells. You can restrict these commands to only cover part of the line. Select This command outputs the value of a data item. Rainflow Half Cycle Count These commands extract spectral density. The object is specified in the Object Name column of the instruction sheet and the data item is specified in the variable column. The Range Graph Min and Range Graph Max commands output just the overall minimum or maximum value respectively. mean. Mean. 4. This is most easily done using the Instructions Wizard. 4. standard deviation. in the Additional Data column.4. Range Graph Summary. Spectral Response Graph Returns the spectral response graph for the specified variable. They are available for any line variable for which a range graph is available in OrcaFlex. "20 to 50". Similarly for Max. Linked Statistics Outputs the same information as the Linked Statistics command on the OrcaFlex results form. In the variable column of the instruction you should specify a number of results variable names. The Range Graph Summary command gives a table having two rows. Parameters for the analysis are specified in the Additional Data column. The StormDuration and ExtremesToAnalyse parameters can be omitted. containing arc length. This is done by listing the columns to be output in the Additional Data column. you can specify a section number in the Additional Data column to restrict results to that section. by specifying a range of arc lengths. The command returns two columns of numbers. e. empirical distribution and rainflow half cycles results of the specified variable. Rainflow Half Cycles. Post-processing The data item is specified using the data name of the data item.com/SoftwareProducts/OrcaFlex/Examples.orcina.9 Instructions Wizard The Instructions Wizard allows you to create OrcaFlex spreadsheet instructions interactively. For example the sea density data item does not depend on wave train so it would not need a Select WaveTrain command. For more details see batch script assignment.w Automation. If the data item appears in a table in OrcaFlex. Prepare a simple OrcaFlex simulation file and an empty OrcaFlex spreadsheet For the purpose of this example you need a simulation file containing at least a vessel and a line. The spreadsheet should now looks like this: 113 . Now create an OrcaFlex spreadsheet and save it in the same directory as the simulation file.e. You could use one of the standard OrcaFlex examples – see www. For example if you want to output wave train data for the Environment and there is more than one wave train then you need to specify the particular wave train. Example commands to do this are given below: Command Object Name Additional Simulation Variable Data Period Select WaveTrain Environment Wave2 Get Data WaveTrainType Environment Select WaveTrain Environment Wave3 Get Data Environment WaveTrainType Select Draught VType1 Draught3 Get Data VType1 CurrentCoeffSurgeArea Select RAOs VType1 Displacement Select Direction VType1 30 Get Data VType1 RAOSwayAmplitude[3] Select Direction VType1 60 Get Data VType1 RAOSwayAmplitude[2] Select RAOs VType1 QTF Select Direction VType1 45 Get Data VType1 RAOSurgeAmplitude[6] Notes: The Select commands must be issued before the Get Data commands. In many ways it is the equivalent of the Select Results form in OrcaFlex. For example if you wanted to output the number of segments in the 3rd section of a line then the variable cell would be "NumberOfSegments[3]". Likewise certain vessel type data requires you to specify a draught and/or an RAO type and direction. The index is always 1-based – i.4. Instructions Wizard Tutorial For a quick introduction to the Instructions Wizard we recommend the following tutorial. then its row number must be given. The Select commands are only needed for certain data items. The Instructions Wizard is found on the OrcaFlex menu in the spreadsheet. Certain objects require special select commands to output certain data items. 4. [1] is the first row of the table. The row number follows the data item name and is given as an index enclosed by either square or round brackets (don't mix them on the same line). w Automation. The top part of the Instructions Wizard should now look as follows: Figure: Load instruction in the Instructions Wizard To add the instruction to the spreadsheet click the "Accept and Close" button and the spreadsheet should now look as follows: Figure: Load instruction on the Instructions Sheet 114 . In the Instructions Wizard click the drop down button and change the command to "Load". Post-processing Figure: Empty instructions table Add a Load instruction using the Wizard The instructions wizard creates and inserts instructions on the currently selected row. Click the browse button and select the simulation file you saved in the first part of this tutorial. A file name field and a browse button will now appear. So the next step is to select the first instruction row by clicking on a cell in row 5. Then open the Instruction Wizard by clicking on the OrcaFlex menu and selecting "Instructions Wizard". Open the Instructions Wizard again and change the command to "Time History". The Variable list now looks as follows: Figure: Multiple selection of results variables Now click the "Accept and go to Next Row" button and you will see 3 instructions being added.w Automation. You should see 4 time histories output on a new worksheet called "Results". "Build Up" and each stage of the simulation. certain results require extra information. one for each variable. e. More than one instruction can be added at once. Now close the Wizard (by clicking the "Close" button) and process all the instructions. Select these from the Variable list using CTRL+CLICK or SHIFT+CLICK. End A. to add the instruction click the "Accept and go to Next Row" button. Sample Times. The available options are: "Whole Simulation". arc length 50. sheet name. "1".g. If you are extracting results for Winches then you may need to specify the winch connection point. There are even commands for reporting model data: Select and Get Data. Suppose that you want time histories of X. In the Wizard you can specify a different simulation period by changing the Period drop down list. open the Wizard again and change the command to Range Graph. Other commands So far we have just looked at time history results but the Wizard allows you to build other instructions. "Static State". For OrcaFlex Lines you also need to specify a point on the line. Spectral Density. Max. Setting Period and Additional Data for the instructions The instructions added so far all specify the default simulation period of "Whole Simulation" and the default line position of "Arclength 0". Labels. Additionally for some Environment results you can specify the name of a disturbance vessel. In the Object list select an OrcaFlex Line (if you are using the "A01 Catenary Riser. All these options are available in the Wizard when you are specifying results for a line. For example.sim" example then select 10" Cat Constant EA) and then select Effective Tension from the Variable list. e. Try selecting different simulation periods and adding instructions. If you are extracting clearance results for Lines then you need to specify the clearance line. Notice how the values in the Simulation Period column reflect your selections in the Wizard. node 12 etc. Notice how slightly different options are available reflecting the fact that range graphs are specified in a slightly different way from time histories. "Specified Period". If you are extracting Supports results for a Vessel or a 6D Buoy then you need to specify the Support Index and possibly the Supported Line Name. If you are extracting Wing results for 6D Buoys then you need to specify the wing. "Latest Wave". Y and Z for the line.g. Post-processing The Load instruction tells the spreadsheet to open the specified file. Standard Deviation and so on. In addition. If you are extracting stress component results for Lines then you need to specify the cross sectional position. If you are extracting results for the Environment then you need to specify the position at which you want results reported. output cell The one part of the Instructions Wizard which we have not discussed is the section titled "Labels" as shown below: 115 . You will see the instruction being added to the worksheet but the Instructions Wizard will remain open allowing you to add yet more instructions. This time. End B. see Vessel Support results and 6D Buoy Support results. Try also experimenting with other commands like Linked Statistics. "0" (same as "Build Up"). Add results instructions using the Wizard Now we need to add some more instructions which specify which results to extract from this simulation file. 10 Duplicate Instructions The Duplicate Instructions form allows you to duplicate sets of OrcaFlex spreadsheet instructions for multiple load cases. Label Cell. There are situations where these column headers are undesirable and if that is so the "Exclude header text" box can be checked to suppress their output. When it first opens it looks as follows: 116 . Post-processing Figure: Labels section of the Instruction Wizard This section determines what gets written into the first 4 columns of the instructions table. If the Overwrite option is checked then the Wizard will output values in each of these 4 columns as specified in the relevant field.. spectral density etc. When instructions are added the Label Cell and Output Cell values on the Instructions Wizard will be incremented automatically. The Duplicate Instructions form can be found on the OrcaFlex menu in the spreadsheet. You can choose to use a default label.4. linked statistics. 4. produce output that includes column headers. Label and Output Cell. Once you have built the spreadsheet instructions for a single load case you typically want to generate the same instructions for each other load case. for example range graphs. Before using it you should create a set of instructions for the first load case – an example is shown below: Figure: Instructions table with instructions for a single load case You are now ready to use the Duplicate Instructions form.w Automation. Alternatively you can choose to specify the label yourself. The Duplicate Instructions form automates this procedure. However. If not checked then the values in the sheet will remain unchanged. Suppose you are analysing a number of different load cases for a variety of environmental conditions. namely Sheet Name. Exclude header text Some results. in which case the label will be assembled based on the particular instruction it is associated with. it generally gives a good first effort which you can modify later. This automatic procedure will not always produce the values you require. however. the instruction’s labels are duplicated in the same way as the Different Sheets method. The results sheets will be assigned names based on the Sheet Names by option. Sometimes. 2. you may specify a prefix for the sheet name by filling in the Sheet Base Name field. Suppose that the results from the first load case took up 20 rows worth of space.w Figure: Automation. it is desirable for all the results to appear on a single sheet – this is achieved with the Single Sheet option. 3 etc. If you select the Load Case option then results sheets will be named based on the load case file name. To do this you set this option to Different Sheets. if your load case files are generated by some other means then you can choose the Specified option and you will then be able to specify each load case file directly. When you select the Single Sheet option you must also specify row and column offsets. We strongly recommend that you use this option since script files make QA much more manageable. The duplication process will generate new instructions with the same Sheet Name. you also have the option whether to Duplicate Labels. In addition. When the selected duplication method is Single Sheet. When checked. but also updated with the given row and column offsets. In this case you would probably specify a row offset of 22 (to allow 2 blank rows between load case results) and a column offset of 0. These offsets allow you to avoid the results from each load case overwriting other load case results. A duplicate set of instructions is generated for each file which is written by the script file. Duplicating the instructions Once you have decided exactly how the instructions are to be duplicated you click the Duplicate button and the instructions table will be modified to look something like this: 117 . Post-processing The Duplicate Instructions form Simulation file selection If your load case files (either OrcaFlex simulation files or OrcaFlex data files) are generated by an OrcaFlex batch script then you should set this option to From Script File and select the script file using the Browse button or by typing the file name into the "Script File Name" field. Duplication Method Usually you will want results for each load case to appear on separate sheets. If not checked then no labels are duplicated allowing you to extract the results from multiple load cases to a single sheet that has only a single set of labels. Alternatively. If you select the Index option then sheets will be named 1. You can then add more instructions to the first load case. 118 . Post-processing Figure: Instructions table with duplicated instructions for multiple load cases Adding / removing instructions Quite often you will find yourself wanting to add more instructions to the each load case. Finally you simply repeat the duplication process outlined above and you will have the extra instructions for each load case. In the screenshot above this would mean deleting all cells from row 9 and below.w Automation. The easiest way to do this is to delete all the instructions apart from those of the first load case. The positions of objects. sway and heave directions for a vessel. The local axes are distinguished from the global axes by using lower case. y and z . such as the surge. Most of the data and results are given relative to the global axes. they are referred to as being either global-relative (and are labelled in upper case) or object-relative (and are labelled in lower case). The local coordinate systems for each type of object are described in the section about that object. Coordinate Systems THEORY 5. Positive rotations are clockwise when looking in the direction of the axis of rotation. such as the mean sea surface Z level and the current and wave direction. In general we use Lxyz to denote a local coordinate system.1 COORDINATE SYSTEMS OrcaFlex uses one global coordinate system GXYZ. This enables you to see the local axes and check that they are as wanted. In addition. but typically the origin is at a selected fixed point on the object and the axes are in special fixed directions.w 5 Theory. with respect to which the seabed shape is defined. for example the local object directions are referred to as x. generally one for each object in the model. The global directions are referred to as the X. which shows the global axes and a vessel with its own local vessel axes Vxyz. All the coordinate systems are right-handed. where G is the global origin and GX. The seabed also has its own seabed origin and local axes. there are a number of local coordinate systems. Y and Z. Whenever data or results are coordinate system dependent. including: Data defining the sea. for example the position of the vessel is defined by giving the global coordinates of the vessel origin V. as shown in the following figure. Another coordinate system that we make widespread use of is the Line End orientation which we denote Exyz. You can therefore choose the position of the global origin G and the horizontal direction GX according to what suits the problem being analysed. The most common object-relative items are: 119 . You can ask OrcaFlex to draw the local axes on the 3D view. z y Sea Surface x V Z Vessel Axes Y Global Axes X G Figure: Coordinate Systems The global frame of reference must be a right-handed system and its Z-axis GZ must be positive upwards. but otherwise it is chosen by the user. GY and GZ are the global axes directions. In other words for these directions the x and y-axes in the above figure are the global GX and GY axes. For directions defined relative to the object axes Oxyz. Hence a relative wave direction of β=0° means a wave coming from astern and a relative direction of β=90° means one coming from starboard. etc. and 180° for the negative z-direction. relative to global axes. that are broadly similar to those used in navigation. Vessel headings are specified as the direction in which the vessel Vx-axis is pointing. relative to global axes. measured positive from the x-axis towards the y-axis. depend on the wave direction relative to the vessel. 120 . and similarly for current and wind. current and wind are specified by giving the direction in which the wave (or current or wind) is progressing. The slope direction for the seabed is specified as the direction that points up the steepest slope. As with positions. A global declination of 0° therefore means vertically upwards. gunnery. such as drag and added mass coefficients. When Declination is 0° or 180°. Declination is the angle the direction makes with the z axis. the azimuth and declination angles are defined as follows: Azimuth is the angle from the x axis to the projection of the direction onto the xy plane. and the positive y axis direction has Azimuth = 90°. Therefore Declination is 0° for the positive zdirection.Vessel Heading).w Theory. moments of inertia. azimuth and declination. for vessel headings the x and y-axes in the above figure are the global GX and GY axes. etc. in degrees.2 DIRECTION CONVENTIONS Directions and Headings Directions and headings are specified in OrcaFlex by giving the azimuth angle of the direction. The slope direction of a plane shape that is Fixed or Anchored is specified relative to global axes. directions are sometimes defined relative to the global axes and sometimes relative to the local object axes. Direction Conventions The coordinates of points that move with the object. 90 150 30 y 180 x 0 330 210 270 Figure: Directions relative to axes Directions and Headings Directions for waves. 90° for any direction in the xy plane. such as the vertices of a vessel or the connection point when something is connected to a buoy. relative to global axes. The slope direction of a plane shape that is connected to another object is specified relative to that object's axes. Directions relative to the global axes are defined in just the same way. Vessel responses to waves. The direction-dependent properties of objects. as shown in the following figure. simply replacing the local xyz directions above with the global XYZ directions. 90° means horizontal and 180° means vertically downwards. Azimuth is undefined (OrcaFlex reports Azimuth = 0° in these cases). In other words for these vessel-relative directions the x axis in the above figure is in the vessel heading direction. For example. vessel type RAOs and QTFs are given for a specified wave direction relative to vessel axes (β = Wave Direction relative to global axes . Azimuth and Declination Directions are defined in OrcaFlex by giving two angles. 5. So again. The positive x axis direction therefore has Azimuth = 0°. 6D Buoy. For example "vertical" does not fully define a direction – it must be either "vertically up" or "vertically down" before the azimuth and declination angles can be derived.Y) data point. Object Connections When a direction is being defined. By using anchored joints you can therefore avoid the need to calculate the seabed Z level at the given X. So for an Anchored joint. When a line's joint is Free. but the Z coordinate is specified relative to the seabed Z level at that X. Links and Winches also have joints at each end (winches can also have extra intermediate joints) and these are connected to other objects in the same way as with lines.4 INTERPOLATION METHODS OrcaFlex uses a number of different methods for interpolating data. Link and winch joints cannot be Free – they must always be connected to some master. When a joint is connected to a master. one at each end. Cubic spline. so the fitted interpolation curve is piecewise cubic. Link and winch joints can be connected to nodes on a line. The data are assumed to follow a straight line between each (X. when the model is in Reset state. 6D Buoys. the "sign" of the direction must also be defined. Each of these line end joints can either be Free or else be connected to a Vessel. These cubics are chosen so that both the first and second derivatives are continuous at each X data point.e. a winch to be attached to the end node of a line so that winching in or out can be modelled. which can be a drawback for some purposes. in other words from End A towards End B. Z=0 means that the connection is exactly on the seabed and Z=1 means it is 1 unit above the seabed. the (X. For Winches and Links. Cubic spline interpolation fits a cubic polynomial over each interval in the data. which are drawn as small blobs on the ends of the line. Because neither the Global Axes nor the seabed move. This allows. But for this method the cubics are chosen so that the only the first derivative is continuous at each X data point. 3D Buoys. Lines cannot be connected to themselves. In other words cubic spline gives a 'non-local' interpolation. 3D Buoy. continuous at the data points. Cubic Bessel (also known as Parabolic Blending). for example. winches and shapes are special objects that can be connected to other objects.Y) data specified at any given data point affects the interpolated curve over the whole range of X values. the connection is made at a specified master-relative position and the master object then determines the position of its slave – the slave is dragged around by its master as the master moves. To distinguish the two ends. the Global Axes or the seabed. that end of the line is free to move and this is indicated by the joint being drawn in the same colour as the line.Y position (not simple with sloping seabeds). To enable connections to be made each line has two joints. These methods are described below: Linear. Curves that are linearly interpolated are continuous but their first derivative is discontinuous at each X data point. 5. the X. axial directions are always defined in the A to B sense.Y position. but with the following exceptions. A consequence of this is that with cubic polynomial interpolation the (X. Thus a link with end 1 directly above end 2 has declination 180°. The second derivative is not. For a connection to the Global Axes. 3D Buoys. 6D Buoys. the Global Axes or the seabed. 5.3 OBJECT CONNECTIONS Lines. Cubic Bessel interpolation is similar to cubic spline in that it is also piecewise cubic. the joint is then referred to as being Anchored.w Theory.Y) pair. axial directions are defined in the sense 'from first end towards second end'. not just over the intervals near that (X. When the joint is connected to another object.Y) values at any given data point only affects the interpolated curve over the intervals near that point. in general. as well as to Vessels. nor to a Link or Winch. the joint at End A is drawn as a triangle and the joint at End B as a square. 121 . a joint connected to either of them is simply fixed in one position. to other lines. For a connection to the seabed the X and Y coordinates are specified relative to the global axes. The difference between them lies in how the connection point is specified. the Global Axes or the seabed. The "sign" conventions used in OrcaFlex for directions are: For Lines. Shapes have a single joint which can be connected to Vessels. First consider connecting a line to another object. links. However cubic Bessel interpolation has the advantage that it gives 'local' interpolation – i. Thus a vertical line with End A at the top has declination 180°. that end of the line becomes a slave and the object to which it is connected becomes its master. Linear interpolation is said to be piecewise linear. In response the slave applies forces and moments to its master – for a line these are simply the end force and moment applied by the line. Y and Z coordinates of the connection point are specified relative to those axes and the joint is called Fixed. The connection is then indicated by the joint being drawn in the colour of its master. If it does not then you usually need to supply more data points. whereas cubic Bessel does not. the interpolated curves for cubic spline and cubic Bessel both exceed this value. For example the following graphs show how each method interpolates a particular set of data. The amount of overshoot is generally less with cubic Bessel than with cubic spline. The other 2 methods are piecewise cubic and they both produce a smooth curve. but in many cases this is not important. Cubic spline interpolation gives a curve that also has a continuous second derivative. Interpolation Methods Choosing interpolation method Sometimes OrcaFlex provides a choice of interpolation method. How serious this overshoot is depends on the data – it can be much more serious than illustrated here or sometimes there can be no problem at all.w Theory. To decide you need to take into account what the interpolated data are used for and the different properties of the interpolation methods. one with continuous first derivative. In general we would recommend that you use the default interpolation method. i. It has the advantage that it is very simple. But if you are using either of the piecewise cubic interpolation methods then you should always check whether the interpolated curve gives an appropriate fit to the data. but in some cases it may be appropriate to use a different method. If continuity of first derivative is not required then linear interpolation is often appropriate.e. Both cubic spline and cubic Bessel produce curves that often have overshoots. 122 . Although the greatest Y value specified in the data is 8. in general. Static Analysis Finally. Finally. hydrodynamic drag. in the sense that each specified (X.Y) data point only affects the interpolated curve over the intervals near that point. 5.5. For details see Buoy and Vessel Statics. 5.Y) data points. These facilities are discussed later. The primary purpose of step 1 static analysis is to provide a good starting point for step 2. the initial positions of the vessels and buoys are defined by the data: these in turn define the initial positions of the ends of any lines connected to them.w Theory. and there are a lot of lines in the model. Occasionally. To help overcome this problem. The equilibrium configuration for each line is then calculated. Static equilibrium is determined in a series of iterative stages: 1. For the majority of systems. then you can make investigation of the problem easier by dragging the line up to the top of the list in the model browser. In most cases. Spline. the static analysis process is very quick and reliable. Note: The lines are analysed in the order they appear in the by types view of the model browser. 123 . with the line ends fixed. To provide a starting configuration for dynamic simulation. etc. So if you are having a problem with the static analysis of a particular line. See Buoy and Vessel Statics. usually for very complex systems with multiple free bodies and many inter-connections. This is useful when modelling towed systems or other systems that have a steady velocity. 2. These methods do not. convergence may be difficult to achieve. The out of balance load acting on each free body (node. find a true equilibrium configuration of the line. cubic Bessel interpolation has the advantage that it gives a 'local' interpolation. buoyancy. OrcaFlex provides facilities for the user to suppress some of the degrees of freedom of the system and approach the true equilibrium by a series of easy stages. etc. Quick. using the method specified on the line data form (either Catenary. Prescribed. However there are occasions where this is not so and OrcaFlex provides facilities for handling these special cases. the static equilibrium configuration is the best starting point for dynamic simulation and these two objectives become one.1 Line Statics When OrcaFlex performs statics it begins with a static analysis of each line in the model. positions for all the nodes on the line). buoy. The static analysis of a given line has two steps: Line Statics Step 1 The first step calculates a configuration of the line (i.) is then calculated and a new position for the body is estimated. or User Specified). The process is repeated until the out of balance load on each free body is zero (up to the specified tolerance). 3. whereas with cubic spline the whole curve is affected to some extent by each of the (X. the static analysis can also be turned into a steady state analysis by specifying non-zero starting velocity on the General Data form. At the start of the calculation.5 STATIC ANALYSIS There are two objectives for a static analysis: To determine the equilibrium configuration of the system under weight.e. even if only by a small amount. especially when bend stiffness is not a major influence. but again this will be corrected by Full Statics. then the line is simply left in the configuration found by step 1. If the bottom end is below the seabed. then it calculates the true equilibrium position of the line. current drag and seabed touchdown (see below) and friction. If Full Statics is included. as specified on the line data form. follows the Bezier curve. Static Analysis Line Statics Step 2 The second step is called Full Statics. in general. Because bend stiffness (and other) effects are not included in the Catenary method. statics and dynamics results from such unstable equilibria are invalid. but it does include all other effects. This will result in part of the line being below the seabed. you can control the maximum number of iterations that are attempted. buoyancy. This will be corrected if Full Statics is enabled. The calculation is iterative and hence it needs a starting configuration – for this it uses the configuration found by step 1.w Theory. an equilibrium position. as far as possible. Nevertheless. but it ignores the effects of bending and torsional stiffness of the line or its end terminations. an equilibrium position. However the Bezier curve may have the wrong length (depending on how accurately you have set up the control points). compression means the line is slack and there is no unique solution. bending and torsional stiffness. Catenary The Catenary method calculates the equilibrium position of the line. The Catenary algorithm is robust and efficient for most realistic cases but it cannot handle cases where the line is in compression. Typically a dynamic run will excite the line enough to kick it out of the unstable equilibrium. the position found is not. Touchdown is only included if the bottom end is on or below the seabed. and so when it is used Full Statics should be included if you want the equilibrium position to be found. Spline The Spline method gives the line an initial shape that is based on a user-defined smooth Bezier spline curve. which may not be an equilibrium position. axial elasticity. then no touchdown will be modelled and the line may hang below the seabed. the Catenary position is often quite close to the true equilibrium position. However. then the Catenary algorithm models touchdown by assuming that the line levels out at the level of the end. including weight. If the bottom end is above the seabed. Therefore Full Statics should normally be included unless it is known that the omitted effects are unimportant. when bending stiffness is ignored. An unstable equilibrium can usually be detected by the presence of large curvature spikes on a range graph. The Bezier curve is specified by the user giving a series of control points – it is a curve that tries to follow those control points – and the Bezier curve and its control points (marked by +) can be seen on the 3D view when in Reset state. with the following limitations: Seabed touchdown can only be included at the bottom end of the line. as well as other aspects of the convergence process – see Catenary Convergence. The Catenary method also ignores contact forces between the line and other objects in the model. Unstable equilibria Sometimes Line Statics Step 2 finds an equilibrium configuration that is unstable. Quick The Quick method simply leaves the line in the position that it was drawn when in Reset state. If necessary. In fact the position set by the Quick method only allows for the 124 . in general. so the Spline method scales the Bezier spline curve up or down until the resulting line shape has the correct As Laid Tension. The smoothness of the spline can be controlled using the spline order. It is therefore not. If Full Statics is not included. The Spline method puts the line into a position that. including buoyancy. drag. and interaction with seabed and solids. Very occasionally OrcaFlex statics converges on an unstable equilibrium. Everyday examples of unstable equilibria include balancing a coin on its edge or balancing a pencil on its tip. This is a crude catenary shape that (for speed reasons) ignores most effects. The algorithm is an iterative process that converges on the solution. The Catenary solution has facilities for including seabed touchdown. This is because. since the nodes below the seabed will be pushed back up by the seabed reaction forces. For example you could perform an in-place analysis of a line using its configuration as calculated by an earlier pull-in analysis. It 125 . Because the Full Statics calculation includes these effects. The default settings (for a new line) are the Catenary method followed by Full Statics. To perform a restart this way you also need to suppress the other parts of the static analysis. so it is not usually an equilibrium position (though for simple cases it may be quite close). These effects are omitted from the Catenary calculation. The track is defined as a sequence of track sections each of which is a circular arc of user-specified length and angle of turn and the line is laid along this track. 1e6. Warning: We recommend that User Specified Statics is only ever used to perform restarts as described above. Y Start of track Track Section 1 Length = 150 Turn = 0 X Track section 2 Length = 100 Turn = -90 10 End A Azimuth = 10 Figure: Track section 3 Length = 100 Turn = 90 Track Section 4 Length = 150 Turn = 0 Continuation of last track section Plan View of Example Track User Specified Starting Shape The User Specified Starting Shape statics method involves no calculation. Full Statics The Full Statics calculation is a line statics calculation that includes all forces modelled in OrcaFlex. when the effects of bend stiffness and shapes are introduced. The Quick method should usually be used only as a preliminary to Full Statics. See Laying out the Line. It provides a convenient way of setting the line up in the as laid (i. Specifically. For other static analysis scenarios. Instead you specify a position for each node and the node is placed there. Full statics needs a starting shape for the line. it then finds the equilibrium position from there. e. no such shock loads should occur when it is used. User Specified Statics commonly results in slow and troublesome statics convergence. pre pull-in) starting position. ready for a time simulation of the pull-in. You should therefore set the Step 1 Statics Method to give a reasonable starting shape. In particular it includes the effects of bend stiffness and interaction with shapes.w Theory.g. and it uses the specified Step 1 Statics Method to obtain this. The starting shape of the line is specified by defining a track on the seabed (see Prescribed Starting Shape). since the Catenary method is fast and in many case gives a good initial estimate of the equilibrium position. Full Statics needs to be disabled. We therefore recommend using Full Statics for most cases.e. This statics method allows you to restart calculations using line configurations that have been calculated by separate OrcaFlex calculations. Static Analysis line's average weight per unit length and axial elasticity. and the General Data Statics Tolerance must be set to a large value. If torsion is modelled then node orientations can also be specified. Which method to use The settings to use for the line data items Step 1 Statics Method and Step 2 Statics Method depend on the type of system being modelled and the type of static position wanted. This is often a good choice. To use Full Statics set the Step 2 Statics Method to Full Statics on the Line data form. Prescribed The Prescribed method is intended primarily for pull-in analyses. and this sometimes results in significant shock loads at the start of the simulation. The convergence process is controlled by the Full Statics Convergence Parameters on the line data form so it may be possible to obtain convergence by adjusting some of those parameters. However. You can then set Full Statics back to "Yes" in order to find the true equilibrium position. and the Prescribed method can be used to define this shape. In particular. However it is normally best to choose the Statics Method that gives the best initial estimate of the desired equilibrium position. But if friction is not sufficient then Full Statics will tend to find a nearby position that is in equilibrium. This approach is not always very robust though. since seabed friction will often be able to hold the pipe in the shape it was originally laid. by running the static analysis and adjusting the control points until the spline shape is close to the desired shape. it would not be included. in principle. it is often useful to first set Full Statics to "No". Static Analysis therefore often provides a good starting point for the Full Statics calculation. The choice of Statics Method is then. It is then optional whether Full Statics is included or not.g. Pipeline Pull-In For a pipe lying on the seabed there are usually many equilibrium positions. if you are analysing multiple load cases it can sometimes be impossible to find a single spline shape that will give the desired static solution for all load cases. Full Statics should be included if you want the true equilibrium position to be found. since this will give the best starting position for Full Statics to work from. There are some cases where the choice of Statics Method is important. 5. which then refines the position to take into account the effects that the Catenary omits.5. the problem may be due to the initial starting position obtained by the specified statics method being a long way from the equilibrium position. or alternatively the Spline method may be needed. In both these cases it may be better to select the Spline method and then specify control points that give an initial shape close to the desired equilibrium position. Normally. in cases where there may be more than one equilibrium position. Contact With Solids The Catenary and Quick methods both ignore contact with solids and so they may well give a poor initial position for the Full Statics to work on. but first here are some general points to bear in mind.e.w Theory. irrespective of the initial starting position. When Full Statics is included. The Quick method may suffice. Some specific cases are described below. Notes: You can also use the Buoy Degrees of Freedom Included In Static Analysis data item. or else converge to the wrong equilibrium position (e. Secondly. to include or exclude all buoys with a single setting. Catenary convergence failure The Catenary method is iterative and may fail to converge. As a result the Full Statics calculation may fail to converge. If this proves difficult. Full Statics Convergence Failure Full Statics is also an iterative calculation and may sometimes fail to converge. such as bending and torsional stiffness and interaction with solids. on the General data form. This allows you to examine and refine the spline shape. then an alternative is to use one of the other statics methods. one in which the line is on the wrong side of the solid). since the final position found will be the equilibrium position. This is controlled by the data item Included in Static Analysis on the object's data form. For pull-in analysis this originally-laid shape is generally known. In both these situations. if friction is sufficient to hold the pipe in that position. not important. Firstly. Note: When setting up the spline control points. the Full Statics calculation will tend to find the one that is closest to the initial starting position found by the Statics Method. the Full Statics calculation is iterative and may have difficulty converging if the initial Statics Method position from which it starts is a long way from the true equilibrium position.2 Buoy and Vessel Statics Each buoy and vessel can be either included or excluded from the static analysis. 126 . In that situation it is often more effective to use a tether to guide the line to the desired contact surface. the first stage Statics Method is only used to give the initial starting shape for Full Statics. it is generally best to choose the Statics Method that gives the best initial estimate of the desired equilibrium position. If it is included then it will have no effect if the Prescribed position is already in equilibrium – i. There are situations where you may need to use other settings. It may be possible to solve this by adjusting the Catenary Convergence Parameters on the line data form. In this case it may be necessary for the user to specify the Spline statics method and specify control points that give a good starting shape for the Full Statics. Key results. If a buoy is excluded from the static analysis. See the diagram below. 5. Often you can obtain good estimates by running static analyses of a simplified model and then using the buoy positions found as the initial positions for the more complex model. for example load-offset curves.3 Vessel Multiple Statics You can use the Multiple Statics command on the Calculation menu to perform a series of static analyses for a grid of different positions of a vessel. Note: If the offset vessel has "Included in Static Analysis" set to "Yes" then in Multiple Statics this setting will be ignored (for the offset vessel only) and the vessel will be placed as specified by the offsets. Note: As an aid to static analysis. you can include just the translational degrees of freedom (X. The remaining stages. The period of simulation is defined as a number of consecutive stages. 3. but in some cases there can be difficulties. To allow you to time-shift one aspect of the model relative to the others. for 6D Buoys. This is sometimes useful as an aid to convergence. are then made available in the form of tables and graphs as a function of the offset distance. and similarly for time-varying wind and any time history files that you use. Ramping of current is optional (see Current Data). There is a button on the general data form for this purpose – see Use Calculated Positions. This iterative procedure usually converges successfully. The vessel positions are specified by a series of offsets about the vessel's initial position (see Vessel Multiple Statics Data).5. The user specifies a series of regularly spaced positions for one vessel in the model and OrcaFlex then carries out separate static analyses for each of these vessel positions. This allows quite complex operational sequences to be modelled. which is specified on the Wave page on the environment data form. simply numbered 1. different parts of the OrcaFlex model have their own user-specified time origins.w Theory. When the calculation is completed the program enters Multiple Statics Complete state. For example. Before the main simulation stage(s) there is a build-up stage. To give the best chance of convergence you should specify buoy and vessel initial positions that are good estimates of the true equilibrium position. No results are given for offsets with failed statics. be the equilibrium position. If any buoys or vessels are included in the static analysis. in general. the velocities and rates of turn of vessels and the releasing of lines. Time is measured in OrcaFlex in seconds.6 DYNAMIC ANALYSIS The dynamic analysis is a time simulation of the motions of the model over a specified period of time. then when the static analysis is done OrcaFlex will simply place the buoy in the Initial Position specified on the buoy data form. 2. All of these time origins are defined relative to the global time origin (which is not user-specified). 127 . The simulation time origin is at the end of the build-up stage. This gives a gentle start to the simulation and helps reduce the transients that are generated by the change from the static position to full dynamic motion. This feature is mainly intended for use in mooring analyses. The figure below shows a simulation using a build-up of 10 seconds. the out-of-balance forces on buoys and vessels can be drawn on the 3D view. links and winches. for example the way winches are controlled. Dynamic Analysis Also.Z) and exclude the rotational degrees of freedom. starting from the position derived by the static analysis.Y. Various controlling aspects of the model can be set on a stage by stage basis. See Vessel Data. so negative simulation time is the build-up stage and the remaining stages are in positive simulation time. using an iterative procedure. This will not. Results cannot be saved. The same applies to vessels. If necessary. Results can only be viewed in this state and are lost upon Reset. … are intended as the main stages of analysis. during which the wave and vessel motions are smoothly ramped up from zero to their full size. A dynamic simulation cannot be carried out after multiple statics – you must Reset first. simulation time is measured relative to the simulation time origin. followed by two stages of 15 seconds each. then the static analysis finds the equilibrium position of those buoys and vessels. Each wave train also has its own time origin. This build-up stage is numbered 0 and its length should normally be set to at least one wave period. If the static calculation fails to converge for a particular offset then this is noted in the Statics Progress Window and the program continues to the next offset. you can also control the buoy convergence process using the statics convergence parameters on the general data form. so if necessary you can use the time origins to time-shift one aspect of the model relative to the others. whose durations are specified in the data. 5. Explicit integration scheme The explicit scheme is forward Euler with a constant time step. Explicit and Implicit.v.w Theory. The forces and moments acting on each free body and node are then calculated.e. p. 10 seconds into stage 1) by either setting the simulation time origin to 2580 or else setting the wave train time origin to -2580. If you use the View Profile facility and find that the wave arrives at the vessel at global time 2590s.a) is the system inertia load. then you can arrange that this occurs at simulation time 10s (i. Dynamic Analysis By default all of the time origins are zero.a) + C(p.v) is the system damping load. F(p. are known from the static analysis. Equation of motion The equation of motion which OrcaFlex solves is as follows: M(p. whereas the latter shifts the wave back to the period the simulation covers. For most cases this simple situation is all you need. The former shifts the simulation forwards to when the wave occurs.v) + K(p) = F(p. Both schemes recompute the system geometry at every time step and so the simulation takes full account of all geometric non-linearities.6. Static Starting Position End of Simulation Build-up -10 Stage 1 Stage 2 0 Simulation Time t 15 30 Wave Train Time 0 Time-history Time 0 T=0 Global Time Origin Figure: Global Time T Simulation Time Origin Wave Train Time Origin Time-history Time Origin Time and Simulation Stages 5. You might want to arrange that a wave crest. including the spatial variation of both wave loads and contact loads. as described below. K(p) is the system stiffness load. v and a are the position. or a particularly large wave in a random sea. including all nodes in all lines.v. the initial positions and orientations of all objects in the model. t is the simulation time. Forces and moments considered include: weight 128 . velocity and acceleration vectors respectively. At the start of the time simulation.1 Calculation Method OrcaFlex implements two complementary dynamic integration schemes.t) where M(p. arrives at your vessel at a particular point in the simulation. C(p. but here is an example where you might want to adjust a time origin. so all of the time frames coincide with global time.t) is the external load. but a local equation of motion for each free body and each line node. The Generalised-α integration scheme has controllable numerical damping which is desirable since it removes this spurious. then the run time is approximately proportional to the square of the number of nodes. vt and at respectively. and then integrated using forward Euler integration. OrcaFlex uses a built-in value of 0. velocity and acceleration at time step t by pt.K(p) This is not the system-wide equation of motion described above. Lines are the most computationally demanding. are calculated in the same way as for the explicit scheme. damping. Finite element models may contain spurious high frequency response. the length of time required for dynamic analysis is approximately proportional to the total number of nodes used multiplied by the total number of inner time steps in the whole simulation. Then the system equation of motion is solved at the end of the time step. To save computing time. The forces. Then the values at the end of the time step.C(p. these loads are updated only over a longer outer time step. This equation is solved for the acceleration vector at the beginning of the time step. the implicit scheme is typically stable for much longer time steps than the explicit scheme and often this means that the implicit scheme is faster. non-physical high frequency response.at pt+1 = pt + dt. If the time step is maintained at the recommended value and nodes are distributed uniformly along the lines. ρ∞. For most models that include lines. This means that solving these equations of motion merely requires the inversion of 3 by 3 or 6 by 6 mass matrices. v and a are unknown at the end of the time step an iterative solution method is required.v. are given by: vt+1 = vt + dt. This numerical damping also leads to much more stable convergence and hence allows for longer time steps and much faster simulations. Consequently each implicit time step consumes significantly more computation time than an explicit time step. and are time-consuming to compute.vt+1 where dt is the time step. a feature inherent in the finite element method. The numerical damping is determined by specifying the level of high frequency dissipation. Both time steps are user-defined and may be set equal for critical cases. Hydrodynamic and aerodynamic forces typically change little over such a short time interval. However. The Line Target Damping data can be used to damp out this high frequency noise. Of the various objects available in OrcaFlex. The Generalised-α integration scheme is designed to minimise the low frequency damping. 129 . At the end of each time step. Implicit integration scheme For implicit integration OrcaFlex uses the Generalised-α integration scheme as described by Chung and Hulbert.w Theory. mass etc.t) . Because p. a feature inherent in the finite element method. at time t+1. Dynamic Analysis buoyancy hydrodynamic and aerodynamic drag hydrodynamic added mass effects. Let us denote the position. moments. the positions and orientations of all nodes and free bodies are again known and the process is repeated.v) . Numerical damping of the integration scheme Finite element models may contain spurious high frequency response. for each free body and each line node. Any integration scheme which includes numerical damping of high frequency response must be careful to avoid damping response at lower frequencies. calculated using the usual extended form of Morison's Equation with userdefined coefficients tension and shear bending and torque seabed reaction and friction contact forces with other objects forces applied by links and winches The equation of motion (Newton's law) is then formed for each free body and each line node: M(p)a = F(p. The time step required for stable integration is typically very short and OrcaFlex gives guidance on an appropriate time step.4 which has been chosen to give fast simulation run times without compromising accuracy. 3D Buoys and 6D Buoys. accumulation of soil in front of the line. To model seabed interaction accurately would require much more information about the soil structure and would involve modelling the soil itself which is beyond the scope of OrcaFlex.4 0. friction on mid-water arches.1 0. time after time zero is normal simulation with the full specified excitation.2 Ramping Simulation time is reduced by the use of a build-up time at the beginning of the simulation. 130 . The objects which can contact with solids are Lines.6 0.5 0.2 0. so time before time zero is build-up time. ramping is also used to smooth the handover from the standard Morison drag force applied in statics to the force given by the VIV model. Hereafter we use the term solid to refer to either the seabed or elastic solids. guide tube friction etc.8 0.9 1 r Figure: The OrcaFlex ramping function This particular ramping function has been chosen so that its first and second derivatives are zero at the beginning and end of the build-up stage. Negative time is shown during the simulation to indicate the build-up time.7 0. 5.4 0.3 0.6 0.6. This gives a gentle start to the simulation which reduces transient responses and avoids the need for long simulation runs. vessel motions and optionally the current are built up smoothly from zero to their full level.5 0. Note: Friction for contact with elastic solids is only included during dynamics. The ramping factor is calculated as follows: Ramping Factor = r3 (6r2 -15r + 10) where r is the proportion of the build-up stage completed.7 0. etc.9 Ramping Factor 0.w Theory.7 FRICTION THEORY OrcaFlex provides a simple friction model that can give an approximate representation of contact friction. During the build-up time the wave dynamics.1 0 0 0.8 0.2 0. This is commonly used to model seabed friction. The build-up stage should normally be set to at least one wave period. Overview of the OrcaFlex friction model OrcaFlex models friction for contact with the seabed or elastic solids. Seabed friction In reality seabed interaction is much more complicated than simple friction – it involves effects such as the soil being displaced by the line as it moves.3 0. 1 0. When using a time domain VIV model. Friction Theory 5. given by: r = (Time + Length of Stage 0) / (Length of Stage 0) Note: Time is negative throughout the build-up stage. Instead we use a modified Coulomb model as illustrated below: Force R Deflection R Force R -Dcrit +Dcrit Deflection R Figure: Standard Coulomb and modified Coulomb friction models 131 . where μ is the friction coefficient and R is the contact reaction force. However. The standard Coulomb friction model states that a friction force of μR is applied. Friction Theory Friction is modelled as Coulomb friction in the solid plane. Every object which is in contact with a solid keeps track of a friction target position (discussed below) and a friction force is applied at which acts towards this target position. this model results in a discontinuous Force / Deflection relationship which would be impossible for a program like OrcaFlex to solve.w Theory. at the end of each time step. If the Step 1 Statics Method is Prescribed then the target positions are laid out along the prescribed shape. Otherwise the target position is set equal to the contact position. If these values are different. The distance between each target position is determined by the unstretched segment length and the As Laid Tension. Target positions in statics Friction is only applied in statics for contact between lines and the seabed. Da = the vector components of D in the node's normal and axial directions. If an object has just come into contact then the target position is set equal to the contact position. If each node was to sit at its target position then the effective tension throughout the line would be the As Laid Tension. 132 . as shown in the following figure. If the target position is a distance greater than Dcrit from the contact position then the target position is placed at a distance exactly Dcrit from the contact position on the vector D. The friction force can be thought of as being ramped from 0 to a maximum value of μR as the deflection increases.w Theory. A is the contact area. 3D Buoys and 6D Buoys and elastic solids the friction coefficient is defined on the Solid Friction Coefficients data form. Here Dcrit is given by: Dcrit = μR / (KsA) where Ks is the shear stiffness data item. For line friction. For contact between Lines. For contact between 3D Buoys and the seabed the friction coefficient is defined on the 3D Buoy data. and vice versa. For contact between 6D Buoys and the seabed the friction coefficient is defined on the 6D Buoy data. for lines in contact with the seabed. Dn. each friction target position is updated using the following rules: At the start of the dynamic simulation. from the node towards the target position. This can be thought of as 'dragging' the target position towards the contact position. both normal and axial coefficients can be defined. Otherwise the target position is not modified. the target position from statics is used. If an object is not in contact then the target position is not defined since no friction is applied. Friction Theory In the modified Coulomb friction model the transition from a friction force of -μR to +μR takes place as a linear variation over the deflection range -Dcrit to +Dcrit. Higher values of Ks lead to the ramping taking place over a shorter distance. OrcaFlex uses a single value of μ defined as: μ = magnitude of the vector μnDn + μaDa where D = unit vector in the plane of the solid. For all other Step 1 Statics Methods the target positions are laid along the seabed in the direction specified by the Lay Azimuth direction. Target positions in dynamics During dynamics. Calculation of friction coefficient The friction coefficient μ is defined as follows: For contact between Lines and the seabed the friction coefficient is defined on the Line Type data. w Theory. Moments in OrcaFlex are reported at the centreline and so the moment arm effect of applying the friction force at the outer edge results in a moment being applied to the node. This feature produces output similar to a frequency domain package but the calculation is based on a random wave time domain simulation. λ is percentage of critical contact damping / 100. Shear damping Objects moving in the solid plane may also experience a damping force. no such moments are applied. Let d be the distance between the contact position and the target position. where p is the point of contact relative to the node origin and F is the applied friction force. Note: This effect is only modelled if torsion is included in the model. The random 133 . 5. For 6D Buoys the friction force is applied at each vertex in contact with the solid. If the vertex if offset from the buoy origin then the appropriate moment. A is the contact area. To do this you must specify a single wave train with wave type of Response Calculation. For lines this is at the line outer edge as defined by the contact diameter. Moments induced by friction (3D and 6D Buoys) Since 3D Buoys do not have rotational degrees of freedom. will be generated. The final output of the analysis is an RAO for the results variable of interest. μR) where S is a scaling factor given by 1 . K is the solid normal stiffness. This frictional moment effect can most easily be visualised by considering a pipe being dragged laterally across a surface with friction.(d/Dcrit). Vs is the component of velocity in the solid plane. It is intuitively obvious that the friction force will result in the pipe being twisted.min(2λ(MKA)½Vs. about the buoy origin. Spectral Response Analysis Old Target position New Target position Vector D Contact position position Figure: Circle of radius Dcrit Updating friction target positions during dynamics Moments induced by friction (Lines) The friction force is applied at the point of contact with the solid.8 SPECTRAL RESPONSE ANALYSIS The Spectral Response Analysis capability of OrcaFlex provides a facility for determining the response characteristics for any OrcaFlex results variable. Time domain random wave for spectral response analysis In order to calculate spectral response you must first perform a random wave time domain simulation of the system of interest. M is the mass of the object. The applied moment is given by the vector cross-product p×F. The results of this simulation are transformed into the frequency domain using a Fast Fourier Transform (FFT) and the spectral response is then derived. If 0 ≤ d ≤ Dcrit then a damping force in the solid plane is applied to the object with magnitude given by: D = S. Spectral response random wave components It is important that the random wave components have frequencies which match those produced by the FFT. the non-linearities are included in the calculation automatically. Depending on the type of system. 2. which has the energy spread evenly over a user-specified range of frequencies. The maximum frequency equals (M/2)Δf = 1/(2t). This frequency is known as the Nyquist critical frequency. Pi) for i = 1. The time history covers the response calculation simulation period as specified on the General Data form. Δf = 1/(tM). This takes the form of a text label which says "The response calculation will use M data points". based on the spectral moments of all the data. M/2 where Pi is understood to be the PSD for frequency fi. M/2 where Ri is the RAO at frequency fi and Si is the spectral density at frequency fi for the response calculation random wave. Comparison with traditional frequency domain methods For frequency domain approaches to calculating system responses each non-linearity in the system has to be handled in special ways. Warning: The generated response RAOs are not always accurate.9 EXTREME VALUE STATISTICS THEORY The theory for the calculation of the extreme value statistics results provided by OrcaFlex depends on which extreme value statistics distribution is chosen: The Rayleigh distribution method uses a direct calculation. or is a product of large primes. with the extremes being selected using the peaks-over-threshold method. with declustering to reduce dependence 134 . Not all these frequencies are used in the response calculation random wave. Spectral response calculation details The spectral response analysis starts from the time history of some results variable of interest. …. The user controls the range of frequencies to be used with the Target Frequency Range data on the Environment data form. t. The values of fi are integer multiples of the FFT's fundamental frequency. The response calculation wave components are selected with frequencies that are also integer multiples of Δf. The effect of leakage is to make the output of the FFT noisy. Extreme Value Statistics Theory wave used has a truncated white noise spectrum. However.e. bespoke linearisation techniques. …. The advantage of the method used by OrcaFlex is that non-linearities can be handled implicitly without the need for special. 5. The Weibull and Generalised Pareto (GPD) distributions are fitted to selected extremes of the data. This is because the FFT calculation is slow when presented with a time history whose size is a large prime. OrcaFlex does not necessarily use all the available samples. OrcaFlex will choose M with the properties that that M ≤ N and the FFT can be calculated quickly and efficiently for M samples. Suppose that N is the total number of available samples. by calculating the RAOs using a fully non-linear time domain simulation and then transforming to the frequency domain using Fourier transform methods. The RAO is calculated as Ri = (Pi/Si)½. it may be impossible to calculate good quality response RAOs using this method. You must use the output with caution. In this way the frequency leakage effect is avoided.w Theory. Having chosen M. The PSD is denoted as the sequence (fi. This is because there could potentially be so many frequencies (i. OrcaFlex then selects the M samples from the original time history that are closest to the end of the simulation. Only the frequencies which lie in the target frequency range are used for wave components. given by f i = iΔf. OrcaFlex then calculates the power spectral density (PSD) of these M time history samples using the FFT. for i = 1. determine the total number of samples available for the FFT. The duration of this period together with the logging interval. 2. This is because of a phenomenon of the FFT known as frequency leakage which would occur if the random wave component frequencies did not match the FFT frequencies. Because of this there may be fewer than M/2 wave components. Notes: Provided that a Response Calculation wave type has been selected the Waves page of the Environment data form reports the value of M. for large values of M/2) that the real-time required to simulate a wave with that many components would be prohibitive. This is because models that are fitted to the entire dataset tend to be driven by features in the body of the data. Mathematical theory (e. Modelling Stationary Series). Weibull and Generalised Pareto Distributions The Weibull and Generalised Pareto (GPD) distributions are both fitted using the maximum likelihood method. For OrcaFlex time history results this is even more important. Note that all the above formulae are for maxima. Extreme Value Statistics Theory between the selected extremes. analysing the upper tail extremes. So OrcaFlex instead calculates the extreme value which will be exceeded with probability α using the alternative formula μ + σ[2ln(-n/ln{1-α})]½ Ochi derives this formula using Cramér's approximation method in his paper On Prediction of Extreme Values. The usual way to do this is declustering: OrcaFlex uses either runs declustering as illustrated by Coles (5. Rayleigh Distribution The derivation and use of spectral moments to fit the Rayleigh distribution is described in detail by Ochi (he calls it the "exact method"). then successive time history values will certainly not be independent. Wooster Temperature Series).3. σ and Tz are the mean. since he describes (Section 4. the peaks over the threshold converge in distribution to a Generalised Pareto distribution. the peaks-over-threshold method (Chapter 4. which may not be relevant to the tail behaviour. The complete model-fitting process is then summarised as: 1. in particular the book by Coles is particularly relevant. We can get much closer to independence by sub-sampling the data. Ochi goes on to show that. Parameter Estimation) its application to the GPD.3. They differ only in the actual statistical distribution that is fitted and then used to predict the extreme values. The technique is widely described in statistical texts. and implementation of. it is safest to use a model that is fitted only to the tails of the data. for low values of risk parameter α.3. of the time history being analysed.2. Both distributions are fitted to extremes of the data that are selected using the peaks-over-threshold method with (optional) declustering. It fits the parameters of the distribution to the data by calculating the parameters that make the observed data most likely under the chosen distribution.e. or defines a cluster to be the set of values between successive up-crossings of the mean value.3. However. respectively. Consider daily temperature for example. where one cold day is likely to be followed by another: successive daily values are not independent. Corresponding formulae for minima (lower tail) are trivially obtained by replacing the plus signs with minus signs in these formulae. 135 . Threshold Models) and declustering (5. Declustering An important assumption underpinning the maximum likelihood method is that the data are independent. The Weibull or GPD distribution is then fitted to those extremes using the maximum likelihood method.1) tells us that as the size of the dataset and the threshold for fitting increase. Ochi shows that. Coles.g. OrcaFlex reports this most probable extreme value for the specified storm duration. the most probable maximum value occurring in storm duration T is given by μ + σ[2ln(n)]½ where n = T/Tz is the number of peaks and μ. the extreme value which will be exceeded only with probability α is μ + σ[2ln(n/α)]½ However this latter formula is approximate and is valid only for low values of α.w Theory. For the Rayleigh distribution to be appropriate for the peak responses. and it gives good results over the whole range of values of risk factor α. i. ensuring that the points we choose are sufficiently far apart as to be approximately independent. under the Gaussian assumption. the response variable must be a stationary Gaussian process. this is often not the case. Coles also documents the motivation for. Use declustering to identify clusters of exceedences. but values a week or a month apart might well be considered independent. since unless the log interval is extremely long. Maximum likelihood Maximum likelihood estimation is a standard general-purpose statistical technique for fitting a given parametric distribution to an arbitrary set of data. standard deviation and mean up-crossing period. Threshold models When the object of primary interest is extrapolation into the tails of the data. Theorem 4. specifies how the object's volume changes with pressure. Normally the density increases with depth.1 Buoyancy Variation with Depth The buoyancy of an object is normally assumed to be constant and not vary significantly with position. 6D Buoy or Line Type by giving the following data on the object's data form. x=μ+y). which is taken to be the density value at the sea density origin. Determine the maximum excess within each cluster. The bulk modulus has the same units as pressure F/L 2 and the above formula can be thought of as saying that the volume reduces linearly with pressure. y. where (1+ξy/σ)+ = max(0.w Theory. added mass. The buoyancy is equal to ρVg. Note: The bulk modulus and density variation facilities in OrcaFlex only affect the buoyancy of objects. Compressibility of Buoys and Lines All things are compressible to some extent. use maximum likelihood to fit the chosen distribution to them. or else because of temperature or salinity variations. In reality the buoyancy does vary due to the following effects: If the object is compressible then its volume V will reduce with depth due to the increasing pressure. V is the volume and g is the acceleration due to gravity.e. The above formula breaks down when P>B. The effect is usually not significant. is FGPD(y) = 1 . since otherwise the water column would be unstable (the lower density water below would rise up through the higher density water above). This is equivalent to applying the three-parameter Weibull distribution FW3(x) = 1 . However. where σ = Weibull distribution scale parameter ξ = Weibull distribution shape parameter. 1+ξy/σ) FGPD(y) = 1 . Assuming independence between these maxima.10. The calculation of hydrodynamic effects use the uncompressed volume and a nominal sea density value.exp[{-(x-μ)/σ}ξ] to the original values x unadjusted for the threshold (i. For an incompressible object the bulk modulus is infinity. the relationship between pressure and volume would become inaccurate well before the pressure exceeded the bulk 136 . Generalized Pareto distribution The Generalized Pareto distribution function. OrcaFlex does not allow for compressibility or density variation when calculating hydrodynamic effects such as drag. Bulk Modulus The bulk modulus. and this is the default value in OrcaFlex. for the excesses y above threshold. For buoys and lines these effects can be modelled in OrcaFlex. If we denote by V the compressed volume of the object then V is given by: V = V0(1-P/B) where V0 is the uncompressed volume at atmospheric pressure.exp{(-y/σ)ξ} to the declustered excesses over threshold. you can specify the compressibility of a 3D Buoy. B. To allow these effects to be modelled. where the location parameter μ is the userspecified threshold value and is not fitted by the maximum likelihood calculation. and at a rate that would see the object shrink to zero volume if the pressure ever reached B. etc.(1+ξy/σ)+-1/ξ for ξ≠0. In this case OrcaFlex uses a compressed volume V of zero. 5. The water density ρ can vary with position.exp(-y/σ) for ξ=0 where σ = GPD scale parameter ξ = GPD shape parameter. Weibull distribution OrcaFlex fits the two-parameter Weibull distribution with distribution function FW2(y) = 1 . where ρ is the water density. Environment Theory 2. but in some cases it can have a significant effect on the object's buoyancy.10 ENVIRONMENT THEORY 5. and P is the pressure excess over atmospheric pressure. 3. either because of the compressibility of the water. The penetration resistance force depends on the choice of seabed model used – for details see either Linear Seabed Model Theory or Non-linear Soil Model Theory.Y). so the object normally only experiences pressures that are small compared to B. Linear interpolation is used for intermediate depths. the current must be extrapolated above the still water level.10. This gives a model where each vertex behaves rather like a pad (such as the landing pad on a lunar module). 5. A line interacts when one of its nodes penetrates the seabed. Exponent is the power law exponent. If the specified profile does not cover the full depth then it is extrapolated (see Extrapolation above). The seabed friction force is calculated using the buoy seabed friction coefficient. Environment Theory modulus. Note: If Z is below the seabed (e.Sb) x ((Z-Zb) / (Zf-Zb))1/Exponent where Sf and Sb are the current speeds at the surface and seabed. If a sloping seabed is specified. Power Law Method Current direction is specified and does not vary with depth. in OrcaFlex we adopt the convention that the surface current applies to all levels above the still water level.g.3 Seabed Theory The seabed reaction force is the sum of a penetration resistance force in the seabed normal direction and a friction force in the direction tangential to the seabed plane and towards the friction target position. variable in magnitude and direction with depth.10. A 3D Buoy interacts when the buoy origin penetrates the seabed.Z) according to the formula: S = Sb + (Sf . respectively. in a wave crest) then current speed is set to S f.2 Current Theory Extrapolation In the presence of waves. and the forces are applied at that vertex. This effect is not usually important and is uncorrected in OrcaFlex.Y. Zf is the water surface Z level. based on the penetration of that vertex and displacement of that vertex from its friction target position.g. In practise B is normally very large. Each penetrating vertex experiences its own seabed normal reaction and lateral friction force. Normal Seabed Stiffness Force The normal stiffness reaction force has magnitude = KnAd and is applied in the outwards normal direction. and are applied at the buoy origin. A 6D Buoy interacts when any of its vertices penetrates the seabed. The seabed reaction forces are calculated using the penetration of the lower outer surface of the line (based on the line type contact diameter) and the seabed forces are applied at that point. Linear Seabed Model Theory In the Linear seabed model the seabed behaves as a linear spring in the normal direction. with spring strength equal to the Normal seabed stiffness specified in the seabed data. The seabed lateral friction force is calculated using the line type seabed friction coefficient. the boundary is inconsistent with a horizontal current. Zb is the Z level of the seabed directly below (X. Other objects are not affected by it. where: Kn = seabed normal stiffness A = penetrator contact area d = depth of penetration into the seabed. The profile should be specified from the still water surface to the seabed.w Theory. seabed damping forces are applied in the normal and tangential directions. If explicit integration is used in the dynamic analysis then. Interpolated Method Horizontal current is specified as a full 3D profile. Speed (S) varies with position (X. The seabed reaction forces are calculated using the penetration of the buoy origin. 5. The current at the greatest depth specified is applied to all greater depths. in addition. has penetrated the seabed) then the current speed is set to S b and if Z is above the surface (e. Drag chain interaction with the seabed is calculated differently – see drag chain seabed interaction. For details of the friction force see Friction Theory. 137 . Objects Affected 3D Buoys and 6D Buoys. lines and drag chains interact with the seabed. The main aspects of the model are: It models the seabed normal resistance using four penetration modes.2(MKnA)½Vn if Vn > 0 Dn = 0 if Vn ≤ 0 where λ = seabed percent critical damping / 100 M = mass of the object (e. is applied in the direction opposing the tangential component of the velocity of the penetrator. as shown in the diagram below.10. such as those proposed by Bridge et al and Aubeny et al. Please contact Orcina if you have any feedback and comments on the model or ideas for improvement. the mass of a node of a line) Kn = seabed normal stiffness A = penetrator contact area Vn = component of velocity normal to the seabed. In each penetration mode the seabed reaction force per unit length. as follows. Note: The non-linear soil model is currently experimental and we are working on comparing the model against experimental results for pipe-seabed contact. See Penetration Resistance Formulae below. In Not In Contact mode the resistance P(z) is zero. It is applied in the seabed outward normal direction and has magnitude D n given by: Dn = λ. In the other 3 modes the formula for P(z) uses a term of hyperbolic form. Full details of the non-linear soil model are given in Randolph and Quiggin (2009). P(z). Mark Randolph FRS (Centre for Offshore Foundation Systems. It is given by Dt = -λ2(MKtA)½Vt where Kt = seabed shear stiffness Vt = vector component of penetrator velocity tangential to the seabed. positive when travelling into the seabed and negative when coming out. The normal seabed damping force is only applied when the penetrating object is travelling into the seabed. For details of the data used by the non-linear soil model and its suitability for different seabed types see Non-linear Soil Model. where z = penetration and D = penetrator contact diameter. 6D Buoy Theory and Line Interaction with Seabed and Solids. not when it is coming out of the seabed. 5. For details on how the penetrator contact area is calculated see 3D Buoy Theory. Normal Seabed Damping Force If implicit integration is used in the dynamic analysis then no seabed damping forces are applied. It is a development from earlier models that proposed and used a hyperbolic secant stiffness formulation. These features are now described in more detail in the sections below. is modelled using an analytic function of the non-dimensionalised penetration z/D. but ensures that as the penetration z increases or decreases from its value when this episode of penetration or uplift started. then the resistance P(z) asymptotically approaches the soil ultimate penetration resistance (for penetration) or ultimate suction resistance (for uplift) at that penetration depth. which provides a high stiffness response for small reversals of motion. Dt.4 Seabed Non-Linear Soil Model Theory The non-linear soil model has been developed in collaboration with Prof. If explicit integration is used in the dynamic analysis then.g. Environment Theory For details on how the penetrator contact area is calculated see 3D Buoy Theory. The tangential seabed damping force. University of Western Australia). 138 .w Theory. seabed damping forces are applied in the normal and tangential directions. 6D Buoy Theory and Line Interaction with Seabed and Solids. so the penetrator starts the simulation in either Not In Contact mode or Initial Penetration mode. These ultimate penetration and suction asymptotic limits are given by Pu(z) = Nc(z/D)su(z)D Pu-suc(z) = -fsucPu(z) 139 . a node on a line. Repenetration mode persists until the penetrator starts to lift up again. and it then changes to Uplift mode. in which case it changes to Repenetration mode. z. The effect of this is that the static position found is based on the assumption that any static penetration occurred as a single progressive penetration. when it changes to Uplift mode. The penetrator then stays in Uplift mode until either the penetration falls to zero. Ultimate Resistance Limits The resistance formulae are arranged so that as penetration z increases (for penetration) or decreases (for uplift) then the resistance asymptotically approaches the ultimate penetration resistance P u(z) (for penetration) or the ultimate suction resistance Pu-suc(z) (for uplift). OrcaFlex cannot allow for such effects since it only has limited information about how the line was originally laid. in which case it breaks contact and changes to Not In Contact mode. Once initial penetration has occurred in the dynamic simulation. and it does not allow for the effect any of uplift and repenetration that might have occurred during first installation.w Theory. and in the dynamic analysis by whether the penetration has increased or decreased since the previous time step. a vertex of a 6D Buoy or the origin of a 3D Buoy) is determined by its penetration. In the static analysis the Uplift and Repenetration modes are not used and the penetration mode is set to Initial Penetration if the penetration is +ve or to Not In Contact otherwise. So if the penetrator stays in contact with the seabed but oscillates up and down then it switches back and forth between Uplift and Repenetration modes.g. the penetrator then stays in Initial Penetration mode until it starts to lift up. If the penetrator breaks contact and then later makes contact again then it enters Repenetration mode. If it starts in Not In Contact mode then it changes to Initial Penetration mode the first time the penetration becomes +ve. The details are as follows. or else until the penetration starts to increase again. Similarly. This is because the model assumes that second and subsequent periods of contact are making contact with the same area of seabed as was previously disturbed by the initial penetration. Environment Theory Penetration Modes Not in Contact Break contact First contact only Uplift Start of first uplift only Initial Penetration Figure: Start of second or subsequent uplift Second or subsequent contact Start repenetrating when still in contact Repenetration Soil Model Penetration Modes The penetration mode of a given penetrator (e. The dynamic simulation starts from the results of the static analysis. not Initial Penetration mode. z 0 and P0. Nc(z/D) = bearing factor. See the green curve in the model characteristics diagram below. which approaches the ultimate penetration resistance limit (upper grey curve) as penetration gets large compared to D/Kmax. The penetration resistance is then given by P(z) = HIP(ζ). where Kmax is the Normalised Maximum Stiffness parameter of the model. Suction Limit Experiments (Bridge et al) have found that suction resistance can only be sustained for a limited displacement past the point where the net resistance becomes negative. i. which gives a good approximation to the theoretical bearing factor for shallow penetration. both of which are specified in the Seabed Soil Properties data. where su0 is the undrained shear strength at the mudline and ρ is the undrained shear strength gradient. i.ζ) is a hyperbolic factor that equals 0 when ζ = ζ0 at the start of this uplift. Penetration Resistance Formulae In Not In Contact mode the penetration resistance P(z) is zero. and suction then decays as uplift continues. fsuc = non-dimensional Suction Resistance Ratio parameter of the model. if ζ gets large (i. as specified in the Soil Model Parameters.1 the formula Nc = Nc(0.Pu-suc(z)] / Pu(z0) The term HUL(ζ0 . Initial Penetration Mode For Initial Penetration mode the starting penetration and resistance values. and asymptotically approaches the (negative) ultimate suction resistance Pu-suc(z) if the non-dimensional uplift (ζ0 .ζ ) / [ AUL(z) + (ζ0 .e. The purpose of this factor is to provide a high initial stiffness while ensuring that the penetration resistance P(z) rises smoothly from zero when contact first starts (when ζ and z are both 0) and asymptotically approaches the ultimate penetration resistance. the value at the time the latest transition into this contact mode occurred.w Theory. This is the penetration.Pu(z) (1) where HIP(ζ) = ζ / [1 + ζ] The term HIP(ζ) is a hyperbolic factor that equals 0 when ζ = 0 when initial penetration starts. and asymptotically approaches 1 if the non-dimensional uplift (ζ0 . To model this the 140 . Uplift Mode For Uplift mode the penetration resistance is given by P(z) = P0 . as specified in the Soil Model Parameters.1)(10z/D)½ is used instead.HUL(ζ0 .ζ)(P0 . and asymptotically approaches 1 as penetration gets large compared to D/K max. as specified in the Soil Model Parameters.ζ) gets large compared to AUL(z). if z gets large compared to D/K max). For z/D ≥ 0.e. This is illustrated by the blue curve in the model characteristics diagram below. For Lines the contact diameter is as specified in the Line Type Contact Data. equals ½ when ζ = 1. In the other three modes the resistance P(z) is modelled using formulae that involve the following variables: ζ = z / (D/Kmax).ζ) = ( ζ0 . So in uplift mode the resistance given by equation (2a) drops from its value P0 when this uplift started. Pu(z). P0 = resistance P(z) at which the latest episode of this contact mode started. z0 = penetration z at which the latest episode of this contact mode started.1 this is modelled using the power law formula N c(z/D) = a(z/D)b. where a and b are the non-dimensional Penetration Resistance Parameters of the model. D = penetrator contact diameter.e.ζ) ] AUL(z) = [P0 . For 3D Buoys and 6D Buoys the contact diameter is taken to be the square root of the contact area (see 3D Buoy contact area and 6D Buoy Theory).Pu-suc(z)) (2a) but subject to a suction limit – see below. when z = D/Kmax. This is given by s u(z) = su0 + ρz. are both zero. ζ0 = z0 / (D/Kmax) = non-dimensionalised penetration at which the latest episode of this contact mode started.ζ) gets large compared to AUL(z). Environment Theory where su(z) = undrained shear strength at penetration z. but non-dimensionalised to be in units of D/Kmax. Here: HUL(ζ0 . For z/D < 0. zP=0) / (λsuc zmax)}] zmax = largest ever penetration z for this penetrator zP=0 = largest penetration z at which suction has started during any uplift λsuc = non-dimensional Normalised Suction Decay Distance parameter of the model. if this repenetration started from a zero or negative resistance Pu* = Pu(z*) if P0 > 0. Here ζ0 and P0 = non-dimensional penetration and resistance at the start of this repenetration HRP(ζ .e. This models the suction decay effect that experimental evidence has found.ζ0) in equation (3a) is a hyperbolic factor that equals 0 when ζ = ζ 0 at the start of this repenetration. so ERP(z) ≤ 1.λrep + (z .ζ0) = (ζ .zP=0) / (λsuc zmax)}] zmax = largest ever penetration z for this penetrator zP=0 = largest penetration z at which suction has started during any uplift λsuc = non-dimensional Normalised Suction Decay Distance parameter of the model. So the repenetration mode resistance given by equation (3a) rises from its value P 0 when this repenetration starts. The exponent in the expression for ERP(z) is zero or negative. until the penetration z exceeds zP=0 by a certain amount.e. The expression for ERP(z) gives a value < 1.P0) (3a) but subject to a repenetration resistance upper bound – see below. i. (z . at which suction has ever occurred during uplift. so EUL(z) ≤ 1. as given by equation (1) ERP(z) = exp[min{0. no more suction than) a negative lower bound Pmin(z). Environment Theory resistance given by equation (2a) is limited to be no less than (i. as specified in the Soil Model Parameters.ζ0) gets large compared to ARP(z). but as the penetrator lifts up higher (relative to the maximum penetration at which suction has ever occurred during uplift) then the suction is limited more. where z* is the penetration when the preceding episode of uplift started The term HRP(ζ .ζ0) ] ARP(z) = ( Pu(z)-P0 ) / Pu* Pu* = Pu(z) if P0 ≤ 0. z P=0. and asymptotically approaches 1 if the non-dimensional repenetration (ζ . as specified in the Soil Model Parameters. and asymptotically approaches the ultimate penetration resistance P u(z) if the non-dimensional repenetration (ζ . quantified by λrep. 141 .ζ0) gets large compared to ARP(z). as specified in the Soil Model Parameters. The exponent in the expression for EUL(z) is zero or negative. Repenetration Mode For Repenetration mode the penetration resistance is given by P(z) = P0 + HRP(ζ . This models the effect that repenetration following large uplift movement shows reduced resistance until the previous maximum penetration is approached.ζ0)(Pu(z) . and so limits the repenetration resistance to be less than the ultimate penetration resistance Pu(z). To model this the repenetration resistance given by equation (3a) is limited to be no more than an upper limit P max(z) given by: Pmax(z) = ERP(z)PIP(z) (3b) where PIP(z) = penetration resistance that initial penetration mode would give at this penetration.w Theory.EUL(z) equals 1 when z ≥ zP=0. given by: Pmin(z) = EUL(z)Pu-suc(z) (2b) where EUL(z) = exp[Min{0. The effect of this is that the term Pmin(z) limits suction to be no more than Pu-suc(z) when the first uplift starts. See the purple curve in the model characteristics diagram below.ζ0) / [ ARP(z) + (ζ . Repenetration Resistance Reduction After Uplift Experiments (Bridge et al) have found that when repenetration occurs following large uplift movement the repenetration resistance is reduced until the previous maximum penetration is approached. . but decays towards zero if the penetration z is less than the largest penetration. λrep = non-dimensional Repenetration Offset After Uplift parameter of the model. see note (1) in diagram) that increases as the pipe sinks into the seabed. Pu Normal seabed reaction force (1) Initial penetration (6) Further repenetration (2) Uplift 1 2 3 4 5 15 10 O 20 Non-dimensional Penetration. Then.e. Ultimate penetration resistance. as specified on in Soil Model Parameters data. and asymptotically approaches the ultimate penetration resistance Pu (upper dashed grey curve). The suction reduces as the uplift continues. or if uplift continues -ve reaction (ie suction) Figure: 25 (3) Further uplift is resisted by suction Ultimate suction resistance.. Soil Extra Buoyancy Force The seabed resistance formulae given above model the resistance P(z) due to the soil shear strength. Pu-suc Soil Model Characteristics The model starts in Initial Penetration mode and gives a resistance (blue curve. see note (2) in diagram) and asymptotically approaches the ultimate suction resistance Pu-suc (lower dashed grey curve). the uplift ends and repenetration starts. in addition to the resistance P(z). note (5) in diagram) and the suction rapidly falls and soon instead becomes +ve resistance. Further cycles of uplift and repenetration would give further episodes of Uplift and Repenetration modes and so give hysteresis loops of seabed resistance. Environment Theory Model Characteristics The following diagram illustrates the effect of the above equations as penetration changes. If.. In this case the uplift is enough that the resistance becomes negative – i.w Theory. then the model enters Repenetration mode (purple curve. however. In addition to this there is an extra buoyancy force due to the fact that the penetrator displaces soil that has a higher saturated density than the water. for a catenary line moving up and down on the seabed. suction (note (3) in diagram). If the uplift continues and the pipe lifts off the seabed then the model stays in Uplift mode and the model follows the green curve further (note (4) in diagram). when the pipe starts to lift up again the model enters Uplift mode and the resistance falls (green curve. vertically upwards. and drops to zero when the penetration drops to zero.ρsea)g where fb is a non-dimensional soil buoyancy factor. ζ (5) suction releases if repenetrates . As repenetration continues increases the resistance rises (note (6) in diagram) and again asymptotically approaches the ultimate penetration resistance. To model this the following extra buoyancy force is applied. 142 . Extra Soil Buoyancy Force = fbVdisp(ρsoil . (4) . 5 Morison's Equation OrcaFlex calculates hydrodynamic loads on lines. ρsea = sea water density at the seabed origin. Soil Model Parameters Several non-dimensional constants are used in the formulae given above for the seabed normal reaction force.ρsea)g that would apply if the soil was fully fluid. and one related to water particle velocity. A higher value causes suction to persist over greater uplift distances. Normalised Maximum Stiffness This is the factor Kmax that determines the reference penetration. should normally be greater than 1. 5. ζ and ζ0. See Ultimate Resistance Limits above. See Soil Extra Buoyancy Force above. but we recommend that these parameters are normally left at their default values. as specified in the sea density data. A higher value leads to greater penetration before the bounding curve is reached. and also how fast the penetration resistance asymptotically approaches its limiting value. Suction Resistance Ratio This is the factor fsuc that controls the ultimate suction resistance Pu-suc(z). The effects of the parameters are now described. Normalised Suction Decay Distance This is the factor λsuc that controls the suction decay limit term Pmin(z) in equation (2b) in Uplift mode. and hence the ultimate penetration and suction resistance limits Pu(z) and Pu-suc(z). but instead tends to heave locally around the penetrating object.w Theory. See Ultimate Resistance Limits above. Johnson and Schaaf. the inertia force. The buoyancy factor. D/Kmax. A lower value gives less suction.A. See Morison. fb. that is used to calculate the nondimensional penetration values.Vr|Vr| where Fw is the fluid force 143 . the drag force. 3D Buoys and 6D Buoys using an extended form of Morison's Equation. Penetration Resistance Parameters The parameters a and b control how the bearing factor Nc(z). P IP(z). Environment Theory Vdisp = displacement volume = volume of the part of the penetrating object that is below the seabed tangent plane. vary with penetration z.Cd. A higher value means the resistance more rapidly approaches the limit as penetration changes.ar) + ½. Their values can be edited on the Seabed Soil Model page of the Environment data form. the same principle is applied. This models the fact that when seabed soil is displaced it does not disperse thinly across the seabed plane. Soil Buoyancy Factor This is the factor fb that controls the modelling of the extra buoyancy effect that occurs when a penetrating object displaces soil.aw + Ca. O'Brien.ρ. ρsoil = saturated soil density. and so gives a stiffer seabed model. The extended form of Morison's equation used in OrcaFlex is: Fw = (Δ. This parameter also affects the repenetration limit term P max(z) in equation (3b) in Repenetration mode. a higher value gives more. by causing suction to decay after less uplift. that are used in the hyperbolic factors in the Penetration Resistance Formulae above. Repenetration Offset After Uplift This is the parameter λrep that controls the penetration at which the repenetration resistance limit Pmax(z) in equation (3b) in Repenetration mode merges with the bounding curve for initial penetration resistance. For moving objects. It therefore controls the maximum stiffness during initial penetration or on reversal of motion. These are parameters that control how the soil response is modelled by the non-linear soil model. A smaller value results in less penetration past z P=0 before the repenetration resistance after uplift merges with the bounding curve of initial penetration resistance. There are two force components.10. as specified in the Soil Properties data.Δ. to model the fact that the displaced soil tends to heave locally around the penetrating object. g = acceleration due to gravity for the units being used The factor fb is normally greater than 1. one related to water particle acceleration. A lower value gives less suction effect. The effect of this is that the extra buoyancy is greater than the standard theoretical buoyancy force V disp(ρsoil . Morison's equation was originally formulated for calculating the wave loads on fixed vertical cylinders. but the force equation is modified to take account of the movement of the body. Environment Theory Δ is the mass of fluid displaced by the body aw is the fluid acceleration relative to earth Ca is the added mass coefficient for the body ar is the fluid acceleration relative to the body ρ is the density of water Vr is the fluid velocity relative to the body Cd is the drag coefficient for the body A is the drag area The term in parentheses is the inertia force. 1991 and Faltinsen. a random wave or specified by a time history file. A simple way to understand it is to consider a body accelerating through a stationary fluid. This water would have mass Δ and be undergoing an acceleration a w.Δ) has the dimensions of mass and has become known as the added mass. It should not be viewed as a body of fluid trapped by and moving with the body.Δ) is a constant related to the shape of the body and its displacement a is the acceleration of the body. but the inertia force can cause confusion.) The added mass component is due to the distortion of the fluid flow by the presence of the body. Torsethaugen and Gaussian Swell. Waves are specified in terms of height and period.a) and Ca. To understand the Froude-Krylov component. Another way of looking at the problem is in terms of energy. The inertia force consists of two parts. The total energy required to accelerate a body in a stationary fluid is the sum of the kinetic energy of the body itself. undisturbed by the presence of the body. This is equivalent to saying that the Froude-Krylov force is the integral over the surface of the body of the pressure in the incident wave.Δ. Trapped water should be treated as part of the body: the mass of the trapped water should be included in the body mass. 144 . Ochi-Hubble. Random Waves OrcaFlex offers five standard frequency spectra: JONSWAP. and direction of propagation. and its volume should be included in the body volume.a respectively.w Theory. linear Airy wave (including seabed influence on wave length) or non-linear waves using Dean.aw. These energies correspond to the terms (m. The drag force is familiar to most engineers.a where F is the total force on the body m is the mass of the body (Ca. one proportional to fluid acceleration relative to earth (the Froude-Krylov component).10.6 Waves Wave Theory Each wave train can be a regular wave. and the kinetic energy of the flow field about the body. the integral of the fluid pressure over the wetted surface must exactly balance the weight of the water displaced by the body. Now remove the water and put the body back: the same force must now act on the body. the other term is the drag force. This is an unfortunate name which has caused much confusion over the years. ISSC (also known as Bretschneider or modified PiersonMoskowitz). 5. The force required to sustain the acceleration may be shown to be proportional to the body acceleration and can be written: F = (m + Ca. Trapped Water The term (Ca. It must therefore be experiencing a force Δ. Trapped water occurs when the body contains a closed flooded space. (Note the parallel with Archimedes' Principle: in still water. but this trapped water is a completely different matter. Some bodies are so shaped that this does occur. For a more complete description of Morison's equation and a detailed derivation of the added mass component see Barltrop and Adams. and one proportional to fluid acceleration relative to the body (the added mass component). 1990.Δ). Regular Waves OrcaFlex offers a choice of a long-crested. imagine the body being removed and replaced with an equivalent volume of water. regular. or where a space is sufficiently closely surrounded to prevent free flow in and out. Stokes' 5th or Cnoidal wave theories (see Non-linear Wave Theories). The facilities include: A profile graph plotting the wave elevation for a selected period and A table listing all the waves in a selected time interval whose height or steepness is large by comparison with the reference wave Hs.w Theory.> δfmax is then recursively subdivided into multiple bands. which for clarity is for only n=10 components (the default value of n is much larger). See the illustration below. near the tails of the spectrum where the spectral energy is low) representing a wide range of frequencies. We define fm. at least for the default values of rmin and rmax. OrcaFlex provides special facilities to assist in selecting an appropriate section of random sea. so the same user data will always give the same train of waves.= rminfm-.to be the frequency of the spectral peak with the lowest frequency. Wave components An irregular wave train is constructed by linear superposition of a number of linear wave components. and the components resulting from subdivision will no longer have the same energy as the non-subdivided components. The wave spectrum plotted below illustrates the effect of the equal energy approach. and any component that covers a wider frequency range is then subdivided into multiple components (which then have lower energy. and the effect of this can be seen in the wider component frequency ranges in the low and high frequency tails of the spectrum. is chosen so that there is equal spectral energy either side of it in the frequency band represented by that component. The phases associated with each wave component are pseudo-random: a random number generator is used to assign phases. The wave component frequency. Note: When the spectrum discretisation method is set to Legacy or 9. fi] and [fi. Likewise define f m+ to be the frequency of the spectral peak with the highest frequency. n. A wave component is then created for each resulting frequency band. rmaxfm+]. The nature of wave spectra means that the energy outside the range is negligible.and fm+ are defined differently. fi. so they are no longer have equal energy) until all the components satisfy the specified maximum frequency range. Different wave component phasing for the same spectrum can be obtained by shifting the simulation time origin relative to the wave time origin. 3. The wave component frequencies are chosen using an equal energy approach – see below. the spectral peak frequencies are calculated internally by the program as described in the Torsethaugen and Haver paper. For the OchiHubble spectrum. OrcaFlex creates the components using an equal area approach. For single peaked spectra this is identical to the behaviour described above. the values of fm. but the sequence is repeatable. In addition we have not applied the maximum component frequency range δfmax. These are available on the Waves Preview page of the Environment data form.and fm+ are set to the nominal value of fm. For the Ochi-Hubble spectrum the nominal fm is defined to be fm1. However this approach can result in some components (e. The overall frequency range considered is [rminfm-. We denote by rmin and rmax the minimum and maximum relative frequencies.3a. Here f 1. To solve this the user can specify a maximum component frequency range. 145 . For single peaked spectra f m. 4. 2. fi+] for which fi+ . fn+ = rmaxfm+ and fi+ = f(i+1)-. Any such subdivision will result in the number of components. fi+] (i = 1 to n). fi+]. until the frequency width of each band is less than the specified maximum δf max. Both fm. since a wide frequency range of spectral energy is then concentrated at a single frequency. The vertical lines represent the component frequency ranges. For the Torsethaugen spectrum the nominal f m is user input data. increasing. Such components can result in poor modelling of system responses. This overall frequency range is then broken into n component frequency bands [fi-. The wave components are created as follows: 1. and by δfmax the maximum component frequency range.g. In other words there is equal spectral energy in the ranges [fi-. or by specifying a different random number seed. Any frequency band [fi-. 5. For simplicity we have only used 10 components but you would typically use a lot more than this in order to give a much better discretisation of the spectrum. such that each band contains the same amount of spectral energy.= fm+ = fm.fi. Tz. For the Torsethaugen spectrum. Environment Theory The program synthesises a wave time history from a user-determined number of linear wave components. over a user-specified range of the frequency spectrum. and n is the userspecified number of components. the spectral peak frequencies are data items named fm1 and fm2. This method of allocating wave components is now described in more detail. a normalising constant.3 Frequency (Hz) Figure: Equal energy approach to choosing wave components The equal energy approach has two significant advantages over a discretisation using equal frequency spacing: 1. 2. This means that the repeat period of the resulting wave train is effectively infinite. θ is the wave direction and θp is the principal wave direction. if n d and nf are the user-specified number of wave directions and number of frequencies per direction.05 0. since that would introduce non-realistic correlations between the frequencies for different directions. To achieve the same level of discretisation with an equal frequency spacing approach would result in a great deal many more components being used. It only applies to Airy waves and to random waves (which are made up of a number of Airy waves). Directional spread spectrum The directional spreading spectrum used by OrcaFlex is: Sd(θ) = K(n)cosn(θ-θp) for -π/2 ≤ θ-θp ≤ π/2 where K(n) = π-½ Γ(n/2 + 1) / Γ(n/2 + 1/2).25 0. 146 . Note: OrcaFlex does not use the same set of frequencies for each of the directions.θ) is then given by S(f.1 0. respectively. Discretisation of the directional spectrum The direction range -π/2 ≤ θ-θp ≤ π/2 is discretised into the user-specified number of wave directions. Since simulation runtimes are increased when more components are used the equal energy approach gives an efficient use of wave components. and then randomly distributes those frequency components over the nd directions in a way that gives nf of them in each of the nd directions. The component frequencies produced by the equal energy approach are not related to each other in a multiplicative way. The total spectrum used by OrcaFlex S(f. using the equal energy strategy. Kinematic Stretching Kinematic stretching is the process of extending linear Airy wave theory to provide predictions of fluid velocity and acceleration (kinematics) at points above the mean water level. Environment Theory Spectral Density (m^2/Hz) 50 40 30 20 10 0 0 0.15 0.2 0. and not correctly represent the continuous spread spectrum. OrcaFlex discretises the directional spectrum using the same equal energy strategy as described above for the frequency spectrum. The equal energy approach results in a finer discretisation being used around the spectral peak. Instead.Sd(θ) where Sf is the frequency spectrum.w Theory.θ) = Sf(f). then OrcaFlex chooses nd x nf frequencies from the frequency spectrum. n is the spreading exponent. The various stretching methods deal with this problem by replacing E(z) with a more realistic term. ω. the peak frequency f m and the significant wave height Hs are data items. angular frequency. For more details see: Barltrop and Adams. page 277. but for z>0. E(z) is replaced by E(0).kx) (1) where a. Wheeler Stretching and Extrapolation Stretching (see below). In other words. Wave Spectra ISSC spectrum The ISSC spectrum (also known as Bretschneider or modified Pierson-Moskowitz) is defined as: S(f) = 5/16 Hs2 fm4 f -5 exp(-5/4 [f/fm] -4) where f is frequency. enabling you to represent sea states that include both a remotely generated swell and a local wind generated sea. JONSWAP spectrum The JONSWAP spectrum is defined as: S(f) = (αg2/16π4) f -5 exp(-5/4 [f/fm] -4) γb where g is the gravitational constant. σ1 and σ2 are data items. Consider. This has the effect of setting the kinematics above the mean water level to be equal to those at the mean water level. respectively. Note that all the stretching methods apply not only to the scaling factor E(z) in the horizontal velocity formula (1). This can give particle velocity predictions that are unrealistically large (the problem being worst for high frequency waves). E(z) is replaced by E(0) + z.1]2). The other two parameters. Tucker 1991. However for z>0 (i. page 108. Extrapolation Stretching This method extends E(z) to points above the mean water level by using linear extrapolation of the tangent to E(z) at the mean water level.w Theory. σ = σ1 for f ≤ fm. above the mean water level) E(z) is greater than 1 so it amplifies the velocity. and OrcaFlex offers a choice of three published methods: Vertical Stretching. where E' is the rate of change of E with z. b = exp(-½σ-2[f/fm . E(z) is left unchanged for z≤0. It is an exponential decay term that models the fact that the fluid velocity reduces as the point goes deeper. Wheeler Stretching This method stretches (or compresses) the water column linearly into a height equivalent to the mean water depth. For more details see Tucker 1991. σ = σ2 for f > fm and the other parameters γ.φ . This formula for z' essentially shifts z linearly to be in the range -d to 0. where d = mean water depth. The term E(z) is a scaling factor given by E(z) = cosh(k(d+z))/sinh(kd).d and ζ is the z-value at the instantaneous water surface. Ochi-Hubble spectrum See the Ochi-Hubble paper for details of the spectral formula. phase lag and wave number. Environment Theory Linear wave theory in principle only applies to very small waves. Vertical Stretching This is the simplest of the 3 methods. The theory therefore needs to be 'stretched' to cover such points.e. x is distance downstream from the wave origin and z is measured positive upwards from the mean water level.E'(0). the horizontal particle velocity u. page 107. Isherwood 1987. This is done by replacing E(z) by E(z') where z' = d(d+z)/(d+ζ) .z) at time t is: u = E(z) a ω cos(ωt . but also to the scaling factors in the corresponding Airy wave theory formulae for the vertical velocity and the horizontal and vertical acceleration. for example. 147 . so it does not predict kinematics for points above the mean water level since they are not in the fluid. In Airy wave theory the formula for u at position (x. but for z>0. for z≤0 equation (1) is left unchanged. φ and k are the wave amplitude. α. The Ochi-Hubble Spectrum allows two peaked spectra to be set up. λ2 for the higher frequency component. the resulting total spectrum typically has only one peak (from the remotely generated swell) plus a shoulder of energy from the local wind generated sea. Gaussian Swell spectrum The Gaussian Swell spectrum is based on the normal (or Gaussian) probability density function and is defined as: S(f) = (Hs/4)2σ-1(2π)-½ exp(-[f-fm]2/2σ2) where Hs. one for the swell component and one for the local wind generated component. however in practice. Dean's stream function theory and Fenton's cnoidal theory which are all available in OrcaFlex. periodic regular waves and random waves. The two component spectra are each specified by a set of three parameters – Hs1. A random wave in OrcaFlex is a superposition of a number of regular linear waves of differing heights and periods. For very small waves in deep water. The component spectrum with the lower frequency peak corresponds to the remotely generated swell and the one with the higher frequency peak corresponds to the local wind generated sea. Warning: The two-peaked Ochi-Hubble and Torsethaugen spectra make no allowance for the directionality of the swell and wind components of the sea state. Airy wave theory (also know as linear wave theory) is valid. This is why the Ochi-Hubble spectrum is often called a two-peaked spectrum. We shall give an outline of these theories here in the form of concise abbreviations of the relevant papers. Environment Theory Example of Ochi-Hubble Spectrum 6 S(r) [m^2] 5 4 3 2 1 0 0 1 2 3 4 Relative Frequency r The Ochi-Hubble wave spectrum is the sum of two separate component spectra – the example graph shows the two components and their sum. or you can simply specify the overall significant wave height Hs and tell OrcaFlex to automatically select the most probable 6 parameters for that value of Hs. where d is the water depth (at the seabed origin). We assume that the wave is long-crested and travels in the x direction and we shall work only in the (x. Torsethaugen spectrum The Torsethaugen spectrum is another two-peaked spectrum. λ1 for the lower frequency component and Hs2. OrcaFlex uses 'most probable' parameters based on formulae given in the Ochi-Hubble paper (table 2b). Thieke R J and Westberg R J. Goodwin P. fm1. In the latter case. Because of this it is more appropriate to model a two-peaked sea state using two separate OrcaFlex wave trains. fm2. These include Stokes' 5th order theory. These conventions are different from those used in OrcaFlex but we use them here in order to agree with the literature. hence the need for non-linear wave theories. 1987. See the Torsethaugen and Haver paper for details of the spectral formula. For an overview of all the theories considered here see Sobey R J. Many waves in practical engineering use do not fall into this category. However. more suited to North Sea application than OchiHubble. The seabed has z = 0 and the mean water level is given by z = d. In reality the separate components frequently come from different directions.w Theory. To fix notation we use the following conventions throughout. In OrcaFlex you can either specify all these 6 parameters explicitly. an OrcaFlex wave train has a single principal direction. Non-linear Wave Theories OrcaFlex models two types of waves. We shall not discuss random waves here. fm and σ are the input data. The horizontal and vertical particle velocities are denoted by u 148 .z) plane. A regular wave is a periodic wave with a single period. The wave is specified by wave height (H) and wave period (T) and the wavelength (L) will be derived. See Data for Ochi-Hubble Spectrum. The constant N is said to be the order of the stream function. This method is also known as Fourier approximation wave theory. We assume a moving frame of reference with respect to which the motion is steady and x = 0 under a crest. satisfies Bernoulli's equation ½ [ (∂ψ/∂x)2 + (∂ψ/∂z)2 ] + η = R.z) whose partial derivatives are the particle velocities of the fluid. convergence for very steep waves cannot be achieved. Dean's original paper Dean (1965) was intended to be used to fit stream functions to waves whose profile was already known. 3. Hence it can be used as a coarse check on the applicability of other theories. Implementing stream function theory requires numerical solution of complex non-linear equations. 2. In all circumstances the stream function method. A stream function is a vector field ψ(x. if it converges. then it is probably wrong! Stokes' 5th The engineering industry's standard reference on 5th order Stokes' wave theory is Skjelbreia and Hendrickson (1961). power series expansions are obtained and then truncated at an arbitrary point. wave height and wave period and we wish to find a wave theory which fits these data. This was quite complicated and Dean's idea was to apply the same idea to a stream function. That is if your preferred wave theory gives significantly different results from Dean's.z) = B0 z + ∑ Bj [sinh (jkz) / cosh (jk)] cos (jkx) where k is the wave number which is as yet undetermined.0) = 0. Dean Stream Function theory A typical approach to wave theory makes use of the idea of a velocity potential.η) = -Q and 4. applied to the same wave. This paper presents a 5th order Stokes' theory with expansion term ak where a is the amplitude of the fundamental harmonic and k = 2π / L is the wave number. If this is the case then it might be worth experimenting with different values. is constant at the free surface z = η(x).w Theory. Thus it is Fenton's theory which is implemented in OrcaFlex. Thus Dean's theory in its original form does not apply and we choose to follow the stream function theory of Rienecker and Fenton (1981). Fenton (1985) gives a 5th order Stokes' theory based around an expansion term kH/2 and demonstrates that it is more accurate than Skjelbreia and Hendrickson's theory. by their very nature. Chappelear devised a wave theory based on finding the best fit velocity potential to the defining wave equations. is zero at the seabed. By standard methods. say ψ(x. Environment Theory and v respectively. For the purpose of OrcaFlex the user provides information on the wave train in the form of water depth. Dean's stream function theory and Fenton's cnoidal theory for a brief overview of each of the nonlinear wave theories available in OrcaFlex and for guidance on how to decide on which wave theory to use in practice. The problem now is to find coefficients B j and k which satisfy equations (3) and (4). It is possible that. Dean's method should cope well in similar circumstances as it is finding a best fit to the governing equations. See Stokes' 5th. It is worth noting that the linear theory of Airy is a 1st order Stokes' theory. 149 . The problem is to find a stream function which: 1. will give sensible results.z) which satisfies ∂ψ/∂x = -v and ∂ψ/∂z = u. That is: ∂φ/∂x = u and ∂φ/∂z = v. In these equations all variables have been non-dimensionalised with respect to water depth d and gravity g. for example a wave recorded in a wave tank. where R is a constant. although we would recommend stream function theory here. Accuracy of method Because the method is a numerical best fit method it does not suffer from the truncation problems of the Stokes' 5th and cnoidal theories. In theory. that is ψ(x. This means that stream function wave theory is very robust. The length a has no physical meaning and by choosing ak as expansion parameter. In very shallow water Fenton believes that his high order cnoidal wave theory is best. which means that the flow is irrotational. For these methods. The number of these equations increases as N increases and there is a short pause in the program while these equations are solved. However. and the summation is from j = 1 to N. If the terms which are being ignored are not small then these methods will give inaccurate answers. for nearly breaking waves the solution method sometimes has problems converging. equations (1) and (2) are satisfied by a stream function of the form ψ(x. For most waves the default value will suffice. satisfies Laplace's equation ∂2ψ/∂x2 + ∂2ψ/∂z2 = 0. Stokes' 5th and the cnoidal theories may give inaccurate results if applied to the wrong waves. This is a vector field φ(x. In fact for Ursell number close to 40 both the Stokes' 5th theory and the cnoidal theory have inaccuracies and the stream function method is recommended. Our recommendations are: Ursell number Recommended wave theory << 40 Dean or Stokes' 5th ~ 40 Dean >> 40 Dean or Cnoidal In general then. Ranges of Applicability Regular wave trains are specified in OrcaFlex by water depth. Thus if the terms which are discarded are significant then this theory will give poor results. The boundary number 40 should not be considered a hard and fast rule. The stream function theory is applicable for any wave. Environment Theory Assuming that the user supplies wave train information comprising water depth. we would recommend the stream function wave theory in most cases. The function takes two parameters. Cnoidal theory This is a steady periodic water wave theory designed to be used for long waves in shallow water. This work has been superseded by Fenton (1990 and 1995). The solution is performed using the bisection method since the equation shows singular behaviour for m ≈ 1 and derivative methods fail. Which wave theory should one use for any given wave train? For an infinitesimal wave in deep water then Airy wave theory is accurate. OrcaFlex has no way of telling if a theory has been misapplied. This equation is known as the dispersion relationship. In his later works Fenton discovered that much better results could be obtained by expanding about a "shallowness" parameter δ. See Ranges of applicability for the waves for which Stokes' 5th theory is valid. The Stokes' 5th order theory is invalid in such water as the expansion term is large and the abandoned terms due to truncation are significant. In order to decide which wave theory to use one must calculate the Ursell number given by U = HL2 / d 3 See Non-linear Wave Theories for notation conventions used. As in the Stokes' theory this equation is the dispersion relationship. This technique is known as Iwagaki approximation and proves to be very accurate. The high-order cnoidal theory of Fenton (1979) has been regarded as the standard reference for many years but it gives unsatisfactory predictions of water particle velocities. Accuracy of method Inherent in the method is a truncation of all terms of order greater than 5. This is a very important point. cn is just cos and the Jacobian elliptic functions can be regarded as the standard trigonometric functions. If another theory is being used then it should be compared against the stream function theory to check its validity.w Theory. but essentially this is a deep water. In practice m is close to 1 and Fenton takes advantage of this to simplify the formulae. x as usual. hence the term cnoidal. We follow this approach. Fenton's original paper gave formulae for fluid velocities based on a Fourier series expansion about the term ε = H / d. steep wave theory. He simply sets m = 1 in all formulae except where m is the argument of an elliptic or Jacobian function. other than giving warnings for obvious abuses – it is up to the user to make sure they are using an applicable theory. By comparing with the stream function theory a reliable check can be made – and if two theories give the same answers then one should be filled with confidence! 150 . Once k is known. In order to do this a non-linear implicit equation in terms of k is solved using Newton's method. For U > 40 we have long waves and the cnoidal wave theory can be used. The initial step of the solution is to determine m and an implicit equation with m buried deep within must be solved. wave height and wave period. For finite waves a non-linear theory should be used. After m has been determined Fenton gives formulae to calculate surface elevation and other wave kinematics. and also m which determines how cusped the function is. In regions well away from Ursell number 40 then the relevant analytic theories (Stokes' 5th or cnoidal) perform very well. wave height and wave period then the wave number k must be computed before the theory can be applied. Fenton shows that the cnoidal theory should only be applied for long waves in shallow water and for such waves m is close to 1. A 5th order stream function representation is used but instead of terms involving cos the Jacobian elliptic function cn is used. The solitary wave which has infinite length corresponds to m = 1 and long waves in shallow water have values of m close to 1. In fact when m = 0. If U < 40 then the waves are said to be short and Stokes' 5th may be used. a number of coefficients are calculated and these are used for power series expansions in order to find the surface profile and wave kinematics. It has not been possible to guard against all such anomalies. Because we are dealing with non-linear waves it is not possible to analyse the wave assuming zero current and then add in the current afterwards. For example if the stream function or Stokes' 5th theories are misapplied then they may predict wave profiles with multiple crests.) We define the fluid motion for a point (x. then apparent and real accelerations are effectively equal and OrcaFlex computes apparent accelerations for Airy wave theory. To 151 . We assume that the water depth is that at the seabed origin for the purpose of deriving the wave information (wave number. There are various different ways of defining Euler angles and the conventions used by OrcaFlex are documented below. It is then up to the engineer to judge the validity of the results. To provide flexibility. Particle kinematics An important consideration for computing the wave kinematics is whether to use apparent or real quantities. Whilst these are valid solutions to the mathematical problem. Tucker (1991) gives an example of a Venturi tube with zero apparent acceleration throughout the tube but a non-zero pressure gradient! For the linear theory of Airy.14L. Seabed Slope In the case of a sloping seabed in OrcaFlex. due to Miche. they are not realistic. as we do for Airy waves. The accelerations are used by OrcaFlex in relation to Morison's Equation in order to compute pressure gradients which in turn result in forces being applied to objects.z) where z < 0 to be the fluid motion for the point (x. in particular the Stokes' 5th theory can predict wave profiles with points of inflection other than at crest and trough. primary and superimposed. This also is physically implausible. That is. stream function etc. is HB = 0. HB.11 VESSEL THEORY 5. In many cases only one of the two types is needed. Vessel Theory Breaking waves All the regular wave theories are suspect for breaking or near breaking waves. For the non-linear theories. Also it is sometimes predicted by each theory that the horizontal fluid velocities under a crest increase with depth. is commonly taken to be 0. OrcaFlex warns if such unrealistic solutions occur. In all cases positive rotation angle means rotating clockwise about the relevant axis direction. The formula is: V = VW .89kd) where k = 2π/L is the local wave number as calculated by Airy wave theory. An expression which covers all depths.CW ) + C. 5. For velocities there is no confusion as the two concepts coincide but there is an issue for accelerations.1 Vessel Rotations The orientation of a vessel is specified by 3 rotation angles that are called Euler angles.88k-1 tanh(0. To calculate the fluid velocity V at any given point in time we must take into account the fluid velocity V W containing uniform current CW together with the current C at the point in question. it is sometimes possible to obtain a solution for a particular wave train which is physically implausible. which is based on the assumption that the wave is very small.0).y. The convention chosen is as follows: The current profile is defined as usual and the current used to analyse the wave is taken to be the component of current in the wave direction at the mean water level. Handling of current Each of the theories implemented allows for a uniform Eulerian current but none is designed to deal with current profiles.CW + C.w Theory. we adopt the following convention for wave theories. If the wave factor is λ then V = λ (VW . In deep water the height of a breaking wave. A similar formula is used during the build up. real accelerations are used in all cases. Physically implausible solutions The non-linear wave theories implemented in OrcaFlex each have their own ranges and limitations as previously discussed.11. as specified by the current profile. where L is the wave length.y. OrcaFlex reports a warning if the wave height exceeds this breaking wave height. So we have to reach some compromise. do we compute velocities and accelerations relative to a fixed point in the fluid (Eulerian) or relative to an individual water particle (Lagrangian). However. a vessel in OrcaFlex can be given two types of motion. The total motion of the vessel is the combination of the two. Call this current component C W. For superimposed time history motion the rotations are applied about the vessel axes. and a phase.5° per metre in the same wave means that the vessel pitches from -1° to + 1°. Vessel Theory distinguish between the primary.11. and finally the roll is applied as a rotation about the new primary heading x axis direction. and then finally the rotation about the new x-axis. These rotations are applied starting from the vessel orientation resulting from the primary motion. The rotations start with the vessel axes Vx.5 (and earlier versions) applied the roll. the rotation about the z-axis is done first. Here is more detail of how the vessel rotations are applied.w Theory. However for vessels the heading angle rotation about z can be large. superimposed and total motion. The primary motion rotation angles are applied first. then pitch about new y direction. roll about x direction. and finally Primary Rotation 1 is applied about the resulting new Vx direction. The superimposed motion is then applied. pitch and yaw for superimposed motion in the 'forward' order. For this the angles are called Rotation 1. Rotation 2 and Rotation 3. followed by the rotation about the new y-axis. in which case the order of application of the rotations is more significant. See What's New in 8. a pitch RAO of 0. That is. Notes: The order of application of rotations is not significant when all the angles are small. the rotations are applied in the reverse order. i. Example: A surge RAO of 0. The total motion results report the combination of the primary and superimposed motion.5 in a wave of height 4m (and hence wave amplitude 2m) means that the vessel surges to and fro -1m to +1m from its static position. pitch and yaw. GZ. so it sets the heading of the vessel. Each displacement RAO consists of a pair of numbers that define the vessel response. Vy. QTF and harmonic motions are applied. The change in order of application of rotations changes results for cases with non-zero roll or pitch. Primary Rotation 3 is applied about the initial Vz-direction (= global GZ direction). Order of application of rotations For each of these sets of vessel rotation angles. 152 . is always applied about a vertical axis.2 RAOs and Phases Displacement RAOs Vessel motions in waves can be defined by displacement RAOs (Response Amplitude Operators) that are specified on the Displacements RAOs page of the vessel type data form. OrcaFlex 8. The initial orientation of the vessel specifies the initial values of the primary rotation angles. and it is in these directions that the RAO. which defines the timing of the vessel motion relative to the wave. then the pitch rotation is applied as a rotation about the new primary heading y axis direction. The two numbers are an amplitude. the reverse order of application is used. So.6 for details. It has the advantage that the z rotation. and these are called the initial Heel. That is. as follows: For primary motion the rotation angles are called Primary Rotation 1. to one particular wave direction and period.e. But this order had the disadvantage that when vessel yaw is large it was applied about an axis that could have already been rolled or pitched and so would no longer be horizontal. in reverse order. For displacement RAOs and harmonic motion they are called Roll. then yaw about final z direction. then Primary Rotation 2 is applied about the resulting new Vy direction. Pitch and Yaw. Note: The first of these 3 primary rotations is about the vertical. The superimposed motion rotations are called roll. different names are used for the 3 rotation angles. Trim and Heading. 5. Vz aligned with the global axes directions GX. which relates the amplitude of the vessel motion to the amplitude of the wave. first the yaw rotation is applied as a rotation about the primary heading z direction (= vertically upwards direction = global GZ direction). The vessel axes directions after this first rotation are called the Primary Heading Axes. Primary Rotation 2 and Primary Rotation 3. For superimposed displacement RAOs and harmonic motion the rotations are applied about the primary heading directions (see above) and the reverse order is used. for one particular degree of freedom. which is most likely to be large. GY. Once again. The reverse order of application of rotations described above is the most commonly used convention for vessel motions. pitch or yaw direction). which direction is positive. It is important to obtain accurate values for the RAO amplitude and phase if the dynamics of the system are to be correctly modelled. sway. RAOs can be obtained either from model tests or from specialist computer programs. the meaning of the phase remains unchanged. in particular. That is whether surge is positive forward or aft. 153 . ω are wave amplitude (in length units) and frequency (in radians/second) t is time (in seconds) R. In this case. The coordinate system used to define vessel motions and. whether heave is positive up or down and whether pitch is positive bow up or bow down. rather than to directly specify its motion.w Theory. sway. can also be used to represent the load (force and moment) on a vessel due to waves. in degrees for roll. and the reporting convention used (e. sway. forward speed and wave period (or frequency). Again. heave. so the RAO data consists of 6 amplitude and phase pairs for each wave period and direction. The only safe course is to obtain a complete description of the system used for the data in each case. Although OrcaFlex allows the RAO input data to use a wide range of systems. pitch. the amplitude represents the magnitude of the force (in the surge. The reference time for phase angles.g. The Orcina convention is to use the amplitude of response (in length units for surge. There are many different conventions for defining RAOs. In OrcaFlex 0° means waves approaching the vessel from astern and 90° means waves coming from the starboard side. sway or heave direction) or moment (in the roll. in degrees for roll. and for a given vessel type they vary with draught. and to use the phase lag from the time the wave crest passes the RAO origin until the maximum positive excursion is reached (in other words.a.cos (ωt . all OrcaFlex results use a right-handed system in which the positive movements are as follows: Surge positive Forward Sway positive to Port Heave positive Up Roll positive Starboard Down Pitch positive Bow Down Yaw positive Bow to Port Wave Load RAOs RAOs.φ) where x is the vessel displacement (in length units for surge. pitch. In addition to the actual RAO data you therefore also need to know: The coordinates of the RAO origin and of the phase origin. Vessel Theory The vessel has 6 degrees of freedom: 3 translations (surge. yaw). pitch. There have been attempts at standardisation but these have not been successful so there remain differences between the main computer programs and model basins: some establishments even use different conventions for reporting model and computed data. However. The system used to define wave direction. the phase origin being at the RAO origin). whether phases are reported as lags or leads). yaw) per unit wave amplitude. OrcaFlex can accept RAO data using a wide range of different conventions so you can input your RAO data in its original form and simply tell OrcaFlex what conventions apply to those data. Mathematically. or in degrees (radians) per degree (radian) of wave slope or wave steepness. heave. The RAO amplitude and phase vary for different types of vessel. heave) and 3 rotations (roll. φ are the RAO amplitude and phase. yaw) a. this is given by: x = R. wave direction. but if a different convention applies to your data then you must allow for this when entering the data. The data may be presented in tabular or graphical form: tables of numbers are better for our purposes since they can be imported directly into OrcaFlex (see Importing Hydrodynamic Data). OrcaFlex allows a range of options. Whether the rotational RAO data are in degrees (or radians) of rotation per metre (or foot) of wave amplitude. as described above. OrcaFlex uses these forces and moments. and they will have dimensions of moment per unit length. a pitch moment RAO of 1E6 kN. the vessel inertia suppresses response. Vessel Theory Example: A surge force RAO of 300 kN/m in a wave of height 6m (and hence wave amplitude 3m) means that a vessel experiences a surge force varying harmonically between -900kN and +900kN over each wave cycle. carries over to wave load RAOs with just one minor difference: rotational wave load RAOs must be expressed per unit of wave amplitude. In very long waves (typically wave periods over 20 seconds for ships or 30 seconds for semisubmersibles) the vessel will move like a raft on the wave surface. even from the most respected sources. Expected RAOs for a vessel in very long waves From ahead (180°) From astern (0°) From port (270°) From starboard (90°) Amp. The most obvious and useful ones are responses at very short and very long wave periods.m.3 RAO Quality Checks RAOs (particularly the phases) are difficult.m to +3E6 kN. The tables below give the expected displacement RAO amplitudes and phase lags for a free-floating vessel in very long waves.11. RAOs and phases. Phase Lag Amp. Wave load RAOs do not completely define the vessel motion as do displacement RAOs: they merely define the force and moment which a wave exerts on the vessel. together with any other loads on the vessel and data on the vessel's mass and inertia. Phase Lag Surge 1 -90° 1 +90° 0 ~ 0 ~ Sway 0 ~ 0 ~ 1 -90° 1 +90° Heave 1 0° 1 0° 1 0° 1 0° Roll 0 ~ 0 ~ 1 -90° 1 +90° Pitch 1 +90° 1 -90° 0 ~ 0 ~ Yaw 0 ~ 0 ~ 0 ~ 0 ~ Towards direction β Amplitude Phase Lag Surge | cos(β) | +90° if cos(β)>0 -90° if cos(β)<0 Sway | sin(β) | +90° if sin(β)>0 -90° if sin(β)<0 Heave 1 0 for all β Roll | sin(β) | +90° if sin(β)>0 -90° if sin(β)<0 Pitch | cos(β) | -90° if cos(β)>0 +90 if cos(β)<0 Yaw | ½ sin(2β) | 180° if sin(2β)>0 0° if sin(2β)<0 154 . for displacement RAOs. 5. there are a few natural points of reference where we know what must be going on. Phase Lag Amp. since the same difficulty applies to the people who derived the data in the first place. to determine the vessel motion from its equation of motion. abstract concepts which makes them difficult to check. The description of RAO conventions above.m/m in the same wave means that the vessel experiences a moment about the y axis varying from -3E6 kN. Displacement RAOs In very short period waves. Phase Lag Amp. so for all degrees of freedom the expected displacement RAO amplitude is zero (and phase is then irrelevant). It is extremely important to check them. are notoriously error-prone! Fortunately.w Theory. so that +90° means that the maximum positive motion occurs 90° after the wave crest passes the vessel. First. The best view direction is horizontal. but they can be significant in some cases. and run a short simulation (say 10 seconds build up plus 2 wave periods). positive roll is starboard down. Generally speaking. Broadly speaking. The second order terms are non-linear effects that are generally much smaller. With the waves coming from the right on screen. This is an excellent check for phases. positive sway is to port. these loads excite the vessel's first order motion. If the wave is very long compared to the ship. When the run is finished (a few seconds only for such a trivial case) replay the last wave period and watch to see whether the motion of the ship is realistic. the ship should be at maximum surge forwards into the wave and maximum pitch angle with the bow up. and vice versa in the trough. It is not quite so good for amplitudes. Set up a simple OrcaFlex model with the vessel only – nothing else – set the vessel's primary motion to None. positive pitch is bow down and positive yaw is bow to port. In these tables we use the conventions of positive surge is forward.g. The linear first order terms are the largest. secondary motion to RAOs + Harmonic. with smaller time steps. superimposed motion to None. Second. the total of all of these terms is called the wave drift load. then the ship should move like a small particle in the water surface. then think again! Wave Load RAOs Since we can relate wave load RAOs to displacement RAOs. say 0. which can be modelled in OrcaFlex using either displacement RAOs or load RAOs. Vessel Theory Warning: The expected yaw RAOs given in the above table only apply to slender vessels whose displacement is distributed along the vessel x-axis. 5. then in the wave crest the ship should be at maximum heave up and moving to the left. leads have been read as lags) then the motion is obviously wrong and you should go back and re-examine the data. You can check RAOs in two ways. The phases given are lags relative to the wave crest. Surge amplitude should also be equal to wave amplitude in deep water. If the phase convention has been misunderstood (e. They can be applied to a vessel and are calculated based on the dimensional Quadratic Transfer Function (QTF) data specified in the user's Wave Drift QTF and Sum Frequency QTF data. second order and even higher order terms. Yaw phasing for a ship in seas off the bow should be such that the ship yaws towards the broadside on position as the wave crest passes: this is easiest to see in a near-plan view.1 seconds. Note: You may need to run a longer simulation. Notes: In these tables. Similarly. roll and pitch phasing should be such that the components of rotation about an axis normal to the wave direction reinforce each other. The check can be extended to other wave directions. you can run quick simulations with only the vessel in the model and then check that the motions you see are sensible. For a detailed description of the theory see Faltinsen's book. The first order load is the sum of a contribution from each individual wave component in the sea state. If not. There are two types of second order contributions: Difference frequency terms from each wave component pair.4 Wave Drift and Sum Frequency Loads The wave drift load and sum frequency load are second order wave loads that act on objects subject to waves. At the point of maximum wave slope as the crest approaches. Heave amplitude should be equal to wave amplitude and pitch motion should keep the deck of the ship parallel to the water surface. but it is nevertheless worth pursuing. to allow the model to 'settle down'. if it looks right in long waves. The contribution from a given pair of wave components has frequency equal to the difference 155 . positive heave is up. The simple model-building exercise described above also works well for wave load RAOS: just set primary motion to Calculated (6 DOF). we can similarly determine the long-wave limit for wave load RAOs. which are usually the most troublesome to get right. normal to the direction of travel of the waves. it probably is right. but will be greater in shallow water in which the wave particle orbits are elliptical. for calculated vessel motion than for displacement RAOs.11. the translational amplitudes are non-dimensionalised against wave amplitude and the rotational amplitudes are non-dimensionalised against maximum wave slope. The second order load is quadratic with wave amplitude and consists of contributions from each pair of wave components in the sea state. with the phasing of surge and sway such that the components in the wave direction reinforce each other. Use a large wave height (20m) and long time step. see Checking RAOs. We neglect terms higher than second order. The wave loads on a vessel can be expressed as a sum of first order. When the amplitude is zero the phase value is irrelevant. Consider a ship in waves coming from ahead. OrcaFlex does this for the RAO graphs to facilitate checking wave load RAOs. or confirm your interpretation with the data source. we may expect the motion to be predominantly in the wave direction. this is indicated in the tables by '~' . OrcaFlex provides RAO graphs that help spot errors.w Theory. Here we give a summary and the details of the formulae used in OrcaFlex. which gives rise to a mean static offset of the vessel. β2.} denotes taking the real part of a complex number.[(ωi+ωj)t . Qd(βi. Let the properties of the i'th wave component be: βi = direction. τi. roll.. All the other second order load contributions are time-varying loads. But whereas RAOs are applied to each individual wave component to give that component's contribution to the first-order wave load.. heave. relative to the simulation time origin. and within each of these data sets there are separate columns for each of the 6 degrees of freedom (surge. pitch. τ1. which can be significantly higher than the typical wave frequencies. QTFs are applied to each pair of wave components to give that pair's contribution to the second-order wave load. yaw). the user data specify the QTF amplitude and phase. at the low frequency position of the vessel's QTF origin.(φi+φj)] } where Re{. These second order loads can be included in.n Σ j=1. Then the QTF for that given degree of freedom is a complex-valued function of the directions β1 and β2 (relative to the vessel) and periods τ1 and τ2 of the wave components in the pair. Second Order Load Theory Second order loads are calculated by applying the QTF data to all pairs of the wave components in the sea state.exp( i. sway. QTFs specified as Full QTFs QTF values for user-specified directions and periods For sum frequency QTFs. of the regular wave components present in all the wave trains specified. If the wave drift load is included then the mean wave drift load is included in both the static and dynamic analyses. Consider a single degree of freedom. which can excite slow drift motion of the vessel. τi. β2. and for wave drift QTFs when the QTF Specification Method is Full QTFs.aj. these are generally less important to model. τj) .n Re{ Qs(βi. There are separate sets of QTF data. These QTFs are derived from the user data. The contribution from a given pair of wave components has frequency equal to the sum of the frequencies of the two wave components. give constant (zero frequency) contributions.n Re{ Qd(βi. in complex-valued form Qs(β1. τ2) = wave drift QTF.. ai. τi. the sum of all these contributions gives the mean wave drift load..n Σ j=1. given by: Wave drift load = Σ i=1. τ2) = sum frequency QTF. is therefore aicos(ωit . βj. in complex-valued form Then the wave drift and sum frequency second order wave loads are sums of load contributions from all paired combinations of wave components in the sea state. Wave component pairs of equal frequencies. one for the difference frequency load (wave drift) and one for the sum frequency load. such as TLPs. n. Wave component pairs that are near each other in frequency give low frequency load contributions. Let the wave drift and sum frequency QTFs be distinguished by subscripts 'd' (for 'drift' or 'difference') and 's' for 'sum': Qd(β1. βj. the derivation depends on how the QTF data are specified and is described below. which is a superposition of a number.w Theory. Vessel Theory between the frequencies of the wave components in the pair. or excluded from. τi. such as each wave component paired with itself. relative to the low frequency heading of the vessel ai = amplitude φi = phase lag. the total of which is called the sum frequency load. The QTFs are similar to Wave Load RAOs – they specify scaling and phasing that are applied to wave components to give the contributions to the wave load. where they can excite high frequency natural modes of the system. βj. the analysis by specifying that 'Wave Drift Load (2nd order)' and 'Sum frequency load (2nd order)' are in the Included Effects on the vessel data form Calculation page. Sum frequency terms from each component pair.[(ωi-ωj)t . so they are included (if specified) only in the dynamic analysis.exp( i. The complex-valued wave drift and sum frequency QTFs are then given by: 156 . τj) . τj) and Qs(βi.(φi-φj)] } Sum frequency load = Σ i=1.φi). τj) are the wave drift and sum frequency QTFs for interaction of wave components i and j. at the low frequency position of the vessel's QTF origin τi = period ωi = 2π/τi = angular frequency The wave component elevation above mean sea level at simulation time t. τ1. βj. Wave component pairs that differ more in frequency give higher frequency contributions.aj. ai. called 'ringing' modes. These can be important to model for some systems. these determine the slowly varying part of the wave drift load. | denotes absolute value (|x| = x if x≥0. exp[ -i. β2. τ1. so the full QTF method is preferable in such cases.τ2) Qd(β1. the calculations detailed above are very computationally intensive. but sometimes full QTF data are not available for all pairs of directions (β1. Vessel Theory Qd(β1. 157 . τ2) = sum frequency phase lag. The justification for the various forms of Newman approximation has two parts: First. τ2) where β1≠β2 or τ1≠τ2. When the Newman approximation method is used. so the user specifies these values directly as a signed real value. For the wave drift load. τ2) . ad and as. both of these issues can be addressed by using the Newman approximation (Newman 1974). if sgn(Qdiag(β1. The QTF amplitudes here. β2. τ. on theoretical grounds. the near-diagonal QTFs should be continuous in both τ 1 and τ2.φd(β1.τ2)|. τ2) . are then approximated from the specified diagonal QTFs that are on the same 'row' and 'column'. τ1. for each of a number of wave directions and periods. τ1. in complex-valued form Qs(β1. This approximation only requires QTF data for equal pairs of directions (β 1 = β2 = β) and equal periods (τ1 = τ2 = τ). which uses the geometric mean instead of the arithmetic mean: Qd(β1. τ2) = as(β1. as specified in the data φs(β1. Second. τ2). β2. not to n2. β2. τ2) = sum frequency amplitude. For the wave drift load OrcaFlex therefore provides a choice of QTF Specification Method: Newman's approximation or Full QTFs. β2. and the phase conventions specified for the Vessel Type do not apply. β2. 0 if x=0). β. -1 if x<0. For details see Interpolation and extrapolation of QTF data. Wave drift QTFs specified by Newman's approximation The above theory uses the full QTF matrix.w Theory. but OrcaFlex uses the following variant formulation developed later by Standing. β2. which are the diagonal entries in the full QTF. The time taken to calculate the second order wave loads using the full QTF theory is therefore proportional to n 2. τ1. Brendling and Wilson. τ2) ] = wave drift QTF. so the full QTF must be specified and the full double summation calculation performed. then the further-from-diagonal QTF values are less important. τ1.τ1. a -ve value corresponds to an exactly out-of-phase contribution. Warnings: Shallow Water: The Newman approximation can be poor in shallow water. A +ve data value gives an in-phase QTF load contribution. They should therefore be well-approximated by the mean of the diagonal values on the same row and column. The approximation method also enables the double summation to be simplified to calculating the square of a single summation.τ1. since they give difference frequency load contributions with higher frequency that are not normally as significant. Even if all the full QTF data are available. which are the 'diagonal' values of the full wave drift QTF function (the mean wave drift load data).τ2) = 0.τ1).τ) = Qd(β. β2.β2. in radians. The offdiagonal wave drift QTF values.β2. providing there is not a significant spreads of wave directions. τ2) = wave drift amplitude. and sgn(x) is the sign function (sgn(x) = +1 if x>0. The phase lag values φd and φs are derived from the user's data allowing for the phase conventions specified on the Vessel Type Conventions page. since they involve double summations over all wave components in the sea state. τ1. which are the 'diagonal' entries in the full QTF matrix.φs(β1. in radians. Newman approximation for off-diagonal QTFs Newman QTF data only specifies the mean wave drift QTFs. τ) must be real. √|Qdiag(β1. relative to the sum frequency crest.τ2) = sgn(Qdiag(β1. in complex-valued form where ad(β1. τ1. β2) and periods (τ1.τ1)) = sgn(Qdiag(β2. τ2) = ad(β1. Qd(β1. τ1. -x if x<0). No separate phase values are specified. the square of the number of wave components in the sea state.τ1)) ≠ sgn(Qdiag(β2. The Newman method then approximates the 'off-diagonal' QTF values for component pairs with different directions or different periods by using an average of the 'diagonal' QTF values for those directions and periods. if sgn(Qdiag(β1. so it also reduces the calculation time to being only proportional to n. τ1. β2. exp[ -i.τ2)) where |. are as specified in the user QTF data. β2. Newman's original approximation method used the arithmetic mean of the two diagonal QTFs. τ2) ] = sum frequency QTF. as specified in the data φd(β1. relative to the difference frequency crest as(β1.τ1)) . These diagonal QTF values Q diag(β. τ1. on theoretical grounds. β2. τ1. the user data specifies only the mean wave drift QTFs.Qdiag(β2. τ2) = wave drift phase lag. QTF values for other directions and periods OrcaFlex uses linear interpolation and extrapolation to derive the diagonal QTF values for directions β and periods τ not specified in the user's data. For the sum frequency wave load there is no equivalent to the Newman approximation. where n is the number of wave components in the sea state. for τ > largest finite period specified in the data. Default Limiting Values The default limiting value at τ=Infinity is Q=0. the interpolation is only needed for a QTF function Q(βmean. Because of this. Q. τ1 and τ2. but the computational load of using the full QTF method is proportional to n2. τ1. and then using linear interpolation between these values. This interpolation is done using a 4-dimensional linear interpolation in the space whose coordinates are β1. This interpolation is done by treating the complex-valued QTF Q as a linear function of the directions and periods. For bi-directional full QTFs (wave drift or sum frequency). τ1.τ1.β2. The default limiting value at τ=0 is taken to be equal to the Q value for the lowest period specified in the data. rather than linear with direction and period. Qd(β1. This default long period QTF limit is theoretically correct for a freely floating body. since the QTF is only needed for wave component pairs with equal directions. OrcaFlex now obtains the QTF value. However this performance penalty only applies to one particular calculation. since wave pairs with very different directions use far-from-diagonal QTF values but still give low frequency drift load contributions if their periods are close to each other. simulation might be significantly slower if the full QTF method is used when a large number of wave components are used to model the sea state. τ2 that are not specified in the user's data.τ1. with small non-zero values.τ2) that is a function of 4 variables. which is a function of two variables only. In practice this means that the only reliable way to determine how practical it is to use full QTFs is to run both with Newman's approximation and with full QTFs to see how the run times are affected for your model. for any specified direction or direction pair. the first being according to period τ (or frequency ω=2π/τ if τ is larger than the longest period specified in the data). τ2) and Qs(β1. β2. since the body behaves like a cork and does not disturb the propagating wave. so the second order wave load tends to zero for long periods (low frequencies). So the full QTF method is also preferable in cases with a spread of wave directions. interpolation is only needed for the diagonal QTF. β2. Interpolation and Extrapolation of QTF data OrcaFlex uses complex-valued linear interpolation to derive the QTF values. and in most simulations the run time is usually determined much more by the other objects in the model (for example calculations for lines). by finding the specified directions and periods either side of the wave component directions and periods. the user data do not specify the limiting QTF value for period τ=0 or for period τ=Infinity. then a default limiting value of Q is assumed at that limit. Vessel Theory Spread Waves: The second argument of the above justification breaks down if the vessel is subject to a significant spread of different wave directions.τ2) that is a function of only 3 variables. Performance of Full QTFs versus Newman's approximation As explained above. So users can easily run trial simulations with full QTFs by simply entering a small amount of dummy full QTF data.βmean. 158 . then the interpolation towards that limit is done according to frequency instead of according to period. to use for directions β1.β2 or periods τ1. In this case the interpolation is done using two separate 1-dimensional interpolations. β2. the interpolation is needed for a QTF Q(β1. The effect of this is that if the user does not specify the QTF limit for τ=Infinity then for periods greater than the longest period specified in the data the user data will be linearly extrapolated (on frequency) towards zero QTF at infinite period (zero frequency). For wave drift QTFs specified using the Newman approximation. So in this case the interpolation is done using a 3-dimensional linear interpolation space whose coordinates are βmean. Qdiag(β. the complex-valued QTF Q is treated as being a linear function of direction and frequency. except if one of the periods either side is Infinity. The effect of this is that if the user does not specify the QTF limit for τ=0 then the QTF given for the shortest period specified in the data will be used for all periods less than that shortest specified period. or what the data values are (provided that they are not zero) – the performance depends much more on the total number of wave components in the model. for the interaction of wave components i and j. In other words. and then the second according to direction β. to see what effect this has on simulation run time. the computational load with the Newman approximation method is proportional to n.w Theory. before deciding whether to obtain and use correct full QTF data. τ2).τ). βmean. τ1 and τ2. For details see Default Limiting Values below. For uni-directional full QTFs (wave drift or sum frequency). Fortunately the performance when using full QTFs is not particularly sensitive to the amount of QTF data. This interpolation is done as follows: If. but extended according to the results of Malenica et al to be applicable to all water depths. roll.τ. and there is not yet a widely accepted method of modelling yaw wave drift damping. roll or pitch. and of course for all degrees of freedom if wave drift damping is not included. OrcaFlex also only applies wave drift damping in the surge and sway directions. 159 .τ. Qde(β.τe) where Ae = 1 + (ω ∂α/∂ω . at the wave drift QTF origin UL. Qd(βe.(4 ω / g) UL = Aranha scaling factor βe = β + (2 ω / g) UT = encounter heading ωe = ω . The wave drift damping is calculated using an encounter effects approach developed by Molin from Aranha's original analysis in deep water.(ω2 / g) UL = encounter frequency When wave drift damping is included. Wave Drift Damping Theory OrcaFlex will calculate the wave drift damping effect on the wave drift load if both Wave Drift Load and Wave Drift Damping are in the included effects.τ). respectively. so the wave drift damping includes both the current effect on wave drift load and the damping effect on vessel low frequency motion. The unmodified QTF values are always used for heave. where the extra subscript 'e' has been added to denote that they allow for the encounter effects. for surge and sway.τ). The effect of wave drift damping is implemented by using modified wave drift QTF values.βe.τ) = Ae . The velocity used in this calculation is the vessel low frequency velocity relative to the current. The limiting QTFs for zero and Infinity periods should therefore be specified in the data if the default limits are not suitable. Note: These encounter effects are only applied to the wave drift load.β. OrcaFlex uses these modified QTF values. since there is not normally significant slow drift motion in heave. UT = components of U in the wave component direction and transverse to that direction.2kh/tanh(2kh)] / [Cg sinh(2kh)] In the case of deep water. Wave Drift Damping with Newman Approximation Method Molin uses the same form of Newman's approximation as OrcaFlex. Q de(β.τ. In addition.w Warning: Theory. Vessel Theory QTF extrapolation could introduce significant errors if a significant amount of wave energy is outside the range of wave periods specified in the QTF data.2)UL/Cg = Aranha scaling factor βe = β + UT/Cg = encounter heading τe = 2π/ωe = encounter period ωe = ω(1 . not to the sum frequency load. pitch and yaw.UL/Cp) = encounter frequency Cp = ω/k = wave phase velocity Cg = ∂ω/∂k = wave group velocity k = wave number α = Cg/Cp U = vessel low-frequency velocity .β. The modified diagonal QTF values are given by: Qde(β. It could be poor for a fixed or moored vessel (especially if firmly moored). the default zero QTF value for long period waves is only theoretically valid for a free-floating vessel.current velocity.τe. For water of depth h we have: ω = √[g k tanh(kh)] g = acceleration due to gravity Cp = √[g tanh(kh)/k] α = ½[1 + 2kh/sinh(2kh)] ∂α/∂ω = h [1 . the above equations reduce to: ω = √(g k) Cp = √(g/k) α=½ ∂α/∂ω = 0 which gives: Ae = 1 .β. the wave drift load contribution can be completely cancelled out. In OrcaFlex this is done by using the geometric mean of the mean drift Aranha factors for the two components. In other words. the Aranha scaling factor [1 .w Theory. before applying Newman's approximation. Velocity Potential Disturbance Consider a single Airy wave component. 5. Disturbance effects can therefore be represented by data specifying how the velocity potential and its gradient are affected by the disturbance. p. However. then the velocity potential function for that component would be that of the undisturbed wave component.t).y. for i = 1 and 2 ωie = ωi (1 . At this point the assumptions have broken down and the theory is no longer valid.UL/Cp.β2. for both Newman QTFs and full QTFs.β2e. for i = 1 and 2 βie = β + UT/Cg. In particular.i) = encounter frequency for component i. motion and pressure distributions due to a given wave component are all based on a complex-valued potential function. The Z-axis is vertically upwards. for a sufficiently fast-moving vessel and slow-moving wave component. This is only likely to arise for short-wave components. in the literature the Aranha factor is only defined for the mean drift QTFs. g/ω. but not reversed. In this approach the fluid elevation. ∇P(p. as follows: Qde(β1.5 Sea State Disturbance Sea state disturbance modelling is based on the potential theory of inviscid fluids.τ1e. exp[ i(ωt . i . And for an even higher vessel speed the encounter frequency. where the two components in the pair have the same frequencies. for i = 1 and 2 τie = 2π/ωie = encounter period for component i.cosh(k(Z+h)) / [ ω. 160 . if it is not then these formulae can result in unreasonable encounter effects.(4 ω / g) UL ] will be negative if UL exceeds a quarter of the wave crest speed. by using the QTF values for the encounter directions and encounter periods of the two wave components in the pair and then scaling by an Aranha factor. Wave Drift Damping with Full QTFs Method With full QTFs OrcaFlex uses the same approach as with the Newman approximation method described above.A. so -Z is the depth of the point below the mean sea surface level. P(p. ω e. A = the undisturbed wave elevation amplitude. not just the constant mean value. which is a function of position.11. OrcaFlex is able to incorporate the time-varying effect of wave drift damping. velocity and acceleration) can be derived from the velocity potential function and its gradient. t.cosh(kh) ] = amplitude of the undisturbed velocity potential at p. OrcaFlex limits the Aranha factor to be non-negative.φu(p)) ] (2) where p = (x. by the wave drift damping. for i = 1 and 2 Warning: Limitation of Wave Drift Damping Effect The theory of wave drift damping assumes that the vessel velocity is small compared to the wave speed.t) = au(p) . since they travel more slowly. To avoid this problem. which is clearly not meaningful.τ1. so for full QTFs this needs to be extended to wave component pairs with different frequencies. in the above formula for Q de in deep water.t) } (1) All the desired properties of the wave component (surface elevation. au(p) = g. and time. which is the approach used in vessel response diffraction programs. could become negative.τ2) = Ae Qd(β1e.t) = Re{ ∇P(p. given by: Pu(p. and whose axes are parallel to the low frequency vessel primary heading axes. This effectively says that the wave drift damping effect for a given wave component can be no greater than (and opposite to) the wave drift load itself for that component.i = encounter direction for component i. Vessel Theory By modifying the diagonal values of the QTFs in this way.Z) = position coordinates. relative to a horizontal frame of reference whose origin is at the mean sea surface level at the low frequency horizontal position of the vessel origin. The velocity field of the wave component is given by the real part of the gradient of this complex velocity potential: v(p.τ2e) where Ae = √(A1eA2e) = geometric mean of the mean drift Aranha scaling factors for the two wave components Aie = 1 + (ωi ∂αi/∂ωi .t).i = mean drift Aranha factor for component i.t). Pu(p. OrcaFlex will issue a warning if this happens for a significant proportion of the wave energy in the sea state.2)UL/Cg. If there was no vessel present. All the desired properties of the disturbed wave component can then be derived from this disturbed velocity potential and its gradient. OrcaFlex can calculate D(p) from these data. Ṗu([x.t) = ad(p) . and the resulting disturbed velocity potential function is Pd(p.t) with respect to t. t) } (8) where Ṗ(p. Substituting equation (5).6 Stiffness. and its gradient. t) ] } (9) This shows that the velocity potential disturbance RAO at any position in the plane of the mean sea surface. of this complex-valued disturbance RAO and its gradient. given by: Pd(p.y. Added Mass and Damping The stiffness load. OrcaFlex can calculate the disturbed velocity potential of each wave component from D(p).t).t) = Re{ D([x. ∇Pd(p.y. arg[D(p)] and |∇D(p)|. ω = wave component angular frequency = 2π / wave component period.y. The complex-valued disturbance RAO.φu(p)) ] (4) Note that this disturbance RAO is independent of time. Note: The gradient data specify the amplitude and phase of ∇ D(p). D([x. D(p). exp[ -i. the contributions from a particular wave component are given by: Disturbed Velocity(p.t).(φd(p) . Pd(p. φu(p) = phase lag (in radians) of the undisturbed velocity potential at position p. Vessel Theory g = acceleration due to gravity. not the gradients ∇ (|D(p)|) and ∇ (arg[D(p)]) of the amplitude and phase of D(p). determined by Airy wave theory) by D(p) for that component: Pd(p. exp[ i(ωt . t) (6) Disturbed Wave Field The user disturbance RAO data (after allowing for whether the vessel type phase convention is leads or lags) specify the amplitudes and phases. The properties of the whole wave field then follow from summing over all wave components in the sea state.t) = D(p) . given by: D(p) = Pd(p. [ (-1/g) . and hence use the above equations to calculate the disturbed velocity potential. since the time variation exp[i(ωt)] has cancelled out in this ratio.11.0]) . and noting that the complex factor D(p) in that equation is time-invariant. ∇Pu(p.t) + ∇D(p) . h = water depth. are calculated using the formulae given below.t) is the derivative of P(p. by multiplying the known undisturbed potential (equation (2). i .y) position. arg[∇D(p)]. k = wave number = 2π/wavelength. Pu(p. 5. The frequency.t) / Pu(p.0]. ω.t) = Re{ ∇Pd(p. Pu(p. and constant-frequency added mass and damping loads.φd(p)) ] (3) where subscript d denotes the values for the disturbed wave component. Ṗd([x.t) } (7) Disturbed Surface Elevation(p. is not affected by the disturbance. equation (8) can be re-written as: Disturbed Surface Elevation(p. at simulation time zero.w Theory.t) = [ ad(p) / au(p) ] . t = simulation time.t) (5) OrcaFlex can also calculate the disturbed potential gradient from the spatial derivative of that equation: ∇Pd(p. is then the ratio of the disturbed potential to the undisturbed potential. So a d(p) and φd(p) are the amplitude and phase lag (at simulation time zero) of the disturbed velocity potential at position p. The presence of (and response of) the vessel (or multibody group of vessels) disturbs the wave component. t). is also the surface elevation disturbance RAO at that (x. |D(p)|. and the direction and period/frequency of the wave component. For example. 161 . for the wave component.0]. p.t) = D(p) .t) = Re{ -(1/g) . as a function of position relative to the vessel.y.0]). Surface Elevation Disturbance RAO This last equation involves the time derivative of Pd. Whilst OrcaFlex cannot account for the waterplane area effects in a non-linear fashion (since it does not have detailed information about the shape of the vessel hull). So P[1] = Z coordinate of reference origin . after the removal of the appropriate moment arm contributions. Stiffness Load The hydrostatic stiffness matrix specifies how the net weight+buoyancy load (force and moment) on the vessel varies with heave.P where L = [Fheave.(mean surface Z + datum Z relative to surface).K'.m zg)g from the roll-roll and pitch-pitch components of K. K. in general. roll and pitch components of the matrix are specified. when the mass of water displaced by the vessel in its datum position is not equal to structural mass of the vessel. And P[2] and P[3] are the roll and pitch (in radians) needed to rotate the vessel from its datum Heel and Trim orientation to its current orientation. L d will be a pure force acting vertically. WAMIT. Two effects contribute to K: the change in load due to the change in the submerged volume of the vessel as it heaves. to do this it must subtract the linearised approximation to the moment arm effects from the user's stiffness matrix. Centre of Buoyancy Specified The buoyancy load arising from waterplane area effects is calculated using the following matrix equation: L = . encodes how the weight and buoyancy loads on the vessel change due to small changes in the vessel's position and orientation. the change in moment caused by movement of the vessel's centre of gravity and centre of buoyancy as the vessel surges and sways (moment arm effects).L)/L (F. OrcaFlex applies a weight force 162 . and M roll and Mpitch are about the vessel primary heading x. P = column 3-vector containing the heave position and roll & pitch angles (in radians) at the reference origin.~). the components for the surge. it is a linearisation of what is. Added Mass and Damping reference origin unless otherwise stated. K = the user-specified hydrostatic stiffness matrix. sway and yaw directions are all zero. it is able to capture the moment arm effects during a simulation by simply applying the weight and buoyancy forces at the instantaneous position of the centre of gravity/buoyancy respectively (under the assumption that the volume of water displaced by the vessel remains constant).L)/radian pitch (F.P where K' is the user's stiffness matrix. respectively. m d the displaced mass of water and z b/g is the vertical distance of the centre of buoyancy/gravity above the reference origin when the vessel is in its datum position. Otherwise.L)/radian (F. a non-linear problem.and y-directions through the reference origin.) Ld = value of L when the vessel is in its datum position. The hydrostatic stiffness matrix. simply to turn the row-vector written into a column vector. relative to the user-specified datum Z.~. As stated.L)/radian (F.Mpitch]T is a column 3-vector containing the heave. heel and trim of that reference origin. Vessel Theory All these loads are applied at the Stiffness. (The superscript T denotes transpose. Here Fheave acts vertically upwards. the hydrostatic stiffness matrix is only applicable for small changes in the vessel's position and orientation. AQWA) account for both of these contributions.g. then OrcaFlex will not know the length of the moment arm needed to adjust K. The moment arm contributions are removed by subtracting a term of the form (m d zb . meaning that it is at an unspecified position on the same vertical line as the centre of gravity. The hydrostatic stiffness matrices output by most diffraction packages (e. This will be zero if the datum position is a freefloating equilibrium position of the vessel when no other objects are attached. where m is the structural mass of the vessel. roll and pitch relative to the vessel in its datum configuration. K.K.L)/L (F. so the units of the stiffness matrix are: heave roll pitch heave F/L F/radian roll (F. Only the heave. roll and pitch components of the net weight + buoyancy load that acts on the vessel at the reference origin. However. surges and sways (often referred to as waterplane area effects). The angular offsets in P are in radians. OrcaFlex therefore has two modes of calculation: Centre of Buoyancy Unspecified The net weight+buoyancy load is calculated using the following matrix equation: L = Ld .L)/radian F/radian where F and L denote the units of force and length.Mroll. This is only possible if vessel's centre of buoyancy has been specified explicitly: if it has instead been input as (~. In addition.w Theory. My.) V = [vx.Fy. which means that the non-linear effects of the shift in the moment arm between the centres of gravity and buoyancy will be captured precisely. (The superscript T denotes transpose. L and T denote the units of mass.L2 where M.L) / (rad/T) where F. in the vessel primary heading axes directions. having only heave.Fz. of the vessel translational and angular acceleration at the reference origin.vy. and is described in Vessel Theory: Impulse Response and Convolution.vz.Mx.Mz) that acts on the vessel at the reference origin. etc. These two forces are applied by OrcaFlex at every time-step of the simulation.ωx. Added Mass and Damping Loads The theory below gives details of the added mass and damping loads when using the Constant Added Mass and Damping Method. Note: If the vessel's Primary Motion is set to Calculated (3 DOF) then reduced added mass and damping matrices are used. but the units given below apply in both cases. respectively.V. so the units of the damping matrix elements are: surge/sway/heave roll/pitch/yaw surge/sway/heave F / (L/T) F / (rad/T) roll/pitch/yaw (F.Fz) and moment (Mx. and a buoyancy force Fb = md g at the vessel's centre of buoyancy. 163 . roll and pitch directions. The angular velocities here are in radians per unit time. surge-roll as surge force per unit roll rate. roll-surge as roll moment per unit surge velocity. damping and stiffness data. surge-sway as surge force per unit sway velocity.My.L) / (L/T) (F. consider the surge-surge element as surge force per unit surge velocity. L and T denote the units of force. having only surge.Fy. in the vessel primary heading axes directions. The calculation for frequency-dependent added mass and damping loads is more complex.ωz]T is the column 6-vector containing the components. sway and yaw components. Damping Load When using the Constant Added Mass and Damping Method. simply to turn the row-vector written into a column vector. in the vessel primary heading axes directions. The damping load is calculated using the following matrix equation: L = -D. The added mass and damping load (force and moment) at the reference origin is therefore equal to -Ma. relative to earth. Note: All components referred to here are in the directions specified by the conventions data. where D is the specified damping matrix and V is the (6 degree of freedom) vector of vessel velocity and angular velocity relative to the earth at the specified reference origin. the added mass load calculation is analogous to the damping load described above. To see this. 'Unit roll rate' means a roll rate of 1 radian/sec. respectively. where Ma is the specified added mass matrix and A is the column 6-vector containing the components.L roll/pitch/yaw M. so the units of the added mass matrix elements are: surge/sway/heave roll/pitch/yaw surge/sway/heave M M. Added Mass Load When using the Constant Added Mass and Damping Method. and the angular velocity (ωx. and the damping and added mass loads are not calculated in the heave. For details see added mass. length and time. The angular accelerations are expressed in radians/T2. length and time.L M. the damping load is equal to -D.V where L = [Fx. and roll-roll as roll moment per unit roll rate. Vessel Theory Fg = -m g at the vessel's centre of gravity.vy. of the damping force (Fx. of the velocity (vx. is not used at all in this case. roll and pitch components.ωy.ωy.w Theory.ωz) of the vessel.vz) at the specified reference origin. The stiffness matrix.Mz]T is the column 6-vector containing the components.A. but it does involve some approximation in the levels of damping and added mass applied. The damping data B(f) and the resulting IRF(τ) are matrix-valued functions. in the case of a multibody group) is given by the following convolution integral equation: F(t) = -A(∞) x''(t) . OrcaFlex uses a method proposed by Cummins (1962). involves integrating all the way back to the start of the simulation. 164 . But fortunately impulse response functions decay to zero as the time lag τ goes to ∞. due to primary motion of the vessel(s) τ is a time lag integration variable.2. This can cause long simulations to run slower and slower as the simulation time progresses. at each calculation time t in the simulation the total added mass and damping load (force and moment) on the vessel (or vessels. As a result the danger of energy feed-in is virtually eliminated. at each time step. i=1. where the integral is truncated. Truncating the integral improves performance significantly. of the added mass and damping reference origin relative to the global origin. The convolution integral in equation (2) is calculated numerically using the following assumptions about the form of the damping: B(f) is assumed to vary linearly with f between the frequencies {fi. B(f) is assumed to decay as f -3 to zero at infinite frequency.Integral(τ=0 to ∞) IRF(τ) x'(t-τ) dτ (1) where x'' and x' are the vessel acceleration and velocity.7 Impulse Response and Convolution To implement frequency-dependent added mass and damping in the time domain.3. for a multibody group they are 6N x 6N matrices. τ = Tc. A(∞). In addition. For frequencies below the lowest frequency specified in the data. of frequency and time lag respectively. For a single vessel (not in a multibody group) these matrices are 6 x 6 matrices. This method involves calculating the Impulse Response Function (IRF) for the vessel and then applying that IRF at each time step using a convolution integral to account for the past motion of the vessel. by applying the following cutoff scaling function: c(τ) = exp[ -(3τ/Tc)2 ] in equation (2) above. B(f) is assumed to decay linearly to zero at zero frequency.m} that are specified in the data. This load is applied at the added mass and damping reference origin.….cos(2πft)] df (2) where B(f) = frequency-dependent damping matrix. so that the IRF is virtually insignificant beyond the cutoff time. the infinite-frequency added mass matrix. must be calculated and included in the vessel total inertia matrix. but this scaling does introduce approximation errors that can be significant for small values of Tc. where N is the number of vessels in the multibody group.B(f). Tc. respectively.11.w Theory. OrcaFlex therefore truncates the impulse response function at the Cutoff Time. To avoid this OrcaFlex instead smoothly scales down the IRF function as τ approaches Tc. For details of how to manage these errors. (1) above. so there comes a point beyond which the rest of the integral can safely be neglected. see Cutoff Time. Impulse Response Function Cutoff The convolution integral equation. c(τ) = is a cutoff scaling function. and implemented by Wichers (1979). at frequency f. See Impulse Response Function Cutoff below. Vessel Theory 5. And simply cutting off the integral sharply at τ = T c can result in negative damping (energy feed-in) being applied at low frequencies. The effect of this scaling by c(τ) is that the impulse response function is smoothly scaled down for large τ. Impulse Response Function (IRF) OrcaFlex calculates the IRF using the following Fourier integral equation: IRF(τ) = c(τ) * Integral(f=0 to ∞) [4. In more detail. For frequencies above the highest frequency specified in the data. For a single vessel (not in a multibody group) the matrices A(∞) and A(f i) are 6 x 6 matrices. the results of the calculation may not be reliable. which characterises the response to past motion). So the manoeuvring load is calculated using the low-frequency components only of the velocity and angular velocity of the vessel relative to the current. A(∞) can be estimated from the IRF and any one of the added mass matrices specified.F3) and moment (F4.A6ju5uj ] F5 = Σj=1…6 [ A3ju1uj . Lamb §124). If the vessel is in a multibody group then the matrix used will be that vessel's diagonal block in the multibody group's longest period added mass matrix.A2ju1uj + A4ju5uj . To reduce these approximation effects OrcaFlex calculates each of the above m separate estimates of its value. if the data could be specified for all frequencies and full integration used to calculate the IRF and these estimates.m} specified in the data.A3ju5uj ] F2 = Σj=1…6 [ A3ju4uj .F6) arise from the classical theory of rigid body motion in an inviscid fluid (see. Vessel Theory Infinite-Frequency Added Mass A(∞) The infinite-frequency added mass matrix gives the vessel's instantaneous response to acceleration (as opposed to the IRF. 165 .A2ju4uj ] F4 = Σj=1…6 [ A2ju3uj .A5ju4uj ] – but see double-counting below where A ij = the added mass matrix coefficients specified by the vessel type data.A1ju3uj + A6ju4uj .A4ju6uj ] F6 = Σj=1…6 [ A1ju2uj . They can play an important role in the damping of slow drift motion.2. where N is the number of vessels in the multibody group. i. for a multibody group they are 6N x 6N matrices. obey the Kramers-Kronig relations. In these circumstances. on the Calculation page of the vessel data form. i=1. added mass and damping are mathematically related through the Kramers-Kronig relations (see Kotik and Mangulis). No further data are needed. If the data are consistent.F5. then this may indicate that the data are not consistent. and at wave-frequency some of these terms are already included in the 2nd order wave load specified by the wave drift QTFs. using the following equation: Estimate of A(∞) from A(fi) = A(fi) + 1/(2πfi) Integral(s=0 to Tc) IRF(s) sin(2πfis) ds where {A(fi).F2. relative to current.3.3. to the estimated infinite frequency added mass A(∞). Manoeuvring loads are a low velocity effect (at higher velocities viscous effects dominate). and then takes A(∞) to be the mean of those estimates. If the vessel type length differs from the vessel length.A3ju2uj + A5ju6uj . then all of these estimates would give the same value.…. The manoeuvring force (F1. so interpolation approximation errors arise.…. In fact.A1ju6uj ] F3 = Σj=1…6 [ A1ju5uj . and then uses the IRF in conjunction with the added mass data to estimate the infinite-frequency limit of the added mass. But in practice the data are only specified for a finite set of frequencies and the integrations have to be done numerically. at the added mass and damping reference origin.8 Manoeuvring Load Manoeuvring loads are second-order forces and moments that are functions of the low frequency added mass of the vessel and the low frequency part of its translational and angular velocity. Damping page of the vessel types form. for example. They are given by: F1 = Σj=1…6 [ A2ju6uj . In theory. with increasing frequency. i=1. You can choose whether manoeuvring loads are included.m} are the user-specified added mass matrices for the m frequencies {fi. Added Mass. If they appear to be converging to a limit which differs significantly from the estimated value A(∞). 5. If frequency-dependent added mass and damping is used then these coefficients will be taken from the added mass matrix associated with the longest period specified (lowest frequency).11.2. u j = low frequency velocity (j=1…3) and low frequency angular velocity (j=4…6) of the vessel. To include them select Manoeuvring Load in the Included Effects applied to the vessel. since the manoeuvring load is based on the added mass data that is already specified for added mass purposes on the Stiffness. Consistent Added Mass and Damping The added mass and damping data are not independent. then the graphs of added mass against frequency should appear to be converging. and using the added mass coefficients (A ij) for the longest period specified in the data (if frequency-dependent added mass and damping is used). OrcaFlex uses the damping data to determine the IRF. then these data will be automatically Froude-scaled to the vessel length.e.w Theory. or the single added mass matrix specified (for constant added mass and damping). with a vertical axis: Fx = . It is only calculated if Other Damping is specified as included on the vessel data form. Vy.Lpitch Ωy .Lpitch Ωy . However these factors are assumed to only include viscous loads. which is outlined below. and the damping force.Qroll Ωx |Ωh| My = . For further details see Oil Companies International Marine Forum.Lheave Vz .Qsway Vy |Vh| Fz = . If the vessel type symmetry is Circular. and angular velocity. and moment. Vessel Theory Dangers of double-counting The expression above for F6 contains the following Munk moment terms that are quadratic in the surge and sway velocity components. of the wavefrequency part of the vessel primary motion velocity relative to the earth. For a discussion of the various damping sources see Damping Effects on Vessel Slow Drift. The damping load is then applied at that reference origin. F. 0) = horizontal vector component of Ω. Drag Loads due to Translational Relative Velocity The drag loads due to translational velocity of the sea and air past the vessel are calculated using the standard OCIMF method. respectively subscripts x.Lsway Vy . The loads are split into those due to translational relative velocity and yaw rate.Qpitch Ωy |Ωh| Mz = . at the reference origin.A22u1u2 If Current Load is included then these Munk moment contributions are assumed to already be included in the load specified by the OCIMF current load data. V.10 Current and Wind Loads These loads are an important source of damping when modelling vessel slow drift.Qpitch Ωy |Ωy| Mz = .Qyaw Ωz |Ωz| where Vh = (Vx. 5.11. as follows. 5.Qheave Vz |Vz| Mx = .Lsurge Vx . z denote the vessel primary heading directions (so x & y are horizontal and z vertical).Lroll Ωx .Qyaw Ωz |Ωz| where L and Q are the linear and quadratic other damping coefficients.Lyaw Ωz .Qsurge Vx |Vx| Fy = .Lroll Ωx . 0) = horizontal vector component of V Ωh = (Ωx.Qheave Vz |Vz| Mx = . The velocity vectors used in the calculation are the translational velocity. are given by: Fx = .Lsurge Vx .Lsway Vy . If the symmetry is not Circular then the damping model treats each degree of freedom independently. 1994.Lyaw Ωz .Qroll Ωx |Ωx| My = .w Theory. Ω. Ωy. M. The damping model used depends on the vessel type symmetry. So to avoid double-counting these terms. if manoeuvring load and current load are both included then these Munk moment terms are omitted from the manoeuvring load. The current and wind drag loads on a vessel are calculated using the data specified on the Current and Wind Load pages on the vessel type data form.11. and to not include any potential theory loads. 166 .Qsway Vy |Vy| Fz = .A21u12 . u1 and u2: + A11u2u1 + A12u22 . then the quadratic term instead uses a cross-flow drag model. Warning: There is also a danger of double-counting if the u62 terms in the above expressions for F 1 and F2 are non-zero and were also included in the surge and sway yaw rate drag factors that are specified on the current load page. y.Qsurge Vx |Vh| Fy = .Lheave Vz .9 Other Damping The other damping load on the vessel is the sum of linear and quadratic terms that are calculated using the other damping coefficients specified on the vessel type data form. Ksway. the relative velocity used is the current (or wind) velocity. but the OCIMF method described above does not include this drag load (since the OCIMF method is designed for stationary vessels). The drag loads due to surge and sway relative velocity are calculated as given by the following OCIMF formulae. then the current velocity at the surface is used). and the yaw moment acts about the vessel Vz-direction. where L is the length between perpendiculars and D is the draught. For wind drag these yaw rate terms are insignificant and so are omitted by OrcaFlex. since there is none for a stationary vessel. sway and yaw drag loads on a stationary vessel.w Theory. and for wind to the exposed areas above the waterline. Notes: The OCIMF method is intended for tankers. For current loads (not wind loads) the OCIMF standard method uses LD for both the surge and sway areas. In other words the relative velocity includes the current but not the waves. Nor does the OrcaFlex extension of OCIMF add these yaw rate drag terms. Drag Loads due to Yaw Rate A vessel rotating in yaw will generate a drag moment resisting the yaw rate. The surge and sway forces act in the vessel Vx and Vy-directions. respectively. using the formulae Surge Force = (½ρ|ω|ω)Ksurge Sway Force = (½ρ|ω|ω)Ksway Yaw Moment = (½ρ|ω|ω)Kyaw (1) where Ksurge. Asway and Ayaw are the surge and sway areas and the yaw area moment. V is the magnitude of the relative velocity of the sea or air past the vessel. the wind velocity at 10m above mean water level). For current these correspond to the exposed areas below the waterline. For hydrodynamic drag. but does not include any wave-frequency or superimposed motion. Csurge. Note that the OCIMF method does not include any drag due to yaw angular velocity of the vessel. Note: The OCIMF standard method uses L2D for the yaw area moment for current loads. The surge force. Kyaw are the yaw rate drag factors (specified on the Current Load page on the vessel type data form). since the OCIMF method has no framework for them. V is based on the current velocity at the low-frequency instantaneous position of the load origin (if this is above the water surface. ρ is the water density (for current drag) or air density (for wind drag). but could be applied to other vessel types providing suitable data are obtained. ω is the vessel yaw rate. but not the wavefrequency motion or the superimposed motion.e. Vessel Theory The OCIMF method calculates the surge. Warning: The current and wind loads are based on theory for surface vessels and are not suitable for submerged vessels. The wind load is only included if the Include wind loads on Vessels option is enabled in the Environment data. relative to the low-frequency primary motion of the vessel. Csway and Cyaw are the surge. due to any low-frequency primary motion of the vessel 167 . at the specified current (or wind) load origin. sway force and yaw moment act at the current or wind load origin. Surge Force = ½CsurgeρV2Asurge Sway Force = ½CswayρV2Asway Yaw Moment = ½CyawρV2Ayaw where Asurge. sway and yaw coefficients for the actual current or wind direction relative to the low-frequency vessel heading. and LA sway for the yaw area moment for wind loads. OrcaFlex extends this to a moving vessel by replacing the current (or wind) velocity used in the OCIMF method with the relative translational velocity of the current (or wind) past the vessel. V is based on the wind velocity specified in the data (i. But for current drag they are important so OrcaFlex models them. For wind loads. More precisely. In both cases V is taken relative to the vessel: it includes allowance for the translational velocity of the load origin due to any low-frequency primary motion of the vessel. and it includes the low-frequency primary motion of the vessel. They are therefore calculated separately in OrcaFlex – see Drag Loads due to Yaw Rate below. in radians per second. Interaction with sway rate Further complications arise if the vessel is swaying as well as yawing. 1988) and developed a more accurate empirical approach based on model test data. unless the C d value was increased to about 5. Indeed Wichers (1979) found that the strip theory results significantly underestimated the actual yaw drag measured in model tests. which we assume to be the same for all the strips. and that for simplicity we choose to put the load origin at the centre of that area. However. Consider the simplest situation where the vessel centre is stationary but the vessel is yawing at rate ω about that centre. We now divide the drag area into vertical strips of width δx and consider the sway drag load on the strip at distance x forward of the centre. These yaw rate drag loads are then applied at the current load origin. The reason for this is that it is difficult to model. Orcina is studying this. He returned to the problem in his PhD thesis (Wichers. This is an interaction between sway velocity and yaw rate and its effect is to significantly increase the yaw moment.12 LINE THEORY 5. giving a significant yaw drag moment. then we can estimate the yaw rate drag factors by: Ksurge = Ksway = 0 Kyaw = (CdDL4/32) where Cd is some appropriate drag coefficient. Yaw Moment = (½ρω2)(CdDL4/32) (2) The same argument can be applied to the drag forces in the surge direction. However the method has some theoretical difficulties. Comparing equations (1) and (2) we see that the Kyaw corresponds to the bracketed term (CdDL4/32) in equation (2). so we can estimate the sway drag load on it by ½ρCdDδx(ωx)|ωx| where Cd is the drag coefficient. To avoid counting these contributions twice. but as described above the model's results did not match experimental results particularly well. See the papers by Wichers for further information. This is in fact a combination of a drag coefficient and the 3rd moment of drag area about the centre. Estimating the Yaw Rate Drag Factors The above formulae (1) are based on a simple strip theory estimate of the drag loads on a yawing vessel. 5. OrcaFlex does not yet include this interaction effect.12. there are a lot of questionable assumptions in the strip theory argument. 168 . In this case the integral in the above strip theory argument turns out to give an extra term involving vω. In fact the integral gives the following yaw moment. as given by Wichers (1979). This strip theory argument therefore concludes that for a slender ship. if manoeuvring load and drag loads due to yaw rate are both included then you must ensure that the yaw rate drag factors only include the contributions due to viscous effects. so they reinforce. and their moments about the centre. which is rather high for a drag coefficient. with the hydrodynamic drag load origin at the centre. from model test. So if more specific data are available. When we do this integral the sway forces from corresponding strips forward and aft of centre have the same magnitude but opposite direction. with a view to implementing a more accurate yaw rate drag model in a future release of OrcaFlex. Let us also assume that the area exposed to sway drag is a simple rectangle of height D (the draught) and length L (the length between perpendiculars). These sway drag loads from each strip. are then integrated to give the total sway force and a contribution to yaw moment. e.1 Overview OrcaFlex uses a finite element model for a line as shown in the figure below. so the surge force contribution to yaw moment is generally negligible. The strip's area is Dδx and its sway velocity due to the yaw rate is ωx. However the yaw moment terms from forward and aft of centre have the same magnitude and same direction. so they cancel and the total sway drag force is therefore zero. But for a slender vessel W is much less than L. Warning: Danger of double-counting: If manoeuvring load is also included then it may include potential theory surge and sway force contributions that are quadratic in ω. with length L being replaced by width W. In the meantime we recommend that you specify yaw rate drag factors that are appropriate to the conditions prevailing in the case being modelled.g. since the formulae break down when ω is zero. Line Theory ρ is the water density. then we recommend setting the yaw rate drag factors to values that best fit your data.w Theory. Wichers (1979) included them in his strip theory model. Forces and moments are applied at the nodes – with the exception that weight can be applied at an offset. 169 . drag) are calculated allowing for the varying wetted length up to the instantaneous water surface level. as indicated by the arrows in the figure above. buoyancy. buoyancy. added mass.) are all lumped to the nodes. 2. The other properties (mass. drag etc. 3. and so represent just one halfsegment. Where a segment pierces the sea surface. Each line segment is divided into two halves and the properties (mass. The model segments only model the axial and torsional properties of the line. The exception to this is end nodes. … sequentially from End A of the line to End B. all the fluid related forces (e.w Theory.) of each halfsegment are lumped and assigned to the node at that end of the segment.g. Line Theory Discretised Model Actual Pipe End A Node 1 Segment 1 Segment 1 Node 2 Segment 2 Segment 2 Node 3 Segment 3 Segment 3 End B Figure: OrcaFlex Line model The line is divided into a series of line segments which are then modelled by straight massless model segments with a node at each end. weight. Nodes and segments are numbered 1. which have only one half-segment next to them. weight. So segment n joins nodes n and (n+1). Nodes Each node is effectively a short straight rod that represents the two half-segments either side of the node. buoyancy etc. 5. The line does not have to have axial symmetry. This section has given only an overview of the line model. there are 3 types of spring+dampers in the model: 170 . since different bend stiffness values can be specified for two orthogonal planes of bending.2 Structural Model Details The following figure gives greater detail of the line model. Line Theory Segments Each model segment is a straight massless element that models just the axial and torsional properties of the line.w Theory. See structural model for full details. The figure includes the various spring+dampers that model the structural properties of the line.12. Torsion spring + damper Sx1 Sy1 Sz Sx1 Axial spring + damper Sx2 Sy2 Sz 2 Node Nx Bending springs + dampers Ny Nz (axial direction) End B Figure: Detailed representation of OrcaFlex Line model As shown in the diagram. The bending properties of the line are represented by rotational spring+dampers at each end of the segment. A segment can be thought of as being made up of two co-axial telescoping rods that are connected by axial and torsional spring+dampers. between the segment and the node. showing a single mid-line node and the segments either side of it. and also shows the xyz-frames of reference and the angles that are used in the theory below. Shear Forces. respectively (see Line Pressure Effects) Ai. Po = internal pressure and external pressure. and also calculates the segment axial direction Sz. The bending properties are represented by rotational spring+dampers either side of the node. It is the vector in direction Sz whose magnitude is given by: Te = Tw + (PoAo . spanning between the node's axial direction Nz and the segment's axial direction Sz. Bend Moments. Torsion Moments. Line Theory The axial stiffness and damping of the line are modelled by the axial spring+damper at the centre of each segment. This effective tension force vector is then applied (with opposite signs) to the nodes at each end of the segment.PiAi) + EAnomC(dL/dt)/L0 where 171 .2ν)(PoAo . 5. which is the unit vector in the direction joining the two nodes.3 Calculation Stages OrcaFlex calculates the forces and moments on a mid-node in 5 stages: 1. can be negative. To do this.λL0) / (λL0) L = instantaneous length of segment λ = expansion factor of segment L0 = unstretched length of segment ν = Poisson ratio Pi. Each mid-node therefore receives two tension forces. Te. 5. Total Load. as specified on the line types form (= effective Young's modulus x cross section area) ε = total mean axial strain = (L . 5. indicating effective compression.12. one each from the segments on each side of it. which applies equal and opposite torque moments to the nodes at each end of the segment.PiAi) where Te = effective tension Tw = wall tension = EA. If torsion is not included then this torsional spring+damper is missing and the two halves of the segment are then free to twist relative to each other. in seconds (this is defined below) dL/dt = rate of increase of length.2ν(PoAo . 3.w Theory. Linear axial stiffness In the case of linear axial stiffness the tension in the axial spring+damper at the centre of each segment is calculated as follows.12. 4. which applies an equal and opposite effective tension force to the nodes at each end of the segment. The variables are given by: EA = axial stiffness of line. Ao = internal and external cross sectional stress areas.4 Calculation Stage 1 Tension Forces Firstly the tensions in the segments are calculated. For the relationship between effective tension and wall tension see Line Pressure Effects. Non-linear axial stiffness When the axial stiffness is non-linear then the tension calculation is as follows.PiAi) + EA.ε . Tension Forces. It is the vector in direction Sz whose magnitude is given by: Te = Var Tw(ε) + (1 . OrcaFlex calculates the distance (and its rate of change) between the nodes at the ends of the segment.C(dL/dt)/L0 In this equation for Tw. the first term is the contribution from axial stiffness. Note: The effective tension. the second term is the contribution from external and internal pressure (via the Poisson ratio effect) and the third term is the axial damping contribution. respectively (see Line Pressure Effects) C = damping coefficient. If torsion is included (this is optional) then the line's torsional stiffness and damping are modelled by the torsional spring+damper at the centre of each segment. 2. z at the end nearest End A. The segment has two frames of reference: Sx1.w Theory. There are bending spring+dampers at each side of the node.and y-directions that are specified by the Gamma angle on the line data form (see End Orientation). Isotropic bend stiffness means that the bend stiffnesses for the x and y-directions are equal. The implicit integration scheme includes in-built numerical damping. as specified on the general data form Ccrit = (2ML0/EA)½ is the critical damping value for a segment M = segment mass. isotropic bending stiffness In the case of linear. generated by the bending spring+damper is calculated. z at the other end. Line Theory Var Tw is the function relating strain to wall tension. then the above equation is separated into its components in the Sx2 and Sy2 directions. and whose magnitude is α 2 / (½L0). one each from the segments on each side of it. which is the direction that is orthogonal to Sz and Nz. where b2 = unit vector in direction (Sz × Nz) and whose magnitude is given by |M2| = EI. Each mid-node therefore receives two effective tension forces.Dcrit λb = target bending damping. Linear. If the axial stiffness is non-linear then we use the nominal axial stiffness EAnom in the formula for e.|C| + D.EI. but not the mass of any attachments The bend angle (α1) and bend moment vector (M1) on the other side of the node are calculated similarly. As in the linear case the effective tension force vector is then applied (with opposite signs) to the nodes at each end of the segment. These axial directions are associated with the frames of reference of the node and segment. non-isotropic bending stiffness If the bend stiffnesses for bending about the x and y-directions are different. giving: 172 . isotropic bending stiffness the bend moment. including contents. as specified on the line types form D = (λb/100). M2. as specified on the general data form. The effective curvature vector C is then calculated: it is the vector whose direction is the binormal direction. including contents. as specified by the variable data source defining axial stiffness.12.d|C|/dt where EI = bending stiffness. which was calculated in stage 1. b2. y1. but not the mass of any attachments Notes: This numerical damping term is only included when using the explicit integration scheme. Dcrit = the bending critical damping value for a segment = L 0(M. These two frames have the same Sz direction. It is calculated automatically using the formula: C = (λa/100)Ccrit where λa = target axial damping. 5. so the bend angle α2 between Nz and Sz can now be calculated.L0)½ M = segment mass.5 Calculation Stage 2 Bend Moments The bend moments are then calculated. EAnom is the nominal axial stiffness which is defined to be the axial stiffness at zero strain. Damping coefficient C The damping coefficient C represents the numerical damping in the line. The implicit integration scheme includes in-built numerical damping. spanning between the node's axial direction Nz and the segment's axial direction Sz. one each from the segments on each side of it. Linear. Notes: The damping term represents numerical damping and is only included when using the explicit integration scheme. so the node experiences two bend moments. The node's frame of reference Nxyz is a Cartesian set of axes that is fixed to (and so rotates with) the node. The bend moment M2 is the vector in the binormal direction. where L0 is the unstretched length of segment. and Sx2. Nz is in the axial direction and Nx and Ny are normal to the line axis and correspond to the end x. y2. Each of these spring+dampers applies to the node a bend moment that depends on the angle α between the segment axial direction Sz and the node's axial direction Nz. as specified on the line types form Cx.Cy + Dy.L0)½ Dy = (λb/100)L0(M.EIx. isotropic bending stiffness (Elastic or Hysteretic) In this case the bend moment magnitude |M2| is given by: |M2| = Var BM(α2 / [½ L0]) + D'. The curvature used in the calculation of bending moments is the value in the true plane of bending.D'c D'c = the bending critical damping value for a segment = L 0(M. The bend angle (α1) and bend moment vector (M1) on the other side of the node are calculated similarly. Non-linear. A non-linear stress-strain relationship for a homogeneous pipe.L0)½. This approach results in a non-linear elastic bend stiffness model.EIy. Var BM can be specified by either: A tabular variable data source that defines the bending stiffness. taking full account of the 3D motions of the adjacent nodes. Non-hysteretic Non-hysteretic means that the data are applied using a simple elastic model. Elastic or Hysteretic Bending Model For non-linear bend stiffness you can choose whether the curvature-moment data are interpreted hysteretically or not. The bend angle (α1) and bend moment vector (M1) on the other side of the node are calculated similarly.L0)½ EInom is the nominal bending stiffness which is defined to be the bending stiffness at zero curvature. without any allowance for the history of curvature.d|C|/dt where Var BM is the function relating curvature to bend moment. So if the curvature increases and then decreases again then the bend moment goes up and down the same non-linear moment-curvature curve. 173 .EInom. In this case the bend moment function Var BM in the above equation is simply the specified function of the current curvature magnitude. The variable data source can be specified as either hysteretic or elastic as described below.dCx/dt component of M2 in the Sy2 direction = EIy. Cy = components of the curvature vector C in the Sx2 and Sy2 directions Dx = (λb/100)L0(M. EIy = bending stiffnesses of segment. Line Theory component of M2 in the Sx2 direction = EIx.Cx + Dx. D' = (λb/100).w Theory. This is illustrated in the following diagram which shows the bend moment M that results when the non-hysteretic model is used and a simple sinusoidally varying curvature C is applied.dCy/dt where EIx. w Theory. The data are taken to specify the bend moment that results when the line is bent with slowly increasing curvature. In other words the hysteretic model treats curvature as being made up of a series of curvature increments and corresponding moment increments. etc. and it undoes them on a first in first out basis. The left-hand diagram shows the bend moment that results from a sinusoidal curvature history. the first increment of curvature that was applied). as shown in the following diagrams. The right-hand diagram shows what happens if a small curvature cycle is followed by another curvature cycle of greater amplitude. But that if the curvature reduces again then the bend moment does not come back down the same curve. Instead when the curvature reduces again the bend moment comes down the curve that is obtained by first undoing and reversing the first bit of curvature (i. the arrows on the curve show the direction of change of the curvature and moment. i. effects of the history of curvature applied. 174 . Line Theory M C Figure: Elastic Non-linear Bend Stiffness Hysteretic The hysteretic model includes hysteresis effects.e. M M C Figure: C Hysteretic Non-linear Bend Stiffness The hysteresis model is described in detail by Tan. then the second bit of curvature. The effect of this hysteretic model is that the bend moment follows a hysteresis curve. Quiggin and Sheldrake (2007).e. as opposed to the last in first out basis that non-hysteretic bend stiffness uses. w Warning: Theory. It is not suitable for modelling rate-dependent effects. Sx2 and Sy2 must first be calculated. 5.e. they involve no twisting. Linear torsional stiffness In the case of linear torsional stiffness the torque generated by the torsion spring+damper can then be calculated – it is a moment vector whose direction is the segment axial direction Sz and whose magnitude is given by: Torque = K. Note that this twist angle is also the angle between Sy1 and Sy2. since so far only the segment axial direction Sz has been found. y1. the shear force in the segment can be calculated. the directions Sx1.τ / L0 + C. differ by just a twist through angle τ. as specified on the general data form 175 . but starting from the orientation of the node at that other end of the segment. the direction that is orthogonal to both Nz and Sz). This shear force vector is applied (with opposite signs) to the nodes at each end of the segment. The directions Sx2 and Sy2 at the end of the segment are determined from the orientation Nxyz of the adjacent node.(dτ/dt) where K = torsional stiffness. the bend moment varies linearly along the segment and the shear force in the segment is the constant vector equal to the rate of change of bend moment along the length. at the two ends of the segment. The twist angle τ in the segment can then be calculated – it is the angle between the directions Sx1 and Sx2. Each model segment is a straight stiff rod in which the bend moment vector varies from M 1 at one end (the end nearest End A of the line) to M2 at the other end. This rotation is therefore through angle α 2 and it is a rotation about the binormal direction (i.(dτ/dt) where Var Torque is the function relating twist per unit length to torque as specified by the variable data source defining torsional stiffness. The shear force is therefore given by: Shear Force Vector = Sz × (M2 . Non-linear torsional stiffness If the torsional stiffness is non-linear then the calculation of torque is as follows.7 Calculation Stage 4 Torsion Moments The torsion is then calculated (providing torsion has been included).M1) / L where L is the instantaneous length of the segment. (Note that rotations about the binormal direction are bending rotations only – i. between directions Sx1 and Sx2 L0 = unstretched length of segment dτ/dt = rate of twist (in radians per second) C = torsional damping coefficient of the line (this is defined below) Te = effective tension in the segment This torque moment vector is then applied (with opposite signs) to the nodes at each end of the segment.6 Calculation Stage 3 Shear Forces Having calculated the bend moments at each end of the segment.12. Sy1. z. 5. y2. Line Theory You must check that the hysteretic model is suitable for the line type being modelled. z and Sx2. To do this. It is intended for modelling hysteresis due to persisting effects such as yield of material or slippage of one part of a composite line structure relative to another part. as specified on the line types form τ = segment twist angle (in radians). It is a moment vector whose direction is the segment axial direction Sz and whose magnitude is given by: Torque = Var Torque(τ/L0) + C. Damping coefficient C The damping coefficient C is calculated automatically using the formula: C = (λt/100)Ccrit where λt = target torsion damping. so this is a vector formula that defines both the magnitude and direction of the shear force. by rotating Nxyz until its z-direction is aligned with Sz. In other words the orientations Sx1.12. where these bend moments are calculated as described above. Note that Sz.e.) The directions Sx1 and Sy1 at the other end of the segment are derived in the same way. Because the model segment is stiff in bending. M 1 and M2 are vectors. each mid-node experiences two tension forces. it is best to check that the resulting Exyz directions are correct by drawing the local axes on the 3D view. not the mass of any contents. (90.180. End Direction Results If the end orientation Exyz is defined. Azimuth. To define how this is done we need to define a frame of reference Exyz for the end fitting. Ey along GY.w Theory.9 Line End Orientation At line ends. since the contents are assumed to not twist with the pipe. we usually need to define not only the axial direction of the end fitting but also the twist orientation about that axial direction. The angles offered are as follows: The "Ez-Angle" is the angle between V and the Ez-direction (i. then it is either Fixed.) to give the total force and moment on the node. drag. Ey along GZ. (0. The implicit integration scheme includes in-built numerical damping. Together.12.) Start with Exyz aligned with Lxyz.e. Declination and Gamma. where: E is at the connection point. Ez along GY. This measures how far V is away from the end fitting axial direction. as follows.90. In this case we define Knom to be the torsional stiffness at zero twist per unit length. and then integrates to obtain the node's velocity and position at the next time step. towards GX. specify the orientation of Exyz relative to the local axes Lxyz of the object to which the end is connected. declination and gamma fully define the rotational orientation of the end fitting. This is done by first specifying the azimuth and declination of the axial direction and then specifying the twist orientation by giving a third angle called gamma. See End Orientation. OrcaFlex then calculates the resulting translational and rotational acceleration of the node. (90. (0. two shear forces and two torque moments (one each from the segments either side of the node). a positive angle means rotation clockwise about the positive direction along the axis of rotation.0. Now rotate by Declination degrees about the resulting Ey direction. For ends connected to other objects. and a negative angle means anti-clockwise.12. When setting the azimuth. Notes: This numerical damping term is only included when using the explicit integration scheme. Ey along -GX.0) sets Exyz to be aligned with GXYZ. Ez at 30° to GZ. Then rotate Exyz by Azimuth degrees about Ez (= Lz at this point). Here are some examples of the effect of various values of (Azimuth. This is the angle V makes with Ez when viewing the zx-plane. Ez along -GZ.0) sets Ex along -GX. The "Ezx-Angle" is the angle from Ez to the projection of V onto the Ezx plane (measured positive from Ez towards Ex). The 3 angles. In these cases the angles define Exyz relative to the global axes GXYZ. then OrcaFlex offers various results relative to those axes. replace GXYZ by Lxyz in these examples.90) sets Ex along -GX. Ez is into the line at End A. two bend moments.30. Iz allows only for the structural mass of the line.0) sets Ex at 30° below GX (in the GXZ plane). added mass etc. (If the line end is not connected to another object. but out of the line at End B. See Calculation Method.e. Gamma) for a Fixed end. the 3 angles azimuth. Declination. Finally rotate by Gamma degrees about the resulting (and final) Ez direction. These loads are then combined with the other non-structural loads (weight. Ez along GY. 176 . Ez is the axial direction of the fitting. axial direction). Anchored or Free. For a given vector V (such as the end force) these include the components of V relative to Exyz and the angles that V makes with the various axes of Exyz (see Line Results: Angles). declination and gamma.0) sets Ex along -GZ. Ey along GY. In all these rotations. using the "A to B" convention – i.8 Calculation Stage 5 Total Load As described above.90. If the torsional stiffness is non-linear then we use the nominal torsional stiffness Knom in the formula for C. 5. Ex and Ey are perpendicular to Ez. Three-dimensional rotations are notoriously difficult to describe and visualise. (0. 5. Line Theory Ccrit = (2IzK/L0)½ = the critical damping value for a segment Iz = rotational moment of inertia of the segment about its axis Here. Pz is in the axial direction. and is reported by the azimuth and declination angles. towards End B. The segment Euler load is shown on effective tension range graphs and infringement warnings are given on the results form and in the statistics tables. Note: OrcaFlex does not model flow friction effects. Compression causes the line to deform laterally. At other points on the line the calculation of the local orientation depends on whether torsion is included: If torsion is included then the local Pxyz directions are calculated using the specified torsional properties of the line. This theory is technical and specific to the way pipes are modelled in OrcaFlex. which can support little or no compression. The "Exy-Angle" is the angle between the Ex-direction and the projection of V onto the Exy plane (measured positive from Ex towards Ey). the compression is limited to the segment Euler load value for the segment π2EI/L02. This is the preferred model except where the bend stiffness is insignificant.12. This is the angle V makes with Ez when viewing the zy-plane. 5. OrcaFlex will correctly represent this deformation. If compression exceeds the segment Euler load of an individual segment. Line Theory The "Ezy-Angle" is the angle from Ez to the projection of V onto the Ezy plane (measured positive from Ez towards Ey). The published literature show that there are three extra forces introduced by contents flow – a centrifugal force.12.10 Line Local Orientation At any point P. Theory This section documents the theory behind the modelling of the centrifugal and Coriolis forces in OrcaFlex. If contents flow is included then the resulting centrifugal and Coriolis effects are modelled. However for pipes carrying high contents density at rapid flow rates the flow effects can be significant. 5. the line orientation is defined by its local axes Pxyz. 5. the bending stiffness is set to zero. OrcaFlex includes the facility to specify contents flow. For more details see Modelling Compression in Flexibles and Limit Compression. using the no-twist assumption at each step to calculate the next node's local orientation. If torsion is not included then the local directions at P are calculated by assuming that no twisting occurs anywhere along the line between End A and P. OrcaFlex calculates the local orientation at P by starting with the orientation at End A (as specified by its end orientation angles) and then stepping along the line from node to node. Note: If End A is free or if it is released then the local orientations are calculated as if End A was connected to an object aligned with the global axes.11 Treatment of Compression A segment is said to experience compression if the effective tension is negative. a Coriolis force and a flow friction force. In more detail. Given adequate segmentation. This is the angle V makes with Ex when viewing the xy-plane. this indicates that the wavelength of deformation is shorter than can be represented by the chosen segmentation and the results may be unreliable. and the segment Euler load limit is also zero.12. depending on the setting of the Compression is Limited data item on the line types form. 177 . Compression is Limited: Yes The segment is treated as an elastic Euler strut. where EI is the bending stiffness of the pipe and L 0 is segment unstretched length. or contents pressure effects due to changes in inner diameter along the length of a line. and their directions are specified by the end orientation angles on the line data form. Accordingly you should exercise caution when interpreting results which depend on the local orientations of the line. The segment Euler load provides a check on the ability of the model to represent compressive loads and the deformations which result. the deformation being controlled by bending. Compression is Limited: No The segment is treated as a strut which can support unlimited elastic compression. This correctly models a chain or very flexible rope.12 Contents Flow Effects Introduction Contents flow effects are normally neglected when modelling pipes in OrcaFlex. At the ends of the line.w Theory. these local axes are referred to as the end axes Exyz. Px and Py are normal to the line axis. OrcaFlex has two modes for handling this. In the case of a chain. The model should be re-run with shorter segments in the affected area. For the first node ui is the end direction – this is taken to be the same as uo if the end is free and otherwise is taken to be the nomoment direction. respectively.u)(v2 . laρ. Contents flow into the node at velocity siui so the rate of input of momentum is ρaisi2ui. When multiplied by the mass of contents in the segment. The force on the contents that is required to achieve this change in flow direction must therefore be the rate of output of momentum minus the rate of input of momentum. 2lr (ω×u). to be the same as the internal cross section area of the end segment – i. For a midnode ui and uo are simply the unit vectors in the directions of the segments before and after the node.v1)) × u = 2r ( (u. uo. and ao for the last node. Similar treatment is applied to uo at the last node.v1) / l so the Coriolis force is given by 2r (u × (v2 .e. We define ai for the first node. Likewise the rate of output of momentum is ρaoso2uo.uo) This result agrees with the centrifugal term included in equation 10 of Gregory & Paidoussis.e. is the term 2ω×p' = 2ω×(r/aρ)u. i. 1996.(v2 . that is dependent on the rate of flow p' rather than p. Coriolis force due to movement of a segment Now consider a segment between two nodes n1 and n2 and consider the following two frames of reference: a fixed global frame and a moving local frame whose origin moves with node n 1 and whose z-axis always points in direction u = unit vector from n1 towards n2. For the common case of a uniform internal cross section the equation simplifies to Centrifugal Force on Node = ρas2(ui .(u. ui say. But ω is given by ω = u×(v2 .e.ρaisi2ui The resulting centrifugal force on the node must be equal and opposite to this. i.v1) . Line Theory Notation ρ = contents density a = internal cross sectional area s = contents flow velocity r = mass flow rate = ρas l = segment length p = position of node relative to fixed axes v = velocity of node relative to fixed axes u = unit vector in downstream direction of line ω = angular velocity of moving frame relative to fixed frame dx/dt = rate of change of any variable x relative to fixed axes x' = rate of change of any variable x relative to moving axes Centrifugal force on a node due to flow through a node First consider a node with flow arriving from one direction.e. and leaving in another direction. i. Similarly let ai and ao denote the internal cross sectional areas on the input side and output side. ρaoso2uo . so Centrifugal Force on Node = ρ(aisi2ui . this gives the Coriolis force on the segment.w Theory.aoso2uo) The theory above caters for the fully general situation where the internal cross section may vary along the line.v1))u ) 178 . we assume no change in internal cross sectional area at the line ends. Consider the contents of a segment. Its velocity relative to the moving axes is p' = (r/aρ)u So its velocity relative to the fixed axes is v1 + dp/dt = v1 + p' + ω×p Therefore its acceleration relative to fixed axes is d( v1 + p' + ω×p) )/dt = (v1 + p' + ω×p)' + ω × (v1 + p' + ω×p) = 0 + 0 + ω'×p + ω×p' + ω×v1 + ω×p' + ω×(ω×p) = ω'×p + 2ω×p' + ω×v1 + ω×(ω×p) and of these terms the only new one. These two tensions are related by the formula Tw = Te + (PiAi . We believe it is suitable for many cases of attached buoyancy and for non-structural linings. Te PiAi Tw PiAi PoAo node n Figure: Te Tw PoAo node n+1 segment mid-point Tension and Pressure forces 179 . (component of (v2 .PoAo) where Pi = internal pressure. The nodes either side represent a length of pipe plus its contents. a force of r .w Theory. (component of (v2 . The diagram below illustrates this and shows the tension and pressure forces present.(u-direction component of (v2 . to calculate Ai and Ao.StressOD2/4. Paidoussis M P & Deksnis E B. not the line type diameters.v1)) ) = 2r . 1976. Explanation of Wall Tension Formula To understand this formula and the difference between effective tension and wall tension. Ao = internal and external cross section areas of the stress annulus. This is equivalent to assuming that the annulus between the stress OD and line type OD carries an axial load which matches the ambient external pressure. More importantly.v1) . consider the forces acting axially at the mid-point of a segment. Below there it is calculated allowing for the static pressure head due to the instantaneous height difference between the point and the mean water level. the equation above is simply the force balance equation for this diagram. Other relevant references include: Paidoussis M P. OrcaFlex uses the stress diameters. 1970. Po is assumed to be zero at and above the mean water level.e. Pi is calculated from the contents pressure. If it is not suitable you should do your own separate calculation of wall tension and stresses.v1)) normal to u).13 Line Pressure Effects OrcaFlex reports two different types of tension – the effective tension (Te) and the wall tension (Tw).12. Line Theory = 2r ( (v2 . the forces on them are calculated as if the length of pipe represented had end caps which hold in the contents and which are exposed to the internal and external pressure. We then apportion this total Coriolis force on the segment into two equal parts – i.v1)) normal to u) on each of the two nodes at the ends of the segment. 1996. 5. Warning: Before using the wall tension and stress results you should confirm that this model is suitable for the case you are modelling. surrounding fluid) pressure. where StressID and StressOD are the stress diameters of the line type. Po = external (i.StressID2/4 and Ao = π. Paidoussis M P & Lathier B E. Note: Where the stress ID or OD differ from the corresponding line type diameter. 1970. and the annulus between the stress ID and the line type ID carries an axial load which matches the ambient internal pressure. The above result agrees with the Coriolis term included in equation 10 of Gregory & Paidoussis.e. Note: A mid node therefore receives two Coriolis force contributions – one each from the segments either side – but an end node only receives one such contribution. but it may not be suitable for bonded buoyancy or structural linings. given by Ai = π. Ai. respectively. allowing for the static pressure head due to the instantaneous height difference between the point and the specified reference Z level. local buckling of the pipe wall is determined by wall tension. Effective tension and resulting wall tension. Line Theory Notes: Both effective tension and wall tension are relevant to the question of pipe buckling. and the actual tension in the cable is the wall tension as defined above. which is a vector in the xy-plane. The pipe stress results are therefore only valid for things like steel or titanium pipes – they do not apply to composite structure flexible pipes.(ODstress2 . respectively. Pi and Po respectively.) For cables.(ODstress4-IDstress4) Iz = 2nd moment of stress area about Oz = 2Ixy 180 . It also assumes that the cylinder is made of a uniform material. with components Cx and Cy in the Ox and Oy directions. which is a vector in the z-direction with magnitude τ.w Theory. Torque. These are both vectors in the z-direction. the pressure terms do not apply and the effective tension is the true tension in the chain. the stress calculation assumes that the loads on the line are taken by a simple cylinder whose inside and outside diameters are given by the stress diameters specified on the line-types form. Consider a cross section through a mid-segment point. Shear force. at the cross section. which depends critically on details of the pipe construction and is therefore beyond the scope of the program. Curvature. For buckling of the pipe as an Euler strut. (Note that OrcaFlex does not model local buckling. Bend Moment. Oz along the pipe axis (positive towards End B) and Ox and Oy normal to the pipe axis (and so in the plane of the cross section). with magnitude M and components M x and My in the Ox and Oy directions. which is a vector in the xy-plane. On the other hand. with magnitude S and components Sx and Sy in the Ox and Oy directions.14 Pipe Stress Calculation OrcaFlex provides stress results that apply only to simple pipes. 5.IDstress2) Ixy = 2nd moment of stress area about Ox (or Oy) = (π/64). the internal pressure term P iAi does not apply. More precisely. For chains. which is also a vector in the xy-plane. The diagram shows the frame of reference used for the cross section. respectively. respectively. the external pressure term PoAo is still applicable.12. as specified on the line types form. as shown in the following diagram. In addition we define the following terminology: ODstress and IDstress = stress diameters. which has origin O is at the pipe centreline. A = cross sectional stress area = (π/4). the following values: Internal and external pressures. which are inherently discontinuous. effective tension is the governing parameter – when it is negative the strut is in effective compression. However. y y (Theta=90) R P C r End A Stress ID O z Stress OD Side View Figure: Theta O x (Theta=0) Cross-Section Frame of Reference for Stress Calculation The program calculates. umbilicals and ropes. with magnitudes Te and Tw respectively. C2 = bending.Z) where R is radially outwards.b/(ODstress/2)2 = -Po. In this case the above calculation is equivalent to assuming that the material in between ID and ID stress. σRR. are the radial. is transparent to pressure. C4 = stress loading factors (C1 = tensile. Notes: IDstress and ODstress are by default equal to the ID and OD specified on the line type form. as specified on the line types form. The wall tension is assumed to be uniformly distributed across the stress area. Consider the point P in the cross section shown as a black dot in the diagram.b/r2 σCC = Hoop Stress = a + b/r2 where a and b are the values that satisfy a . C2. which can be identified by its polar coordinates (r. circumferential (or hoop) and axial (or longitudinal) stresses. we define a local set of axes (R. Line Theory C1. σCC and σZZ. as specified on the line types form.15 Pipe Stress Matrix The pipe stress matrix at point P (see Pipe Stress Calculation) can be written as: σRR σRC σRZ σRC σCC σCZ σRZ σCZ σZZ These stress components are calculated as follows. Instead it is calculated directly from σ(·). Axial Stress (non-linear stress-strain) For a homogeneous pipe with non-linear stress-strain σZZ cannot be split into tensile and bending components because of non-linearity.C. they can be set to be different to ID and OD. This gives: σRR = Radial Stress = a . respectively. the stress at P is a symmetric 3×3 matrix of stress components (see Pipe Stress Matrix). that σRR = σCC = -Po. the specified stress-strain relationship: σZZ = σ(εZZ) where εt is the direct tensile strain εZZ is the axial strain. At P.Cycosθ) 181 .e. and between ODstress and OD. The internal pressure therefore applies right through to the ID stress and the external pressure applies right through to ODstress.12. OrcaFlex calculates this matrix and then derives stress results from it. 5. However. C3 = shear.b/(IDstress/2)2 = -Pi and a . If IDstress is zero. The stress generated by the above loads varies across the cross section. Radial and Hoop Stresses σRR and σCC are due to the internal and external pressure. C3. They are calculated using Lamé's equation for a thickwalled cylinder whose internal and external diameters are ID stress and ODstress. With respect to these axes. Axial Stress σZZ is the axial stress and is given by: σZZ = Direct Tensile Stress + Bending Stress where the Direct Tensile Stress is the contribution due to wall tension and Bending Stress is the contribution due to bend moment. C4 = torsional). then OrcaFlex assumes that external pressure applies throughout the structure – i. εZZ = εt + r(Cxsinθ . Diagonal Terms The three diagonal entries of the stress matrix.w Theory.Mycosθ)/Ixy where C2 is the bending stress loading factor. θ). For terminology see Pipe Stress Calculation. so its contribution is given by: Direct Tensile Stress = Tw/A The contribution due to bend moment varies across the cross section and is given by: Bending Stress = C2r(Mxsinθ . C is in the circumferential direction (positive in the direction of Theta increasing) and Z is parallel to Oz. above Fy = same as standard formula for Fy. The formulations are reviewed in Casarella and Parsons. above Fz = ±½Pρ(πDaL)Cdz|V|2 where the sign of Fz. Reber and Wilson.Sxsinθ)/A where C4 is the torsional stress loading factor. This formulation is preferred by some analysts for systems with near-tangential flow. then it is zero. including Richtmyer.w Theory. is the same as the axial component of the relative flow vector. and Vz parallel to the line axis. The drag forces applied to a line are calculated using the cross flow principle. That is.12. The formulations differ in how the drag force components vary with the incidence angle φ between the flow and the line axial direction. If torsion is not included in the model. using Morison's Equation are applied to the line. In the formulae below ρ = fluid density P = proportion wet or proportion dry. The other contributions are both due to the shear force. Cdx. It is appropriate for general flow conditions. Finally. Standard Formulation Fx = ½Pρ(DnL)CdxVx|Vn| Fy = ½Pρ(DnL)CdyVy|Vn| Fz = ½Pρ(πDaL)CdzVz|Vz| This formulation is the most commonly-used and was the formulation used by versions of OrcaFlex before a choice of formulation was introduced. since then the axial component of the flow vector is zero and so the direction of Fz is undefined. For the axial direction the drag area is taken to be the skin surface area πD aL where Da is the axial Drag / Lift diameter.e. The components of drag force normal to the line axis are then based on V n. There is a choice of the following three possible drag formulations for the drag force components (F x. whether it is towards End A of the line or towards End B. the fluid velocity relative to the line Vr is split into its components Vn normal to the line axis. 182 . Fz) in the local line directions. It has been proposed or used by various authors. and its x and y-components Vx. as appropriate. The contribution C4τr/Iz in the above equation is the shear stress contribution due to torque. Cdy and Cdz. Fy. since the matrix is symmetric. σCZ = C4τr/Iz + C3(Sycosθ . but there are in fact only 3 independent terms. For the directions normal to the line axis (x and y) the drag area is taken to be the projected area D nL where Dn is the normal Drag / Lift diameter and L is the length of line represented by the node. Pode Formulation Fx = same as standard formula for Fx.16 Hydrodynamic and Aerodynamic Loads Drag Both hydrodynamic and aerodynamic drag forces. but can also be modified to model wake interference from other lines upstream. Warning: The Pode formula for Fz is discontinuous at φ = 90. Note: Aerodynamic drag is only included if the Include wind loads on Lines option is enabled in the Environment data. which is assumed to be uniformly distributed across the stress area. i. 5. and the drag areas appropriate to each direction. The same drag formulation is used for hydrodynamic and aerodynamic drag forces. They are given by: σRC = 0 σRZ = C3(Sxcosθ + Sysinθ)/A where C3 is the shear stress loading factor. see Sparks (1980) and Sparks (1984). The drag force formulae use drag coefficients. The drag coefficients are specified on the line type data form. Vy. Line Theory Off-Diagonal Terms The 6 off-diagonal terms are the shear stresses. The component of drag force parallel to the line axis is based on Vz. for two useful references on this subject. In this case OrcaFlex sets Fz to zero. Standard: |Fn| = Rsin2φ |Fz| = Rμ.w Theory. Cd2 is the Drag Coefficient away from the Seabed. This scaling factor is equal to cos θ where θ is the angle of the line axis to the seabed plane. Also. The drag coefficients Cd1 and Cd2 can be specified as varying with Reynolds number which allows specification of a drag force which varies with both Reynolds number and Height above seabed.e. and let φ be the incidence angle between the flow vector V and the line axis.|Vn|) Fy = ½Pρ(DnL)CdyVy|Vn| + ½Pρ(πDaL)CdzVy(|V| . This is the transverse direction that is normal to the line axis and in the seabed plane. Reynolds number can be calculated in a number of different ways. Then the formulations can be expressed as follows. The actual drag coefficient used by the OrcaFlex calculation is given by: Cd = λCd2 + (1-λ)Cd1 where Cd1 is the Drag Coefficient on the Seabed. i. You should set the Reynolds number calculation data to match the data source used for your variable drag coefficient data. The drag variation factor λ is a function of the normalised height above the seabed. Then Vz = Vcos φ and Vn = Vsin φ. allowing for contact diameter. h. ut is the flow direction for lift purposes = (un × uz)/|un × uz|. These data are all defined on the variable data form. Vt is component of Vr in the transverse direction ut.cos2φ Pode: |Fz| = Rμ Eames: |Fn| = Rsin2φ |Fn| = R{(1-μ)sin2φ + μsin φ} |Fz| = Rμcos φ Drag coefficient variation with Reynolds number and Height above seabed The normal drag coefficients Cdx and Cdy can be specified to vary with Reynolds number. Cd(Re). λ is the Drag Variation Factor. This is the direction normal to the line axis and in the plane of that axis and the seabed normal. uz is the unit vector in the node z-direction. ul is the unit vector in the lift force direction = (uz × ut)/|uz × ut|.|Vn|) Fz = ½Pρ(πDaL)CdzVz|V| Drag Force Variation with Incidence Angle The above formulae for the drag force components can be re-written in a form that highlights how the drag force varies with incidence angle. Lift The hydrodynamic lift force is defined to be: FLIFT = P|un × uz|(½ρ(DnL)Cl|Vt|2)ul where un is the unit vector in the seabed outward normal direction. Similarly. as specified by the Reynolds number calculation data. for nodes well away from the seabed we expect Cd to be equal to Cd2 and so λ should equal 1 for large values of h/Dn. h/D n. We define h to be the vertical height above the seabed of the underside of the node. Line Theory Eames Formulation for bare cables Fx = ½Pρ(DnL)CdxVx|Vn| + ½Pρ(πDaL)CdzVx(|V| . Alternatively the normal drag coefficients can be specified to vary with Height above Seabed. The purpose is to scale down the lift force as the line axis becomes more inclined to the 183 . The variable data table specifies the drag coefficient as a function of Reynolds number. For nodes lying on the seabed Cd should equal Cd1. Consider the case where the line is axially symmetric. The lift force magnitude has been scaled by |u n × uz|. let: R = ½Pρ(DL)Cdn|V|2 μ = πCdz/Cdn = (drag force in axial flow) / (drag force in normal flow of same velocity) Fn = the normal component of the drag force. Cl is the lift coefficient. In this case h/d=0 and so λ(0) should equal 0. Cdx = Cdy = Cdn say. the line is subject to two added mass effects: Its effective mass is increased by CaMF where MF is the mass of the fluid displaced (taking into account the proportion wet) and Ca is the added mass coefficient specified for that direction. This direction is determined by the relative velocity of the water past the chain – the faster the flow then the greater the angle of the drag chain to the vertical. 5. In this case h/d=0 and so α(0) should equal 1. where AF is the component (in that direction) of the acceleration of the fluid (relative to the earth) and C m is the inertia coefficient for that direction. In this case the actual lift coefficient used by the OrcaFlex calculation is given by: Cl = αCl1 where Cl1 is the Seabed Lift Coefficient. instead of per unit arc length. The effect of the factor is equivalent to assuming that the standard lift force formula gives the lift force per unit projected length. If the line axis is parallel to the seabed plane this factor is 1 and so it has no effect. By projected length we mean the length of the projection of the node onto the seabed plane. You should set the Reynolds number calculation data to match the data source used for your variable lift coefficient data. For each of these directions. Reynolds number can be calculated in a number of different ways. 184 . If the fluid is accelerating then the line experiences a fluid acceleration force given by C mMFAF. The force consists of the tension in the drag chain and so is in the direction in which the chain is hanging. until when θ = 90 the factor is zero and so no lift force is applied. Note that pressure effects of flow rate are not included. For nodes well away from the seabed the lift effect dies away and we expect Cl to be equal to 0. The lift coefficient decay factor α is a function of the normalised height above the seabed. Added Mass The added mass effects on a line are calculated separately for the local x. if the line accelerates then it experiences an extra inertial force (due to added mass) given by -CaMFAL where AL is the component (in that direction) of the acceleration of the line (relative to the earth). The lift coefficient Cl1 can be specified as varying with Reynolds number which allows specification of a lift force which varies with both Reynolds number and Height above seabed. But as the line axis inclines to the seabed plane the factor reduces. h/D n. As a result. These data are all defined on the variable data form. α is the Lift Coefficient Decay Factor. Fluid Flow If the mass flow rate of the Line is non-zero then the centrifugal and Coriolis effects due to this flow are included.17 Drag Chains A drag chain is an attachment to a line that applies a force to the node to which it is attached.w Theory.12. Another way of thinking about this factor is that it generalizes the standard lift force formula F LIFT = (½ρDnLCl|Vt|2)ul to cases where the line axis is inclined to the seabed. So α should equal 0 for large values of h/D. Typically Cm = 1 + Ca and in this case the fluid acceleration force can be written as MFAF + CaMFAF where the first term is called the Froude-Krylov force and the second term is called the added mass force. Line Theory seabed plane. This is now described in more detail. Lift coefficient variation with Reynolds number and Height above seabed The lift coefficient can be specified to vary with Reynolds number in an identical manner to drag coefficients. y and z-directions. Alternatively the lift coefficient can be specified to vary with Height above Seabed. For nodes lying on the seabed Cl should equal Cl1. as specified by the Reynolds number calculation data. 90 and the normal and axial drag forces are given by: Fn = normal drag force = ½ρ(LD)Cdn(α)Vn|Vn| Fa = axial drag force = ½ρπ(LD)Cda(α)Va|Va| where Vn = normal component of relative velocity = |V|sin α Va = axial component of relative velocity = |V|cos α ρ = water density Cdn(α). Because the tensile force being applied by the line is axial to the chain. is then applied to the line. The fluid drag on the chain. In other words. The remaining net force on the chain in the axial direction. the direction in which the drag chain hangs is that in which the chain is in force balance in the direction normal to the chain.w Theory. W. in OrcaFlex. OrcaFlex therefore hangs the chain in the same vertical plane as the relative velocity vector V and at angle θ to the vertical. OrcaFlex calculates the angle θ by iterating until the sum of the normal components of drag force and wet weight is zero. Line Theory Vn V A Va Connection to Line -90 Drag Chain Wa Wn W Figure: 180- Drag Chain Consider the drag chain shown in the above diagram. the wet weight of the chain is steadily reduced as the chain becomes supported by the seabed. Let D = drag chain effective diameter L = drag chain length θ = drag chain declination from vertical V = horizontal relative velocity = (horizontal fluid velocity at A) – (horizontal node velocity at A). that as the chain is lowered down onto the seabed. interact with the seabed in a fairly simplistic way that is designed to achieve the following two primary effects of seabed interaction: Firstly. Then the incidence angle α between the horizontal relative velocity vector V and the drag chain is α = θ . 185 . Cda(α) = normal and axial drag coefficients for this incidence angle. The inertia of the drag chain is assumed to be small enough to be neglected. The tension being applied by the line at the top of the chain. Drag Chain Seabed Interaction Drag chains. so we assume that the drag chain is always in equilibrium under the action of 3 forces: The chain's wet weight. Fa. the components of wet weight and drag normal to the chain must balance. OrcaFlex reports a value for End Force and End Ez-Angle.12. and so is done with the chain vertical. the diagonal line switches corners but the proportion wet varies continuously. 5. See Modelling Line Ends.12. and the various forces are attributed to nodes at each end. the supported chain also moves laterally (but below the node) and so generates a friction force that is then applied to the node.PW. As the node moves laterally. and the hydrostatic and dynamic forces are attributed to the appropriate node. This means that if current drag causes the chain to hang at an angle to the vertical then the supported length will generally have been overestimated and the hanging length correspondingly underestimated. we use the diagonal line joining the highest point on the segment circumference. where μ is the friction coefficient and R is the seabed reaction. The end force and angle values provide the basis for the design of end fittings such as bend stiffeners. Note that the division of the drag chain into a hanging length and a supported length is done before the hanging length is analysed. the Proportion Wet could be calculated from the intersection of the segment centreline axis with the free surface. with the lowest point at the 'wet' end. that if the chain is dragged across the seabed then an opposing friction force μR is generated. A B Proportion Wet = B / (A+B) Figure: Proportion Wet for a surface-piercing segment This surface-piercing model enables OrcaFlex to model systems such as floating hoses. The intersection of the diagonal line with the surface continues to give the appropriate Proportion Wet result. It assumes that the chain hangs vertically straight down from the line. However please note the following points when modelling such systems: 186 . OrcaFlex uses a simple but effective modification of this concept. As the segment passes through the tangent position. OrcaFlex first calculates how much of the drag chain would be supported by the seabed. Line Theory Secondly. this simple approach breaks down when the segment is tangent to the surface. If the curvature is large. the connection at the line end is modelled as an isotropic ball-joint with a rotational stiffness and a preferred no-moment direction.19 Interaction with the Sea Surface OrcaFlex Lines are subdivided into segments. For a partially submerged segment. the hydrostatic and hydrodynamic forces are proportioned depending on how much of the segment is submerged – the Proportion Wet (PW). Proportion Wet is available as a line result variable. the calculated value is accurate only if sufficiently short segments have been used to model the line near its end. see the diagonal line in the figure below. at the 'dry' end. For this reason. The seabed interaction model used is as follows: At any given time. The inclusion of end stiffness allows the program to calculate the curvature and bending moment at the termination. However. Instead of using the centreline axis. The supported part of the chain is modelled as if it is lying on the seabed directly beneath the node to which the chain is attached. and the magnitude of the angle between the end force vector and the no-moment direction. 5. For a segment whose axis is normal to the surface. This is an inaccuracy that cannot easily be avoided at the moment. A rotational stiffness of zero simulates a freely rotating end.w Theory. and a value of Infinity simulates a clamped end. The drag chain is then considered as being made up of two parts – the supported part and the remaining hanging part. containment booms and wave suppression systems. Vessel motion is automatically accounted for. We also define Proportion Dry (PD) as PD = 1 .18 Line End Conditions Except for Free Ends. The hanging part of the chain is then analysed as described above. These are the magnitude of the end force. and these are the two points that are minimum 187 . you must set Clash Check to "Yes" and set the Contact Stiffness to a non-zero value. The facility to suppress clash modelling (by setting Clash Check to "No") has been included because the clashing algorithm is time consuming.a line can clash with itself. d. for both lines. as follows.w Theory. Note: Line clashing is not modelled during statics. It is therefore best to suppress clash modelling on all sections that will never clash with other lines. allowing for the contact diameter. which is taken to be contact diameter multiplied by the length of line represented by the node. when the explicit solver is in use. For cases of practical dynamics. If your hose is flexible. A = contact area. Let p 1 and p2 be the two points of closest proximity – i. Multiple contact points along the line length are allowed for. The program uses constant drag and added mass coefficients for the floating hose. or if you are not interested in the effects of clashing. Let the radii of the two segments be r1 and r2 (as defined by the line type contact diameter). First OrcaFlex calculates the shortest separation distance. Calculating the Clash Force OrcaFlex checks for clashing between any two line segments for which clash checking is enabled and the contact stiffness is non-zero (for both segments involved). nodes experience a damping force.12. Line Theory A consequence of this model is that a hose floats in still water as a wall-sided body. or just awash. In addition.12. Line Clashing Data To include clash modelling between two lines.e. between the centrelines of the two segments.21 Clashing OrcaFlex provides two different ways of modelling contact between lines: the Line Contact model and the Line Clashing model. The clash check between segment S1 (on line L1) and segment S2 (on a different line L2) is done as follows. and neglects friction. For details see Seabed Theory and Shapes Theory. This is a developing area and we would appreciate feedback from users. Finally. In this case OrcaFlex applies equal and opposite clash contact forces to the 2 segments to push them apart. When modelling floating hoses. If d < (r1 + r2) then the lines are in contact. OrcaFlex assumes constant spring stiffness and damping values. and fewer segments are required. The force algorithm is described below. If d ≥ (r 1 + r2) then the lines are not in contact and no contact force is applied. The two segments do not need to be in different lines . p1 is on the centreline of segment S1 and p2 is on the centreline of segment S2. The clashing model is described below. but it does mean that if you check the immersion depth of a hose in still water you may find the answer slightly wrong if the hose is very buoyant. and it permits lines to separate again after contact. Clashing behaviour can be difficult to understand and it is not always obvious what the results mean and how they should be used in practice. 5. The contact occurs at the outer edge of the line. it is important to have enough segments to model the local curvature. friction forces can also be included. You can also specify the Contact Damping value. in other words OrcaFlex does not take account of the variation in water plane area with draft that arises from the circular cross section. For a summary of the differences. and the waves are short. 5.20 Interaction with Seabed and Shapes Nodes are also subjected to reaction forces from the seabed and any Shapes with which they come into contact. d = depth of penetration. we would be very pleased to hear of it. The reaction force is given by: Reaction = KAd where K = stiffness of the seabed or shape. as specified by the contact diameter. advantages and disadvantages of the two models see Line Contact versus Line Clashing. and the user has to select appropriate values based on the average immersion depth. then you will need at least ten and preferably twenty segments per wave to model the curvature properly. this simplification is of minor importance. The following notes expand on the way the calculations are carried out by the software and give our suggestions on interpretation. It pushes lines apart again if they try to pass through another. However a stiff hose tends to bridge the wave troughs. Unfortunately the literature is of limited help – if you know of any good data source. w Theory, Line Theory distance d apart. Also, let u be the unit vector in the direction from p 1 towards p2. Then the magnitude of the clash contact force applied is given by: F = (Stiffness Term) + (Damping Term) where the two terms on the right are documented below. A force of this magnitude F is applied to segment S 1, at p1, in direction -u. And the equal and opposite force is applied to segment S2, at p2, in direction +u. The stiffness term is given by: Stiffness Term = k(d - [r1 + r2]) where k = 1 / (1/k1 + 1/k2) is the combined contact stiffness of the segments. Here k 1 and k2 are the contact stiffnesses of the two segments, as specified in the Line Types data. The damping term is based on the rate of penetration, v, which is the u-direction component of p1's velocity relative to p2. If v≤0 then the two segments are moving apart and then no damping force is applied. If v>0 then the penetration is increasing and the damping term is then given by: Damping Term = cv where c is the combined contact damping value of the two segments, which is given by: c = 0 if c1=0 or c2=0 c = 1 / (1/c1 + 1/c2) otherwise. Here c1 and c2 are the contact damping values of the two segments, as specified in the Line Types data. How the Clash Force is Applied and Reported In general, clashing will take place between one segment of one line and one segment of another (the probability of a clash occurring exactly at a node is very small unless you take special measures to make it happen). OrcaFlex determines the force as just described, and reports the force as a segment variable – i.e. when you ask for the clash force at a particular arc length along the line, the force reported is the clash force for the segment which contains the specified point. If multiple clashes occur simultaneously on the same segment then the Line Clash Force reported is the magnitude of the vector sum of the clash forces involved. In the OrcaFlex model, all forces act at the nodes, so the clash force has to be divided between the two nodes at the ends of the segment in which the force acts. The force is divided in such a way that the moments of the two forces about the contact point are equal and opposite. Interpreting the Results Contact between lines can be a violent impact at high relative velocity, or a gentle drift of one line against another, or anything in between. We need to view the results in different ways for different sorts of contact. The following notes give some general guidance based on our experience, but in difficult cases it is essential that users develop their own understanding of the underlying physics, and confirm it by sensitivity analysis. OrcaFlex provides three measures of the severity of a clash event: Clash force. Clash impulse (integral of contact force times time – a measure of momentum transfer). Clash energy (calculated by integrating the magnitude of clash force with respect to depth of penetration). There are 3 types of OrcaFlex results which can be used for analysing clashing: 1. Time Histories of Clash force and Clash impulse. 2. Range Graphs of Clash force. 3. The Line Clashing Report contains Clash force, Clash impulse and Clash energy, together with a host of other details about clash events. Low Speed Contact Where one line drifts quite slowly against another as a result of weight or drag forces, then the contact is essentially quasi-static. The clash force at the point of contact is the best measure of what is happening, and will be insensitive to segmentation and contact stiffness. High Speed Impact The case of violent impact at high speed is much more complicated. Contact forces arrest the relative movement of the lines over a very short time interval. Momentum is transferred from the faster moving to the slower moving line. Kinetic energy at the moment of impact is converted partly to local strain energy at the point of contact, and partly to axial and bending strain energy elsewhere in the lines. 188 w Theory, 6D Buoy Theory If the discretisation of the lines is sufficiently fine, the contact stiffness value is correct, and contact damping is small, then OrcaFlex models the impact correctly, and all the reported results (force, impulse, energy) are correct. In practice, however, contact stiffness is rarely known with any precision, and it may not be practicable to discretise the line sufficiently to represent the deformation of the line axially, or particularly in bending, following a violent impact. (Deformation of the colliding cross sections is represented by the contact stiffness.) Under these circumstances, we need a measure of clash severity which is both meaningful for engineering purposes, and insensitive to discretisation and contact stiffness. Of the three measures available: Maximum clash force reduces with reducing contact stiffness and is usually the least reliable measure. Impulse is generally insensitive to changes in contact stiffness, though this may be masked where the change in stiffness causes a change in the character of the impact. (For example, a high contact stiffness may give rise to a single impact followed by a large rebound. Reducing stiffness can reduce the rebound to such an extent that the single impact is replaced by a double impact.) Impulse is also fairly insensitive to changes in segmentation. Unfortunately, however, impulse is not a convenient measure for engineering purposes. Energy is the most convenient practical measure of potential damage. This may be sensitive to contact stiffness, where there is a fairly equal distribution of strain energy between contact and other elastic deformations of the system, but if contact strain energy is the dominant component, then sensitivity is reduced. Contact strain energy is also sensitive to discretisation: longer segments give higher values of contact strain energy. This means that the reported strain energy for a coarsely segmented model is generally conservative. In practical cases, it may be possible to reduce segment length sufficiently to show that contact strain energy is below damaging levels, without needing to go to the very fine discretisation which might be required for an accurate value. Sensitivity to time step Clash events are often intermittent and short lived. Consequently, simulations of clash events can be sensitive to the choice of time step. For explicit integration this is usually not an issue because use of the explicit solver typically necessitates the use of short time steps. However, when implicit integration is used, you should take extra caution when interpreting clashing results because of the longer time steps allowed by the implicit solver. We recommend that you carry out sensitivity studies to show that the time step in use is sufficiently short. Damping Linear damping is included in the OrcaFlex contact model, and contributes to the reported clash force, impulse and energy results. 5.13 6D BUOY THEORY 5.13.1 Overview This and subsequent topics give the formulae used for the forces and moments applied to a 6D Buoy. Note that for a spar buoy there is also some more detailed documentation available on our website: www.orcina.com/Resources/TechNotes/SparBuoyEquationOfMotion.pdf. The buoy is treated as a rigid body with 6 degrees of freedom, 3 translational and 3 rotational. The equation of motion has the following contributions. Weight The weight force of Mass . g is applied at the centre of mass. Buoyancy Lumped buoys The buoyancy force on a lumped buoy is given by: Buoyancy Force = ρgVwet and this buoyancy force is applied vertically upwards at the centre of wetted volume, which is taken to be (1-PW)H/2 below the specified centre of volume. In these formulae: ρ = sea density g = acceleration due to gravity Vwet = wetted volume = PWV 189 w Theory, 6D Buoy Theory PW = proportion wet = Hwet/H V = volume is as specified on the buoy data form Hwet = wetted height = ½H + (depth of the specified centre of volume below the surface), where depth here is negative if the centre of volume is above the surface, and then 0 ≤ Hwet ≤ H H = height as specified on the buoy data form. These formulae make the proportion wet PW, the buoyancy force and the point of application of that force, all vary linearly with vertical position of the centre of volume relative to the surface, as follows: When the centre of volume is H/2 or more above the surface, PW = Hwet = Vwet = 0, and the buoyancy force is zero. When the centre of volume is on the surface, PW = ½ and the buoyancy force is half the fully-submerged Archimedean buoyancy, and it is applied H/4 below the surface, i.e. half way along the assumed Hwet. When the centre of volume is H/2 or more below the surface, then P W = 1 and the buoyancy force is the fullysubmerged Archimedean buoyancy, and it is applied at the centre of volume. This model behaves as if the specified Buoy Volume is in the shape of a cylinder, of length equal to the specified Buoy Height and with its centre attached to the buoy at the specified centre of volume, but such that the cylinder pivots about that centre of volume in order to always keep its axis normal to the instantaneous water surface tangent plane. Warning: This lumped buoy surface-piercing model is not realistic or accurate – OrcaFlex does not have enough geometry information for lumped buoys to model the surface-piercing accurately. It is just a simple way to give a buoyancy force, wetted volume and centre of wetted volume that vary in the right sort of way as the buoy passes through the surface. The model gives no contribution to roll and pitch stiffness from free surface effects when the buoy pierces the surface, so static stability of a floating Lumped Buoy is therefore not correctly represented. To model surface-piercing accurately you will need to use a Spar Buoy or Towed Fish, or multiple such buoys connected together to represent the actual buoy geometry. Spar buoys and Towed Fish For spar buoys and towed fish, separate buoyancy forces are calculated and applied to each cylinder. The buoyancy force on an individual cylinder is given by: Buoyancy Force = ρgVwet where Vwet is the volume of that part of the cylinder that is below the water surface. This force is applied vertically upwards at the centroid of that wetted volume. Note: If added mass and damping of a Spar Buoy or Towed Fish is specified by Values for Each Cylinder then the instantaneous water surface is used for this buoyancy calculation. But if the added mass and damping is specified by RAOs and Matrices for Buoy then the (horizontal) mean water surface is used; this excludes wave buoyancy effects, which are assumed to be included in the RAOs. Hydrodynamic Loads In general, the hydrodynamic loads are calculated using Morison's equation with additional components as discussed below. The exception to this is if the added mass and damping effects on a spar buoy are specified by giving wave load RAOs and added mass and damping matrices. For a lumped buoy the hydrodynamic loads on the buoy are calculated using the fluid kinematics at the buoy centre of wetted volume. These loads are scaled by the buoy Proportion Wet and applied at the centre of wetted volume. For details of the hydrodynamic loads see Lumped Buoy Theory: Added Mass, Damping and Drag. For a spar buoy or towed fish the calculation of hydrodynamic loads depends on the form of added mass and damping chosen. If the added mass and damping are specified by Values for each cylinder, then all the hydrodynamic loads are calculated and applied separately on each cylinder. The hydrodynamic load on a cylinder is applied at the centroid of wetted volume of the cylinder and is scaled by the Proportion Wet of the cylinder. The water surface is assumed to be the tangent plane to the instantaneous wave surface directly above the centre of the cylinder; this therefore allows for the buoyancy variation due to the wave. If the added mass and damping are specified by RAOs and matrices, then the wave loads, added mass and damping are calculated for the whole buoy, using the specified RAOs and matrices, and they are applied at the specified RAO, Added Mass and Damping Origin. The buoyancy and drag loads are calculated and applied for each cylinder, as described above, except that in this case the buoyancy load is calculated using the (horizontal) 190 w Theory, 6D Buoy Theory mean water surface instead of the instantaneous wave surface. The effect of this is to exclude the wave contribution to buoyancy load, which is assumed to be included in the specified wave load RAOs. For details see Spar Buoy and Towed Fish Theory: Added Mass and Damping and Spar Buoy and Towed Fish Theory: Drag. Hydrodynamic Damping (linear) You can apply additional damping forces and moments that are directly proportional to the fluid velocity and angular velocity relative to the buoy. See Lumped Buoy Damping and Spar Buoy and Towed Fish: Added Mass and Damping. The main use of these terms is to represent wave radiation damping for surface buoys. Values may be obtained theoretically from a 3D diffraction model of the body or, more commonly, from empirical results such as a roll decay test. Hydrodynamic Moments Rotation of the body relative to the fluid generates hydrodynamic moments which are analogous to the hydrodynamic forces given by Morison's equation. OrcaFlex includes facilities for calculating these moments. For Lumped Buoys, rotational hydrodynamic properties are included for damping, drag and added inertia components. For Spar Buoys, drag moment data only are included. In all cases, the fluid moments are calculated based on the angular velocity and acceleration of the buoy, without any contribution due to angular velocity and acceleration of the fluid. This is because the sea is treated as being irrotational, so there is no unique definition of fluid angular velocity and angular acceleration at a point. The sea angular velocity and acceleration are therefore taken to be zero. If you are in any doubt as to the correctness of the model, then we recommend setting the moment terms to zero. Hydrodynamic moments will then be omitted completely for a Lumped Buoy. For a Spar Buoy represented by several cylindrical sections, moments will be generated automatically as a result of the distribution of hydrodynamic forces along the buoy axis. Estimation of Hydrodynamic Properties See technical note Buoy Hydrodynamics. 5.13.2 Lumped Buoy Added Mass, Damping and Drag Added Mass and Inertia Specified by diagonal values The buoy inertia for translational motion is increased, for each local axis direction, by: Added Mass = PW . Ca . HydroMass where HydroMass and Ca are the reference hydrodynamic mass and added mass coefficient for translations in that direction. The buoy inertia for rotational motion is increased, for each local axis direction, by: Added Inertia = PW . Ca . HydroInertia where HydroInertia and Ca are the reference hydrodynamic inertia and added mass coefficient for rotations about that direction. Specified by full matrices The buoy inertia, considered with respect to local axes and applied at the centre of wetted volume, is increased by: Added Mass = PW . AM where AM is the full 6×6 added mass matrix. Fluid Inertia Loads Specified by diagonal values The fluid inertia force applied in each local axis direction is given by: Force = PW . Cm . HydroMass . A where HydroMass and Cm are the reference hydrodynamic mass and Cm coefficient for that direction, and A is the component, in that direction, of the local water particle acceleration relative to the earth. No fluid inertia moment is applied, since the sea is treated as irrotational so its angular acceleration is taken to be zero. 191 w Theory, 6D Buoy Theory Specified by full matrices The fluid inertia load, considered with respect to local axes and applied at the centre of wetted volume, is given by the matrix equation: Load = PW . IM . af where Load is the vector [Fx, Fy, Fz, Mx, My, Mz]T where Fx, Fy, Fz, Mx, My and Mz are the components of force and moment with respect to local axes, IM is the full 6×6 fluid inertia matrix, af is the vector of fluid acceleration components [af,x, af,y, af,z, 0, 0, 0]T, af,x, af,y and af,z are the components in the local buoy axes directions, of the local water particle acceleration relative to the earth, and the three zeros in af are the fluid angular acceleration components, which are taken to be zero since the sea is treated as irrotational. Damping The damping force applied in each local axis direction is given by: Fx = - PW.UDFx.Vx Fy = - PW.UDFy.Vy Fz = - PW.UDFz.Vz where UDF is the Unit Damping Force and V is the buoy velocity, either relative to the earth or relative to the fluid velocity (as specified in the buoy data). Similarly, the damping moment applied about each local axis direction is given by: Mx = - PW.UDMx.ωx My = - PW.UDMy.ωy Mz = - PW.UDMz.ωz where UDM is the Unit Damping Moment and ω is angular velocity of the buoy. Note that ω does not include any contribution from fluid angular velocity, since the sea is treated as irrotational so its angular velocity is taken to be zero. Drag The drag force applied in each local axis direction is given by: Fx = - PW.½.ρ.Cdx.Ax.Vx.|V| Fy = - PW.½.ρ.Cdy.Ay.Vy.|V| Fz = - PW.½.ρ.Cdz.Az.Vz.|V| where A is the Drag Area, Cd is the Drag Coefficient and V is the buoy velocity relative to the water velocity. The drag moment applied about each local axis direction is given by: Mx = - PW.½.ρ.Cdx.AMx.ωx.|ω| My = - PW.½.ρ.Cdy.AMy.ωy.|ω| Mz = - PW.½.ρ.Cdz.AMz.ωz.|ω| where AM is the Moment of Area, Cd is the drag coefficient for rotation and ω is angular velocity of the buoy. Note that ω does not include any contribution from fluid angular velocity, since the sea is treated as irrotational so its angular velocity is taken to be zero. 5.13.3 Spar Buoy and Towed Fish Added Mass and Damping The first order hydrodynamic loads on a spar buoy or towed fish can be modelled in two different ways: either by values for each cylinder or by wave load RAOs and matrices for the whole buoy. Loads specified by Values for Each Cylinder When you choose values for each cylinder, the added mass and damping effects are calculated separately for each cylinder. The resulting effects (force, moment, increased mass and rotational inertia), for each cylinder, are applied at the wetted centroid of the water displaced by that cylinder. Added Mass – constant coefficient In its simplest form, the added mass load on each cylinder follows Morison's equation, the relevant part of which may be written as 192 w Theory, 6D Buoy Theory F = (Δ + Δ Ca)af - Ca Δ ac where F is the added mass load on the cylinder Δ is the reference mass, the mass of fluid displaced instantaneously by the cylinder Ca is the constant added mass coefficient for the cylinder af is the fluid acceleration relative to earth ac is the cylinder acceleration relative to earth. The first term in this expression can also be written as (1+C a) Δ af, and this is the form which is applied when the added inertia coefficient Cm is assigned the value '~'. The '1' in (1+C a) represents what is known as the FroudeKrylov force; the 'Ca' term gives rise to the added mass force. C m may also take a numerical value, and so the more general form for the added mass load on a cylinder is F = Cm Δ a f - C a Δ a c where '~' for Cm is understood to mean the usual (1+Ca) form. Thus far, we have only considered translational added mass and inertia. The rotational effects are simpler: since we deem the sea to be irrotational, the rotational fluid acceleration is zero and there is no rotational analogue of the C m Δ af term. We are left with an added moment of inertia due to the cylinder's angular acceleration: M = - PW Ia Ω'c where M is the added inertia moment on the cylinder PW is the instantaneous proportion wet of the cylinder, ie the proportion which is submerged Ia is the added moment of inertia for the cylinder Ω'c is the cylinder angular acceleration (relative to earth). In terms of components in buoy local axes directions then, consider a spar buoy, for which the cylinder axis direction is the buoy z-direction. The total force and moment in these directions, due to added mass, are Fx = Cmn Δn afx - Can Δn acx Fy = Cmn Δn afy - Can Δn acy Fz = Cma Δa afz - Caa Δa acz Mx = - PW Ian Ω'cx My = - PW Ian Ω'cy Mz = - PW Iaa Ω'cz where the subscripts n and a denote the normal and axial components respectively. The components of the displaced reference mass, Δn and Δa, need particular care for hollow cylinders; these are described below For a Towed Fish the cylinder axis direction is instead the buoy x-direction. So for a Towed Fish the subscripts x and z in the above equations are interchanged, so that the axial values of the coefficients and reference masses and inertias are used in the equations for Fx and Mx, and the normal direction values are used in the equations for F z and Mz. Added Mass – variable coefficient You may, if you wish, specify the normal added mass coefficient Can in a more elaborate form, using tabular variable data. Using a constant value, as above, means that the variation with depth of the added mass load is calculated by OrcaFlex through the displaced mass (for force) and proportion wet (for moment); choosing instead a variable form for Can means that the data become the source of the variation with depth. Specifically, you define the values of C an corresponding to a range of values of normalised submergence, h/s, in a generalisation of DNV RP-H103 3.2.13. This allows a more precise definition of the variation of added mass with submergence than the constant coefficient. It also lets you define the nature of any variation when the cylinder is fully submerged, which is not possible for the constant coefficient case (since, when fully submerged, the displaced mass is constant). As all the variation is in the coefficient values, the reference mass is constant in this case; we take it to be the mass of fluid displaced by the whole of the cylinder volume were it to be fully submerged, regardless of its actual instantaneous submergence and (for a hollow cylinder) as if its ends were closed (see Reference Fluid Mass below). We denote this fully-submerged reference mass by Mn. Since the axial added mass coefficient Caa and the added inertia Cm and added moment of inertia Ia are here always of the constant form and not allowed by OrcaFlex to be variable, only the normal translational components differ under variable added mass. For a spar buoy, these components are F x and Fy, and writing Can(h/s) to signify the variable data form for Can, these components become for Cm ≠ ~ 193 w Theory, 6D Buoy Theory Fx = Cmn Δn afx - Can(h/s) Mn acx Fy = Cmn Δn afy - Can(h/s) Mn acy and for Cm = ~ Fx = (Δn + Can(h/s) Mn) afx - Can(h/s) Mn acx Fy = (Δn + Can(h/s) Mn) afy - Can(h/s) Mn acy. Again, for a towed fish we simply interchange the x- and z-directions, so the axial terms are used in the equations for Fx and Mx, and the normal terms for Fz and Mz. Notes: If you choose to use variable added mass, you must provide data for at least two values of normalised submergence h/s. The smallest value of h/s must be -1 (corresponding to the cylinder just about to enter the water), and on physical grounds the corresponding C a value must be zero. There is no upper limit on the range of h/s: the data will be truncated at both ends of the range. Added mass is frequency-dependent, so you should take care to use data which correspond to the response frequency for your particular model. DNV, RP-H103, 3.2.13, for instance, provides a graph of Ca against h/s, but this represents the high-frequency limit so may well be inappropriate for your own model. Reference Fluid Mass and Inertia For motion normal to the cylinder axis, the value used for the displaced reference fluid mass Δ n is the mass of the fluid displaced by the submerged part of the whole of the cylinder cross section. So, if the cylinder is hollow (i.e. inner diameter is non-zero), Δn includes the fluid trapped inside the part of the cylinder that is below the surface. The fully-submerged reference mass Mn for the normal direction follows the same rule: if the cylinder is hollow, then Mn includes the fluid trapped inside the whole cylinder. In effect, a hollow cylinder is treated as if it were solid when determining the normal reference fluid mass Δn or Mn. For motion parallel to the cylinder axis, the value used for the axial reference fluid mass, Δ a, does depend on whether the cylinder is hollow. If it is not hollow, then Δa is the same as the value used for motion normal to the cylinder axis, Δn, i.e. equal to the mass of the fluid displaced by the submerged part of the cylinder; if the cylinder is hollow, then Δa is the mass of the fluid displaced by the submerged part of just the cylinder annulus, excluding the fluid trapped inside the part of the cylinder that is below the surface. (There is no variable data form of the coefficient Caa, so no corresponding fully-submerged Ma) These values for the reference fluid mass and inertia are based on the assumption that for a hollow cylinder the trapped fluid contents are free to translate and rotate axially relative to the cylinder, but not free to move normal to the cylinder axis. Damping Forces and Moments For each of the buoy local axes directions, each cylinder is subject to a damping force and damping moment given by: Damping Force = -PW.UDF.V Damping Moment = -PW.UDM.Ω where PW = proportion wet of this cylinder UDF, UDM = specified Unit Damping Force and Unit Damping Moment for this direction of motion (normal or parallel to the cylinder axis) V = component, in this direction, of the translational velocity of the buoy at the instantaneous position of the centroid of the submerged part of this cylinder, either relative to the earth or relative to the fluid velocity (as specified in the buoy data). Ω = component, in this direction, of the angular velocity of the buoy relative to the earth. (The fluid is treated as irrotational so its angular velocity is taken to be zero.) Note: If damping relative to fluid is specified in the buoy data, then the velocity V used in the damping force formula is the buoy velocity minus the fluid velocity (including current and waves) at the instantaneous position of the centroid of the submerged part of the cylinder. The angular velocity Ω used in the damping moment formula is not affected by this – it is always the buoy angular velocity relative to the earth, since the fluid is treated as irrotational so its angular velocity is taken to be zero. Loads specified by RAOs and Matrices Note: This option is only available for Spar Buoys. 194 w Theory, 6D Buoy Theory When you choose RAOs and Matrices for Buoy, the added mass and damping effects are calculated from the specified wave force and moment RAOs and added mass and damping matrices. In addition, the buoyancy force is calculated using the mean water level, rather than the instantaneous water surface. This excludes the wave-related buoyancy effects, since these are assumed to be accounted for in the loads specified by the RAOs. Warning: The drag force is also calculated using the mean water level, although (non-linear) drag can't be completely accounted for in (linear) RAOs. The RAOs are used to calculate force and moment vectors that are proportional to the amplitude of the wave component. They are applied at the instantaneous position of the RAO, Added Mass and Damping Origin, but are specified relative to a frame of reference that has x horizontal in the wave direction, y horizontal and normal to the wave direction, and z vertically upwards. The surge RAO therefore specifies a force that acts at the RAO, Added Mass and Damping Origin in the wave direction, the heave RAO specifies a vertical force, and the pitch RAO specifies a moment acting about the horizontal line normal to the wave direction. The added mass and damping matrices are also applied at the RAO, Added Mass and Damping Origin, and they are applied in the buoy axes directions, i.e. the surge added mass is applied in the buoy local x-direction, etc. The added mass matrix is simply added into the buoy's inertia (also known as the virtual mass matrix). The damping load is calculated using the following matrix equation: [Fx,Fy,Fz,Mx,My,Mz]T = -D [Vx,Vy,Vz,Ωx,Ωy,Ωz]T where Fx, Fy, Fz, Mx, My, Mz = components in the buoy local axes directions, of the resulting damping force and moment. D = damping matrix specified in the data. Vx, Vy, Vz = components, in buoy axes directions, of the buoy velocity at the RAO, Added Mass and Damping Origin, relative to the earth or relative to the fluid velocity (as specified in the buoy data). Ωx, Ωy, Ωz = components, in buoy axes directions, of the buoy angular velocity. Note: If damping relative to fluid is specified in the buoy data, then the velocity V used here excldues the fluid velocity due to waves, because the damping effects due to waves are assumed to be included in the RAOs. V is therefore taken to equal the buoy velocity minus the current velocity at the instantaneous position of the centroid of the submerged part of the cylinder. And Ω is simply equal to the buoy angular velocity relative to the earth, since the current has no angular velocity. 5.13.4 Spar Buoy and Towed Fish Drag The second order hydrodynamic loads on Spar Buoys and Towed Fish are calculated and applied separately for each cylinder. The loads on each cylinder are calculated as follows. The proportion wet P W, referred to below, is calculated for each cylinder according to its level of immersion. Drag Forces The drag forces are calculated using the "cross-flow" assumption. In the local x and y directions, i.e. normal to the cylinder axis, the drag forces are given by: x Drag Force = - PW.½.ρ.Cdn.An.Vrx.|Vrxy| y Drag Force = - PW.½.ρ.Cdn.An.Vry.|Vrxy| where An is the drag area for the normal direction Cdn is the drag coefficient for the normal direction Vrx and Vry are the x and y-direction components of the buoy velocity relative to the water |Vrxy| is the absolute magnitude of the relative velocity in the x-y plane. And in the z direction, i.e. parallel to the cylinder axis, the drag force is given by: z Drag Force = - PW.½.ρ.Cda.Aa.Vrz.|Vrz| where Aa is the drag area for the axial direction Cda is the drag coefficient for the axial direction Vrz is the z direction component of the buoy velocity relative to the water |Vrz| is its absolute magnitude. 195 w Theory, 6D Buoy Theory Drag Moments Drag moments are also calculated using the cross-flow assumption. About the local x and y directions the drag moments are given by: x Moment = - PW.½.ρ.Cdn.An.Ωr,x.|Ωr,xy| y Moment = - PW.½.ρ.Cdn.An.Ωr,y.|Ωr,xy| where An is the drag area moment for the normal direction. Cdn is the drag moment coefficient for the normal direction Ωr,x and Ωr,y are the x and y components of the angular velocity of the buoy relative to earth. And |Ω r,xy| is the absolute magnitude of the component in the xy plane of the angular velocity of the buoy relative to earth. (The water is treated as irrotational, so its angular velocity is taken to be zero.) And about the local z direction the drag moment is given by: z Moment = - PW.½.ρ.Cda.Aa.Ωr,z.|Ωr,z| where Aa is the drag area moment for the axial direction. Cda is the drag moment coefficient specified for the axial direction Ωr,z is the z component of the angular velocity of the buoy relative to earth, and |Ω r,z| is its absolute magnitude. (The water is treated as irrotational, so its angular velocity is taken to be zero.) Drag Area Moments The drag area moments in the above equations are the rectified 3rd moments of drag area about the axis of rotation. So drag area moment = Sum(A.|r|3) where A is an element of drag area at an (absolute) distance |r| from the axis of rotation. The modulus |r| arises from the drag term in Morison's equation. The area moment should have dimensions L5. Note that the axial Area Moment is about the cylinder axis, and the normal Area Moment is about the normal to that axis through the cylinder centre. We have derived the following results for simple bodies: For a rectangle of length L and width W, the 3rd moment of area about the line in the plane of the rectangle and through its centre in the length direction is (L.W4) / 32. And the 3rd moment of area about the line in the plane of the rectangle and through its centre in the width direction is (W.L4) / 32. For a circular disc of diameter D, the 3rd moment of area about a line in the plane of the disc and through its centre = (D5) / 60. We can use the two results above to calculate reasonable Drag Area Moment values to use for a cylinder in a spar buoy. Let L be the length of the cylinder and D be the diameter, and first consider the Area Moment for the Normal direction, i.e. about a line through the cylinder centre and normal to the cylinder axis. If the curved surface of the cylinder is exposed to drag then we can account for its contribution to the Area Moment by using its projection onto the plane made by the line and the cylinder axis. This projected area is a rectangle of length L and width D and the line crosses it in the width direction, so the contribution to the Area Moment is (D.L 4) / 32. If either of the end discs of the cylinder are also exposed to drag then we also need to account for their contribution to the Area Moment. Munk Moment Slender bodies in near-axial flow experience a destabilising moment called the Munk moment. This emerges from potential flow and is distinct from (and additional to) any moments associated with viscous drag. It is only well defined for a fully-submerged body. Newman (1977, page 341) derives the term and points out that it "acts on a non-lifting body in steady translation". Thwaites (1960, pages 399-401) gives an alternative derivation and provides numerical values for spheroids. Note that for bluff bodies the flow tends to separate over the afterbody. This has the effect of reducing the Munk moment to a value less than the potential flow theory would suggest. See Mueller (1968). The Munk moment effect can be modelled in OrcaFlex by specifying a non-zero Munk moment coefficient for a Spar Buoy or Towed Fish. OrcaFlex then applies a Munk moment given by: Munk Moment = Cmm.M.½.sin(2α).V2 where Cmm is the Munk moment coefficient 196 in order to separately control the slam forces that arise from these two situations. These are the userspecified constant slam data values. For spar buoys and towed fish the slam area is taken to be the instantaneous waterplane area. 5. at the point on the stack axis that is half way between the ends of the stack. Aw = slam waterplane area. used with that coefficient is not specified by the user. Spar Buoy and Towed Fish slam load data are specified on the Drag & Slam page of the buoy data form. However the total impulse due to the slam force. 6D Buoy Theory M is the mass of water currently displaced. Lumped buoy slam load data are specified on the Properties page of the buoy data form. Ce = slam coefficients for entry (subscript s for slam) or exit (subscript e) respectively. which is calculated by OrcaFlex. note that the value of Cmm is ill-defined for a partially submerged body. And the relative velocity (vn) is the instantaneous value at the wetted centroid of the object. the slam or water exit force is only applied while the buoy or cylinder is surface-piercing. α is the angle between the relative flow velocity V and the buoy axis. will often be less sensitive and so the overall effect on the motion of the object will in general be modelled more accurately. Slam force can be applied for both water entry and water exit. the surface outward normal (n) is the instantaneous value at the surface point vertically above or below the centre of volume of the object. Because of this the slam and water exit force models might give poor results if the object is wide enough horizontally to be a significant fraction of wavelength for a sufficiently large portion of the wave spectral energy. Note: In the slam models described below. vn = component in the surface normal direction of the buoy velocity relative to the fluid velocity.13.5 Slam Force Slam forces in OrcaFlex can be applied to 6D Buoys by setting non-zero slam data. Because of this the slam force time history and peak slam force are hard to model accurately. If a constant non-zero slam coefficient is used for either entry or exit then you must also specify the slam waterplane area (Aw) to be used with that coefficient. and different slam data can be specified for water entry and exit. except that in order to avoid giving a discontinuous force the Lumped Buoy slam area is ramped as the buoy enters or leaves the water and as it becomes fully-submerged. n = unit vector in water surface outward normal direction. and each can either be specified as a constant slam coefficient or as slam data that are variable with submergence relative to the surface. and the same value is used throughout the buoy’s penetration of the water surface. however see below for special treatment for hollow buoys. Separate slam data are specified for each cylinder of the buoy. no allowance is made for the variation in surface slope and water velocity across the diameter of the object that occurs due to waves. This slam area is not used if the entry and exit slam data are both either variable or zero. 197 . If the buoy is surface-piercing then this allows for the proportion of the buoy that is in the fluid. However. For lumped buoys the slam area is user-specified. in the direction that tries to increase the angle α. The slam data for water entry and exit can be specified independently. We therefore recommend that short waves should be suppressed when modelling slamming on a large buoy in a random sea. since OrcaFlex calculates and uses the instantaneous waterplane area for each cylinder for the slam area. When a constant slam or water exit coefficient is used. In particular. no force is applied when the buoy or cylinder is fully-submerged. Constant Slam Data If a constant slam coefficient is specified for water entry or exit then the slam or water exit force is given by: Entry Slam Force = +½ ρ Cs Aw vn2 n Exit Slam Force = -½ ρ Ce Aw vn2 n where ρ = water density Cs. This can be done by using the Maximum Relative Frequency data on the waves data form. such as the exact angle between the object and the sea surface at the time of entry.w Theory. see Lumped Buoy Slam Area Ramping below for details. This ensures that the slam force opposes the buoy’s penetration of the water surface. When a constant slam coefficient is used the slam area. A w. which corresponds to the transfer of momentum between the water and the buoy. The moment is applied about the line that is normal to the plane of the buoy axis and the relative flow vector. In reality the slam force might be very sensitive to precise local conditions at the time the object enters the water. V is the flow velocity relative to the buoy. w Theory. where the program must solve for dynamic equilibrium.6 0.4 0. since it may prevent such an equilibrium position from existing.6 Ramped 0. based on the buoy cylinder inner diameter. which cannot be permitted in a time domain simulation.|cosθ| Ai where θ = angle between the buoy cylinder axis and the sea surface outward normal. DNV RP-H103 (sections 3.2.11) or Faltinsen (chapter 9) provide more detail on the theoretical arguments.e. Ai = area of water surface intersection of the hollow void within the cylinder. so that the total slam impulse over a complete submergence or emergence is correct. OrcaFlex cannot apply the full user-specified Slam Area immediately the buoy makes contact with the surface. This ensures that the slam force varies continuously at the start and end of penetration.2 Proportion Wet Figure: Lumped Buoy slam force ramping For spar buoys and towed fish using constant slam coefficients.2 0. No ramping is therefore applied to the slam force on spar buoys and towed fish. Similarly OrcaFlex cannot reduce the slam force to zero the instant the buoy becomes fully-submerged.8 1 1.) Hollow Spar Buoys & Towed Fish when using Constant Slam Data When constant slam data are used. The ramping function that is applied to do this is shown in the following figure. For such hollow buoys the slam area A w is given by: Aw = Ao . the slam area used is slightly increased during the middle 80% of the penetration through the surface. based on the cylinder outer diameter and including the intersection area of the hollow void. 1. This is because it would give a discontinuous step change in load applied to the buoy when it made contact with the water. A w. And in order to compensate for the slam force being reduced over this first and last 10% of the penetrstion.4 0.2 Slam force ramping 1 0. Ao = area of water surface intersection of the whole cylinder. special treatment is applied to the slam waterplane area. i. 198 .e. 6D Buoy Theory Using simple constant slam coefficients for the slam data in OrcaFlex leaves detailed considerations of the physics behind slamming outside the program. i. and give information on suitable values for the slam coefficients. but in practice this situation is so unlikely to occur that we have not found it to be a problem. and ramped down again to zero over the last 10% of the passage through the surface. that is used for hollow spar buoys and towed fish.2 0 -0. (The waterplane area could in theory change discontinuously if the buoy end cylinder face hit the water exactly parallel to the surface. Lumped Buoy Slam Area Ramping For a Lumped Buoy using constant slam data. the discontinuity problem does not arise in practice since the water plane area naturally rises from and returns to zero continuously as the buoy's passage through the surface starts and ends.2 0 0. To avoid this the user-specified Slam Area (constant-coefficient lumped buoy only) is ramped up to its full value over the first 10% of the buoy's passage through the surface.2.9 and 3. It is a smooth ramping function that has been calculated so that it has the correct integral (one).8 Idealised 0. n. This is the rate of change of added mass coefficient with non-dimensional submergence h/s. h/s. then you should specify two sets of variable slam data. For variable slam data used for water entry. h/s = normalised (non-dimensional) submergence.9 and 3. i. the halfspan is taken to be half the user-specified Lumped Buoy Height. For a Lumped Buoy. Variable Slam Data Alternatively you can specify slam data that are variable with submergence of the centre of volume of the Lumped Buoy or cylinder (of a Spar Buoy or Towed Fish) below the surface. This varies from -1 when the Lumped Buoy or cylinder is just about to enter the water.11). For a horizontal cylinder this is the same as the nondimensional quantity shown by the dotted line in DNV Recommended Practice RP-H103 Figure 3. If the hollow buoy enters the water side on. measured +ve in the inwards surface normal direction.0 when it is just fully-submerged. then A w = Ao = waterplane area of the whole cylinder. since now that area of water is penetrated. L is cylinder length and θ is the angle between the cylinder axis and the outward surface normal direction (0 ≤ θ ≤ π/2). with its axis normal to the water surface.2. And the other should specify the rate of change of low frequency added mass coefficient and be specified as the slam data for water exit.2.9 & 3. One variable data set should specify the rate of change of high frequency added mass coefficient and be specified as the variable slam data for water entry. where ρ is water density and VT is total Lumped Buoy or cylinder volume. either because it moves both up and down relative to earth or because of the surface moving up and down due to waves. h = submergence of the centre of volume of the Lumped Buoy or cylinder. 6D Buoy Theory This formula for Aw for a hollow buoy is not theoretically based – it is simply an approximation that varies continuously between the following sensible limiting values: If the hollow buoy enters the water end on. For intermediate piercing angles the formula excludes a proportion of the intersection area of the hollow void.11.w Theory. this is given by s = r sinθ + ½ L cosθ.e. The user-specified variable slam data are therefore the gradient of the added mass coefficient when viewed as a function of the non-dimensionalised submergence. This therefore excludes the intersection area of the hollow void. This therefore includes the intersection area of the hollow void. The high frequency added mass typically increases with increasing submergence. on the grounds that this area of water is not penetrated. so the values specified for rate of change of added mass coefficient used for water exit should normally be negative. s = half-span of the Lumped Buoy or cylinder in the surface normal direction. relative to the total fully-submerged displaced mass. Notes: Added mass is frequency dependent. If your simulation involves the object moving both up and down relative to the surface.2. For a cylinder of a Spar Buoy or Towed Fish the half-span s is half the instantaneous span of the cylinder in the surface normal direction. then Aw = Ao . ρVT. with its axis parallel to the water surface. where r is cylinder outer radius. and the high frequency added mass coefficient should be used for variable slam data that are used for water entry. and continues increasing with depth of the fully-submerged buoy or cylinder below the surface. i.5.Ai = waterplane area of the cylinder annulus. The slam data are then specified by giving the rate of change of the added mass with submergence in the following non-dimensional form: dCa(h/s) / d(h/s) = user specified non-dimensional variable slam data. so the values specified for rate of change of added mass coefficient for water entry should normally be positive. whereas for water exit it should be the low frequency limit of added mass coefficient (see DNV Recommended Practice RP-H103 sections 3.e. 199 . This is the added mass for motion normal to the surface. whereas the low frequency added mass coefficient should be used for water exit. divided by the fully-submerged displaced mass. This is the distance from the surface to the centre of volume. which will equal the projected area of the cylinder (product of outer diameter and cylinder length). to 0 when it is half submerged. for a cylinder inclined to the surface it is the natural generalisation of that quantity. However the low frequency added mass typically decreases with increasing submergence. Ca = added mass coefficient. the added mass coefficient Ca for which rate of change is specified should be the high frequency limit of added mass coefficient.2. See DNV RP-H103 sections 3. to +1. Data Requirements with Variable Slam Data If you use variable slam data then your data must satisfy the following requirements: You must provide data for at least two values of normalised submergence. Whereas for water exit the user-specified variable slam data are the rates of change of the low-frequency added mass coefficient with normalised submergence. respectively. The formula for entry slam force is based on conservation of added momentum. whereas the rates of change of added mass specified for slam/water exit force should be for the high/low frequency added mass limits.w Theory. which are normally +ve and so the entry slam force is upwards. Force Formulae with Variable Slam Data When using variable slam data.13. The above formula for slam force is then exactly equivalent to that given for f s (which is slam force per unit length) in DNV Recommended Practice RP-H103 section 3. 200 . The data are truncated at both ends of the range. as in our example. by using the half-span s in place of the cylinder radius r.9 . and the specified rate of change of Ca for this value of Normalised Submergence must be zero. This corresponds to the object just about to enter the water. For a cylinder whose axis is parallel to the surface plane. the rate(s) of change of added mass specified for variable slam data might well not match any variable added mass data that you specify for the added mass effects on the object.2. dCa/d(h/s) = user-specified non-dimensional variable slam data.7. And the above formula for water exit force is exactly equivalent to that given for F e (water exit force per unit length) in DNV RP-H103 section 3. This ensures that the slam or water exit force is zero when the object is out of the water. whereas the formula for water exit force is based on conservation of energy. n = unit vector in water surface outward normal direction. The variable added mass data you specify should be for the expected dominant frequency of oscillation of the object. When variable slam data are used the variation of force with submergence is therefore modelled by the variation of the rate of change of added mass coefficient with Normalised Submergence. the half-span s is equal to the radius r of the cylinder. For a cylinder whose axis is inclined to the surface plane. and that the force also reduces to zero once the object gets far enough below the water surface. so the rate of change of added mass will be taken to be zero outside the range of values of Normalised Submergence that you give. where the dependence of the force on submergence is modelled through the variation of the applied slam area during passage through the surface (for a Lumped Buoy the user-specified slam area is ramped and for a cylinder of a Spar Buoy or Towed Fish the slam area used is the instantaneous waterplane area. The smallest value of Normalised Submergence for which data are specified must be -1. Notes: For water entry the user-specified variable slam data are the rates of change of the high-frequency added mass coefficient with normalised submergence. over a short range of Normalised Submergence h/s.13. the slam or water exit force is given by: Entry Slam Force = ρVT dCa/d(h/s) (1/s) vn2 n Water Exit Force = ½ ρVT dCa/d(h/s) (1/s) vn2 n where ρ = water density VT = total volume of Lumped Buoy or cylinder.2. But it must ramp up from zero at h/s=-1 in order to avoid a discontinuous slam or water exit force as the object enters or leaves the water. This is in contrast to when constant slam data are used. vn = component in the surface normal direction of the buoy velocity relative to the fluid velocity. This gives rise to the extra factor ½ that appears in the formula for water exit force. which are normally -ve and so the water exit is downwards. the above formulae generalise those given by DNV. 6D Buoy Theory Because of the frequency-dependence of added mass. h/s. The rate of change of Ca specified for the largest value of Normalised Submergence given must also be zero. which almost always varies as the object passes through the surface). This ensures that the slam force opposes the buoy’s penetration of the water surface. The rate of change of C a may well rise very quickly as the object enters the water. so the variable slam data specified should be for the buoy orientation expected when the slam or water exit forces apply. one at each vertex. and axis oriented in the instantaneous surface normal direction. 6D Buoy Theory There is no upper limit on the values of Normalised Submergence for which data are specified. for example if it penetrates the surface with its axis close to being parallel to the surface so that multiple cylinders pierce the surface at the same time. as with other hydrodynamic loads. However in order to to cater for the more general situation covered by OrcaFlex. Therefore the velocity used. the wave velocity vertical component is allowed for (3.13. Because the vertices are (in general) offset from the buoy origin. So if for some reason you want slam or water exit force to be applied even when the object is far below the surface then you can enter a large value as the highest Normalised Submergence for which you specify data. by setting a non-zero seabed friction coefficient or solid friction coefficient. In DNV RP-H103. the DNV slam force is always in the vertical direction. 5.6 Contact Forces Contact Forces from Interaction with Seabed and Shapes Interactions with shapes and the seabed are calculated as if the buoy consists of a series of lumps. the slam force is calculated separately for each cylinder of the buoy. The total volume VT referred to above in the formulae for the variable slam data case is calculated using the outside diameter of the cylinder and does not allow for it being hollow. where s is the half-span of the object in the surface normal direction. For a spar buoy or towed fish. the slam force is correctly distributed along the length of a spar buoy or towed fish. v n. Contact friction forces can also be included.w Theory. we therefore take them for this purpose to be cylindrical in shape. When variable slam data are used the Normalised Submergence. When constant slam data are used the instantaneous waterplane area is used for the slam area. If the hollow buoy is free-flooding then the rate of change of added mass coefficient with Normalised Submergence will depend on the inclination of the cylinder axis to the surface. In both cases. which is h/r in DNV RP-H103.13.2. Note: This analysis of submergence is specific to circular cylinders. the OrcaFlex model extends that of DNV RP-H103 in a number of ways described above.7). these seabed or shape reaction forces give reaction moments about the buoy origin. If any buoy vertex penetrates the seabed or an elastic solid then it experiences a reaction force at that vertex. a still. 201 . To apply variable slamming data to lumped buoys. With variable slam data the force is applied at the instantaneous centre of wetted volume of the cylinder. This applies for both constant and variable slam data. These vertices are used even if the Draw circular cylinders option is selected.3). If you specify no vertices then the 6D Buoy will not react to contact with the seabed or with any solids.2. when used with a hollow Spar Buoy or Towed Fish. See Seabed Theory and Shapes Theory for details. with radius consistent with their volume and height. Hollow Spar Buoys & Towed Fish when using Variable Slam Data User-specified variable slam data.9. for constant coefficients. Point of Application of Force For lumped buoys the force is applied at the instantaneous centre of wetted volume of the buoy.2. Differences from DNV RP-H103 This slam force model used in OrcaFlex closely matches that given in DNV-RP-H103. In DNV RPH103 (section 3. is the normal component of buoy velocity relative to the water surface allowing for the velocity of the surface due to waves. the vertices used are the vertices which are automatically created for the Draw square cylinders drawing option. as described here. In either case then. With constant slam data that force is then applied at the instantaneous centre of waterplane area of that cylinder. horizontal sea surface is assumed in the variable coefficient case (3. Notes: For a lumped buoy you can specify the number and location of the vertices. must include any effect due to the cylinders being hollow. For spar buoys and towed fish. These are summarised here: In OrcaFlex the model includes surface movement due to waves.9) the projected area is used. is generalised to h/s. Aw. This generalises the model to allow for non-horizontal cylinder orientation. and the slam force is applied in the surface normal direction allowing for waves. VrX. In addition. Drag Drag forces are calculated separately for each of the global X. At. All of the fluid related effects are calculated allowing for what proportion of the buoy is currently immersed in the sea. drag. A v.V. of the projected lateral area = cylinder diameter × cylinder length. Default total contact area If At is set to '~' then OrcaFlex calculates and uses a default value of A t that is based on the buoy geometry as follows.A in each of the global axes directions.½. The forces applied are as follows.PW. buoyancy.ρ. divided equally amongst all the buoy vertices: Av = At / (number of vertices) If At is set to zero then the buoy experiences no contact forces.PW. for the X direction Vr is the velocity vector of the fluid relative to the buoy and |Vr| is its absolute magnitude VrX is the component of Vr in the X direction. Weight and Buoyancy Weight = Mg Buoyancy = PWρgV where M = mass ρ = fluid density V = volume. where Ca is the Added Mass Coefficient for that direction A is the acceleration of the fluid in that direction. This force is often considered as being made up of two parts: 1.PW. Fluid Inertia Effects Fluid acceleration force = (1+Ca). the inertia of the buoy in each of the global axes directions is increased by: Added mass = ρ.A. and then scaling all of the fluid related forces by this proportion. For the X direction (and similarly for the Y and Z directions) the drag force applied is Drag Force = PW. PW. 3D Buoy Theory Contact area The reaction force at a vertex depends on the contact area of the vertex.V. This is done by calculating a proportion wet. For Spar Buoys and Towed Fish the default total contact area is given by: At = max(Aaxial. respectively.V. The Froude-Krylov force = ρ.CdX. The added inertia force = Ca. added mass and reactions from shapes.A 2. 5. For a Lumped Buoy the default total contact area is given by: At = Volume / Height where Volume and Height are as specified on the buoy data form.V where Ca is the Added Mass Coefficient for that direction. 202 .AX. over all cylinders. Y and Z directions.w Theory.14 3D BUOY THEORY The effects included for a 3D Buoy are weight.ρ. This vertex contact area is taken to equal the specified total contact area of the buoy.|Vr| where CdX and AX are the Drag Coefficient and Drag Area. Alateral) where Aaxial = maximum cylinder cross sectional area Alateral = sum.Ca.ρ.PW. L0) / L0 K = Wire Stiffness data value. the Value specified in the data is used as a target nominal constant tension that the winch drive attempts to achieve. Dynamic Analysis If Specified Payout is specified (length control mode) for a stage of the simulation. 3D Buoys receive a contact damping force (for details see Seabed Theory and Solids Theory) and friction forces. and the wire tension t and winch drive force f are both set to equal: t = f = Kε (1) where: ε = Wire Strain = (L .CV2 if dL0/dt = 0: f(V) = f(0) if dL0/dt > 0: f(V) = f(0) + Deadband + BV + DV2 (3) where V = rate of payout = dL0/dt Deadband = the winch drive deadband data item 203 . given by: Reaction = KAd where K is the Stiffness of the seabed or elastic solid A is the contact area d is the depth of penetration of the buoy origin B. so if the value for t given by equation (2) is negative then the winch wire is considered to have gone slack and t is set to zero.Deadband + AV . and the unstretched length paid out. In addition to this reaction force. then the unstretched length of winch wire paid out. The drive force f applied is then given by: if dL0/dt < 0: f(V) = f(0) . specified on the winch data form L = total length of the winch wire path L0 = unstretched length of winch wire paid out Alternatively. opposing the wire tension being applied to the other side. Winch Theory Contact Forces Finally.w Theory.15 WINCH THEORY Static Analysis If the Statics winch control mode is set to Specified Length then for the static analysis the unstretched length of wire paid out. then for the static analysis the winch drive force f and the wire tension t are both set to the Value specified. is then set to match this wire tension according to equation (1) above. For Detailed winches the winch drive tries to achieve the target tension by applying a drive force to one side of the winch Inertia. is set to the Value specified.dL0/dt) / L0 L = total length of the winch wire path Note: The winch wire is not allowed to go into compression. 5. If Specified Tension mode is specified for a stage of the simulation. so the Value specified is used for the actual winch wire tension. if the Statics winch control mode is set to Specified Tension. 3D Buoys are also subjected to a reaction force from the seabed and any elastic solid with which they come into contact. negative Value means haul in. L0. L0. is steadily increased or decreased during that stage so that the total change during the stage is the Value specified. Positive Value means pay out. For Simple winches the winch drive is always assumed to achieve the target tension. L0. The winch wire tension t (which is applied to each point on the wire) is then given by t = Kε + CKdε/dt (2) where K and C are the Wire Stiffness and Wire Damping data values specified on the winch data form dε/dt = Wire Strain Rate = (dL/dt . in the direction of the vector p o-ps.Deadband 2 + A. L0.V Drive Force f Deadband f(0) = Nominal Tension + Stiffness (Payout since simulation started) Deadband 0 Payout Speed V (-ve = hauling in) f(V) = f(0) .16 SHAPE THEORY Elastic Solids Consider an object which penetrates the surface of an elastic solid. D should be non-zero. where: K = stiffness of the material A = contact area d = depth of penetration. and with magnitude of KAd. 204 .(L0 . f(0) = Value + Stiffness. a line node) then this closest point may be on an edge or corner of the shape.V . the common value of f and t is then found by solving the simultaneous equations (2). D = the winch drive drag term data items. (3) and (4) may have no solution.w Theory. Shape Theory A.C.L00) Value = the nominal constant tension Value given Stiffness = the winch drive stiffness data item L00 = original value of L0 at the start of the simulation (set by the static analysis) f(V) = f(0) + Deadband 2 + B. since otherwise the simultaneous equations (2).V + D.V Figure: Force Control Mode for Detailed Winches If the winch Inertia M is non-zero. Note: If the winch inertia is set to zero then at least one of the damping and drag terms A. then the winch wire tension is set as in equation (2) above and the winch inertia reacts by paying out or hauling in wire according to Newton's law: Md2L0/dt2 = t . If the winch inertia is set to zero. C. A warning is given if this is attempted.f so the wire tension therefore tends towards the winch drive force and is hence controlled by the given Value. The outwards reaction force on the penetrating object acts outwards. B = the winch drive damping term data items C.g. then the winch is assumed to be instantly responsive so that f = t at all times (4) Given the current value of L0. 5. B. (3) and (4) for the payout rate dL0/dt. Denote by p o the position of the penetrating object and by ps the closest point on the surface of the solid to po. is then altered at the calculated rate dL0/dt as the stage progresses. The unstretched length of winch wire out. Note that if the penetrating object has non-zero contact diameter (e. when Vn is positive). pressure difference effects and the local geometry. and is given by: D = 2λ(MKA)½ Vn where λ = percentage of critical damping / 100 M = mass of the penetrating object Vn = component of object velocity in direction into the solid. for realistic cases. Finally. Notes: If the shape intersects the water surface then the surface is assumed to pass through the shape unaltered. Thus a wave in the open sea also appears inside the shape. then the trapped water is assumed to move and rotate with the vessel. a moonpool with an open connection at the bottom will suppress most of the wave and current action. for example. depending on the size of the opening to the sea.w Theory. Shape Theory For details of the way the contact area is calculated. We make this assumption because of the difficulty in predicting. if explicit integration is used then a reaction damping force D is also applied when the object is travelling into the solid. if a non-zero friction coefficient is specified. However there will be some flow in and out of the moonpool.e. But if the shape is connected to a moving vessel. then a lateral friction force is applied. For example. The damping force is only applied when the object is travelling into the shape (i. but it is attenuated to some extent and lags behind the surface outside. 3D Buoy Theory and 6D Buoy Theory. The surface elevation in the moonpool therefore does respond to the wave outside. For details of the friction model see Friction Theory. This damping force is in the same outwards direction. how the surface will behave inside the trapped water volume. So if the trapped water shape is Fixed or Anchored then no fluid motion occurs inside the shape. 205 . Trapped Water Inside a trapped water shape the fluid translational velocity and acceleration are calculated on the assumption that the trapped water moves and rotates with the shape. In addition. see Line Interaction with Seabed and Solids. . Each line can also have a number of attachments. mooring lines. Tethers are simple linear elastic ties that can take tension but not compression. or drag chains. and ends can be disconnected in the course of a simulation. planes and cylinders) are available and a number of shapes may be placed together to build up more complex compound shapes. Several different elementary shapes (cuboids. Links are mass-less connections linking two other objects in the model. The winch drive can be operated in either constant speed mode.Y and Z). Winches are also mass-less connections linking two (or more) objects in the model.1 MODELLING INTRODUCTION To analyse a system using OrcaFlex. cables. they are made of an elastic material and so apply a reaction force to any object that penetrates them. in which it applies a user-specified tension to the winch wire. barges etc. The objects represent the structures being analysed and the environment determines the current. or else in constant tension mode. These are elements attached to lines at user-specified locations. or attached to other objects such as Vessels or Buoys.w 6 System Modelling: Data and Results. Spring / Dampers can take both compression and tension and both spring and damper components can be non-linear. They are rigid bodies whose motions are prescribed by the user. 3D Buoys are simple point bodies with just 3 degrees of freedom – the translational degrees of freedom (X. They can also be driven around the sea surface. etc. Trapped Water shapes can be used to model parts of the sea. The following types of objects are available in OrcaFlex. etc. The model consists of the marine environment to which the system is subjected. for modelling different sorts of marine object. to which the objects are subjected. They may be fixed or attached to other objects such as Vessels or Buoys. Line properties may vary along the length. floating platforms. Unlike a vessel. or indirectly by giving first order wave load RAOs or second order wave drift QTFs. clump weights. sway. at user specified velocities and headings. heave. plus a variable number of objects chosen by the user. Elastic Solids can be used to act as physical barriers to restrict the movement of the other objects in the system. pitch and yaw). roll. you must first build a mathematical model of the real-world system. the motion of a buoy is calculated by OrcaFlex. Note: Although called buoys. (Detailed descriptions of each type of object are given later. Two types are available. using the various modelling facilities provided by OrcaFlex. Several different types of 6D Buoy are available. which is fed from and controlled by a winch drive mounted on the first object. wave excitation. Modelling Introduction SYSTEM MODELLING: DATA AND RESULTS 6. in which it pays out or hauls in the winch wire at a user-specified rate. Shapes are geometric shapes and three types are available. 6D Buoys are much more sophisticated than 3D Buoys – they are rigid bodies with the full 6 degrees of freedom. That is. Drawing shapes can be used purely for visualisation and have no influence on or interaction with the rest of the model. such as moonpools. flexible hoses. or a combination of the two. that are shielded from the waves. The connection is by a winch wire.) Vessels are used to model ships. 3D and 6D Buoys do not need to be buoyant and so can readily be used to model any rigid body whose motion you want OrcaFlex to calculate. whose response to waves is defined by the data. Lines are catenary elements used to represent pipes. for example to allow a buoyant section to be represented. during the course of the simulation. and provide a convenient way of modelling items such as floats. placed in the environment and connected together as required. The motion can be specified in a number of ways: directly by a time history motion data file or specifying Response Amplitude Operators (RAOs) for each of 6 degrees of freedom (surge. 3D Buoys are not allowed to rotate and are intended only for modelling objects that are small enough for rotations to be unimportant. Line ends may be fixed or free. OrcaFlex calculates both their translational and rotational motion. 207 . 6. 208 .System Modelling: Data and Results. Static analysis. If you want to specify time-varying data for more than one object (e. links and winches have the special property that they can be used to connect together other objects.2 DATA IN TIME HISTORY FILES For certain data you can use time history files to specify time-varying values. or for the wave and a vessel) then you can either put all the data in one file (using multiple columns in a single table) or you can use separate time history files for the different objects. in which OrcaFlex calculates the static equilibrium position of the model. links or winches that are attached to an object. but not wave loads. Dynamic analysis. You can either specify the full path or a relative path. Fatigue analysis. though at the cost of increased analysis time. as required. Similarly. Example files are provided with OrcaFlex. A choice of implicit and explicit integration scheme is offered. and then set up a model that includes those features. Time history file data are specified on a page control: Figure: Time history data Source page The Input File is the name of the time history input file that contains the data. in which OrcaFlex carries out a time simulation of the response of the system to waves. the lines. See Object Connections for details. links and winches to connect the other objects together. in which OrcaFlex calculates and reports the undamped natural modes of the model. and allows you full control over how the variable changes with time. in which OrcaFlex calculates and collates fatigue damage. Data in Time History Files w Of these various object types. This is available for wave elevation. current and a range of user-defined inputs. for both the wave and wind. The first model of a system might be quite simple. wind speed and vessel motion. or of an individual line in the model. The number of objects in the model is only limited by the memory and other resources available on the computer being used. Later. there are no built-in limits to the number of lines.g. OrcaFlex offers a variety of analyses: Modal Analysis. current and wind loads are included. Computer programs cannot exactly represent every aspect of a real-world system – the data and computation required would be too great. thereby giving more accurate predictions of its behaviour. Once the model has been built. As a result very complex systems can be modelled. the model can be extended to include more features of the system. though of course the more complex the model the longer the analysis takes. So when building the model you must decide which are the important features of the system being analysed. Assembling the model therefore consists of creating objects and then using the lines. so that early results and understanding can be gained quickly. only including the most important aspects. Y. So. simulation time -40 to 0) followed by 200s of simulation (simulation time 0 to 200) will cover time history time from 260s to 500s.01s intervals and the minimum time sample interval was 0. Note: If you are using more than one time history file (e. Cubic Bessel interpolation typically gives step changes in acceleration at the specified time samples. Such acceleration effects can manifest themselves as steps or spikes in the inertial forces on any objects attached to the vessel. with respect to vessel local axes. Files of this format can easily be produced with commercial spreadsheet programs by using "Save As" and selecting tab-delimited text format. Y. Data in Time History Files For vessel time history files you must specify an Interpolation Method. This sub-sampling technique has proved to be very effective at smoothing interpolated time histories and so improving the quality and stability of simulations. the point on the vessel at which the motion time history applies.g. in other words it must be a text file in which the time history data columns are separated by single tab characters. For vessel time history files the Datum Point specifies. Time History File Format Time History files must conform to the following formatting rules: The file must be a tab-delimited text file. The Time Origin gives you control of how the times given in the time history file relate to the times in OrcaFlex.2s then OrcaFlex would use every 20th row of time history data. the time history time origin and the simulation time origin can be used to control of how the times given in the time history file relate to the times in OrcaFlex. Preview page The preview page presents graphs of the data contained in the time history file. or if the sample interval in the file is very small. The simulation time origin is also specified relative to global time. This is done on the Data page using a series of drop down lists. X. Note: The values plotted on the graphs are the raw data contained in the time history input file. if both do) then you may find that the interpolated time history values cause the simulation to contain unrealistic noise. one for a wave train and one for motion of a vessel) then they each have their own time origins. The time origin is specified relative to the OrcaFlex global time origin.) are fixed by specifying None in the drop down list. If either of these conditions hold (or worse. Data page You must tell OrcaFlex which columns in the time history file correspond to Time. For a superimposed motion time history the degree of freedom will be fixed as zero. Z etc. for example. Z etc. The Minimum time sample interval can be useful to smooth time history data in some situations: if the time history values have been truncated to a small number of significant figures. Note that the time history file must contain data to cover the whole of the simulation. which you can use to time shift each time history independently of the others. 209 . Note: If you do not wish to sub-sample the time history input file then you should use a value of 0. The time axis of the graphs use the raw data contained in the input file. For most purposes we recommend using Cubic Spline interpolation. As described above. so you can simulate different periods of the time history by adjusting either the time history time origin or the simulation time origin. You can also specify that vessel degrees of freedom (X. These graphs can therefore be used to check that the time origin data items are set correctly. For example if the time history file contained data sampled at 0. Using a non-zero minimum time sample interval results in the time history data being sub-sampled at the specified period. since it gives continuity of vessel velocity and acceleration. if the time history file's time origin is set to 100s and the simulation time origin is set to 400s. This can provide a quick check that the column data has been correctly specified. Each graph contains two vertical lines to represent the beginning and end of the simulation.e. For a primary motion time history the degree of freedom will be fixed as the value at the end of the static calculation. so it specifies the global time that corresponds to zero time in the time history file. and Linear interpolation gives zero acceleration between the times specified and then an infinite acceleration when the velocity changes at a specified time sample. then a simulation consisting of 40s of build-up (i.w System Modelling: Data and Results. No interpolation is applied before plotting the curves. but if you have a large number of data points (>1000) the data (on the preview graph only) may be subsampled. The data values must be in standard decimal or scientific form. so in this case constant data specifies dy/dx. Different data items can use the same variable data source much in the same way that.) can precede the data but once the data begins it cannot be interrupted with any more text. i. Before saving the text file. The different possibilities are described below. For a wave time history the time values must be equally spaced since a fast Fourier transform is used which requires equal spacing. Note: If you generate your time history text file from a spreadsheet program such as Excel. so you can then specify the drag coefficient to be a function of Reynolds number. To edit the name of a data source double click the name or select the name and then press F2. or the name of a variable data source (which you do by typing in the name or by selecting it using the down-arrow button). The data are assumed to start at the first numeric entry in the time column and blank rows are not allowed once the data has started. The named data source must already have been defined – see the next section. But for some numerical data items you can choose to instead specify variable data. As an example consider the drag coefficient of a line. which is designed to be used from left to right. y say. What form these data take varies. If x varies during the simulation then y varies accordingly. and the actual value y(x) used by OrcaFlex then depends on the value of x at the time. These are the numerical data items that have a small downarrow button to the right of the data item value. and their names. each time the drag coefficient is needed OrcaFlex will first calculate the Reynolds number (the x in the above description) and then derive and use the corresponding drag coefficient y(x). 6. In Excel you can get all significant figures by selecting all the cells and then using the Format Cells command (on the Format menu) to set the number format to scientific with 15 decimal places. Then. whereas variable means non-linear and you specify y as a function of x. Cases like this are documented in the description of each data item. since otherwise the time history text file will lose some significant figures. This means that textual information about the file (titles etc. Using Variable Data Variable data can only be used for certain data items. For example data for drag coefficients are kept separate from data for axial stiffness. This structure is indicated by the layout of the form. for instance. But sometimes the Reynolds number variation is important.3 VARIABLE DATA Most OrcaFlex data are constant – i. In this context constant means constant slope. Setting up Variable Data Sources All the variable data sources are specified on the Variable Data form. Typically the data item's value y is then specified as being a function of some other value x. For many applications this variation is not significant so a fixed constant drag coefficient is sufficient. This form can be opened using the model browser or using the popup menu on any data form. different sections of a Line can use the same Line Type. Note that some data items use variable data in a slightly different way. it is therefore important to set the number format to one that displays all the significant figures. Each table on the Variable Data form is given a name and the tables are grouped according to the type of data they contain. rather than y. using the tree view in the left-hand section of the form.e. In the real world this isn't a fixed constant value – it depends on the Reynolds number. 210 . The right-hand section of the form is where the data for the data source is entered. To add a new table. But for wind velocity or vessel motion time history files variable time intervals can be used since the interpolation methods used do not require equal spacing. is a fixed specified value. please note that the number of significant figures in the text file will depend on the number format of the cells in the spreadsheet. For these you can specify either a fixed constant numerical value in the usual way. So first select the type of data you want. The centre section of the form then shows how many data sources have already been defined for that selected type of data.e. and the constant value you specify is dy/dx. Variable Data One column must contain the time values and these must be given in ascending order. linear. where y is tension and x is axial strain. To delete a data source select it and press the DELETE key. The data must be given in the same units as used in the OrcaFlex model.w System Modelling: Data and Results. a value. increment the Number of Data Sources. For example the axial stiffness of a line type is the slope of the tension-strain curve. The function can use this value as its starting value if it so chooses. For native code DLLs. Initial Value When OrcaFlex calls the external function for the first time it passes this value to the function. The following data items are required to specify an external function data source: File Name The file name containing the external function. the system DLL search order is used if the DLL is not found relative to the directory containing the latest OrcaFlex file. We refer to these two types of external functions as native code external functions and Python external functions.3 will be used. Horizontal Variation Factor Data Sources These data sources specify a variation along a user-prescribed axis. it is relative to the directory containing the latest OrcaFlex file that you have opened or saved. (xn. log scales are used. Note: This value is used by OrcaFlex when drawing the model in Reset state. Function Name The name of the external function. This can be the name of a DLL for a native code external function. The data will be automatically sorted into order of increasing x when they are used or when you use the Profile button. Truncation means that OrcaFlex uses y 1 for all x ≤ x1 and yn for all x ≥ xn (the table already having been sorted so that x1 is the lowest x-value specified and xn is the highest). i. (x2. The function must then recalculate and update the value of the variable data item. For values of x outside the range specified OrcaFlex either extrapolates or else truncates.. If the file name uses a relative path.w System Modelling: Data and Results. .2 or 3. If Python 2 is selected then either version 2. For a native code external function this is the name of a function exported by the external DLL. then the most recent. Time Step This specifies how frequently the external function is called to update the value of the variable data item. This table defines a function y(x). If there is no such file (because it is a new model which has not yet been saved) then the file name is relative to the value of the working directory when the program started. This table is specified in the same way as for tabular data sources.1 External Functions External Function Data Sources are yet another variety of variable data source.0.1. if more than one of these versions is present on your system. Variable Data Tabular Data Sources These data sources are specified by giving a table of corresponding values (x 1. These data sources allow data to be specified by a user-defined function provided in an external DLL.y2).y1). This axis is defined by the X. Python Version For Python external functions only. For details on how to implement external functions please refer to the OrcaFlex programming interface documentation. The variable data form reports the method of interpolation and whether extrapolation or truncation is used. This function is called repeatedly during the OrcaFlex simulation and is passed the current value of the variable data item. or a Python script. or the name of a Python script in the case of a Python external function. the outer time step or a user-specified time step. where the table's left-hand column is the independent variable x and its right-hand column is the dependent variable y. 6. 3. Where appropriate.3.Y coordinates of an origin and an azimuth direction. this determines which version of Python is used. this data item is ignored and the external function is called on each iteration of each time step. The Profile button displays a graph of the currently selected data. You can use either the inner time step. 2. Note: When using implicit integration.e.yn). 211 . Alternatively it can ignore this value and substitute a different value. If both of these versions are present on your system. then the most recent will be used. Again.6 or 2. For a Python external function this is the name of a class defined in the Python script. For intermediate values of x OrcaFlex interpolates. 3.7 will be used. Together with the axis you also specify a table of values defining the horizontal variation factor as a function of distance along the axis. If Python 3 is selected then one of version 3.. This is useful for data checking purposes.7 will be used. If you choose a user-specified time step then you input a target time step and the program uses the nearest whole multiple of the inner time step. respectively. dll. External Function Parameters The external function facility provides a general purpose method of passing parameters to external functions. Current reference speed and reference direction. mass. you must have 32 bit version of Python. Alternatively these example functions can be downloaded from www. For more details please refer to the OrcaFlex programming interface documentation. Selecting US gives length in feet. you must have them compiled as 32 bit. time and temperature. You can.w System Modelling: Data and Results. Selecting SI gives length in metres. the Environment etc. compile both 32 bit and 64 bit versions: these should be located in the same directory and the 64 bit version given the suffix of 64. Winch tension and winch payout rate. the parameters are passed in the ObjectParameters attribute of the info object. Data which can be controlled by External Functions The following data items can be controlled by External Functions: Vessel. You may. These parameters are passed to the external function. If the parameters are hard coded then the external function DLL will have to be recompiled each time you experiment by changing the parameters. the parameters are passed to the external function in the lpObjectParameters member of the TExternalFunctionInfo data structure. time in seconds and temperature in Celsius.dll then the 64 bit DLL must be named ExtFn64. you must have a 64 bit version of Python. the bitness of OrcaFlex and Python must match: to use Python external functions from 64 bit OrcaFlex. force in kips.g. they must be compiled as 64 bit. by default. Likewise. The parameters are specified as a free form multi-line text field. External Function Examples A selection of example external functions are supplied on the OrcaFlex installation disc. A PID controller has a number of parameters and these could be hard coded into the external function. have both 32 and 64 bit versions of OrcaFlex installed. force. the External Function Examples illustrate the procedure involved in passing parameters to external functions and are a useful source. Units are defined for length. For native code external functions. General Data 32 and 64 bit Environments The bitness of OrcaFlex and compiled native external functions must match: to use native external functions from 64 bit OrcaFlex. Units Data This may be SI. OrcaFlex does not use this text. 6. a Vessel. have both 32 and 64 bit versions of Python installed simultaneously. This means that the external function has to do some work to decode and interpret the text before it can access the parameters. a 6D Buoy.com/Support. Instead OrcaFlex allows you to specify parameters for the external function as part of the OrcaFlex data. a Winch. Also. mass in tonnes. mass in kips. However. you will.orcina. Bend stiffness for Line Types. 212 .4 GENERAL DATA The General Data form is used to specify data that apply to the whole model. and to use Python external functions from 32 bit OrcaFlex. For Python external functions. Please refer to the OrcFxAPI help file for full details. if you wish. For example. in OrcaFlex you may want to experiment by varying these parameters to see how they affect a simulation. 6D Buoy and Line applied loads. However. if you need your external function to work with both 32 and 64 bit versions of OrcaFlex. this also means that there is a great deal of flexibility in the parameter passing mechanism. force in kN. If you follow this naming convention. US or User Defined (multiple choice). Vessel primary motion. Comments A free form multi-line text field that can be used to store notes about the model.) uses an external function then a page titled External Functions is available on that object's data form. if the 32 bit external function DLL is named ExtFn. The parameters are specified in the text field contained in this page. and to use native external functions from 32 bit OrcaFlex. For an example of why this is desirable consider an external function which implements a PID controller used to model the active control system for a heave compensating winch. Wing orientation angles. then OrcaFlex will load whichever external function DLL matches the architecture of the OrcaFlex process. Whenever an OrcaFlex object (e. time in seconds and temperature in Fahrenheit. time and temperature units on offer and in addition you can specify the value of g (gravitational acceleration). together with individual settings on each buoy's data form. When using such a system you should note that the equations in this manual. when it is excluded OrcaFlex simply places the buoy at the position specified by the user. provided a reasonable length build-up stage is specified. force and time units there is a corresponding inertial mass unit. mass. are written in a form which assumes that any terms involving mass units (e. by running a simulation with no waves and starting from a non-equilibrium position. especially if the initial estimated position given in the data is far from being an equilibrium position. In fact the simulation can then often be used to find the true static equilibrium position. 6. You may need to set this data item to None if the model is statically indeterminate. as well as finding the static equilibrium position of the other objects. For 6D Buoys you can also choose whether the rotational degrees of freedom are included or excluded.4. for 6D Buoys. but excludes rotational degrees of freedom for 6D Buoys. Which buoys are included in the static analysis is determined by the data item "Buoy Degrees of Freedom Included in Static Analysis" on the General Data form. just the rotational degrees of freedom) from the static analysis. F (force units) and T (time units). The static analysis is an iterative calculation and for some complex systems this calculation may fail to converge. mass. If this happens you can exclude some or all buoys (or. OrcaFlex automatically allows for this when you use US units or any User Defined system where the mass unit is not the inertial mass unit.1 Statics Buoy Degrees of Freedom Included in Static Analysis Buoys can either be included or excluded from the static analysis. or if the static analysis fails to converge.w System Modelling: Data and Results. but instead simply places the buoys at the initial starting position specified in the data. magnitude) and direction. Normally the starting speed is zero. In this manual the units of data items are denoted using the capital letters L (length units). once it is found. If a non-zero speed is specified (e. density etc.) are expressed in the inertial mass unit. It is defined by giving the speed (i. by running a simulation with no waves. You may then select individually from the length. force and time units. for example a free-floating buoy.e. moment of inertia. so the inertial mass unit is 1 kiloslug (= 1000 slugs = approximately 32000 pounds mass). General Data If neither of these systems meets your requirements then select User Defined. US units. For example in the US units system the unit of acceleration is 1 ft/s 2 and the unit of force is 1 kip force. for modelling a towed system) then the static analysis becomes a steady state analysis that finds the steady state equilibrium position in which the whole 213 . use mass units that are not the inertial mass unit corresponding to the length. When a buoy is included OrcaFlex calculates the static equilibrium position of the buoy. Z includes all buoys in the static calculation. since a 1 kip force applied to a 1000 slug mass would give an acceleration of 1 ft/s 2.g. whether that buoy should be included in the static equilibrium calculation. A value of Individually Specified allows you to specify individually on each buoy data form. force. Y. the true static equilibrium positions of the buoys can then be input as their starting positions for subsequent runs. Starting Velocity Specifies the velocity of the whole model for the static analysis and for the start of the simulation. not the 'non-inertial' mass unit used by the unit system. If the units are changed. and many of the possible User Defined units systems.g. it does allow the simulation to proceed and the initial nonequilibrium errors will normally be dissipated during the build-up stage of the simulation. Although the simulation then starts from a non-equilibrium position. as described below: A value of None means that OrcaFlex does not find the true static equilibrium position of the buoys in the model. M (mass units). One example of this is to use the simulation to determine the damping properties of the system. mass per unit length. This data item should normally be set to All. as in most text books. A value of X. in which case the static analysis will attempt to find the static equilibrium position of all the buoys in the model. Another reason for using None is if you specifically want the simulation to start from a non-equilibrium position. Note: For any given length. this simplifies the static analysis and should enable convergence. which is the mass that would be accelerated at 1 unit of acceleration when one unit of force was applied. then OrcaFlex converts all the data in the model into the new units. so for example a mass density has units of M/L^3. w System Modelling: Data and Results, General Data model is moving with the specified velocity. The static position is therefore then referred to as a steady state position, and the calculation of this position allows for any drag loads due to differences between the starting velocity and the current velocity. Note: The model will start the simulation from the calculated steady state; i.e. with the specified starting velocity. So you should normally ensure that each vessel in the model has its prescribed motion for stage 0 (the build-up stage) set to match the specified starting velocity. Otherwise the simulation will start with a sudden change in vessel velocity, which will cause a "kick" which may take some time to settle down. Statics Convergence Parameters When buoys or vessels are included in the static analysis, their equilibrium positions are calculated using an iterative algorithm that is controlled by the convergence parameters on the General data form. They do not normally need to be altered. However if the static calculation fails to converge it is sometimes possible to improve the behaviour by adjusting the convergence parameters. Max Iterations The calculation is abandoned if convergence has not been achieved after this number of steps. For some difficult cases simply increasing this limit may be enough. Tolerance This controls the accuracy of the solution, for Lines, 3D Buoys, 6D Buoys and Vessels. Min Damping, Max Damping For some cases it is necessary to control the convergence process by damping down (i.e. reducing) the step taken at each stage. The program includes an automatic damping system that chooses a suitable damping factor for each iteration, but the user can set the minimum damping and maximum damping factors that are used. Normally the default values will suffice but for difficult cases the default values can be altered. For cases that appear to make the convergence unstable (e.g. giving very bad line positions on the screen) try increasing the Min Damping factor to a value greater than 1, say values in the range 1 to 10. You can also try increasing the Max Damping factor, say to values in the range 10 to 100. Note: Convergence will be slower with larger damping values so you should use the smallest values that result in statics converging. Mag. of Std. Error, Mag. of Std. Change For some cases it may be necessary to reduce one or both of these values from their defaults. Doing so is likely to slow down the convergence, but it may be necessary in order to achieve convergence! 6.4.2 Dynamics Simulation Stages The simulation proceeds in a Number of Stages each of a given Duration. See Figure: Time and Simulation Stages in Dynamic Analysis. Before the first stage is a Build-Up Period during which the sea conditions are slowly ramped up from zero in order to avoid sudden transients when starting a simulation. Time during the build-up stage is reported by the program as negative, so that the first stage proper starts at time t=0. When using regular waves, it is usual to define the whole simulation as a single stage and results are presented on a cycle-by-cycle basis. In random waves there is no meaningful "wave cycle". By dividing the simulation time into stages you are free to collect results for specific time periods of interest. Logging OrcaFlex stores the results of a simulation by sampling at regular intervals and storing the samples in a temporary log file. When you save the simulation OrcaFlex writes the data to the simulation file, followed by a copy of the log file, so that the sampled values can be read back in again at a later date. You can control the time interval between log samples by setting the Target Sample Interval on the general data form. The Actual Sample Interval will be the nearest whole multiple of the dynamic time step. You can obtain more information about the logging by using the Properties command on the popup menu on the general data form. This reports the number of log samples that will be taken and the size of the resulting simulation file. Logging Precision You can also control the Precision with which samples are logged. 214 w System Modelling: Data and Results, General Data Single precision uses 4 bytes to represent each value and gives about 7 significant figures, which is quite accurate enough for almost all applications. Double precision uses 8 bytes per value, giving about 16 significant figures but uses twice as much disk space. Double precision logging is usually only needed in very particular cases. We therefore recommend that you use single precision logging unless you see signs of precision problems in the results. The typical signs of precision problems are that the curvature or bend moment time histories for a line look more like a step function than a smooth curve. If you see such results then try using double-precision logging to see if precision is the cause. The typical case where precision problems can occur is where the model contains a pipe or riser that has an extremely high bend stiffness and which experiences large displacements during the simulation. The reason is that OrcaFlex logs the positions of each node but in order to save space in the simulation file it does not log the curvature, bend moment etc. Instead OrcaFlex recalculates results like curvature and bend moment from the node positions whenever you request these results. When both the bend stiffness and the node displacements are very large then this calculation can greatly amplify the small steps in node position (8th significant figure) that are present in a single precision log, giving a bend moment graph that has steps rather than being smooth. 6.4.3 Integration & Time Steps Integration Method OrcaFlex implements two complementary integration schemes: Explicit and Implicit. Theoretical details are given in Dynamic Analysis: Calculation Method. Explicit Integration The explicit scheme used by OrcaFlex is forward Euler. Like all explicit schemes this is conditionally stable. In practice this means that in order to achieve stability the time step must be small compared to the shortest natural nodal period. By default OrcaFlex will automatically set the time step. Implicit Integration For implicit integration OrcaFlex uses the Generalised-α integration scheme which is unconditionally stable for linear systems. Constant and variable time step options are available. OrcaFlex provides two results variables (Implicit solver iteration count and Implicit solver time step) which can be used to track the performance of the implicit integration scheme. Limitations of Implicit Integration Some of OrcaFlex's features have not been adapted for the implicit scheme. Because of this implicit integration cannot be used with models that use any of the following features: Vessels using Calculated (3 DOF) primary motion or Calculated (6 DOF) primary motion when some superimposed motion is also applied. Note that implicit integration can be used with vessels using Calculated (3 DOF) primary motion or Calculated (6 DOF) primary motion when no superimposed motion is applied. Tension-controlled detailed winches with non-zero inertia. Time domain VIV models. Also, note that implicit integration does not include seabed damping, solid damping or line clash damping. Advantages and disadvantages of the two integration schemes The explicit scheme is extremely robust and flexible. Its main drawback is that the stability requirements can result in very short time steps and correspondingly long computation times. This tends to be most significant for stiff systems, or for systems with fine segmentation. For such systems the implicit scheme can be faster, sometimes by orders of magnitude. It is essential to consider accuracy as well as computation time. For the explicit scheme, if the simulation is stable then, in our experience, it is rare for the results to be inaccurate. We recommend that you conduct time step sensitivity studies to confirm this. Implicit schemes, on the other hand, can quite easily achieve stability and yet produce inaccurate results. For rapidly varying physical phenomena (e.g. snatch loads, impact, sudden line on line clashing etc.) results accuracy is more likely to be an issue. We recommend that time step sensitivity studies are carried out to ensure accuracy of results. Comparisons with the explicit scheme are particularly useful for this purpose. 6.4.4 Explicit Integration Inner Time Step, Outer Time Step For efficiency of computation, OrcaFlex uses 2 integration time steps when explicit integration is used in the dynamic simulation: an inner time step and a larger outer time step. Most calculations during the simulation are done every inner time step, but some parameters (the more slowly-varying values such as wave particle motion and 215 w System Modelling: Data and Results, General Data most hydrodynamic and aerodynamic forces) are only recalculated every outer time step. This reduces the calculations needed and so increases the speed of simulation. The usual effect of setting one of the time steps too large is that the simulation becomes unstable, in the sense that very large and rapidly increasing oscillations develop, usually very near the start of the simulation. OrcaFlex detects and reports most such instabilities; the time steps can then be reduced and the simulation retried. However, it is generally worth repeating important simulations with smaller step sizes to ensure that no significant loss of accuracy has occurred. Note: High values of Seabed stiffness may shorten the natural period of parts of the system lying on it. This in turn leads to shorter inner time steps being required. Beware that the effects of seabed stiffness will not be accounted for if touchdown does not occur until dynamics are run. Recommendations for setting time steps Both time steps must be short enough to give stable and accurate simulation. Experience indicates that the inner step should not exceed 1/10th to 1/20th of the shortest natural nodal period of motion for any degree of freedom in the model. The shortest natural nodal period is reported in the Full Results for statics. The outer step can usually be set to 10 times the inner time step; this gives a good saving in computing time without risking instability. In addition, the outer time step should generally not be more than 1/40th of the wave period (or 1/40th of the zero crossing period for a wave spectrum). If you are using a Wake Oscillator VIV model then we recommend that the outer time step is no more than 1/200th of the minimum Wake Oscillator Strouhal Period. Always use recommended time steps OrcaFlex helps you set the simulation time steps using the above criteria. There are 2 modes of operation: If Always use recommended time steps is checked (the default setting) then OrcaFlex will calculate recommended time steps and use these values directly. This means that any values that you specify will be overwritten. The main advantage of using this option comes during the design phase. If you make changes to the model's properties which alter the shortest natural nodal period then OrcaFlex automatically modifies the time steps accordingly. This is particularly useful when you make a change that allows the use of longer time steps. When not using this option it is all too easy to forget to lengthen the time steps and suffer unnecessarily long simulation run times. The other significant benefit of this mode of operation comes when preparing a large number of similar simulations using batch script methods. Suppose that the different models involved have differing shortest natural nodal periods. The Always use recommended time steps option allows you to use appropriate time steps for each individual model without having to set them manually. Alternatively, if Always use recommended time steps is not checked then OrcaFlex first of all calculates the recommended time steps. If these are shorter than the values specified on the General Data form then OrcaFlex issues a warning and gives you the option of using the recommended values. You are free to disregard the warnings if desired, but if either time step (though especially the inner step size) is set too large there is danger of instability or inaccuracy in the simulation. The main situation where this mode of operation is to be preferred is when OrcaFlex recommended time steps are too long and lead to an unstable simulation. Sometimes the only solution is to set the time steps manually and this option gives you that flexibility. Recommended time step settings Inner time step (fraction of shortest natural period) Our experience is that for most cases the inner time step can safely be set to 1/10th of the shortest natural nodal period. However, for some models you may find you need to use a shorter time step to achieve a stable simulation. By changing this value you can control what fraction of the shortest natural nodal period OrcaFlex uses to calculate the recommended inner time step. The default value is 10, which equates to a recommended inner time step of 1/10th of the shortest natural nodal period. A value of 20 would give a recommended inner time step of 1/20th of the shortest natural nodal period, and so on. Outer time step (multiple of inner time step) The recommended outer time step will be no greater than this value times the inner time step. Outer time step (fraction of wave period or Tz) The recommended outer time step will be no greater than T divided by this value, where T is either the wave period (for regular waves) or Tz (for random waves). 216 w System Modelling: Data and Results, General Data Outer time step (fraction of Wake Oscillator Strouhal period) This data item is only available if you are using a Wake Oscillator VIV model. The recommended outer time step will be no greater than the minimum Wake Oscillator Strouhal Period divided by this value. 6.4.5 Implicit Integration Implicit Integration Parameters Use variable time step For the implicit solver OrcaFlex offers both constant and variable time step algorithms. The default is to use a constant time step and in general this is to be preferred. Variable time step schemes can introduce high frequency noise into a system which in turn can lead to inaccurate results, for example noisy time histories, non-physical spikes in results etc. Note that this is a feature of all variable time step algorithms. For the majority of systems no problems arise when using a variable time step. However, if you are using variable time steps then we do recommend that you check the quality of your results. The variable time step algorithm chooses the time step based on the number of iterations used for previous time steps. If a large number of iterations were required for previous time steps then the time step is reduced. Conversely, if a small number of iterations were required then the time step is increased. The results variables Implicit solver iteration count and Implicit solver time step can be used to track the performance of the variable time step algorithm. Time step / Maximum time step If you are using a constant time step then this data item determines that time step. OrcaFlex has a default value of 0.1s. However, different systems will require shorter time steps and indeed some systems can give perfectly accurate answers with longer time steps. If you wish to optimise run times then you may need to experiment with different time step values. If you are using a variable time step then this data item limits the time step used by OrcaFlex and it will never exceed this value. Warning: Implicit solvers can produce inaccurate results, even for stable simulations, if the time step is chosen to be too large. Because of this we strongly recommend that you carry out sensitivity studies on your time step to ensure accuracy. A very useful additional technique is to compare results from the implicit solver and the explicit solver. Maximum number of iterations The implicit integration scheme uses an iterative method to solve the dynamic equilibrium equations. The calculation is abandoned if convergence has not been achieved after this number of iterations. If you are using a variable time step then this results in the time step being reduced rather than the simulation being aborted. Accordingly we recommend that a relatively small value is used, we recommend using the default value of 20. This allows OrcaFlex to abandon the current iteration quite early and try again with a shorter time step. Conversely if you are using a constant time step then the simulation is aborted if convergence cannot be achieved inside this number of iterations. Because of this we recommend using a larger value than for variable time steps. The default value of 100 is usually a good choice. Tolerance A non-dimensional value which controls the accuracy of the solution. Increasing this value can result in reduced computation time since fewer iterations are needed to solve the dynamic equilibrium equations. However, doing so may also result in inaccurate results. Notes: We recommend that you use the default tolerance value. Should you choose to increase it then we strongly recommend that you perform sensitivity studies to confirm the accuracy of your results. For systems where the only responses are extremely slowly varying (e.g. drift motions, Spar VIM) you might need to use a smaller tolerance than the default value to obtain accurate results. 6.4.6 Numerical Damping Line Target Damping Finite element models may contain spurious high frequency response, a feature inherent in the finite element method. Line Target Damping specifies damping whose effect is usually only to damp down this high frequency noise. The value gives the % critical damping level that will be achieved for oscillations at the shortest natural period of each node. These oscillation periods are typically very short and depend on the segment length and stiffness values of the line section involved. 217 w System Modelling: Data and Results, General Data The % critical damping generated for longer oscillation periods is inversely proportional to the period, and for typical response periods (usually much longer) the damping level is usually insignificant. To achieve a significant level of damping at wave period usually requires a very high Line Target Damping value to be calculated and specified, and this in turn often requires shorter time steps and so longer simulations. Because of this we recommend that you use Rayleigh Damping to model the effects of structural damping. The target damping can be specified independently for tension, bending and torsion. Within broad limits, this damping has little influence on the results of a simulation unless the system is subject to very rapid variations in tension or bending, for example when snatch loads occur. A value between 5% and 50% of target damping is usually assumed. For details on the use of these data, see the theory documentation for tension, bending and torsion. Note: These data are only available when using the explicit integration scheme. The implicit integration scheme has built-in numerical damping. 6.4.7 Response Calculation Simulation Period used for Response Calculations These data items determine the period of the simulation to be used for the Spectral Response Analysis. This period is specified by giving From and To simulation times. A value of '~' for the From time is interpreted as simulation time 0. A value of '~' for the To time is taken to mean the simulation time at the end of the simulation. These are the default values and in most cases are the values which you should use. Note: These data items are only available when you have selected the Response Calculation wave type. 6.4.8 Results Spectral Density Fundamental Frequency Determines the fundamental (minimum) frequency for Spectral Density graphs. The default value is usually quite reasonable. However, smaller values are sometimes required to achieve good resolution of the spectral form. Wall Clock Time, CPU Time These two output values, found on the properties report, can also be obtained from one of the OrcaFlex automation interfaces. Both variables report the time taken to perform the dynamic simulation. Wall Clock Time measures the real time, in seconds, that elapsed between the start and finish of the simulation. CPU Time measures the total CPU time, in seconds, summed over all processors in the system. The results can be extracted using the OrcaFlex post-processing spreadsheet. Use the Get Data command with object name General and variable name WallClockTime or CPUTime. From the Python or MATLAB interfaces use the following code: WallClockTime = model.general.WallClockTime CPUTime = model.general.CPUTime From C or C++ you should call C_GetDataDouble passing the handle the General data object and a data name of "WallClockTime" or "CPUTime". Log file location(s) This value, also found on the properties report, can be obtained with the automation techniques described above using the name LogFileLocation. This value is the location of any log files used by an OrcaFlex simulation. Results variables For details on how to select results variables see Selecting Variables. The available variables are: Time The simulation time. Implicit solver iteration count The number of iterations used by the implicit integration scheme to solve the dynamic equilibrium equations. Implicit solver time step The time step used by the implicit integration scheme. This is most useful when you are using a variable time step. 6.4.9 Post Calculation Actions Post Calculation Actions provide a means to include post-processing as part of your wider OrcaFlex automation process. The data are described below and are specified on the General data form. 218 w System Modelling: Data and Results, General Data For example, consider the batch processing capability. This is typically used to run large numbers of dynamic simulations. The input data files are added to the batch form, and then OrcaFlex performs the simulations using as many processors are available on the machine. The next step is to post-process the simulations to extract the desired results. This can also be a time consuming task and it is very desirable that it be automated. If the post-processing is performed using the OrcaFlex spreadsheet, then the spreadsheet can also be added to the list of batch form jobs. The post-processing will then be performed after all the simulation files have been generated. So, if your post-processing uses the OrcaFlex spreadsheet then it can be integrated into your automation process. However, if you do not use the OrcaFlex spreadsheet for post-processing, then you need a different mechanism to integrate your post-processing. Post calculation actions meet that need. A model can define one or more post calculation actions. The actions can be executed after a static analysis is completed or after a dynamic analysis is completed. Post calculation actions are executed when you perform a calculation using batch mode or Distributed OrcaFlex (requires version 5 or later). Post calculation actions can also be invoked from the OrcaFlex programming interface. Note that post calculation actions are not executed when an analysis is performed interactively in OrcaFlex. There are two types of post calculation action: In-process Python actions and Command script actions. In-process Python actions This action type takes advantage of the Python interface to OrcaFlex. The script is run inside the OrcaFlex process, by an embedded Python interpreter. The benefit of using an in-process execution model is that the script has direct access to the same model that OrcaFlex used to perform the analysis. This is in contrast to the command script actions which need to start separate processes to execute the script, and then load the model and simulation file into memory. In fact an in-process Python action is executed before the simulation file is saved. The action is specified by a script file containing Python code. The script file must use the .py file extension, and must define a function named Execute which receives a single parameter. The sequence of events that are carried out around the action's execution is as follows: 1. The OrcaFlex analysis, either statics or dynamics, is performed. 2. The embedded Python engine is loaded into the process. 3. The action's specified script file is imported. 4. The Execute function is called. 5. Control returns to OrcaFlex which then saves the simulation file. The single parameter that is received by the Execute function can be named whatever you like. But for the sake of discussion, we adopt the convention of naming it info. The info object defines the following attributes: model, params, modelDirectory and modelFileName. The model attribute is an instance of the Model class defined in the OrcFxAPI module. Through this object you can perform your post-processing in exactly the same way as with a standalone Python script. The params attribute is a string containing the Parameters text specified on the data form. The other attributes, modelDirectory and modelFileName, provide information about the file on which the analysis was performed. The modelFileName attribute contains the absolute path of the simulation file. Note that the simulation file is yet to be saved. You would typically use modelFileName to create the file name for any output files that your post-processing script saves. For example you might simply change the file extension from .sim to .txt. The modelDirectory attribute is simply the name of the directory that contains modelFileName. Of course, modelDirectory could be obtained by simple text processing of modelFileName, but we provide modelDirectory for the sake of convenience. Post-processing actions can be quite time-consuming. If you wish to report progress to the user then you can call model.ReportActionProgress(progressText). OrcaFlex will then display these progress strings in the batch form's list of jobs. If the action is executing in the context of Distributed OrcaFlex, then the progress text will appear in the Distributed OrcaFlex viewer's list of jobs. Command script actions If your post-processing tool of choice is other than Python, then you must use the command script action type. This action type executes in a separate process. Whilst this is perhaps somewhat less efficient than the in-process Python actions, the command script actions are extremely flexible. The sequence of events is a little different for command script actions: 1. The OrcaFlex analysis, either statics or dynamics, is performed. 2. OrcaFlex saves the simulation file. 219 w System Modelling: Data and Results, General Data 3. A new command interpreter (cmd) process is created. 4. The command interpreter executes the commands in the action's script file. Since the command interpreter cannot perform OrcaFlex post-processing, your script file will typically contain a command to launch another process that can. For example you may launch a MATLAB process. Note: Command scripts that invoke MATLAB cannot be used when processing using Distributed OrcaFlex. Distributed OrcaFlex runs as a Windows service which does not allow interaction with the desktop, and the MATLAB executable always interacts with the desktop. The command script has access to the same information that is passed to in-process Python actions. However, for a command script these values are passed using environment variables with the following names: PostCalcActionParams, PostCalcActionModelDirectory and PostCalcActionModelFileName. Progress is reported simply by writing to the standard output device. If your process buffers the standard output then you will need to flush those buffers in order for the progress to be delivered to OrcaFlex in a timely manner. Note: MATLAB uses its own console which captures the standard output and standard error output buffers. Consequently these outputs are not available to OrcaFlex to display. Data Each post calculation action is defined by the following data. Run after Determines whether the action is run after the static analysis, or after the dynamic analysis. Note: Command script actions that are scheduled to run after statics are sometimes not executed. If the overall analysis is a dynamic analysis, then a command script action will not execute after the statics calculation. The issue is that the static calculation is performed as a pre-requisite step for the ultimate dynamic analysis, but the simulation file is not saved until the dynamic simulation is completed. On the other hand, in-process Python actions can run because they are not dependent on the existence of the simulation file. Typically this issue is not a problem. Commonly a set of OrcaFlex data files is designed with either static analysis or dynamic analysis in mind. And the post calculation actions would be configured to run after statics or dynamics respectively. What's more, both types of action can extract static results when run after a dynamic simulation. Action Type Specifies whether the action is an In-process Python action or a Command script action. Python Version For in-process Python actions only, this determines which version of Python is used to execute the script. If Python 2 is selected then either version 2.6 or 2.7 will be used. If both of these versions are present on your system, then the most recent, i.e. 2.7 will be used. If Python 3 is selected then one of version 3.0, 3.1, 3.2 or 3.3 will be used. Again, if more than one of these versions is present on your system, then the most recent will be used. Script File Name The file name of the action script. You can either specify the full path or a relative path. Parameters Text that is passed to the action. This text can be used for whatever purposes you like. For example, you could specify a list of results variables that are to be extracted. Skip dynamic simulation file save Suppresses the saving of dynamic simulation files when running in batch mode or Distributed OrcaFlex (i.e. whenever post-calculation actions are active). This is useful if the post-calculation action extracts all the output you need from the simulation. Skipping the saving of the simulation file allows you to reduce storage and bandwidth demands. Note that this data item is only available if there are some actions defined. And the data item can only be checked if all of the actions are in-process Python actions. This is because command script actions rely on the existence of a simulation file. Examples In order to complement the formal descriptions above, we present concrete examples for each type of post calculation action. These actions should be assigned to a model that contains a line named Line1. 220 w System Modelling: Data and Results, General Data In-process Python actions Save the following code to a text file named script.py in the same directory as your OrcaFlex data file. import os.path def Execute(info): line = info.model['Line1'] tension = line.TimeHistory('Effective Tension', objectExtra=OrcFxAPI.oeEndA) outputFileName = os.path.splitext(info.modelFileName)[0] + '.txt' with open(outputFileName, 'w') as f: f.write(line.name + ' End A Effective Tension\n') for value in tension: f.write(str(value) + '\n') Note: You must not explicitly import the OrcFxAPI module in post-calculation action code. This import is performed implicitly by the host OrcaFlex process. The import needs to be performed by the host OrcaFlex process to ensure that the imported OrcFxAPI module correctly references the host OrcaFlex process. The post-calculation action code can access the implicitly imported OrcFxAPI module in the usual way, as is demonstrated in the above example. Add a single post calculation action and set its data as follows: Save the data file and run it via the OrcaFlex batch form. Once the dynamic simulation completes, a text file will be created containing the Effective Tension time history values for End A of the line. Command script actions Save the following code to a text file named PostProcess.m in the same directory as your OrcaFlex data file. try modelFileName = getenv('PostCalcActionModelFileName') model = ofxModel(modelFileName) line = model('Line1') tension = line.TimeHistory('Effective Tension', ofx.oeEndA) [pathstr, name, ext] = fileparts(modelFileName) outputFileName = fullfile(pathstr, [name '.txt']) outfile = fopen(outputFileName, 'wt') fprintf(outfile, '%s End A Effective Tension\n', line.name) fprintf(outfile, '%f\n', tension) fclose(outfile) catch exit(-1) end This MATLAB script performs the exact same operation as the Python script above. The script assumes that the MATLAB interface to OrcaFlex is available. You may need to add it to your global MATLAB path, or include an addpath statement in the .m file above. We also need to create a simple command script to call the MATLAB script. Save the following to a text file named script.bat, again in the same directory as your OrcaFlex data file. rem Requires that matlab.exe is on the system path. rem Alternatively, set the PATH variable here: rem set path=path\to\matlab\bin;%path% matlab.exe -wait -nodesktop -minimize -r "PostProcess, exit" 221 w System Modelling: Data and Results, General Data Note: If there is no explicit exit command then MATLAB will remain open and not return to OrcaFlex. If an error occurs within the script then the exit command in the script.bat file will not be reached, so we need to include try…catch statements around our code to trap an error and exit with an error code to OrcaFlex. Add a single post calculation action and set its data as follows: Save the data file and run it via the OrcaFlex batch form. Once the dynamic simulation completes, a text file will be created containing the Effective Tension time history values for End A of the line. Development, debugging and testing Post calculation actions cannot be invoked interactively. Because of this it can be a little awkward to debug actions. An effective way to work is to use the Python interface to help. The typical workflow when developing a post calculation action looks like this: 1. Run dynamic simulation in the batch form. When the simulation completes, the actions are invoked. 2. Look at the output and results of the actions. 3. If the action has worked as intended, development is complete. Otherwise, refine the action and go to step 1. In an ideal world we would all write perfect code at the first time of asking and never need to go around the above loop. Of course, the reality is quite different. The big problem with the workflow above is that running the dynamic simulation can take time. One very simple solution is to add the simulation file to the batch form rather than the data file. When the batch form processes this it finds that there is no need to do any dynamic simulation and proceeds immediately to the post calculation actions. An alternative is to use a short Python script to load the simulation file and then invoke the post calculation actions. For example: import sys import OrcFxAPI for file in sys.argv[1:]: model = OrcFxAPI.Model(file) model.ExecutePostCalculationActions(file, OrcFxAPI.atInProcPython) Save this script in the same directory as your simulation files and give it an appropriate name, for example ExecuteActions.py. Now you can execute the script passing the simulation files as arguments: python ExecuteActions.py SimFile1.sim SimFile2.sim This approach avoids having to interact with the OrcaFlex batch form. What's more, if you are using a Python debugger you can step through your post calculation action using that debugger. Debugging MATLAB command scripts As noted previously, MATLAB does not output to the conventional standard output and error buffers. To capture error information from a script, the following methods can be used: 1. Run your script in the MATLAB GUI first to test for obvious errors. You will need to change the working directory of MATLAB to the location of your model and script, and you will need to substitute values for the environment variables set by OrcaFlex. 2. Modify your scripts to remove the exit commands and run the model in the OrcaFlex batch form. If an error occurs in your script, the MATLAB console will remain open for you to see the error message. 3. Modify the catch statement in your script to output the error details to a file, for example: 222 . Small log files are stored in memory to improve performance and larger files are stored in your machine's temporary directory. 223 . elevation and centre) can be specified directly. exit(-1) end 6. it consists of the sea. a value of 90° is the positive Y direction etc. For certain models the estimate may be inaccurate. The CPU time is the sum of CPU times over all CPUs used and the wall clock time is the real time that elapsed whilst simulating. err. Total number of log samples equals Simulation duration including build-up / Actual log sample interval Log sample frequency This equals 1 / Actual log sample interval. 6.4. This is because the number of vortices is variable and depends on the simulation.5 ENVIRONMENT The environment defines the conditions to which the objects in the model are subjected. If the Calculated based on the model extent option is selected then the default view is a wire frame view.. catch err errfid = fopen('matlab_error. Log file location(s) This reports the location of any log files used by an OrcaFlex simulation. the scale bar and the compass in 3D Views. '%s\n'. the view axes. If the Specified option is selected then the default view parameters (graphics mode. North direction If this direction is defined then a compass is drawn on the 3D View. waves and seabed. Actual log sample interval. It equals Wave Period / Actual log sample interval. So a value of 0° is the positive X direction. Simulation CPU time.w System Modelling: Data and Results. Actual Sample Interval is the nearest whole multiple of the inner time step.message) fclose(errfid). Target log sample interval. Usually this would be specified by first setting up the desired view parameters in a 3D View window and then using the Set as Default View menu item.10 Drawing Pen The pen used to draw the global axes. Environment try your script code. current. Default View Parameters These data determine the default view for this model. It reports the following: Simulation duration including build-up The sum of the stage durations. size. azimuth. Log samples per wave cycle This is only available when the Wave Data specifies a single regular wave train. Total number of log samples Target log sample interval is the data item specified on the data form. 6. Estimated simulation file size An estimate of the simulation file size.4. The compass is only drawn for plan views. Simulation wall clock time The time taken to perform the simulation.11 Properties Report The General Data properties report is available from the popup menu on the data form. in elevation. 'a+') fprintf(errfid. When a new 3D view window is opened it will start with these view parameters. In particular the size of simulation files for models using vortex tracking and which log vortices are difficult to estimate. The direction is an azimuth direction.txt'. and sized so that the entire model will be displayed. is defined by setting V = |Vr| and L = D. Note that the division by cos(α) means that Reflow can be arbitrarily large when the relative flow is very near axial. which in turn affects the Reynolds number. Kinematic Viscosity This value is used to calculate Reynolds number. Reynolds number calculation Reynolds number. Vr = Vfluid . the environment is defined relative to the global axes. but this does not matter since the normal component of relative velocity is then very small. in turn. Re. This. Accordingly the characteristic velocity is based on the relative flow velocity at a node. The viscosity can either be a constant or vary with temperature. That is Renom = |Vr|D/ν. and ν is the kinematic viscosity of the fluid.Vnode and the characteristic length is always related to the normal drag / lift diameter of the node. OrcaFlex calculates Reynolds number in order to calculate drag and lift coefficients for lines that are specified as varying with Reynolds number. so the drag and lift forces are also very small. from which it follows that Recross ≤ Renom ≤ Reflow. is defined by setting V = |Vr| and L = D/cos(α). So for example the seabed and the current and wave directions are specified relative to the global axes. Environment Datum Current Direction Z Wave Direction Still water surface Surface Z-level Y G Water Depth X Global Axes Seabed Direction of Slope Seabed Origin Figure: Environment As shown above. Reflow. 6.w System Modelling: Data and Results. is defined by setting V = |Vn| and L = D where Vn is the component of Vr normal to the line. Reynolds number is available as a line results variable. These can all be related by the equation Recross/cos(α) = Renom = Reflowcos(α). The temperature can affect the kinematic viscosity (if that is specified as varying with temperature). 224 . Cross Flow Re.5. the length of the line cross section in the relative flow direction. Temperature The temperature of the water can either be constant or vary with depth below the mean water level. can affect the drag and lift coefficients used for a line. Recross. D. If we define α to be the angle between the relative flow direction and the normal to the line then we can write Recross = |Vr|Dcos(α)/ν since |Vn| = |Vr|cos(α). Flow Direction Re. Different values of Re result from different selections of characteristic velocity and length. is a measure of the flow regime defined as Re = VL/ν where V and L are velocity and length parameters chosen to characterise the flow.1 Sea Data Sea Surface Z Specifies the global Z coordinate of the mean (or still) water level. Renom. This gives Reflow = |Vr|D/νcos(α). OrcaFlex offers the following options for characteristic velocity and length: Nominal Re. Environment Which method you select for calculating Reynolds number is in many ways arbitrary. since in most models the effects of density variation are not significant. 0. added mass. This is specified as a dimensionless multiplicative factor. For these effects a nominal sea density value is used. This is the most common value to use. density variation is important because it causes buoyancy variation. By default the sea density is constant. To neglect density variation with horizontal position this data item should be set to '~'. Thus. and at levels beyond the ends of the table the density value at the end of the table is used.w Note: System Modelling: Data and Results. To model density variation with horizontal position you must define a Horizontal Variation Factor variable data source.5. For example. which can be horizontal or sloping. Note: Density variation only affects the buoyancy of objects. Seabed Shape Data Shape Type Three types of seabed shape are available: A Flat seabed is a simple plane. The key factor is that the method chosen matches the data source used for the variable drag and lift coefficient data.5) allows you to apply a scaling factor to the vertical density profile. Horizontal Density Variation Density variation with horizontal position can also be modelled. Linear interpolation is used to obtain the density at intermediate levels. 225 . 6. for all hydrodynamic calculations other than buoyancy OrcaFlex uses a single sea density value. Interpolated allows you to specify a density profile as a table giving the density at a series of depth levels.5. Constant allows you to specify a single density value that applies at all depths. OrcaFlex does not allow for density variation when calculating hydrodynamic effects such as drag. the sea density value used is the sea density at the still water level. and how. The water's bulk modulus specifies how a given mass of water shrinks under pressure. Y. The vertical density variation can be set to Constant. Using a numeric value (e. Where a variation of density with depth has been defined the factor will be applied at all depths. Interpolated or Bulk Modulus. etc. For some systems. 0.3 Seabed Data The seabed data divides into two groups: Data specifying the shape of the seabed surface.2 Sea Density Data Sea Density The sea density can be constant at all positions in the sea or it can vary with depth and/or horizontal position. You must specify the water's Surface Density and Bulk Modulus. Since there is no variation of density with horizontal position the choice of X and Y coordinates here is arbitrary. 6. Different data sources may make different choices. using the same volume formula as for buoys and line types – see Bulk Modulus. which is taken to be the density value at the sea density origin. Vertical Density Variation Vertical Density Variation specifies whether. Here X and Y are the origin coordinates for the horizontal variation axis. ESDU 80025 provides curves relating drag and lift coefficients to Reflow. Sea Surface Z). The horizontal variation factor is assumed to be constant in the direction normal to the axis. Data specifying the seabed resistance model that OrcaFlex uses to calculate the forces acting on objects that contact the seabed. Sea Density Origin As explained above. A dry land system can be modelled by using Constant density and setting the density to zero. OrcaFlex then derives the density variation with depth on the assumption that the water column has the given bulk modulus and is at uniform temperature and salinity. Bulk Modulus specifies that the density varies with depth purely because of the compressibility of the water. If there is horizontal density variation then the sea density origin is defined to be (X.g. the water density varies with depth. Sea Surface Z). however. This is the sea density value at the sea density origin which is defined as follows: If there is no horizontal density variation then the sea density origin is defined to be (0. Environment A Profiled seabed is one where the shape is specified by a 2D profile in a particular direction. However you can specify a near-vertical cliff.Y positions. The model is only applicable to small slopes. You should check that the interpolated shape is satisfactory. and vice versa. Profile seabed data Profile The profile table defines the seabed shape in the vertical plane through the seabed origin in the seabed direction.e. note that to avoid interpolation overshoot you may need to specify several extra points just either side of the cliff. Note: You cannot model a true vertical cliff by entering 2 points with identical Distance from Seabed Origin but different Z coordinate – the second point will be ignored. and the other of those two values is updated to match. Direction The Seabed Direction is measured positive anti-clockwise from the global X axis when viewed from above (see Directions). Beyond the ends of the table the seabed is assumed to be horizontal. Flat seabed data Slope This is the maximum slope upwards. based on the specified Sea Surface Z. See Choosing Interpolation Method. or else use linear interpolation. A 3D seabed allows you to specify a fully general 3D surface for the seabed. For a profile seabed the direction specified is the direction in which the 2D profile is defined. where the interpolated seabed is significantly higher or lower than desired. Seabed Origin. with a choice of linear or cubic polynomial interpolation in between.w System Modelling: Data and Results. The seabed is assumed to be horizontal in the direction normal to the seabed profile direction. so if the water is shallow and the depth varies then the seabed origin should normally be chosen to be near the main wavesensitive parts of the model. The meaning of this data item depends on the type of seabed in use: For a flat seabed the direction specified is the direction of maximum upwards slope. Depth The seabed origin is a point on the seabed and it is the origin relative to which the seabed data are specified. If you do this. Warning: The depth at the seabed origin is used for all the wave theory calculations. in degrees above the horizontal. If you are having problems with static convergence or unstable simulations then you should try one of the other interpolation methods. Warning: Linear interpolation can cause difficulties for static and dynamic calculations. For a Flat seabed you can type in either the seabed origin Z coordinate or the water depth at the seabed origin. For Profile and 3D seabeds the Z coordinate and water depth at the seabed origin are displayed but they are not specified directly. or else the Depth. together with the interpolated shape in between profile points. in particular that the interpolation has not introduced overshoot – i. relative to which the seabed data points are specified. Overshoot can be solved by adding more profile points in the area concerned and carefully adjusting their coordinates until suitable interpolation is obtained. with a choice of Interpolation Method. It can be chosen by the user and is specified by giving its coordinates with respect to global axes. 226 . The seabed is horizontal beyond the ends of the graph. Normal to that profile direction the seabed is horizontal. The Distance From Seabed Origin is measured from the seabed origin in the seabed direction (negative values can be given to indicate points in the opposite direction). For a 3D seabed the direction and the seabed origin together define a frame of reference. 0° means sloping upwards in the global X direction and 90° means sloping up in the in the global Y direction. The specified profile points are shown. A flat seabed is modelled as a plane passing through the seabed origin and inclined upwards at this angle in the seabed direction. For example. Seabed Z values in between profile points are obtained by interpolation. If a Z coordinate is entered then the Depth is updated to match. by specifying the depth at a series of X. View Profile The View Profile button provides a graph of the seabed profile. since they are determined from the Z values specified in the profile or 3D geometry data and the specified Sea Surface Z. The program will accept slopes of up to 45° but the model becomes increasingly unrealistic as the slope increases because the bottom current remains horizontal. at a series of points specified by their Distance From Seabed Origin. The shape is specified by giving the either the seabed Z coordinate relative to global axes. Seabed damping is always zero when using the implicit integration scheme. a low value models a soft surface such as mud.g. A high value models a surface such as rock. The linear method has been provided for the special case of an analysis where your seabed data consists only of depth and slope at each line anchor point.w System Modelling: Data and Results. The x and y coordinates are given with respect to a right-handed frame of reference with origin at the seabed origin. provides a degree of control over the triangulation. The non-linear soil model gives a more sophisticated model of the seabed resistance in the normal direction. On the other hand you may find that specifying α>0 results in significant portions of your seabed being removed. note that there is no seabed damping contribution when implicit integration is used. alternatively be specified as a Depth. Linear Model The Linear model treats the seabed as a simple linear spring in both the seabed normal direction and the seabed shear directions (i. y and Z coordinates of the seabed. per unit depth of penetration. When explicit integration is used. and at any horizontal position outside the area specified the sea is considered to be infinitely deep. and vice versa. x-axis horizontal in the specified seabed direction and y-axis horizontal and normal to that x-direction. but it is unlikely to give any useful information on embedment. In this case you may find that specifying α>0 helps. The linear interpolation method allows you to build a seabed which is effectively a number of different flat sloping seabeds for each line. for convenience. so the model does not model any suction effect. including modelling of suction effects when a penetrating object rises up sufficiently. The minimum edge triangulation angle. The Seabed Damping is the constant of proportionality of the damping force. a node on a line) from its undisturbed position. and a seabed lateral resistance that is proportional to the lateral displacement of the contact point (e. not when penetration is reducing.e. (If a depth is entered then the Z coordinate is updated to match. The linear damper in the normal direction only acts when penetration is increasing. The linear model can be tuned to give specified uniform stiffness responses in the normal and tangential directions. The stiffness equals the spring reaction force. This provides a smooth interpolation which makes both static and dynamic calculations more stable and robust. α. Z vertically upwards. Linear Model Data The Normal Seabed Stiffness is the constant of proportionality of the spring force in the seabed outward normal direction. This gives a seabed normal resistance that is proportional to the penetration. For information on the suitability of the non-linear soil model see Non-linear Soil Model below. For the directions tangential to the seabed plane the non-linear model behaves as a linear spring with user-specified stiffness. and is a percentage of critical damping. The Shear Seabed Stiffness is used by the friction calculation. A value of '~' results in the Normal Seabed Stiffness being used. Some data sets (for example concave data sets) can result in strange artifacts around the edges of the data. Environment 3D seabed data The 3D seabed is defined by specifying a set of x.) The program forms a triangulation of the input data and then uses either Linear or Cubic Polynomial interpolation methods. We would normally recommend using the cubic polynomial interpolation method. The linear spring stiffnesses in the normal and lateral directions can be different. If this is the case then you should set α to 0 which results in no edge triangles being removed. Note: The seabed generated by OrcaFlex only extends as far as the data specified. the axial and lateral directions in the seabed tangent plane). since it models the non-linear and hysteretic behaviour of seabed soil in the normal direction. The stiffness for the seabed normal direction can be specified independently of the stiffness for the tangential directions. as with the linear model. A value of 0 disables friction. 227 . Also. the Linear model also includes linear dampers in the normal and lateral directions. So you must specify seabed data that covers the whole area of seabed that any object in the model might contact. which give an extra damping resistance that is proportional to the rate of penetration (for the normal direction) or the rate of lateral movement (for the lateral directions). Note that the Z coordinate can. a Linear model and a Non-linear Soil model: The Linear model gives a seabed that behaves as a simple linear spring in both the seabed normal direction and the directions tangential to the seabed plane. Seabed Model Data Two types of seabed model are available. per unit area of contact. When α>0 the program removes any triangles at the edge of the triangulation that have internal angles less than α. The Z coordinate is specified relative to the global model origin. 4 to 1.6 te/m 3. and is not suitable for modelling sand without very careful choice of soil data and model parameters to reflect sand response. This default shear stiffnes used is equal to 20/D times the soil undrained shear strength at a penetration depth of z = ½D. for implicit integration the lateral damper strength is zero. Note: The non-linear soil model is currently experimental and we are working on comparing the model against experimental results for seabed contact. The non-linear soil model is suited to modelling soft clays and silty clays. See Soil Model Parameters. The Saturated Soil Density specifies the density of the seabed soil when fully saturated with sea water. and it is particularly relevant for cases (such as typical deep water seabeds) where the mudline undrained shear strength is only a few kPa or less and the seabed stiffness response to catenary line contact is dominated by plastic penetration rather than elastic response. For further details see Non-linear Soil Model Data. For shallow water the seabed soils are typically stronger than in deep water. It is a development from earlier models that proposed and used a hyperbolic secant stiffness formulation. Seabed Theory and Non-linear Soil Model Theory. These data are the same as those described above for the linear model. The non-linear soil model is more sophisticated than the Linear model. The shear stiffness can be specified as '~'. Note that the non-linear model is not suitable for caprock conditions. Beware that the shorter natural periods will not be reported in the statics results table if touchdown only occurs during the simulation. and is documented in Randolph and Quiggin (2009).3 to 2 kPa/m. It is used by the non-linear seabed model to model the extra buoyancy effect that arises when a penetrating object displaces seabed soil. The undrained shear strength at any given penetration distance z is then taken to be su(z) = su0 + ρ. Note: For dynamic analysis using implicit integration you might find that you need to use a shorter time step with the non-linear soil model than with the Linear model. su0.w System Modelling: Data and Results. In the seabed lateral directions the seabed is modelled in the same way as described above for the Linear model. where D is the contact diameter of the penetrating object. Site-specific data should be used. The shear strength is specified by giving the undrained Shear Strength at Mudline. See Soil Extra Buoyancy Force for details. in which case a default shear stiffness value is used. See Non-linear Soil Model Theory for details of how these data are used to model the seabed reaction force. It models the non-linear and hysteretic behaviour of seabed soil in the normal direction. Non-linear Soil Model The non-linear soil model has been developed in collaboration with Prof. ρ. Typical deep water sediments have essentially negligible undrained shear strength at mudline (0 to 5 kPa) and an undrained shear strength gradient of 1. They are non-dimensional parameters that control how the seabed soil is modelled. Mark Randolph FRS (Centre for Offshore Foundation Systems. and this is based on the specified soil shear strength properties. University of Western Australia). Shear Stiffness and Damping These specify the strength of the lateral linear spring+damper that is used to model the lateral resistance. Non-linear Soil Model Data The data for the non-linear soil model divides into three groups: Soil Properties These specify the undrained shear strength and saturated density of the seabed soil. The lateral damper is only used for explicit integration. so it is given by: Default Shear Stiffness = (20/D)[su0 + ρ(½D)] Seabed Soil Model Parameters These appear on a separate page on the Environment data form. and this may require the use of a smaller simulation time step. Environment Warning: If you use the explicit integration scheme then note that a high seabed stiffness will shorten the natural periods of parts of the system lying on it. such as those proposed by Bridge et al and Aubeny et al. Typical saturated soil densities are in the range 1. See Linear Seabed Model Theory for details of how these data are used to model the seabed reaction force. Please contact Orcina if you have any feedback and comments on the model or ideas for improvement. The non-linear modelling only applies to the seabed normal direction. and the undrained Shear Strength Gradient. including modelling of suction effects when a penetrating object rises up sufficiently. They should be obtained from geotechnical survey of the site.z. 228 . Stokes' 5th or Cnoidal. OrcaFlex offers a choice of three methods: Vertical Stretching. and 90° means a wave travelling in the positive Y-direction. Torsethaugen. ISSC (also known as Bretschneider or modified Pierson-Moskowitz). for example. but multiple wave trains can be used for more complex cases. See Dynamic Analysis for details of the time frames used in OrcaFlex.4 Wave Data Number of Wave Trains You can define a number of different wave trains and the overall sea conditions are the superposition of the wave trains. specified by a time history file or specified explicitly by a list of components. a superposition of locally generated waves in one direction and distant storm-generated swell in a different direction). The Cnoidal wave theory is only suitable for long waves in shallow water. Gaussian Swell or User Defined Spectrum. See Data for Regular Waves. Wave Direction For both regular and random waves.e. The Stokes' 5th wave theory is only suitable for short waves in deep water. It defines the global time that corresponds to simulation time t = 0. Data for a Wave Train Each wave train is specified by the following data. These are various different spectra for random waves. Wheeler Stretching and Extrapolation Stretching. For regular waves we recommend the Dean wave – this is a non-linear wave theory using a Fourier approximation method and it is suitable for all regular waves. 229 . With multiple wave trains the direction of the first wave train is taken to be the primary direction and this is reflected in both the way the sea is drawn and the Sea Axes. For further details see Ranges of Applicability. OrcaFlex will give a warning or may report that the wave calculation has failed. Time History allows you to specify the wave in the form of a time history input file. Environment 6. These are various different wave theories for regular waves. this is the direction that the wave is progressing. See Data for Time History Waves. 0 degrees means a wave travelling in the positive X-direction. JONSWAP. Altering the simulation time origin shifts the simulation time relative to all of the wave trains. If the specified wave is not suitable for the selected wave theory. measured positive anticlockwise from the global X-axis when viewed from above. This wave type gives you complete control over the wave train and would typically be used to compare OrcaFlex results with results produced by a different program. Kinematic Stretching Method Kinematic stretching is the process of extending linear Airy wave theory to provide predictions of fluid velocity and acceleration (kinematics) at points above the mean water level. Dean. For details see Kinematic Stretching Theory. So. A truncated white noise spectrum has energy spread evenly over a userspecified range of frequencies.w System Modelling: Data and Results. See Data for User Specified Components. alternatively. so kinematic stretching also applies to random waves. If you are using a directional spreading spectrum then the wave direction is taken to be the principal direction. Simulation Time Origin The simulation time origin allows you to control the period of time that the dynamic simulation covers. The Airy wave theory is a simple linear wave theory that is only suitable for small waves. In most cases a single wave train is sufficient. If this happens please check that the wave theory selected is suitable. such as a crossing sea (i. Note: Random waves are modelled by combining a number of linear Airy waves. See Data for Response Calculation.5. Ochi-Hubble. Each wave train can be given a name and a specified direction. a random wave (with a choice of spectrum). you can also time shift an individual wave train by altering its wave time origin. A wave train can be one of the following: a regular wave (with a choice of wave theory). Wave Type Each wave train can be any of the following types: Airy. Response Calculation is a special type of random wave with a truncated white noise spectrum which is used for Spectral Response Analysis. User Specified Components allows you to specify the wave train as the sum of a number of sinusoidal components. so changing the simulation time origin allows you to shift the period of global time that is simulated. 6. You specify the number of discrete wave directions to be used together with an exponent for the spreading function. the phases of the wave components that make up the wave train are randomly distributed. The spatial origin is specified relative to the global origin and the time origin is specified relative to the global time origin. For most waves the default value will suffice. Gaussian Swell. Wave Origin and Wave Time Origin Each wave train has its own spatial origin and time origin. you can set the order of stream function to be used. Full details are given in the wave theory topic. 6. OrcaFlex uses a random number generator and the user-defined seed to assign phases. Number of wave directions and Spreading exponent These data allow you to model a directional spread spectrum. Torsethaugen Spectrum. but they are fixed relative to the wave time origin. for nearly breaking waves the method sometimes has problems converging. Stream Function Order For the Dean wave theory only. For a regular wave train the wave time origin is the time at which a wave crest passes the wave origin. The Wave Type specifies the type of spectrum and the spectral data then define the actual spectrum within that type. If this is the case then it might be worth experimenting with different values. sea state and simulation time origin. Environment The Horizontal Velocity preview graph can be used to see the effect of the different kinematic stretching methods. See: JONSWAP and ISSC Spectra. The phases associated with each wave component are pseudo-random.5. such as a large wave. Secondly.w System Modelling: Data and Results. However. OrcaFlex uses a cosn spreading function where n is the specified spreading exponent. If a maximum component frequency range is specified then the actual number of components can be greater than the number of components specified here.5. since randomly selecting different periods of the wave train is statistically equivalent to choosing different random phases for the wave components. You can therefore use the origins to arrange that a wave crest passes a particular point at a particular time during the simulation. independently of the other wave trains. you may want to do a series of runs with the same wave train data but different random phases for the wave components.5 Data for Regular Waves A regular wave is a single wave component defined by wave Direction. Height and Period. 230 . For a random wave train. so you can shift a given wave train in space or time. If you are using a directional spreading spectrum then you specify the number of wave components per direction. Otherwise you specify the total number of wave components for the wave train. If the number of wave directions is set to 1 then no spreading is applied. You can therefore arrange that the simulation covers a different piece of the random wave train by changing the wave time origin. see Setting up a Random Sea.6 Data for Random Waves Random waves are specified by giving the energy spectrum of the random sea. The wave train's data specify the wave train relative to its own origins. This can be useful for two purposes: You may want to select a particularly significant event in the wave train. User-Defined Spectrum. Number of Components and Seed Random wave trains are represented by a user-defined number of component waves whose amplitudes and periods are selected by the program to give a sea state having the specified spectrum. by adjusting its origins. Wave height is measured from trough to crest. The sequence is repeatable. OrcaFlex has special facilities to make this easy – see Wave Preview. For more information. Ochi-Hubble Spectrum. so the same seed will always give the same phases and consequently the same train of waves. different wave conditions can be obtained by shifting the wave time origin. For a given spectrum. This can be done by specifying randomly chosen wave time origins for the different runs. Spectrum discretisation method Allows control over the spectral discretisation algorithm. The 9. Peak period and frequency Tp and fm.m22/(m0m4)}½. 231 . m4. The View Wave Components button outputs a spreadsheet giving details of the wave components that OrcaFlex has used to represent a random or time history wave train.0. those in the low and high frequency tails of the spectrum where the spectral density is low) covering a wide frequency range.3a option in its handling of double peaked spectra. If any of the wave components generated by the equal energy discretisation algorithm covers a frequency range wider than the specified maximum component frequency range. For a random wave train the spreadsheet also reports the following properties of the spectrum: Spectral moments m0. Note that T1 is sometimes denoted by Tm. and the maximum component frequency range. In other words this is the temporal frequency and not the angular frequency.7 Data for JONSWAP and ISSC Spectra For the ISSC spectrum you specify Hs and Tz (or alternatively the linked parameters Tp or fm) and the program calculates the other spectral parameters. Spectral Moments The ith spectral moment. Spectral bandwidth parameter ε = {1 . The maximum relative frequency is relative to the spectral peak with larger frequency.5 and rmax = 10. if the component's frequency very closely matches a system response frequency.5. of a process with spectrum S(f) is defined to be mi = ∫0∞ S(f)fi df where frequency f is defined as f = 1/T for corresponding period T. …. The minimum relative frequency is relative to the spectral peak with lower frequency.5 and 10. Minimum and maximum relative frequency (r min. The 9.0 are usually sufficient to produce a good representation of the spectrum.5d option. This might over-excite a system response.g. if the component's frequency is well away from the system response frequency even though that frequency is within the frequency band modelled by the component.5d option differs from the 9.3a option allows minimum and maximum relative frequencies. This data item is provided purely for reasons of backwards compatibility. It allows you to reproduce sea-state realisations generated by earlier versions of the program. Maximum component frequency range (δfmax) This maximum component frequency range places an upper limit on the width of the frequency range represented by each wave component. We recommend that all new analyses use the 9. The 9.5d option discretises the spectrum taking into account both spectral peaks. If the Legacy option is selected then the program reverts to the algorithm used in versions 9. since the spectral energy represented by the component is concentrated at a single frequency. A value of '~' means that the component frequency ranges are not limited in this way. mi. This data item can be used to avoid such problems. Otherwise the program chooses a seed automatically. Spectrum graphs and tables The View Frequency Spectrum button produces a graph of energy spectrum. The minimum and maximum relative frequency are hard-coded to 0. rmax) These data determine the range of frequencies considered by the spectral discretisation algorithm. or fail to excite an important system response. 6. These are the period and frequency at which the spectrum has the greatest spectral density.w System Modelling: Data and Results.2 and earlier. and we recommend that you do limit the frequency range. Each wave component is constrained to cover a frequency range no greater than δf max. This data item is provided because the equal energy discretisation algorithm used by OrcaFlex can result in some wave components (e. The default values of rmin = 0. to be specified by the user. If you are using a directional spreading function then you can plot it using the View Direction Spectrum button. then that component is subdivided into multiple components (which now have lower energy each) until all the components satisfy the specified maximum frequency range. Environment If User specified seeds is checked then the user must specify a seed for each wave train. respectively and no maximum component frequency range is applied. Such wave components can result in poor modelling of system responses. Mean period T1 = m0/m1. m1. those with largest spectral energy. Auto: In this case Hs is specified by the user and the program selects the most probable spectral parameters for that value of Hs. For the ISSC spectrum Tz. Tp and fm are tied together. Tp and fm are tied together. Tz is the zero crossing period. Tz (or alternatively the linked parameters Tp or fm) and γ and the program calculates the other parameters. Spectral energy parameter (α) For the ISSC spectrum α is calculated by the program to give a sea state with the specified H s and Tz. i. Tp and fm depends on γ. but cannot be edited.w System Modelling: Data and Results. fm. Spectral width parameters (σ1. Otherwise α is calculated by the program to give a sea state with the specified Hs and Tz. For Partially Specified parameters Tz. The relationship between Tz. For Fully Specified parameters Tp and fm are tied together. so setting any one of them sets the other two to match. Hs and Tz Hs is the significant wave height and Tz is the zero crossing period. λ1 and λ2 are shape parameters that control the extent to which the spectral energy is concentrated around the modal frequency – larger values give more concentrated component spectra. We treat Tz as the master data item which means that you must set γ before setting Tp or fm. so setting any one of them sets the other two to match. 6. Finally. User: In this case the user specifies the spectral parameters explicitly. 1987 if the parameters are calculated using the Automatic option.e. fm1. The resulting Hs and Tz values are displayed. the overall significant wave height Hs = (Hs12 + Hs22)½. Hs1. λ1. α. Parameters Hs1 and Hs2 are the significant wave heights of the component spectra.07 and 0. For the JONSWAP spectrum γ is automatically calculated by the program using formulae given by Isherwood. σ2) These only apply to the JONSWAP spectrum. but neither can be edited. Fully Specified: You specify all the spectral parameters (γ.8 Data for Ochi-Hubble Spectrum The Ochi-Hubble formulation allows 2-peaked spectra to be set up. Tz. fm2 and λ2 The Ochi-Hubble spectrum is the sum of 2 component spectra. Their values depend on whether you specify Auto or User. Tp Hs is the significant wave height. For the JONSWAP spectrum how these data are used depends on the selected parameter option: For Automatic parameters you set Hs and Tz and the program calculates and reports Tp and fm. If the parameters are calculated using the Fully Specified option you can specify these values. Tp and fm (=1/Tp) are the spectral peak period and peak frequency. Partially Specified: You specify Hs. each of which is specified by a set of three parameters: Hs1. You must also set Hs. You can specify these spectra parameters in two alternative ways: 232 . enabling you to represent sea states that include both a remotely generated swell and local wind-generated waves. The various spectral parameters are documented below: Hs. Parameters fm1 and fm2 are the modal frequencies of the two components. so setting one of them sets the other to match. Environment For the JONSWAP spectrum you have the following options for setting the spectral parameters: Automatic: You specify Hs and Tz and the program calculates the other parameters. Peak enhancement factor (γ) For the ISSC spectrum γ is always 1. Otherwise you can specify the value.5. Otherwise they are fixed at the standard values of 0. λ1 for the lower frequency component and Hs2. fm2. For the JONSWAP spectrum if the parameters are calculated using the Fully Specified option you can specify α and the program reports the corresponding Hs. The resulting Tz is then derived and displayed. σ1. The program calculates and reports Hs and Tz. fm1. σ2 and Tp or fm) and the program calculates and reports Hs and Tz. λ2 for the higher frequency component. Hs2. For Partially Specified parameters you must be careful about the order in which you set parameters.09 respectively. If you enter one the other will be updated according to this equality. Because of this it is more appropriate to model a two-peaked sea state using two separate OrcaFlex wave trains. Hs2. However.5. In reality the separate components frequently come from different directions. f m1 = fm and fm1 > fm2. where S(f) is the spectral energy as a function of frequency f. between those specified in the table) OrcaFlex uses linear interpolation to obtain the spectral ordinate S(f). And for values of f outside the range specified in the table OrcaFlex assumes that S(f) is zero. Hs. where m0 and m2 are the zeroth and second spectral moments. In reality the separate components frequently come from different directions.11 Data for User Defined Spectrum A user defined spectrum is specified by giving a table of values of S(f). OrcaFlex reports on the data form Hs and Tz that correspond to the spectrum specified. Hs. 6. fm and σ. should normally be greater than that of the second.9 Data for Torsethaugen Spectrum The Torsethaugen spectrum is a double peaked spectrum best suited to North Sea conditions. Warning: The Ochi-Hubble spectrum makes no allowance for the directionality of the swell and wind components of the sea state. Environment If you select Automatic the program calculates the parameters of the most probable spectrum.5. The parameters used are as given in the Ochi-Hubble paper. For swell dominated sea states. one for the swell component and one for the local wind generated component.5. one for the swell component and one for the local wind generated component. table 2b. Tz = (m0/m2)½. The fm and Tp data items are linked by the relationship f m = 1/Tp. These are calculated using the standard formulae: Hs = 4m0½.10 Data for Gaussian Swell Spectrum The Gaussian Swell spectrum is typically used to model long period swell seas. If you select Specified you must specify all 6 parameters.096. fm2 = fm and fm1 < fm2. an OrcaFlex wave train has a single principal direction. f m2. Your table should therefore include enough points to adequately define the shape you want (important where S(f) is large or has high curvature) and should cover the full range over which the spectrum has significant energy.12 Data for Time History Waves A time history wave train is defined by a separate text file that contains the wave elevation as a function of time. since most of the wave energy tends to be associated with the lower frequency component. It enables you to represent sea states that include both a remotely generated swell and local wind-generated waves. must be less than that of the second.e.5. Tp and σ The Gaussian Swell spectrum is specified by Hs. The significant wave height of the first component. 6. an OrcaFlex wave train has a single principal direction. The fm and Tp data items are linked by the relationship f m = 1/Tp. fm. For intermediate values of f (i. 6. Notes: The modal frequency of the first component. fm and Tp The Torsethaugen spectrum is specified by Hs and Tp. based on the overall significant wave height Hs that you have specified. For wind dominated sea states. fm1. Because of this it is often more appropriate to model a two-peaked sea state using two separate OrcaFlex wave trains. To use this you need to do the following: 233 . The program then derives and displays the corresponding overall Hs and Tz values. Warning: The Torsethaugen spectrum makes no allowance for the directionality of the swell and wind components of the sea state. The values of f specified do not need to be equally spaced. H s1. 6. However. It is also recommended that fm2 is greater than 0.w System Modelling: Data and Results. If you enter one the other will be updated according to this equality. fm1 and fm2 The frequencies for the primary and secondary spectral peaks. Full details of the formulation used are found in the Torsethaugen and Haver paper. amplitudes and phases that match the Fourier components. The elevation values must be the elevation at the specified Wave Origin. Because of this. where N is a power of 2 that is at least twice the specified minimum number of components. The time values in the file must be equally spaced and in seconds.w System Modelling: Data and Results. OrcaFlex needs at least 2m samples. if possible) until it has 2m samples. Note that the FFT requires the number of samples it uses from the time history file. More details are given below. you must then either provide more samples in the time history file or else reduce the minimum number of components requested. 4. so we recommend that this is avoided by providing more actual samples. This gives N/2 sinusoidal Fourier components. you will be warned if this happens. 234 . SimulationDuration is the length of the remaining stages and T0 = SimulationTimeOrigin . if necessary Let n be the number of samples selected in step 1. N of them say. So if n is less than 2m then OrcaFlex selects more samples from the file (taken equally from earlier and later in the file. In order to achieve the specified minimum number of components.BuildUpDuration) to (T0 + SimulationDuration) where BuildUpDuration is the length of the build-up stage of the simulation. This is likely to introduce spurious high frequencies into the waves. to shift the simulation relative to the time history. The View Wave Components button reports their numerical values and the View Spectrum shows their spectrum. This affects the number of Fourier components that will be used to model the time history wave. OrcaFlex uses a Fast Fourier Transform (FFT) to transform the data into a number of frequency components. So if 2m is not a power of 2 then OrcaFlex again selects more samples from the file (taken equally from earlier and later in the file. measured positive upwards from the still water level specified in the OrcaFlex model. and it produces N/2 components. are converted into frequency domain form using a Fast FourierTransform (FFT). OrcaFlex first selects the elevation values that cover the simulation period To do this OrcaFlex searches the time history file and selects the time samples that cover the simulation period. it adds extra samples of value zero).e. 1. OrcaFlex then includes more samples. then zero-padding will be used to extend the time history until it does. OrcaFlex uses a fast Fourier transform to obtain Fourier components The selected time history samples. Warning: If the time history file does not contain enough samples to achieve this. but note that using a very large number of components may significantly slow the simulation. If OrcaFlex runs out of samples in the file while doing this then it zero-pads (i. the time history file must contain a sequence of N samples that covers the period of the simulation. Each component is then used to define a single Airy wave and these Airy waves are then combined to give the wave elevation and kinematics at all points. These time origin settings allow you. Environment Create a suitable time history text file defining the wave elevation as a function of time. N say. 2. since that is needed in order to use a fast Fourier transform. If OrcaFlex runs out of samples in the file while doing this then an error message is given. if you want. Setup the time history data as described in Data in Time History Files. Set the Minimum Number of Components. The time history wave is then modelled as the superposition of these Airy waves. Set the Wave Time Origin to position the required section of wave time history within the simulation period. with periods. The View Wave Components and View Spectrum buttons on the data form show (in tabular and power spectral density graph form respectively) the Airy wave components that OrcaFlex will use to model the waves. However OrcaFlex also needs the number of samples to be a power of 2. How Wave Time History Data are Used Briefly. You can use the View Profile button (on the Waves Preview page on the environment data form) to see the wave elevation as a function of simulation time. and using the same units as those in the OrcaFlex model. m say. These will be the time samples from time (T0 . to be a power of 2.WaveTimeOrigin. OrcaFlex models the time history wave as the superposition of Airy waves N/2 Airy waves are created. if possible) until the number of selected samples is a power of 2. It should be set high enough to give desired accuracy. 3. Here are more details. 14 Data for Response Calculation Hs The significant wave height of the truncated white noise spectrum used for the Spectral Response Analysis. The relative performance of the Instantaneous Position (interpolated) and Static Position (interpolated) methods in comparison with the Instantaneous Position (exact) method depends heavily upon the number of wave components in the model. It is therefore recommended that the Wave Origin (= the point the time history file data applies to) is placed close to the main wave-sensitive parts of the model. Target Frequency Range These data items determine the frequency range of the truncated white noise spectrum used for the Spectral Response Analysis. This extrapolation introduces errors. With just a few wave components present. You will be warned if the actual frequency range cannot achieve the Target Frequency Range. especially if the static position assumption is not a good one. the expectation is that the bulk of the computational work will be unrelated to wave kinematics. In this scenario we expect the performance benefit to be minor and it will be better to use the more accurate Instantaneous Position (exact) method. that is the total spectral energy. The wave components that OrcaFlex uses to represent this spectrum are carefully chosen. The total energy of the spectrum is determined by H s using the standard formula m0 = (Hs/4)2 where m0 is the zeroth spectral moment. If this happens then as much of the target range is used as is possible. For each component you specify: Frequency or Period You may specify either of these and the other is automatically updated using the relationship Period = 1 / Frequency. A more detailed discussion of the issues involved in choosing H s is given in Load Cases Data for Spectral Analysis. 6. care must be taken to ensure that the predicted wave kinematics are an acceptable approximation to those predicted by the Instantaneous Position (exact) method. to derive surface elevation at other points and to derive fluid kinematics from the surface elevation readings. but this performance gain may come at the cost of reduced accuracy. and yet can still result in significant performance improvements. They are selected to match the frequencies produced by the Fast Fourier Transform(FFT) used to calculate the spectral response. 6. Amplitude The single amplitude of the component – that is half the peak to trough height. 6.5. However.5.13 Data for User Specified Components The User Specified Components wave type allows you to specify the wave train as the sum of a number of sinusoidal components.5. The Instantaneous Position (interpolated) option has more general applicability. The likelihood is that the Static Position (interpolated) method will yield the fastest runtime of the three methods. in a model containing a large 235 . A truncated white noise spectrum has energy spread evenly over the a specified range of frequencies. Environment This last step effectively uses Airy wave theory to extrapolate from the Wave Origin. It is possible for the range of FFT frequencies not to cover the Target Frequency Range. which become worse the further you go from the Wave Origin. where the surface elevation has been defined. OrcaFlex also reports Tz = (m0/m2)½. Phase lag The phase lag relative to the wave train time origin. When using either optimisation.15 Wave Calculation Wave Calculation Method OrcaFlex has three methods of calculating its wave kinematics: Instantaneous Position (exact) Instantaneous Position (interpolated) Static Position (interpolated) The latter two methods are optimisations of the first that apply only to lines – all model objects apart from lines always use the Instantaneous Position (exact) calculation method. This process is described in more detail in the Spectral Response Analysis theory section.w Warning: System Modelling: Data and Results. depending upon the optimisation being used. the performance gain of the Instantaneous Position (interpolated) and Static Position (interpolated) methods may be considerable. Wave Calculation Time Interval Instantaneous Position (interpolated): the time interval determines the temporal separation between the vertices of the regular grid used for interpolating the wave kinematics. Instantaneous Position (interpolated) The wave kinematics are computed only at the vertices of a regular grid. This choice could possibly be based on the specific wavelengths present in the sea state.g. It is also not compatible with Sea State Disturbance RAOs. which extends in both time and space. Care should be taken when choosing the time interval to ensure that it is sufficiently small. based on the values at nearby grid vertices. any lines that experience sea state disturbance will use the Instantaneous Position (exact) method to compute their wave kinematics instead. Note: The Static Position (interpolated) optimisation cannot be used in conjunction with either Wheeler Stretching or Extrapolation Stretching. The kinematics at all other positions and times are then computed by linear interpolation. such that the interpolation between vertices/nodes gives a good approximation to the true kinematics. It may also be related to the geometric properties of the lines in the model (e. which means that the wave kinematics will be recalculated at every timestep and no interpolation between times will be employed. This choice could possibly be based on the specific wave periods present in the sea state. Both optimisations have a time interval and a spatial interval associated with them. This can be useful for models containing lines that remain relatively still during the course of a simulation. Care should be taken when choosing this parameter to ensure that it is sufficiently small. when the node is in its static position). the fluid kinematics of non-linear wave trains are always computed using the Instantaneous Position (exact) method. which can be set by the user. Environment number of wave components (several hundred or more). Static Position (interpolated): the spatial interval is used to reduce the number of nodes at which the wave kinematics are explicitly calculated. which means that the wave kinematics will be recalculated at every node and no interpolation will be employed. 236 . Note that. Note: The Instantaneous Position (interpolated) and Static Position (interpolated) optimisations only apply to wave trains comprising linear wave components. the interpolation parameter being based upon the arclength along the line. even when recalculating at every time-step. by taking advantage of the fact that the node is assumed to be stationary.e. Static Position (interpolated) The standard wave kinematics calculation will be performed once at the start of the simulation for each line node (i. Note: The Instantaneous Position (interpolated) optimisation cannot be used in conjunction with Extrapolation Stretching. Instantaneous Position (exact) Each relevant model object will calculate the wave kinematics (sea surface elevation. At intermediate times the kinematics will be estimated by linear interpolation. The default value of this parameter is zero. The interpretation of these parameters varies slightly. curvature) if the Static Position (interpolated) calculation method is being used.w System Modelling: Data and Results. Wave Calculation Spatial Interval Instantaneous Position (interpolated): the spatial interval determines the spatial separation between the vertices of the regular grid used for interpolating the wave kinematics. the Static Position (interpolated) method will usually still be faster than the Instantaneous Position (exact) method because of the static position assumption. as described below. and at the object's current (instantaneous) position. The default value of this parameter is zero. At other nodes the wave kinematics are linearly interpolated based on the key nodes on either side. The kinematics at future times will then be computed without repeating the full calculation. Static Position (interpolated): the time interval determines how often the wave kinematics shall be recalculated. fluid velocity and fluid acceleration) at every time-step of the simulation. This parameter is not permitted to be zero and the program will report an error at the start of dynamics if this is the case. These nodes are known as key nodes and are chosen such that the spacing between them (defined as the arclength between the nodes when the line is in its static position) is approximately equal to the spatial interval. such that the interpolation between times gives a good approximation to the true kinematics. the autocorrelation is a way of judging whether the discretisation specified is sufficient to give reasonable statistical modelling of the continuous spectrum process. the simulation time origin can then be set to just before the period of interest. For irregular waves. the OrcaFlex calculation is equivalent to evaluating the expectation in the above expression as both: the ensemble average for the stochastic process. which is equivalent to not having a cutoff depth at all. This may reduce the computational effort associated with model objects in regions where the fluid motion is effectively negligible. This saving may be especially noticeable for models containing a large number of wave components. such as a riser top end position. This enables you to search through a period of global time looking for an interesting wave event and then set the time origins so that the simulation covers that event. An example of the use of these commands is to use List Events to scan over a long period of global time (e. a i and ωi are the amplitude and angular frequency of the i th wave component. For a regular wave the autocorrelation doesn't decay – it repeats at wave period – which is just a reminder that a repeating wave process is being modelled. and σ2 is the sea surface variance. i. as defined by the phases that have been specified on the Waves data form.16 Waves Preview When using a random wave or a time history wave. Whilst the autocorrelation is available for regular and irregular waves. i. The cutoff depth is measured downwards from the mean sea surface and its default value is infinity. Environment Wave Kinematics Cutoff Depth In addition to the choice of wave calculation.g. Since wave trains vary in space as well as time you should normally set this point to be close to a system point of interest. due to the discretisation into a finite number of wave components. rather than simulation time. OrcaFlex provides the option of specifying a cutoff depth below which the fluid velocity and acceleration are assumed to be zero. look for large waves and then use View Profile to look in more detail at short sections of interest. namely List Events and View Profile. and the time average of the particular realisation of the wave process in the model. the process of all wave components across all wave trains modelled. so that the simulation covers that period. Somewhat confusingly there are two commonly used definitions of autocorrelation. the realisations that will be executed when the simulation is run. View Profile This plots a time history of wave elevation at the specified Position over the specified interval of global time. The autocorrelation reported by OrcaFlex is equivalent to evaluating the more general expression: ρ(τ) = E[η(t)η(t+τ)]/σ2 where η is the sea surface elevation relative to the still water level and E is the expectation operator. it is only really useful for irregular waves. the real-world continuous spectrum process autocorrelation will decay to very small values after only a few peak wave periods.e.e. 6. See also Setting up a Random Sea. the average taken across all possible realisations of the wave process of all the wave components in the model where the phases are to be sampled from a uniform probability distribution across all phase angles. View Profile and Horizontal Velocity commands apply.e. View Autocorrelation The graph reports the autocorrelation coefficient function of the discretised total wave process.5. Notes: These commands work in terms of global time. Having decided which part of the wave train to use. Position This is the point to which the List Events. i. These are provided on the Waves Preview page on the environment data form and are documented below. The autocorrelation at time lag τ is calculated as: ρ(τ) = Σi ai2cos(ωiτ)/2σ2 where the sum is over all wave components. Because the wave process is ergodic. If you are using multiple wave trains then these commands report the combined sea state from all of the wave trains. The discretised process will decay but then show more significant correlation for longer time lags. 10000 seconds or more). You should specify a number of wave components that is large enough such that the autocorrelation function of the discretised process decays to a reasonably small value and stays small for the period 237 . OrcaFlex provides two preview facilities to aid selection of the wave.w System Modelling: Data and Results. All wave events in the specified interval of global time and at the specified Position which match the specified criteria are reported.17 Modelling Design Waves Design wave heights and periods are commonly provided as a design input.5.5 Tz = 0. and average zero up-crossing period. the maximum storm can be estimated from wind statistics on the assumption that the waves are generated by the local winds. or (providing the sea state is uni-directional) that the wave steepness exceeds the specified steepness S. not any of the higher order parts included if one of the non-linear regular wave types is used. so in practise this should not be a constraint. The governing parameters are fetch (i. at the specified (X. However. for comparison purposes. Finally.3 Duration-limited Hs = 0. and the length and steepness of this equivalent Airy wave are given. The factor k provides for the fact that the highest wave crest and deepest trough in any given storm do not in general occur together. average zero crossing period Tz is Hmax = kHs[½ln(N)]½. These are then used to calculate. This reports the Airy wave whose height and period match the Hs and Tz of that single wave train.0163UX0.4X0. Note: The autocorrelation only includes the principal linear component. H s. and the data are sometimes incomplete or in a different form from that required for OrcaFlex. Tz. The steepness criterion S is only used for uni-directional sea states because steepness is measured in the wave direction and so is only meaningful if all wave components are in the same direction. a reference wave is reported at the top of the table. the highest crest and lowest trough. These include the largest rise and fall. for this water depth. the number of up and down zero-crossings and the sample's estimated Hs and Tz values. where N = T/Tz Most wave statistics are based on measurements taken at 3 hour intervals so T should generally not be greater than 10800s. but this is not always so. and D is duration in hours. the height (total rise or fall) is given and an equivalent period is derived from the time interval between the peak and trough. For a comprehensive discussion.419D3/7U4/7 where X is fetch in km. which are linear by their nature. List Events This command searches for individual waves within a random sea which satisfy specified criteria.Y) Position and specified global time.w System Modelling: Data and Results. For each event. occurring in time T in a storm of significant wave height H s. wind speed and duration. U is wind speed in m/s at 10m above mean sea level. the length of open water over which the wind blows). an Airy wave of the same height and period. 6. Horizontal Velocity This plots how the water horizontal velocity (due to current and waves) varies with depth. the autocorrelation function is only really useful for irregular waves.0146D5/7U9/7 Tz = 0. various wave elevation statistics are reported for the position and period of time specified. Otherwise the simulations will include unrealistic correlation and not be statistically representative of the real world continuous spectrum process. Significant waveheight. compared with the overall parent spectrum. These statistics enable you to measure how "typical" this wave elevation sample is. determined by the Wave Search Method: If the Height or Steepness option is selected then program searches for rises or falls that exceed the specified height H. The maximum crest-to-trough waveheight is generally less than the sum of the maximum 238 . The criteria are be specified in one of two ways. If there is only one wave train then. Maximum Storm In the absence of measured wave data. can then be estimated from equations given by Carter (1982): Fetch-limited Hs = 0. Environment of simulation that you are running.439U0. Maximum Individual Wave Height Expected maximum waveheight Hmax. If the Height or Period option is selected then the program searches for wave events matching (up to specified tolerance levels) both the specified wave height H and the specified wave period T. see Tucker (1991) on which the following notes are based.e. For analysis of permanent systems (e. Whilst the complete operation may take many hours or even days. Set the number of wave components (typically 100). can take a range of values.05Tz < Tass < 1. It would be too conservative to apply 3 hour maximum conditions in such a case.5. JONSWAP. 6. Period of the Maximum Wave The period associated with the maximum wave T ass. Tucker recommends 1.w System Modelling: Data and Results. γ = 3. period Tz or Tp according to preference) for the assumed seastate with a maximum tidal current.18 Setting up a Random Sea This section gives information on how to set up a random sea using OrcaFlex's modelling facilities.41Tz. However alternative requirements are possible and it is sometimes useful to impose additional conditions for convenience in results presentation.40Tz. quicker to run. 2. critical parts such as landing an item of equipment on the seabed may only take a few minutes. The spectral peak period Tp is sometimes specified rather than Tz. Environment crest elevation plus maximum trough depth. using the facilities available in OrcaFlex. 3. The risk of encountering a large wave is only one of many elements to be considered in assessing overall risk. we are left with subjective judgement. then generate suitable wave trains incorporating these waves following the procedures detailed in Setting up a Random Sea.0 for more frequent waves (fatigue waves).01%?). but the cost rises disproportionately as the level of acceptable risk is reduced. For regular wave analysis we recommend that you use the Dean stream function theory. This has no objective basis. use the period range recommended by Tucker. The question comes down to a balance of cost against risk. applying both waves and current from the worst direction. There is a need here for some feedback from practical experience to determine what is in practice acceptable and what is not. Use regular waves for preliminary work. i. If field specific data are not available. For a detailed description of these. the factor varies with the peak enhancement factor γ. we select an appropriate wave train as follows. different criteria apply. Set the significant wave height (Hs) and average period (Tz) for the design storm.9 for the maximum wave. either from other wave statistics (for example a wave scatter table. The overall risk of failure must be small enough to be acceptable (how small – 1%. For the ISSC spectrum Tp = 1.3 and Tp = 1. Having decided what values of Hmax and Tmax are required. Recommendations 1. The height and period of the maximum design wave may be specified by the client. Torsethaugen and Gaussian Swell options are available. see Wave Data. but on occasion we have to derive the appropriate values ourselves. we guess. For the mean JONSWAP spectrum. etc. Ochi-Hubble. A typical requirement is to determine the maximum seastate in which a given operation can safely take place.g. and easier to understand. If random sea analysis is required. and the wave spectrum – ISSC.29Tz Wave Conditions for Short Term Operations For operations lasting from a few hours to a few days. The OrcaFlex random wave data form reports Tp and the spectral peak frequency fm = 1/Tp. The most common requirement is to produce a realistic wave train which includes a "design wave" of specified height Hmax and period Tmax. but is plausible. giving significant wave heights Hs and average periods Tz) or from a more general description of weather (such as wind speed). k = 1. and of operations which were not successful because of weather conditions could provide a calibrated basis for analysis of future operations. Tucker recommends k = 0. We don't know anyone who has done this – until they do. This is a big subject which is rarely addressed rigorously. Regular waves are easier to set up.e. For the JONSWAP spectrum. 239 . flexible risers) use expected maximum wave height with the appropriate return period (commonly 50 or 100 years return period for 5 to 20 year field life) and a range of associated wave periods. determine the heights and period ranges for the maximum design waves as above. Hindcasting of operations which took place successfully in what were judged to be marginal conditions. A common guess is to combine the significant wave (a regular wave of height H s. 0. we should use a full Fourier series representation of the wave system which would typically have several thousand components (the number depends on the required duration of the simulation and the integration time step). If you choose JONSWAP then you can either specify γ or let the program calculate it (see formulae given by Isherwood). Tz. Finding a Suitable Design Wave A frequent requirement is to find a section of random sea which includes a wave corresponding in height and period to a specified design wave. so the same seed will always give the same phases and consequently the same train of waves. The bandwidth parameters are set automatically to standard values).9Hs. Environment Search through the time history of wave height and looking for a particular wave rise (trough to crest) or fall (crest to trough) which has the required total height and period. Suppose that the list shows a wave fall at t = 647s which is close to your requirement. The Ochi-Hubbleand Torsethaugen spectra enable you to represent sea states that include both a remotely generated swell and a local wind generated sea. OrcaFlex uses a random number generator and the seed to assign phases. The JONSWAP spectrum is a variant of the ISSC spectrum in which a "peak enhancement factor". Setting the Number of Components OrcaFlex generates a time history of wave height by dividing the spectrum into a number of component sine waves of constant amplitude and (pseudo-random) phase. However. as noted above. which define the bandwidth over which the peak enhancement is applied. a further infinite set from 101 components and so on. there are advantages in keeping γ constant. OrcaFlex provides preview facilities for this purpose.0 is identical to the ISSC spectrum with the same Hs and Tz. then use the List Events command (on the Waves Preview page of the environment data form) to ask for a listing of waves with height > H=1. five parameters are required. H s. Choice of wave spectrum can cause unnecessary pain and suffering to the beginner. The phases associated with each wave component are pseudorandom. Strictly speaking. When the required design wave has been located. If you are looking for a large wave in a random sea.w System Modelling: Data and Results. and two additional parameters σa and σb (denoted σ1 and σ2 in OrcaFlex). Since short waves travel more slowly than long ones. see Tucker et al (1984). For a discussion of the consequences of this approach.000s. γ. say Hmax = 1. For the North Sea it is common to set γ = 3. Then you can use the View Profile command to inspect this part of the wave train. Ship responses and wave kinematics are also generated for each wave component and added assuming linear superposition.g. say. Ochi-Hubble or Torsethaugen). say. You will then see the large wave with the smaller waves which precede and follow it. This is prohibitively expensive in computing time so we use a much reduced number of components. Setting the Sea State Data The ISSC spectrum (also known as Bretschneider or modified Pierson-Moskowitz) is appropriate for fully-developed seas in the open ocean. then adjust Hs and Tz slightly and repeat. you can set the simulation time origin and duration so that the design wave occurs within the simulation time. The one exception to this sweeping statement may be 2-peaked spectra (e. The time history generated is just one of an infinite number of possible wave trains which correspond to the chosen spectrum – in fact there are an infinite number of wave trains which could be generated from 100 components. with sufficient time before and after to avoid starting transients and collect all important responses of the system to the design wave. this affects simulations of mild sea states more than severe seas. If you have to do a systematic series of analyses in a range of wave heights. 240 . then the simulation may have to be longer to allow time for the principal wave group to pass through the whole system.7Hs. JONSWAP is commonly specified for the North Sea. Two parameters are sufficient to define an ISSC spectrum – we use Hs and Tz for convenience. The wave components are added assuming linear superposition to create the wave train. more components give greater realism but a greater computing overhead. OrcaFlex will then search that time period and list wave rises and falls which meet the criterion you have specified. For present purposes. by asking OrcaFlex to draw the sea surface elevation for the period from t = 600s to t = 700s. A typical random sea simulation may represent 5 or 6 average wave periods (say 60-70 seconds for a design storm in the North Sea) plus a build up period of 10 seconds. is applied to give a greater concentration of energy in the mid-band of frequencies. If the system is widely dispersed in the wave direction. γ. The spectrum is a means to this end. It is worth looking over a reasonably long period of time at first – say t = 0s to 50. the important point is to get the "design wave" we want embedded in a realistic random train of smaller waves. and in practice it matters little what formulation is used. For the JONSWAP spectrum.3. If no wave of the required characteristics can be found. The sequence is repeatable.000s or even 100. this does involve some loss of randomness in the time history generated. Note that a JONSWAP spectrum with γ = 1. OrcaFlex currently allows you to specify the number of wave components to use. even in a stationary sea state. In the real world. then there would be additional scatter. wave elevation at any time and any location is directly proportional to H s. This is often conveniently done by small adjustments to Hs and Tz.Y coordinates). if you have found a wave at the origin at time t which has the height you require but the period between crests is 5% less than you want. In extreme storm conditions. In these 2 cases. It is worth checking that a wave train which gives a design wave at Ship A does not simultaneously include an even higher wave at Ship B. If you want to investigate system response to a specified design wave at both Ship A and Ship B. This capability is intended to help when you are analysing a series of load cases with differing current data. For example. Deriving Hmax from Hs Hmax = kHs[½ln(N)]½ where N is the number of waves in the period under consideration and K is an empirical constant. i. it can be assumed that 1. Wave Statistics The following is based on Tucker (1991). As we noted above. provided the number of wave components and the seed are held constant. if you have found a wave at time t which has the period you require but is 5% low in height. We need make no apology for this. increasing H s by 5% will give you the wave you want. If you are using an ISSC spectrum. For further discussion see Tucker et al (1984). the wave train at X = 0 differs from that at X = 300m. the important point is to get the design wave we want embedded in a realistic random train of smaller waves. For example.e. S = (2πHs)/(gTz2) = 1/18 hence Tz = √[(2πHs)/(gSs)] = 3.19 Current Data Multiple Current Data Sets Multiple sets of current data can be defined. in the batch script which generates the load case simulations.05t. Y = 0) is proportional to Tz.4Tz. then you will usually have to do the analysis twice. You can define the different current data sets in the base data file. so for waves going in the positive X direction (wave direction = 0°). you may be analysing a system in which lines are connected between Ship A at X = 0 and Ship B at X = 300m. Tz in seconds. These scaling rules can be helpful when conducting a study of system behaviour in a range of wave heights. then you can make use of some useful scaling rules at this point. or a JONSWAP spectrum with constant γ. Note: This rule does not apply in general except at the origin of global coordinates.39√Hs for Ss = 1/18 (Hs in metres. also at time t. once with the design wave at Ship A and once at Ship B. For example. you simply set the active current to be one of the pre-defined current data sets. You can use the preview facility to examine the wave at different critical points for your system. If the wave trains were independently derived. However. increasing Tz by 5% will give you the wave you want. A random wave train varies in both time and space.w System Modelling: Data and Results. then adjust H s and Tz slightly and repeat. This gives a systematic variation in wave excitation for which we may expect a systematic variation in response. then: For constant Tz. If no wave of the required characteristics can be found. For extreme storms. 241 . Since wave statistics are usually based on measurements made every 3 hours. K = 1 is usually assumed. it is common to assume a "significant wave steepness" of 1/18. only one set of current data is active at any one time.05Tz < Tass < 1.) Deriving Tass from Tz Generally. the instantaneous wave spectrum varies considerably and H s and Tz with it.9. For constant Hs. but at time 1. 6.5. Then. the time between successive wave crests at the origin (X = 0. but for moderate wave conditions as used for fatigue analysis. We can select a suitable wave train for one wave height and scale to each of the other wave heights. N is usually taken as the number of waves in 3 hours: N = 10800/Tz. K may be taken as 0. Environment Note that when you use the preview facility you have to specify both the time and the location (X. The simulation would then start with the flexible on the wrong side of the pipe. consider a case where a flexible line is to the left of a stiff pipe but current pushes the flexible up against the pipe. vary with simulation time or be given by an external function. Since the OrcaFlex static analysis does not include the effects of contact between lines. To define the current data sets click on the Edit Current Data Sets button. Data for Power Law Method Speed at Surface and at Seabed The current speed at the still water level and at the seabed level. Data for Interpolated Method Speed and Direction The magnitude and direction of a reference current. for example when a sloping seabed is specified. If it is not checked then you define just a single current data set. The direction specified is the direction the current is progressing – for example. If you prefer to enter current speeds and directions directly. Then. For example. respectively. Current speed and direction are interpolated linearly between the specified levels. This data item is only available if you have enabled multiple current data sets. the current at the least depth specified is applied to any depth above this. This problem can be overcome by setting the current to ramp during the build-up stage and setting clash checking for the two lines. relative to reference. if current was included in the static analysis then it would find a static position where the flexible line was to the right of the pipe. The actual current at a given Z level is then defined relative to this reference current by a current profile. Note: Speed at Seabed cannot be greater than Speed at Surface. For example if consecutive rows in the table specify rotations of 350° and 10° then the program interpolates passing through 355°. Note: OrcaFlex interpolates rotations over the shortest route. At each Depth in the table the current speed is the reference current speed multiplied by the Factor for that depth. The build-up stage will then introduce the current effects but will also include the effect of contact between the two lines.w System Modelling: Data and Results. Data for a single Current Data Set Ramp During Build-Up If selected then the static position will be calculated without the effects of current. Active current Specifies which of the multiple current data sets is active in the model. 0° and 5°. simply set the reference current speed to 1 and the reference direction to 0. during the build-up stage of dynamics the current is ramped up to its full value. 0° and 90° mean currents flowing in the X and Y directions. If not selected (the default) then the current is used in calculating the static position and full current is applied throughout. Negative factors can be used which allow you to model reversing currents. the Direction is the reference direction plus the rotation specified. rather than using a reference current and referencerelative profile. generally taken as a surface current. This opens a separate data form where the current data sets can be defined and named. Vertical Current Variation Current Method Can be Interpolated or Power Law. 242 . Similarly. Profile A current profile may be defined by specifying factors and rotations at various depths. Environment Multiple sets of current data can be defined This data item must be checked if you wish to define multiple sets of current data. The current at the greatest depth specified is applied to any depth below this. This facility to omit current effects from the static calculation and introduce them during the build up is useful where the current may cause lines to come into contact. The static position will exclude the effect of current and so will leave the flexible to the left of the pipe. The Power Law method uses an exponential decay formula. The speed and direction can either be fixed. The Interpolated method uses a full 3D profile with variable speed and direction. Air Kinematic Viscosity This is used to calculate Reynolds number. To model current speed variation with horizontal position you must define a Horizontal Variation Factor variable data source. Lines and 6D Buoy Wings Specifies whether wind loads are included for Vessels. Negative factors can be used which allow you to model reversing currents. Lines and 6D Buoy Wings. With a smaller value. the current direction is the same at all levels. measured positive from the global X-axis towards the global Y-axis. 0.20 Wind Data The Wind page on the Environment data form contains data for modelling wind. 6. Environment Direction When using the power law current method. The speed specified should be the value at an elevation of 10m (32. The vectors are non-dimensionalised. then the wind speed V(10) at 10m can be estimated using the formula: V(10) = V(h) (10/h)(1/7). This view is most useful for visualising and checking your current profile rotation data. by setting the Wind Type to one of the following. Wind Direction The direction specified is the direction in which the wind is progressing – see Direction and Headings. Air Density The air density is assumed to be constant and the same everywhere. Using a numeric value (e.5) allows you to apply a scaling factor to the vertical current speed profile.8 ft) above the mean sea surface. These options are primarily intended to maintain compatibility with some older versions of OrcaFlex. In all cases the wind is uni-directional.3 and earlier did not include wind loads on Lines or 6D Buoy Wings. To neglect current speed variation with horizontal position this data item should be set to '~'. Exponent This determines how the current decays. Horizontal Current Variation Current speed variation with horizontal position can also be modelled. The direction specified is the direction the current is progressing. 0 and 90 mean currents flowing in the X and Y directions. The horizontal variation factor is assumed to be constant in the direction normal to the axis. If you have the wind speed V(h) at some other height h (in metres). With a higher value. 243 . For example. When files produced with such versions are loaded the options for Lines and 6D Buoy Wings are not ticked. the decay mostly occurs close to the seabed. Lines and 6D Buoy Wings – that is all these options are ticked.5. This value is fixed and cannot be edited. since that is the height used by the OCIMF vessel wind load model. Where a variation of current speed with depth has been defined the factor will be applied at all depths. Wind Speed Wind speed is assumed to be the same everywhere. The Vertical Profile 3D View shows a 3D View with a number of arrows showing the current velocity vectors at a range of depths. the decay is spread more evenly across the water depth. Include wind loads on Vessels.w System Modelling: Data and Results. Lines – see Line Theory: Hydrodynamic and Aerodynamic Loads. The wind data are used to calculate wind loads on: Vessels – see Vessel Theory: Current and Wind Loads. View Vertical Profile Graph. Version 8. This is specified as a dimensionless multiplicative factor. This means that you cannot use them to tell absolute current speeds but the speed of the current at a particular depth can be compared relative to the speed at other depths. When new models are created in OrcaFlex wind loads are included on Vessels. View Vertical Profile 3D View The Vertical Profile Graph plots Z against current speed which can be useful to help visualise and check your vertical current speed variation. respectively. You can choose to specify wind speed in various ways.g. 6D Buoy Wings – see 6D Buoys: Wing Type Data. You can specify the Number of Components to use. current direction arrow and wave direction arrows are drawn. For details see Data in Time History Files. You should specify enough to give a reasonable representation of the spectrum. Negative factors can be used which allow you to model reversing wind profiles. The View Spectrum button shows a graph of the spectrum. OrcaFlex uses a 'equal energy' algorithm to choose the amplitudes and frequencies. Vertical Wind Variation Wind speed variation with height above the mean water level (MWL) can also be modelled. In both cases: The spectrum is determined by specifying the Mean Speed and the spectrum then determines the statistical variation about that mean. but their frequencies are chosen so that the components are more closely spaced where the spectral energy density is high. For details see Data in Time History Files.e. The phases generated are repeatable – i. The phases of the components are chosen using a pseudo-random number generator that generates phases which are uniformly distributed. Environment Constant The wind speed is then constant in time. Secondary Wave Direction Pen When the Draw Environment Axes preference is ticked a wave direction arrow is drawn in the direction of the wave. The first wave train uses the sea surface pen since it is regarded as the dominant one for drawing purposes. This is an arrow next to the view axes which points in the direction of the wind. The components are sinusoidal functions of time whose amplitudes and frequencies are chosen by OrcaFlex to match the spectral shape. This is specified as a dimensionless multiplicative factor. All subsequent wave trains' direction arrows are drawn in the Secondary Wave Direction Pen. 6. This arrow is only drawn if the current speed is not zero and if the Draw Environment Axes preference is ticked.w System Modelling: Data and Results. 244 . The wave direction arrows are explained below. and more widely spaced where the spectral energy is low.21 Drawing Data These data allow you to control the drawing of the various components which make up the OrcaFlex Environment. The wind speed is modelled by a sum of a number of components. Linear interpolation is used to obtain the wind speed and direction at intermediate times. To model vertical wind speed variation you must define a Vertical Variation Factor variable data source. If there are multiple wave trains whose directions are not equal then a wave direction arrow is drawn in the direction of each wave train.5. Time History (Speed) The wind speed variation with time is specified explicitly in a file. Linear interpolation is used to obtain the wind speed at intermediate times. This can be any integer in the range -232 to +232-1. The View Components button gives a report of the components that OrcaFlex has chosen. Wind Direction Pen Determines how the wind direction arrow is drawn. The current direction arrow is an arrow next to the view axes which points in the direction of the current. and therefore the same amplitude. To neglect vertical wind speed variation this data item should be set to '~'. This allows a vertical wind profile to be modelled. using a choice of either the API RP 2A (1993) spectrum or the NPD spectrum. Time History (Speed & Direction) The wind speed and direction variation with time is specified explicitly in a file. This gives all the components the same energy. Random The wind speed varies randomly in time. For a more general discussion of drawing in OrcaFlex see How Objects Are Drawn. if you re-run a case with the same data then the same phases will be used – but you can choose to use different random phases by altering the Seed used in the random number generator. Sea Surface Pen Determines how the sea surface. This arrow is only drawn if the wind speed is not zero and if the Draw Environment Axes preference is ticked. Wave number. Velocity.Y. The option to select a disturbance vessel will only be visible if there is at least one vessel in the model that has sea state RAO data associated with it. It is also possible to specify that the results should be subject to sea state disturbance due to the presence of a disturbance vessel.Z position. Wind Speed and Wind Direction The wind speed and direction. Statistics and Linked Statistics For details on how to select results variables see Selecting Variables. Elevation The global Z-coordinate of the sea surface at the specified global X. Such models can take a very long time to draw and drawing performance can be improved by omitting the drawing of the data points. A value of 0% gives a solid surface and all objects behind the surface will not be visible. Shaded Drawing Sea Surface and Seabed Translucency Controls how translucent the sea surface and seabed appear in the Shaded Graphics mode. Seabed Profile Pen If you are using a profile seabed then an extra grid line is drawn along each data point used to specify the profile. 6.Z position. Z-Acceleration The magnitude and global X.Y. Z-Velocity. a density of d means that there are d lines per scale bar length.w System Modelling: Data and Results.Y position.22 External Functions Parameters This data item specifies the External Function Parameters. 245 .Y. A value of 100% specifies transparency and leads to a completely see-through surface.Z coordinates of the point for which you want results. A disturbance vessel can also be specified if desired. Static Pressure The pressure due to the static head of water at the specified global X.Z position. This can be used to emphasise the seabed profile data.Y. Y. Ursell number and theoretical Breaking wave height. X. Environment Seabed Pen The seabed grid is drawn in this pen. a free form multi-line text field which is passed to any external function used by the Environment. Density The density of the water at the specified global X.5. Y and Z components of the water particle velocity (due to current and waves) and acceleration (due to waves) at the specified global X. Draw 3D seabed data points This options allows you to omit 3D seabed data points from the wire frame drawing. X. Sea Surface and Seabed Grid Density The density of the grid is specified in terms of the length of the scale bar on the 3D view. If the specified Z position is above the water surface then zero is reported. Time History. For Environment results you must specify the global X. Acceleration. so higher density values give a finer grid (but takes longer to draw). Note that this does not depend on the specified global X. Results are for the sea conditions that apply during the simulation and therefore include the build-up of wave motion during the build-up stage. 6.5.23 Results Summary and Full Results Results tables are available for the Environment reporting Wave length. If the specified Z is below the seabed then the value applicable at the seabed is given.Z position. This can sometimes be useful for models with extremely large numbers of 3D seabed data points. Current Speed and Current Direction The speed and direction of the current at the specified global X.Y. Y.Y. A value of '~' for the Z coordinate is interpreted as meaning the instantaneous sea surface elevation.Z position. Most Recent Files List List of the most recently used files. Sea State Table These data specify the random sea state scatter table. Spectral Form All the sea states are assumed to be of the same spectral form which can be either JONSWAP or ISSC. This option is useful where the regular wave scatter table is pre-determined but you still want to take advantage of the automatic export of text data files. individual) waves. 1983. 246 . New Clears previously entered Wave Scatter data and resets data to default values. Selecting an item on the list causes the file to be loaded.sct). Open Open a Wave Scatter file (. data and output. m1 and m2 using the formula of Longuet-Higgins. The conversion method uses the formula of Longuet-Higgins. batch script and fatigue analysis files. This probability density is determined by the first 3 spectral moments m0. batch script and fatigue analysis files corresponding to the calculated regular wave scatter table.e. 1983. Save Save the data to the currently selected file name (shown in title bar of the window). Units You can select the units of length to be used for the wave scatter data. The wave scatter conversion tool is run by selecting the Wave Scatter Conversion command from the OrcaFlex Calculation menu. but allows you to specify the file name to save to. Regular Wave Scatter If Calculated from irregular wave scatter is selected then the regular wave scatter table is derived from a random sea state scatter table using the formula of Longuet-Higgins. One of the most useful features of the tool is the ability to create text data files. the data relating to the wave scatter conversion. This allows you to take advantage of the automatic export of text data files. Full details of the calculations involved are given in the theory section. batch script and fatigue analysis files. Exit Closes the wave scatter form. with its own menus. The size of the list can be adjusted from the Preferences form. Save As This is the same as Save. If User specified is selected then the regular wave scatter table is input directly. 1983. File Menu commands The commands on the file menu allow you to save.5.w System Modelling: Data and Results. This gives the joint probability density of individual waves in a random sea. It is essentially a self-contained sub-program within OrcaFlex. Any OrcaFlex process active in the main window is paused until the wave scatter form is closed and the wave scatter conversion tool has no effect on existing OrcaFlex data. As an alternative you can input directly the regular wave scatter table. which can be saved to a file. Environment 6. Data The wave scatter conversion tool requires the following data. and then reload.24 Wave Scatter Conversion Introduction The wave scatter conversion tool converts a scatter table of sea states to a scatter table of regular (i. If the Regular Wave Scatter option is User specified then these data are not required. Full details of the calculations involved are given in the theory section. Wave Period. can be saved as an Excel file. Note that this button is not available if you have a user specified regular wave scatter table. The program calculates and reports Hs and Tz. Regular Wave Scatter Table This sheet contains the main output from the wave scatter conversion – a table listing the number of occurrences of waves in each regular wave bin. Total Duration This is the total duration to be covered by the regular wave scatter table. Sigma1 and Sigma2. Sea States You must specify the spectrum for each sea state in your scatter table. Spectral Parameters If you select the JONSWAP spectral form you have 3 options for specifying the spectral parameters: Automatic. Wave Height. For Partially Specified parameters Tz. In order to reduce the amount of computation time required to analyse all the load cases it is customary to ignore such bins. Wave Heights. For Fully Specified parameters Tp and fm are tied together. 1983 method is valid only for narrow-banded spectra. like all such windows in OrcaFlex. Regular Waves (user specified regular wave scatter table) These data specify a complete regular wave scatter table. Number of bins The number of bins in the regular wave scatter table. This value is required to determine the relative likelihood of occurrence of each sea state. Any bins which have occurrences below the occurrence threshold are omitted. Any bin which has an occurrence value lower than this threshold will be ignored. 247 . If you have selected the ISSC spectral form then you enter Hs and one of Tz. Regular Waves (scatter table calculated from irregular wave scatter table) These data specify how the regular wave scatter table is discretised into bins. Occurrence threshold Some of the bins in the regular wave scatter table can have very small occurrence values. so setting one of them sets the other to match. Alpha. Regular Wave Bins The regular wave height and wave period bins are listed here. Normally this value comes from a sea state scatter table where it is usually presented in parts per thousand. You must also set Gamma. Tp or fm.w Note: System Modelling: Data and Results. OrcaFlex automatically constructs bins around these values. The output is presented in a spreadsheet window which. Partially Specified or Fully Specified. If you have selected the JONSWAP spectrum the required parameters depend on the selected parameter option: For Automatic parameters you set Hs and Tz and the program calculates and reports Tp and fm. Number of Occurrences For each sea state in your scatter table you must also specify the number of occurrences of that sea state. Tp and fm are tied together. You must also set Hs. Output To perform the wave scatter conversion you simply click the Show Regular Wave Scatter Table button which is found on the Regular Waves page. Environment The Longuet-Higgins. Number of Occurrences These are specified for each bin in the regular wave scatter table. Thus the Ochi-Hubble and Torsethaugen spectra are not available for this type of conversion. The spreadsheet is made up of the following sheets: Sea State Table This sheet contains the input data which specified the sea state scatter table. This command is also available from the Action menu. This setting applies to all sea states. The output from the wave scatter conversion tool includes a table listing these bins. so setting any one of them sets the other two to match. Wave Periods These are the regular wave heights and wave periods that you wish to analyse. If you do not wish to ignore any bins then you should set the threshold to 0. for l = 1. will need to be input.yml for text data files. Theory Notation Let the list of sea state spectra and associated durations be denoted Z l and Dl respectively. %H will be replaced with the wave height for that load case. The program will supply an appropriate file name. The wave height. Automation Once you have obtained the regular wave scatter table you will usually want to generate a regular wave simulation file for each regular wave bin. From this formula it can be seen that the absolute values of D l are not important. or by the generated batch script file. This file lists each load case together with the corresponding number of occurrences for that load case. However. This allows load cases with longer wave periods to use a coarser logging interval than for those with shorter wave periods and hence reduce the sizes of the simulation files. T=3. Base Case File Name The name of an OrcaFlex data file on which all the load cases are to be based. There are two options available. Simulation File Name Template Each load case file (corresponding to a single regular wave bin) is given a name based on this template. %T will be replaced with the wave period for that load case.dat for binary data files or . Fatigue Having generated a regular wave simulation file for each regular wave bin you will commonly want to perform a fatigue analysis. The Export Batch Script button can be used to write an OrcaFlex batch script file to automate the generation of these simulation files. The probability of occurrence of sea state q is given by P(Zq) = Dq / ∑l Dl. Environment This sheet also displays the total number of bins and the total probability covered by the table. Because different load cases have different wave periods these data are defined as multiples of that wave period. for example: "Case #01. Clicking the Export Fatigue Analysis File button produces an OrcaFlex fatigue analysis file. such as the S-N curve data. Do not specify the file extension as part of the template.dat" and so on for all load cases. H=%H. "Case #02. H=0. Simulation Duration Specifies the duration of the Build-up Stage and Stage 1 for each load case. Note that the sea state duration is only used to specify the distribution of sea states. wave period and simulation duration data will be specified either in the generated text data files. The files are generated when you press the Create Text Data Files button. determined by the Automation Method data item: Text data file: Each regular wave bin is mapped to a corresponding text data file. …. Override base case log interval and Target number of log samples per wave period These data allow you to set the simulation log interval for each load case simulation file by specifying the number of log samples in each wave period. Batch script: A batch script file is created that will generate a data file for each regular wave bin. Notes: You do not need to use all three format strings in your template. The default value of the template is "Case #%N. T=5. either . T=%T" and this will lead to files named. The file produced is not complete and other data. k where k is the number of sea states. However.w System Modelling: Data and Results. This latter value provides an important check that your bins extend far enough along the wave height and period axes. it provides a good starting point for performing the fatigue analysis.5. OrcaFlex will display an error message if the simulation file names are not unique. Alternatively the Create Script Table Spreadsheet button can be used to create a script table spreadsheet which can be pasted into an OrcaFlex Excel spreadsheet. Special format strings can be used to customise the file names as follows: %N will be replaced with the load case number. If the value is significantly less than 1 then your bins need to be extended.5. This data file should specify a regular wave. H=0. 248 . Each load case is assigned a unique number. rather it is their relative values which are significant.dat". you must use enough of them to make the simulation file names unique. The Fatigue Line Name data item can be used to specify the corresponding fatigue analysis data item. If you have already saved the wave scatter data then relative paths can be used when locating this file. This gives the joint probability density p(R. Tjupper] respectively. Z) of individual waves in a given random sea state as follows: p(R. We now have mn individual wave height and period bins which we denote by B ij for i = 1. Hm + (Hm-Hm-1)/2] so that Hm falls in the middle of the last bin. instead it reports the total number of occurrences O ij for each bin Bij. …. Hmupper] = [(Hm-1+Hm)/2. The wave height bins are denoted by [Hilower. m and Tj for j = 1.3. The wave period bins [Tjlower. However this also means that H 1 may not fall in the middle of the bin. R = H/Hrms. Joint probability for individual waves This section is based on Barltrop and Adams section 6. Tz = (m0/m2)½. denoted by P(Bij. mi = ith spectral moment of Z. Zl) OrcaFlex does not report these probabilities. (Hi+Hi+1)/2] for i = 2. Finally the other bins are chosen to be [Hilower. The first bin is taken to be [H1lower.1/S]2/ν2}). These wave heights and periods are ordered to be strictly increasing. the probability of occurrence P(Bij ) of each individual wave height and period bin is calculated as follows: P(Bij) = ∑l P(Zl) P(Bij. Riupper = Hiupper / Hrms. This is given by Oij = P(Bij) Dtotal / Tj where Dtotal is the total duration as specified on the Regular Waves page. Z) = L(ν)exp(-R2{1 + [1 . Tjupper] for j = 1. Hiupper] = [(Hi-1+Hi)/2. …. Each bin Bij represents individual waves whose heights and periods fall in the ranges [H ilower.6 SOLID FRICTION COEFFICIENTS DATA These data are used to specify friction coefficients for contact between Elastic Solids and Lines. …. Zl) dS dR where the integral is evaluated over the region Rilower ≤ R ≤ Riupper. Sjlower ≤ S ≤ Sjupper. …. Solid Friction Coefficients Data Regular wave bins The specified regular wave heights and periods are denoted Hi for i = 1. Zl) = ∫∫ p(R. the specification of these data is necessarily more complex than that for the seabed friction coefficients. …. 3D Buoys and 6D Buoys. It is clearly important that 0 is contained in the bin. m. Hrms = Hs/√2. The last bin is taken to be [Hmlower. Following their lead we use the formula of LonguetHiggins. S = T/Tm. …. and vice versa. S. Individual wave scatter For each sea state Zl we can calculate the probability of occurrence of each individual wave height and period bin. Tm = m0/m1. n. m and j = 1.2R2/(S2ν√π) where Z = spectrum of given random sea state. Hiupper] and [Tjlower. 249 . This should not matter provided that the bin is small enough. Because each Elastic Solid can come into contact with any number of Lines and Buoys. Note: Friction for contact with elastic solids is only included during dynamics. S. n are chosen in an analogous fashion.6. respectively. Hiupper] for i = 1. ν = (Tm2/Tz2 . S. m-1. …. n.1)½ and L(ν) = 2 / (1 + {1+ν2}-½). 1983. Zl) as follows: P(Bij. H1upper] = [0. Sjlower = Tjlower / Tm and Sjupper = Tjupper / Tm. Thus. Rilower = Hilower / Hrms. 6. (H1+H2)/2].w System Modelling: Data and Results. Any node in the model. OrcaFlex deals with this ambiguity by choosing the more specific combination. that is the second row which specifies "Line Type1". A row with named line type and named shape is the most specific combination and the friction coefficients from such an entry will always be chosen over any other entries. Vessels The data comprise three tables as follows: The Line Types table defines friction coefficients for contact between Lines and Elastic Solids. Accordingly the program does not allow you to have rows of both type 1 and 2 in the same table. will use the specified friction coefficients when in contact with the specified shape. The data in the 6D Buoys table and the 3D Buoys table are interpreted in exactly the same way. How the data are interpreted For the most part it should be clear how the data are interpreted. Friction Coefficients Normal and axial friction coefficients.w System Modelling: Data and Results. 2. If the axial coefficient is set to '~' then the normal friction coefficient is used for all directions of motion. 250 . The exception to this statement is when multiple rows specify friction coefficients for the same elastic solid and contacting object. A row with "all line types" and "all shapes" is the least specific combination and other entries will always be chosen over this. OrcaFlex regards such rows as equally specific. with the data specified in the figure above. The 6D Buoys table defines friction coefficients for contact between 6D Buoys and Elastic Solids. Similarly if there are multiple rows with identical Line Type and Shape entries then the program will issue a error message. Rows with "all line types" and a named shape. The Line Type can be specified as "all line types". For example. any contact between nodes and any shape other than "Shape1" will not include friction effects. This is because OrcaFlex has no way of choosing one set of friction coefficients over another. Rows with a named line type and "all shapes". irrespective of the line type it is based on. If no friction coefficients are specified for a particular combination of Line Type and Shape then no friction will be modelled. Line Types table The table contains a user-defined number of rows specifying friction coefficients and each row has the following data: Line Type and Shape The specified friction coefficients will be used for contact between the specified shape and any node which uses the specified line type. Instead of Line Type you specify 3D Buoys or 6D Buoys and there is only a single friction coefficient because Buoy friction in OrcaFlex is isotropic. For example consider the table below: Figure: Solid Friction Coefficients Line Types data table If a node which uses "Line Type1" comes into contact with "Shape1" then OrcaFlex has two choices for friction coefficient since this particular contact satisfies both rows of the table. Similarly the Shape can be specified as "all shapes". 6D Buoys table and 3D Buoys table These tables are entirely analogous to the Line Types table. The 3D Buoys table defines friction coefficients for contact between 3D Buoys and Elastic Solids. The other possibilities are: 1. For full details of the friction calculation see Friction Theory. barges. and for a given draught of that vessel type. In addition. QTFs. at the centre of gravity. respectively. This system allows a given vessel type to be used for similar. floating platforms. but not identical. its RAOs.w System Modelling: Data and Results. Vessels 6. The origin is never specified explicitly. for example where cables or risers are connected. This is effectively chosen by the user when the vessel type is set up. TLPs. Note that these directions must therefore be the directions to which the RAOs apply. are specified on the Vessel data form. Vessel Data and Vessel Type Data A vessel requires a lot of data to define its properties. added mass etc. so these data are instead specified for a Vessel Type. They are principally suitable for modelling floating bodies that are large enough for wave diffraction to be significant. The vessel itself is then set to use that vessel type and draught.g. such as its position and how its motion should be calculated. It is entirely arbitrary and may. The RAOs. be at the bow on the keel. QTFs and other diffraction analysis results.) are not specific to the way the vessel is being used. Vy and Vz must be the directions of surge. On the other hand the two tugs differ in their positions and the way they are driven. each of type 'Tug' but possibly of different lengths. 251 . for instance. so there is no corresponding data item for you to enter its value: it is simply the point on the vessel to which all the vesel type data (or their reference origins) refer. the vessel and the vessel type both have lengths specified. However note that if you specify that the vessel type has symmetry then the vessel origin must be placed on the plane(s) of symmetry or at the centre of circular symmetry. since they allow the vessel motion to be based on RAOs. which can be calculated by a separate program and then imported into OrcaFlex. see Vessel Types: Conventions for details. or for more than one vessel. The case-specific data. Vessel Frame of Reference The vessel is defined relative to a right-handed system of local vessel axes Vxyz illustrated below. since they apply to both tugs. But most of the data (e. sway and heave. semi-subs or any similar floating rigid body. drawing data (defining the tug outline) and many other properties are data of the vessel type. are then defined relative to these vessel axes.7 VESSELS Vessels can be used to model ships. Vx. QTFs. and if these differ then all the vessel type data are automatically scaled to the length of the vessel. so these are properties of the individual vessel objects. for this vessel type. vessels. For example a pipe being towed by two similar tugs can be modelled by creating a vessel type called 'Tug' and then creating two vessels. These points then move with those axes as the vessel moves and rotates relative to the global axes. etc. where: V is the vessel origin for this vessel type. vertex 3 edge joining 3 to 5 vertex 5 z (heave) yaw y (sway) pitch V Figure: x (surge) roll Vessel Model Points on the vessel. and OrcaFlex calculates these motions automatically. Because the different loads depend on different parts of the primary motion. so for simple cases only one of the two motions need be used. Some of the loads depend on only the low frequency primary motion. Vessels Vessel Drawing The vessel is drawn in 3D views of the model. OrcaFlex needs to know how much of the primary motion is low frequency and how much is wave frequency. OrcaFlex superimposes this latter motion on the primary motion to give the total combined motion of the vessel. Other Damping is calculated using the wave frequency primary motion. each of which are optional but when both are present they are applied concurrently. so you can highlight application-specific drawing. To enable this. For an overview see Vessel Modelling Overview and for details of the options see Vessel Calculation Data. In the absence of waves it moves steadily along its course and this would be modelled using Primary motion (probably set to Prescribed or Time History). not any superimposed motion. so in this case you also need to specify a dividing period that is used to filter the primary motion into its low frequency and wave frequency parts. Both means a mixture of frequencies. consider a ship being driven under power along a specified course. with the wave frequency motion superimposed on the low frequency motion. since it is a low frequency effect. and it is then often useful to be able to model them separately. which will also be drawn. Drawing data can be specified for both the vessel and for its vessel type. As with all points on the vessel. The drawing allows a simple visual check that amplitudes. So when primary motion is used you also need to specify whether the primary motion is treated as all low frequency. wave load RAOs. that broadly fall into two categories – low frequency (LF) motions such as slow drift motion due to waves or driven motion due to vessel thrusters. since the current and wind load data are generally obtained from steady state measurements or analysis. as either a "wire frame" of user-specified vertices and edges or using a shaded view drawing file. for a fixed vessel) can be set to None. And each of them (or both. For some cases both types of motion are present. and it will also be automatically scaled if the vessel is a different length. For example the lead tug in the above example might have a special tow-point fitting that you want to draw. and wave frequency (WF) motions such as response to wave loads. OrcaFlex provides two vessel motions. all wave frequency or both. and this allows you to set up vessel-specific drawing. Primary Motion and Superimposed Motion. and can also be used to do a visual check for interference between lines and vessel structure. the drawing coordinates are defined relative to the vessel axes Vxyz shown above. in OrcaFlex they only depend on the Primary motion.1 Vessel Modelling Overview Motion Options Vessels can undergo various different types of motion. Wave drift damping is calculated using the low frequency primary motion. However the vessel can also have its own extra drawing data. wave drift QTFs and sum frequency QTFs. Added mass and radiation damping effects are calculated using all the primary motion. Primary Motion Treatment for Included Effects You can choose which of many different types of vessel load are included in the analysis. Most of these loads are affected by the motion of the vessel. OrcaFlex first draws the vessel type (scaled to the vessel length) and then draws the vessel. Vessel Motion Many options are available for how the vessel position and motion is calculated.w System Modelling: Data and Results.7. as follows: Interpolation of displacement RAOs. It is usually convenient to specify drawing data for the vessel type. since it can then be shared if that vessel type is used for another vessel. As an example. with the latter being superimposed on the former. for both wire frame and shaded views. The range of excitation frequencies that are being modelled should be used to determine the appropriate setting for this data item. since it is a low frequency effect. phases etc. are consistent with the applied wave. The two parts of the drawing can have different colours. The Primary and Superimposed motions each have a choice of different types of motion. 252 . some depend only on the wave frequency primary motion. When the vessel is drawn. Current and Wind loads are calculated using the low frequency primary motion. But when waves are present the primary motion is augmented by wave-generated motion that would often be modelled in OrcaFlex as Superimposed motion specified by displacement RAOs. 6. and the wave phases for applying these. are calculated using the low frequency primary motion. Manoeuvring load is calculated using the low frequency primary motion. and some depend on all the primary motion. Dimensionless items such as translational RAOs (surge. This is useful if you have data for a 70m ship. The default value '~' means that this vessel is the same length as the vessel type. Note also that rotational RAOs (roll. optionally including 1st order wave loads and added mass & damping (these would normally be included). for example. For example force data have units equivalent to Mass*Length/Time2 so are scaled by (R3). applied loads. All masses (and added masses) are scaled by R3. Data items with other units are scaled by writing the units in terms of the fundamental units of mass. sway. If you specify a length that differs from the vessel type length. covering both wave frequency and low frequency. Draught Specifies which Draught of the specified vessel type to use. but want to use a 50m ship that is otherwise very similar. The draught used cannot be changed during a simulation.w System Modelling: Data and Results. but note that Froude scaling does apply to the periods (or frequencies) specified for RAO and QTF data. Vessels If the vessel is subject only to wave frequency excitation. Calculated (6 DOF) primary motion can be used to model the whole motion of a vessel. Type Specifies the Vessel Type. Warnings: If the vessel does not scale uniformly in all dimensions. 253 . Length Specifies the length of this vessel. current and wind drag loads. yaw) are often given in dimensional terms (degrees per metre) and these also scale. then primary motion is treated as should be set to wave frequency. accurate data specific to this vessel should be obtained. If the vessel is subject to a range of excitation frequencies. length and time. Prescribed or Time History primary motion can be used to model a vessel being driven over a predetermined course. then OrcaFlex will scale all the vessel type's data to allow for the scaling factor VesselLength/VesselTypeLength. 6.2 Vessel Data Name Used to refer to the Vessel.5.g. and the displacement RAO data would therefore not be used. Each Vessel Type can have data for a number of different draughts. If the vessel is subject only to low frequency excitation.7. Froude scaling scales each item of data by a factor that depends on the units of that item. If R = ratio of vessel length to vessel type length. Loads from any attached lines or other objects are always included. moored) vessel whose motion is due to the 1 st order wave effects only. heave) and phase angles are unchanged by the scaling process. and the superimposed motion set to RAOs + Harmonic to model the 1st order wave-induced motion. The Vessel Types button allows you to view and edit the Vessel Type Data. then primary motion is treated as should be set to both. then primary motion is treated as should be set to low frequency. Time History primary motion (or Time History superimposed motion but not usually both) can be used to completely specify the motion of a vessel. then this type of scaling introduces errors and should not normally be used. Typical Examples of Vessel Modelling Here are some typical examples of how primary and superimposed motion can be combined to achieve various things. then the scaling factor applied is as follows: All lengths are scaled by R. These scaling rules are the same as those used in deriving full scale ship performance from physical model tests.5)2) = R3. All times are scaled by R0. In this case the superimposed motion would normally be None. The scaling is done using Froude scaling (see Rawson and Tupper). Instead. and are correct if the vessel is a perfect scaled replica of the vessel type in all respects.(R) / ((R0. 2 nd order wave loads. since all motion has already been accounted for in the primary motion. pitch. Primary motion set to None and superimposed motion set to RAOs + Harmonic can be used to model a simple steady (e. and then applying the above factors. This is only used if Prescribed. If Included in Static Analysis is set to 6 DOF then OrcaFlex starts from the user-specified position and adjusts all six degrees of freedom until an equilibrium position is reached. Warning: If you have included any harmonic motion on the vessel (see Harmonic Motion) then the phases of the harmonic motions will normally depend on the vessel Initial Position. sum frequency load. Note that only these 3 free degrees of freedom of the vessel (X. for ships in head and stern seas the RAO scaling errors may be acceptable. The Initial Orientation defines the orientation of the vessel axes Vxyz as three rotations. Trim. If the vessel is not included in the static analysis then this Initial Position is taken to be the static position of the vessel. For an overview see Vessel Modelling Overview Included in Static Analysis You can control whether the OrcaFlex static analysis calculates the static equilibrium position of the vessel. Heading. or simply places the vessel in the user-specified initial position. added mass & damping load. The Initial Position defines the position of the vessel origin V. Z forces and Heel. This means that the Z component of resultant force may be non-zero in the equilibrium position. Initial Position and Orientation These specify the vessel's static position relative to the global axes. so if you change the Initial Position you may need to change the harmonic motion phases accordingly. Likewise the resultant Heel and Trim moments may be non-zero in the equilibrium position. Primary Motion page specifies any further data for any Primary Motion. The other three degrees of freedom (Z. then the Trim rotation about Vy and finally the Heel rotation about Vx. Heading moments will be zero at the equilibrium position. Trim and Heel. The static orientation of Vxyz is that which results from starting with Vxyz aligned with the global axes and applying the Heading rotation about Vz. If the vessel is included in the static analysis. not any slowly varying contribution to wave drift load. so OrcaFlex issues a warning if scaling is used and the wave direction is not close to a head or stern sea.w System Modelling: Data and Results. Note: The vessel Z coordinate can only be changed by editing on the vessel data form. Calculation Data The following settings (on the Calculation page on the vessel data form) control how the vessel's static position and dynamic motion are determined. if included). Y and Heading) are included in the calculation. Heel and Trim) are assumed to be constrained and so are left at the values specified by the user. manoeuvring load and other damping load) will be zero. and any included wave drift load will only include the mean drift load (allowing for wave drift damping. for a series of static analyses. Y and Heading until an equilibrium position is reached. OrcaFlex first places the vessel at the initial position and orientation specified by the user. 254 . Further Vessel Data The remaining vessel data are specified on the following separate pages of the data form: Calculation page specifies how the vessel motion is modelled. If Included in Static Analysis is set to None then OrcaFlex leaves the vessel in this user-specified position. If Included in Static Analysis is set to 3 DOF then OrcaFlex starts from the user-specified position and adjusts the vessel's X. all of the X. This is not necessarily an equilibrium position. This is only used if Harmonic Motion or Time History superimposed motion are used. In the static analysis many of these (first order wave load. since the RAOs for these wave directions depend mainly on vessel length. Y. Dragging in the Z direction with the mouse is prevented. Time History or Externally Calculated primary motion are used. For other cases the RAO scaling is likely to be poor. The loads on the vessel to be taken into account in calculating the equilibrium position are specified by the Included Effects. then this Initial Position is used as an initial estimate of the vessel position and the statics calculation will move the vessel from this position iteratively until an equilibrium position is found. Vessels However. In this case. Drawing and Shaded Drawing pages specify how the vessel will be drawn in the 3D view. Superimposed Motion page specifies any further data for any Superimposed Motion. Multiple Statics page allows you to specify a grid of different positions of the vessel. Primary Y. plus the data for all the included loads. Displacement RAOs + Harmonic. Manoeuvring Load: Has no separate data. for example to model the vessel moving station during the simulation. Damping page. Superimposed Motion The Superimposed motion is applied as an offset from the position given by the primary motion. Sway. each of which is optional. See also Theory. In this option OrcaFlex calculates the vessel primary motion in only 3 degrees of freedom (surge. Included Effects For each of the following vessel load effects. There is no primary motion in the other 3 degrees of freedom (heave. if waves are present and you specify non-zero displacement RAOs for the vessel type. Added Mass. The harmonically varying offset comes from two sources. The vessel's position oscillates harmonically about the primary position. This option allows you to drive the vessel around the sea surface. 255 . The vessel's speed and course are specified by the data on the Primary Motion page. There is no offset and the vessel position is equal to the primary position at all times. It can be one of the following options: None. When both are present they are applied concurrently. Roll.w Note: System Modelling: Data and Results. roll. yaw) based on the included loads plus loads from any lines or other objects that are attached to the vessel. Requires that Wave Load (2nd order) is also included. sway. For this option the user specifies the primary motion in a time history file that defines. you can choose whether they are included in the analysis by ticking the corresponding checkboxes on the calculation page of the vessel data form: Applied Loads: Data for these are on the vessel form Applied Loads page. Primary and Superimposed. Primary Rotation 1. Wave Drift Load (2nd order): Data are on the vessel type form Wave Drift QTFs page. Prescribed. Added Mass and Damping: Data are on the vessel type form Stiffness. See also Theory. Time History. then the offset will include the wave-generated harmonic motions specified by those RAOs. pitch). Calculated (3 DOF). based on the included loads. Firstly. Vessels If multiple statics are being performed on the vessel then no equilibrium calculation is performed on the vessel and its placement is determined by the multiple statics data. See Manoeuvring Load Theory. Calculated (6 DOF). as a function of time. Time History. Primary Z. with the latter being superimposed on the former. Heave. the vessel Primary X. The added mass. The data for all the included loads must be specified. The user specifies the offset in a time history file that defines the vessel Surge. Sum Frequency Load (2nd order): Data are on the vessel type form Sum Frequency QTFs page. Secondly. Wave Load (1st order): Data are on the vessel type form Load RAOs page. It can be one of the following options: None. See the Time History data on the Superimposed Motion page. Externally Calculated. For theory see Wave Drift Damping. Pitch and Yaw as a function of time. The primary motion is defined by an external function that is specified on the Primary Motion page. Wave Drift Damping: Has no separate data. Primary Rotation 2 and Primary Rotation 3. the vessel's superimposed offset also includes any harmonic motions that you specify on the Superimposed Motion page on the vessel data form. In this option there is no primary motion and the primary position of the vessel remains fixed at the position determined by the static analysis. Other vessels in the model are included in the static analysis as specified by their own data. Dynamic Analysis OrcaFlex provides two vessel motions. stiffness and reference origin datum position of the vessel type must be specified. Here OrcaFlex calculates the vessel motion in all 6 degrees of freedom. See the Time History data on the Primary Motion page. See also Theory. plus loads from any lines or other objects that are attached to the vessel. damping. Primary Motion The Primary motion determines what OrcaFlex refers to as the primary position of the vessel. See Vessel Modelling Overview for an introduction and examples of how these options can be used. Time domain digital filters are not perfect (see the filter cutoff graphs). For example. so that the calculation can use the appropriate part for each load. Primary Motion is treated as. so that if the vessel starts at rest then at the start of the next stage the vessel is travelling at 1m/s. if the direction is 0° relative to Vessel heading then the vessel velocity. the velocity (speed and direction) of the primary position and the rate of change of the heading. See also Theory. Vessels Other Damping: Data are on the vessel type form Other Damping page. so the Dividing period should ideally be well above the highest period of the significant wave frequency response of your vessel. Note: Negative speeds can be specified. then the vessel velocity direction varies during the stage. Speed of Motion For each simulation stage the speed of the motion can be specified as either a Constant Speed or a Speed Change. OrcaFlex issues warnings at the start of the simulation if the data specifies a discontinuous velocity. Because of this.1m/s 2 to be applied throughout the stage. Rate of Turn In addition to varying the velocity of the mean position. If the Direction of Motion is specified relative to the Vessel heading and the Rate of Turn is non-zero. or a mixture of both low and wave frequency. Warning: The Prescribed Motion facility can cause discontinuities of velocity at stage boundaries and these may cause transients in the system. This is the angle change per second to be applied to the vessel's heading throughout the stage. Prescribed Motion The prescribed motion data only apply if the vessel's Primary Motion is set to Prescribed. a value of 90° relative to the Global X direction would result in the motion being in the global Y direction. The direction value is interpreted as an azimuth. See also Theory. Broadly speaking. The last of these means that you also need to specify a Dividing period that is used to filter the primary motion into its low frequency and wave frequency components. So. Dividing Period Some of the included effects depend on only the low frequency primary motion.w System Modelling: Data and Results. some depend on only the wave frequency primary motion. It enables you to drive the vessel around the sea surface along a predetermined path. Current Load: Data are on the vessel type form Current Load page. A digital filter (a second-order Butterworth filter. The vessel is driven by specifying. whilst varying. you can specify a Rate of Turn for each stage. Wind Load: Data are on the vessel type form Wind Load page. then you need need to specify whether the Primary Motion is treated as all low frequency. components of the vessel motion with periods longer than this value will contribute to the lowfrequency motion. all wave frequency. if the vessel's heading was 130° and the direction of motion was 50° relative to the Vessel heading then the motion would be an azimuth of 130° + 50° = 180° relative to global. Direction of Motion For each simulation stage the direction of the motion can be specified as either relative to the Global X direction or relative to the Vessel heading. but well below the lowest period of significant slow drift response. Note: The direction of motion is not restricted to be in the same direction as the vessel heading. see Bellanger) is then used to separate the vessel primary motion into low-frequency and wave-frequency parts. that is in the global -X direction. is always in the Vessel heading direction. Note: Loads which are included will only affect the vessel static equilibrium position if Included in Static Analysis is set to other than None. and some depend on all the primary motion. See also Theory. if primary motion is used. And they will only affect the vessel motion if the primary motion is set to one of the Calculated options. 256 . For details see Vessel Modelling Overview. an increment of 1m/s during a stage of length 10 seconds causes an acceleration of 0. Likewise. for each stage of the simulation. by specifying how the vessel's primary position and heading change during the simulation. and those components with shorter periods will contribute to the wave-frequency motion. In addition. based on this dividing period. If Speed Change is selected then the speed is incremented linearly by the specified amount during the stage. If Constant Speed is selected then that speed applies throughout the stage. this applies to all 6 degrees of freedom. The time values in a vessel time history file need not be equally spaced. If you are modelling slow drift. the phases are not specified relative to the phase of a wave – they are the phase lags from the global time origin T=0 until the maximum harmonic motion occurs. as specified by the vessel's primary motion. then note that slow drift normally only applies to surge. in which case the amplitudes for heave. Warning: Harmonic motions can be used to model pre-calculated vessel slow drift. To do this: On the Calculation page set the primary motion or superimposed motion data item (or both) to Time History. For further details of the file format see Time History Files. On the appropriate Time History page. from the vessel's local origin. if your time history data are defined as the displacement of the Datum Point away from its initial position you need to add in the offset of the Datum Point. are set to Time History. Roll.w System Modelling: Data and Results. Sway. These are the positions of the Datum Point measured relative to the global axes. Primary Rotation 1. Heave. Vessels If the direction is specified relative to the Global X direction then the vessel velocity direction is not affected by the Rate of Turn. The whole of the harmonic motion is applied at the displacement RAO origin. Primary Z. subject to any Froude scaling on vessel length. Sway. pitch and yaw). then you will normally also have to adjust the phases of the slow drift. This is because such changes affect the global time at which a particular part of the wave train will reach the vessel and hence will also affect the global time at which maximum slow drift motion is achieved. Time History The Time History data only apply if the vessel's primary or superimposed motion. see order of application of rotations. or if you change the data for the waves (other than changing the simulation time origin). The units used for all the columns must be the same as those used in the OrcaFlex model. The harmonic motion amplitudes (unlike the RAO responses of the vessel) are not specified relative to a wave amplitude – they are specified directly in length units (for surge. measured in the primary motion frame. set up the time history data as described in Data in Time History Files. the phase that should be specified for the harmonic motion is given by 360 × ((Tmax / P) mod 1) where P is the period of the harmonic motion and Tmax is the global time at which you want the maximum of the motion to occur. The harmonic motions are in addition to any wave-generated motion specified by the RAO data. roll and pitch should be set to zero. Primary Y. Primary Rotation 2 and Primary Rotation 3. More precisely. or both. and Heave motion must be inclusive of the offset of the Datum Point from the vessel's local origin. Because the superimposed time history motion defines the position of the Datum Point. into your time history data. sway and yaw. Similarly. These are the positions of the Datum Point measured relative to the primary position of the vessel. Doing so allows you to specify the motion by giving a time history file. so the time values must be in seconds and angles in degrees. the Amplitude and Phase lag of the motion for each of the 6 degrees of freedom of the vessel. Pitch and Yaw. For details of how rotations are applied. 257 . your time history data for the Surge. specified by giving: the Period of the harmonic motion. as described below. sway and heave) or degrees (for roll. Harmonic Motion The Harmonic Motion data only apply if the vessel's superimposed motion is set to RAOs + Harmonic. For superimposed time history motion the degrees of freedom that must be specified are Surge. That is. Contents of Time History File The time history file must contain a time column and columns for all 6 degrees of freedom of the vessel. If you do this then if you move the vessel's Initial Position in the wave direction. so if you only want the wave-generated motion then you should set the number of harmonic motions to zero. Each harmonic motion is a single-period sinusoidal motion of the vessel. It allows you to specify a number of harmonic motions of the vessel. For primary time history motion these are Primary X. Create a tab-delimited text file containing the time history motion you want. vary with simulation time or be given by an external function. for SimulationTime = -BuildUpDuration) will not. orientation. On the Primary Motion page of the vessel data form. Offsets are from the vessel's initial position and are specified by giving a range of azimuth and offset values. Multiple Statics The offsets for multiple statics calculations are specified here. Note: Applied loads will only affect vessel static position if the corresponding degree of freedom is included in the static analysis. Externally Calculated Primary Motion The externally calculated primary motion data only apply if the vessel's Primary Motion is set to Externally Calculated. To use externally-calculated primary motion: On the Calculation page of the vessel data form. You can apply to the vessel external Global Loads that do not rotate if the vessel rotates. This can be done either in a separate time history file for the wave or else in an extra column in the vessel's time history file. set the Primary Motion to be Externally Calculated. If the vessel rotates then the loads do rotate with it. for example. If the vessel rotates then the loads do not rotate with it. The position and velocity specified by a time history file for the start of the simulation (i. For example: 258 . Typically the calculation will be based on values of variables as the simulation proceeds – otherwise it is preferable to use a time history to impose a pre-calculated motion. These components can be constant. Also set the Origin to the vessel axes coordinates of the point on the vessel whose motion your external function specifies. Unlike most standard external functions. These are suitable for modelling thrusters. These are specified by giving the components of Applied Force and Applied Moment relative to vessel axes. These values are returned in a TExternallyCalculatedPrimaryMotionStructValue struct – full details are given in the OrcFxAPI help file. and will only affect the motion if the Primary Motion is set to one of the calculated options which includes the degree of freedom. acceleration and angular acceleration. Again these components can be constant. To handle this OrcaFlex uses ramping during the build-up stage to smooth the transition from the static state to the position and motion specified in the time history file.y. angular velocity. in general. In the External functions section of the Variable Data form. velocity. you can specify external Local Loads that do rotate with the vessel. vary with simulation time or be given by an external function. If you have suitable data for the wave elevation then you can use that to specify the wave by time history. These are specified by giving the components of Applied Force and Applied Moment relative to global axes. Applied Loads You can optionally include applied loads on a vessel. set up an variable data source that specifies the details of your external function.z coordinates relative to vessel axes. In addition. In both cases the Point of Application of the load is specified by giving its x. It enables you to impose a motion on the vessel that is calculated programmatically in your own external function.e. set the Externally calculated primary motion to the external function variable data source that you have set up. the externally calculated primary motion external function returns multiple values per call: position.w System Modelling: Data and Results. match the static state from which OrcaFlex starts the simulation. Vessels Notes: If there is any wave-generated motion present in a vessel's time history motion then the OrcaFlex wave data needs to match the wave that generated that motion. w System Modelling: Data and Results. With the above data. vessels are drawn using the wire frame data. The Offsets table specifies how far in the given direction the vessel is to be placed. The vertices and edges follow the motions of the vessel. by default. Drawing Vessels are drawn as wire frames defined in the data as a set of Vertices and Edges. If the vessel length differs from the vessel type length. edges and pen specified for its vessel type (see the vessel types data form). This allows you to specify a wire frame drawing of the basic vessel type. no edges) if desired. They can also be used to represent a spar or other equipment attached to the vessel. For shaded graphics views. some set to '~') to combine both filled in and framework shapes. 259 . and thus may be used to improve understanding of the motion of the model. for shaded 3D Views. and check visually if other parts of the model pass through it. then the vessel type wire frame is scaled accordingly. Then a further vessel-specific wire frame may be drawn. OrcaFlex uses the following procedure to generate this surface from the wire frame vertices and edges. Note that you can use a mixture of edge diameters (some defined. The vessel is drawn by first drawing a wire frame based on the vertices. Vessels The Azimuths table determines which directions are to be analysed. If the edge diameter is '~' then that edge will be used to build a filled in shape. Shaded Drawing By default. For example during a simulation replay you can adjust the viewpoint to look exactly along the edge of interest. The drawing data do not affect the mathematical model in any way – they are purely for drawing 3D views. You can define wire frame drawing data in two places – for the vessel and also for its vessel type. The Edges are lines drawn between two vertices. Note that either. the offsets analysed by the multiple statics calculation are as illustrated by the dots in the diagram below: Y 90 deg X 45 deg 135 deg 180 deg 0 deg 0m 20m 40m 60m 80m 100m Vessel Initial Position Figure: Example Offsets A diagram showing the selected offsets is drawn on the Vessel Offsets data form. otherwise that edge is drawn as a cylinder with the specified diameter. of these wire frames can be empty (i. to help visualise which offsets will be analysed. edges and pen that you specify on the vessel's data form. As an alternative you can use the vertices and edges to define a frame like structure. using any vertices. so that you can then look for clashing with other parts of the system. The Vertices are defined by giving their coordinates relative to the vessel axes Vxyz. but OrcaFlex needs a solid surface for the shaded graphics representation. or both. The wire frame drawing data comprises vertices and edges. filled-in shape based on the vertices and edges.e. and then optionally add to it (possibly in a different colour) a wire frame drawing of some equipment that is specific to that vessel. the vessel is drawn using a solid. This algorithm does not always generate the shaded drawings that you might expect. e. In the red vessel. the superstructure and hull do not share vertices and so there are two distinct sets of connected vertices. but in shaded mode they differ. Consider the following two wire frame vessels. The remaining edges are used to partition the vertices into sets of connected vertices. This results in two separate convex hulls and a better representation.e. 260 . These edges are now handled and are excluded from the remainder of the procedure.g. Vessels First any edges with specified diameters (i. When drawn in wire frame mode they look the same. Figure: Wire Frame and Shaded Drawing For the green vessel the superstructure and the hull share vertices and so all vertices are connected. Finally. Two vertices are deemed to be connected if there exists a path of edges between the two vertices.w System Modelling: Data and Results. diameters not equal to '~') are drawn as cylinders. crane boom latticework. the smallest convex hull enclosing the set is drawn. This allows you to use such edges to visualise parts of the structure that are not solid. for each set of connected vertices. This results in a single convex hull for all vertices being drawn. It reports the following: Length The length of the vessel. Two different vessels can have the same type. Then the length of the longest side of this cuboid is found.txt.x file by including an auxiliary file called AdditionalInformation. a free form multi-line text field which is passed to any external function used by the Vessel object. The vessel typical force and moment are based on the forces and moments applied by connected objects.w System Modelling: Data and Results. To illustrate this. Vessels Alternatively the object can be represented by an imported 3D model by specifying the Shaded Drawing File. The Use Culling option is normally selected since it can provide a useful performance benefit. Statics force accuracy. The Shaded Drawing Origin defines the origin of the shaded drawing with respect to the vessel's local axis system. Examples of this can be found in the sample shaded drawings provided by Orcina. OrcaFlex accepts a position as a static equilibrium position if the largest out of balance load component is less than the statics accuracy. Disabling the Use Culling option resolves this problem. External Functions Parameters This data item specifies the External Function Parameters. We refer to the resultant force and moment as the out of balance load. You can define a number of different vessel types and each type is given a name. each of type 261 . The static analysis searches for an equilibrium position for the vessel – that is a position for which the resultant force and moment on the vessel is zero. OrcaFlex may not be able to achieve the Tolerance specified if it is too small. If this happens then typically sections of the model will be missing when drawn by OrcaFlex. If there is more than one wave train then the direction of the first wave train is used. but will take more iterations. in order to work it requires that the triangles defined in the . 6.x file directly. Reducing the Tolerance value will give a more accurate static equilibrium position.x file). This is modelled by creating a vessel type called 'Tug' and then creating two vessels. If these coordinates use a different length units system from your OrcaFlex model then you should specify the units used in the . consider a model of a pipe being towed by two identical tugs. Draw Size is provided to allow you to scale the drawing. This longest side is calculated by first fitting the smallest possible cuboid around the vertices of the shaded drawing (these are defined in the . However. Statics moment accuracy These are only reported if the vessel is included in statics.x file have their outward facing directions defined correctly. Note: If you use a value of '~' for Draw Size then OrcaFlex uses the coordinates in the . Specify a value of '~' to display the drawing using the absolute coordinates as specified in the . Wave direction relative to vessel The relative wave direction.x file extension. In the unusual situation where the outward facing directions are not defined correctly then the . All directions are scaled equally to arrange that the longest side in the drawing is drawn to the specified Draw Size. usually with the . Because computers have limited numerical precision the static analysis cannot always find a configuration where the out of balance load is exactly zero.3 Vessel Types Each vessel has a vessel type that determines a lot of its data and which is defined on the vessel types form.x file will not display correctly. This must be a Direct X format file. The Browse button allows you to specify the Shaded Drawing File quickly and also provides quick access to the Orcina sample drawings via the Navigate to Orcina sample drawings button. The Statics force accuracy equals Tolerance * vessel typical force and the Statics moment accuracy equals Tolerance * vessel typical moment. This cuboid is aligned with the shaded drawing's local axes.7. which is then used on the vessel data form to specify the type of that particular vessel. Shaded Drawing Origin is provided because the shaded drawing and the vessel may have different origins. Properties Report The Vessel properties report is available from the popup menu on the data form. since the computer has limited numerical precision. If you use a relative path then the path will be taken as relative to the folder containing the OrcaFlex file. Similarly Shaded Drawing Orientation allows you to reorient the shaded drawing to match the vessel's axis system.x file. The diffraction analysis used 8% extra damping in roll about CG. The default hydrodynamic and wind drag coefficients are based on graphs given in the standard OCIMF book. wave drift QTFs. Vessel Type Data Draughts For each Vessel Type you can enter data for several different Draughts.84 m. so if you have no better data available then this default data might still sometimes be useful even if your vessel is a different length tanker. Block Coefficient 0. but only if you have no better data available. it is given initial default data that corresponds to a particular 103m long tanker. The RAOs. Separate QTFs for each different draught. Added Mass and Damping data. which is modelled in OrcaFlex using non-zero linear other damping. Conventions define the meaning of the RAO and wave drift QTF data. The tanker used in this analysis had the following properties: Length Between Perpendiculars 103 m. A single set of drawing data applies to all draughts. The conventions apply to all draughts. Stiffness.95 m. for example. Such a file can then act as a library of vessel types that can be imported into other OrcaFlex data files. The default data was obtained as follows. Draught 6. added mass and damping matrices. Note that the OCIMF book gives different coefficients for different vessel types and draughts. The default structure data. Longitudinal GM = 114 m. Properties Data The vessel type data are then specified on the following separate pages of the data form: Structure data defines the length of the vessel type (same for all draughts) and its mass. You should replace this with accurate data for the vessel you are modelling. Breadth 15. The default vessel type data are approximate averaged deep water coefficients.g. e. but is otherwise similar. each draught having a user-specified Name. stiffness. For example you can set up a data file that defines a number of vessel types but has no vessels. but a lot of the data are draught-dependent and so separate data are defined for each defined draught.66 m. so these are properties of the individual vessel objects. Current and Wind Load data. You don't have to use all. Wave radiation damping is specified here. The wind drag areas are based on an assumed average upperworks height of 12m for surge and 9m for sway. The hydrodynamic and wind drag areas and area moments are set for the above 103m tanker. It is not possible to use different draughts at different times during the same simulation. Wave Drift QTF data. For modelling other sources of damping. Transverse GM 1. OrcaFlex automatically Froude scales vessel type data to the vessel length you specify. The default displacement RAOs have been calculated from the first order wave load RAOs and the stiffness. Vessels 'Tug'. 262 . and they have been rounded to only 1 or 2 significant figures. since they apply to both tugs. Each vessel in the model must specify (on the vessel data form) which draught to use. Separate values for each different draught. and other damping data all come from an NMIWave diffraction analysis of a 103m long tanker in 400m water depth. On the other hand the two tugs differ in their positions and any prescribed motion. inertia and centre of gravity (draught-specific). Separate RAOs for each different draught. added mass and damping. or even any. are data of the 'Tug' vessel type. Drawing data.804. wave load RAOs.w System Modelling: Data and Results. The vessel origin for these default data is on the centreline at midships and at the mean water level. Separate values for each different draught. However note that the default data tanker has a significant heave resonance in beam seas at 7s period. Displacement and Load RAO data. Separate values for each different draught. Some of the vessel type data apply to all draughts. Other Damping data. of the vessel types you define. viscous roll damping. Default Vessel Type Data When you create a new vessel type. If your vessel is similar to the default data tanker then you might find the default data useful. stiffness. It is vital that you know the conventions that apply to the RAO tables that you are using. the conventions apply to all RAO and QTF data. Mass and Moment of Inertia Tensor The vessel type's mass and moment of inertia tensor with respect to axes through the centre of gravity in the vessel x. you should replace the '~' with an appropriate value for the length of the vessel type.w Note: System Modelling: Data and Results. QTF. Warning: In general. The use of differing coordinate systems and conventions by different suppliers of data is the main source of confusion. Rotational RAO Conventions Roll. which is specified on the Stiffness. This value is no longer permitted and will now cause an error if you attempt to run a simulation. added mass and damping data.g. In this case. If the vessel length differs from this. Structure Vessel Type Length The length between perpendiculars of the vessel type. These should include the structural and contents mass and inertia. Unfortunately. and so have only the few significant figures that are included in the NMIWave output file.g. added mass and damping matrices). radians/foot etc. Translational RAO Conventions Translational displacement RAOs are always non-dimensional (e. e. and (in the case of the direction conventions) stiffness. metres/metre or feet/foot). Instead you can tell OrcaFlex the conventions that apply to those data and OrcaFlex will then automatically allow for those conventions when it uses the data. Different definitions of phase angle and rotational RAOs.g. since they are derived from NMIWave output values with only a few significant figures. Added Mass and Damping page. Vessels Some default data values have been taken directly from NMIWave output. Note: Some old OrcaFlex data files may contain vessels with the default value '~' for the vessel type length. These data only affect the vessel motion if the vessel Primary Motion is set to Calculated (3 DOF). there are separate values for each draught. and the default displacement RAOs are derived from the load RAOs. This enables you to enter these data directly from many other programs without having to convert the values between different sets of conventions. using Froude scaling. a number of complications make them notoriously error-prone and difficult to check in practice. kN/m). Use of vessel symmetry. Conventions The conventions page (on the vessel types data form) contains settings that define the meaning of the RAO. Centre of gravity (CG) The coordinates of the vessel type's centre of mass. OrcaFlex provides easy ways of handling these problem areas. The remaining data on the Structure page on the vessel type form are described below and are draught-specific. Calculated (6 DOF) or Externally Calculated. to obtain motions in seas from the port side given data for seas from the starboard side. e. but they are really no more accurate. i. Translational load RAOs are always given as force per unit wave amplitude (e. not all RAO tables fully document the conventions used: see RAO data checklist for help finding out what conventions apply to your data and see Checking RAOs to check that the conventions are set correctly. pitch and yaw displacement RAOs may be specified using one of the following three possible conventions: As rotation angles per unit wave amplitude. But other default data have been derived from NMIWave output values by calculation (for example non-dimensional NMIWave output values needed dimensionalising for use in OrcaFlex. Although RAOs are simple enough in principle. The values are dimensional. The main issues are: Different coordinate systems. This value is only used if Froude scaling is required for any vessels of this type. relative to vessel axes. in degrees/metre. then the length value is used to scale all the vessel type data to the length of the vessel.e.g. You cannot mix data with differing conventions in the same model (but see rotational RAOs below). the derived default data values have many decimal places. Because of this. 263 . y and z directions. but not the added mass. In each case. the convention on the data form should be specified accordingly. Wave steepness is a commonly used angular measure of a wave. This is relative to the time at which the wave crest.w System Modelling: Data and Results. but of course the RAOs are numerically larger (by a factor of π) than those using the maximum wave slope convention. The Symmetry can be set to: None: The vessel type has no symmetry. Rotational load RAOs must be given as moment per unit length (e. kN. kN. Other damping is also treated in two different ways. the actual numerical values for these non-dimensional RAOs are the same regardless of whether the unit selected is degrees or radians. Therefore. then OrcaFlex (internally) converts them to be relative to wave amplitude using the deep water wavelength. defined by steepness = H/L radians (= (180/π)H/L degrees). Symmetry You can specify symmetry of the vessel type. Waves are referred to by The RAO and QTF data can be specified by period in seconds. of course. Maximum wave slope is the true maximum slope of the wave surface. RAO/QTF tables can only be given for one wave direction. XZ plane (or YZ plane): This specifies that the XZ (or YZ) plane through the RAO origin is a plane of symmetry. the units (degrees or radians) of the max wave slope or wave steepness must be the same as those for the angles of rotation.e. either degrees/degree or (equivalently) radians/radian.m/m). Directions You must specify the directions that correspond to positive motion or load in the RAO and QTF data. XZ & YZ planes: This specifies that both the XZ and YZ planes through the RAO origin are planes of symmetry. For each direction given OrcaFlex uses symmetry to derive tables for the reflected directions in the other 3 quadrants. so long as the units are consistent in this way. The values are non-dimensional.g. Warning: If rotational displacement RAOs are given relative to wave slope or steepness. and OrcaFlex uses symmetry to derive tables for all other directions. The values are again non-dimensional. 2. This is the exception to the above rule that the conventions apply to all RAOs and QTFs. Note: These phase conventions do not apply to Newman approximation Wave Drift QTFs. trough. the angles of rotation may be given in either degrees or radians. RAO & QTF Phases The RAO & QTF phase convention is specified by 3 data items: 1. since they are entered without any phase information. by angular frequency in radians/second or by frequency in Hertz. The directions specified must cover all the wave directions used in the simulation. As rotation angles per unit wave steepness. Note that. 264 . are equivalent. and rotational QTFs as moment per unit length squared (e. Vessels As rotation angles per unit maximum wave slope. The most common convention is as given by the default OrcaFlex vessel type: a right-handed system with Z upwards and clockwise rotations being positive. damping and added mass matrices. zero up-crossing or zero down-crossing passes the phase origin. depending on whether circular or non-circular symmetry is selected. which can be thought of as either degrees/degree or radians/radian which. and in the stiffness. Phases are either leads or lags. 3. which is πH/L radians (= 180H/L degrees) for wave height H and wave length L. or in the case of circular symmetry to derive the RAOs/QTFs for any arbitrary direction from the single direction given. Phases are specified either in degrees or radians. But the phase conventions do apply to Full differencefrequency and sum-frequency QTFs. i. not the wavelength for the water depth specified in the model. The phase defines the time at which the maximum positive value of the motion occurs.m/m2). For each direction given OrcaFlex uses symmetry to derive tables for the reflected direction on the other side of the plane. the degrees/radians switch and the unit amplitude / steepness / maximum slope switch do not apply to load RAOs. For the two non-dimensional cases. OrcaFlex will then use the user-specified RAO/QTF tables for wave directions on one side of the symmetry plane to derive tables for the reflected directions on the other side of the plane. Circular: This specifies that the vessel has circular symmetry about the RAO origin.g. For each direction. RAO Origin The RAO origin is the point on the vessel whose motion is defined by the RAOs. in all 6 degrees of freedom. and on the RAOs page of the vessel type data form each RAO table is labelled with its associated direction. QTF origins and phase origins must be on all the planes of symmetry. We therefore recommend that the RAO directions defined cover all the wave directions that will be used and in steps of 30° or less. using the following data. The periods/frequencies need not be entered in order – they will be sorted before use. Or if you specify circular symmetry then all the RAO origins. select the existing direction's page and click the Insert Direction button. depending on the RAO phase conventions) passes the specified RAO phase origin. They are only used if the 1 st order wave loads are included for the vessel and they only affect the motion if the vessel primary motion is set to one of the calculated options. For further information see Vessel Theory: Wave Load RAOs. For random sea simulations. They are only used if the vessel superimposed motion is set to RAOs+Harmonic. They define the 1st order motion of the vessel in response to waves of given period and amplitude. then OrcaFlex will use linear interpolation to obtain an RAO table for that direction. RAO Data RAO data can be specified for a number of different wave directions relative to the vessel. or for wave periods either side of that period. They define the 1st order wave force and moment on the vessel due to waves of given period and amplitude. as specified in the conventions data. The two types of RAOs are specified in very similar ways.e. Warning: Interpolation is likely to be poor if the interval involved is large. RAO Phase Origin The RAO phase origin is the point on the vessel to which the RAO phase values are relative. RAO Interpolation/Extrapolation On direction You must provide RAO tables that include or span the wave direction(s) involved in the simulation. These harmonic motions are specified by giving the RAO amplitudes and phases. And for both there is a Check RAOs button that provides RAO graphs that help detect errors. RAO data should be specified for a wide enough range of wave 265 .w Warning: System Modelling: Data and Results. It is specified by giving its coordinates with respect to the OrcaFlex vessel axes (not the directions specified on the Conventions page). usually for a range of wave periods and directions. Similarly.or down-crossing. On period For regular wave analysis. using the OrcaFlex direction convention. In this case the phase origin can be set to '~'. To change the value of the wave direction for one of the RAO tables. In the case of a circular symmetric vessel. It is commonly. select the tab for that table and edit the Selected Direction. Displacement RAOs are specified on the Displacement RAOs page on the vessel type data form. The phase values given in the RAOs must be relative to the time that a particular point on the wave (crest / trough / zero up. for all six degrees of freedom. at the centre of gravity. i. But note that some programs (one example being MOSES) generate RAOs where the phase origin is not necessarily the same as the RAO origin. To insert a new wave direction after an existing direction. Wave load RAOs are specified on the Load RAOs page on the vessel type data form. QTF origins and phase origins must be on the vertical axis of symmetry. Different draughts can use different RAO origins. the phases are relative to the time the crest or trough passes the point whose motion the RAOs define. For further information see RAOs and Phases. about its primary position. If RAOs are required for a wave direction (relative to the low frequency heading of the vessel) for which an RAO table has not been supplied. RAOs OrcaFlex uses two different types of RAO (response amplitude operator): Displacement RAOs and Wave Load RAOs. but does not need to be. RAOs are specified for only one wave direction – OrcaFlex will derive RAOs for all other directions. Often the phase origin is the same as the RAO origin. This relative wave direction is the direction in which the wave is progressing. The RAO origin is specified by giving its coordinates with respect to the OrcaFlex vessel axes (not the directions specified on the Conventions page). In the dynamic analysis the vessel moves harmonically. measured positive from the vessel x-direction towards the vessel y-direction. the Delete Direction button deletes the currently selected direction. meaning 'same as RAO origin'. RAO data are only needed for the appropriate wave period. the RAO table covers a range of wave periods or frequencies. Vessels If you specify some planes of symmetry then all the RAO origins. It then interpolates these tables on direction relative to the vessel (which will be changing during the simulation if the vessel heading changes) to obtain the RAOs for the appropriate wave periods and directions. 266 . If you specify an RAO for zero period which has non-zero response.w System Modelling: Data and Results. Linear interpolation is used if RAOs are required for a period that is between the periods given in the table.φ) = [C(a1. See RAO Quality Checks for details.φ).φ2)] / 2 This gives better results than interpolating the amplitude and phase separately.L/L2). Both of these stages are done using complex valued interpolation. For periods shorter than the smallest value in the table. are specified in dimensional form and with respect to waves of unit amplitude. Note: The wave drift load is only calculated for a vessel if the Wave Drift Load (2nd Order) option is checked in the list of vessel Included Effects.φ1) for direction β1 and (a2. simply specify a zero-amplitude response at zero period in your RAO tables. given RAOs (a1. since a non-zero response at zero period is physically implausible. OrcaFlex will issue a warning. these loads will only affect the vessel motion if the vessel primary motion is set to one of the Calculated options. OrcaFlex will override this with a zero response. in which the RAO with amplitude a and phase lag φ is represented by the complex number: C(a. Wave drift loads can be important for moored vessels. Also. such as ringing with TLPs. OrcaFlex will use the RAOs specified for that longest specified period. We strongly recommend that your RAO tables provide data for periods that include or span all the wave periods that will be involved in the simulation. Vessels periods to cover the spectrum. which for a free-floating vessel can be derived from the knowledge that the vessel must follow the surface in a sufficiently long wave. you may specify the RAO for period=Infinity. OrcaFlex will warn if there are wave components in the sea state that will be affected by this. In both of these cases. respectively. then the interpolated RAO for the intermediate direction β=(β 1+β2)/2 is (a. And the sum frequency QTF load is only calculated if the Sum Frequency Load (2 nd order) option is checked in the list of vessel Included Effects. To avoid this warning. where: C(a. Different draughts of the vessel type have their own separate QTF data and QTF origins. OrcaFlex first interpolates on period.exp(-iφ) For example. Complex-valued Interpolation Note that RAO interpolation is done using the complex value representation of the RAOs. For periods longer than the longest period specified in the table. To avoid this warning.φ1) + C(a2.φ2) for direction β2 (where these are directions relative to the vessel). OrcaFlex will assume a zero amplitude response at zero period and apply linear interpolation between that and the shortest period value. Obtaining the data All of the above data can generally be obtained from the results of a diffraction program. Note: If the vessel length differs from the vessel type length then the RAO periods specified on the vessel type form are Froude scaled. to obtain RAO tables whose entries correspond to the wave component periods. and it is these Froude scaled periods that must cover the actual wave period(s). since they include low frequency components that might excite slow drift motion of the vessel on its moorings. Wave Drift and Sum Frequency QTFs The Wave Drift QTFs and Sum Frequency QTFs pages on the vessel type data form contain the Quadratic Transfer Functions (QTF) data that OrcaFlex uses to calculate a wave drift load and sum frequency QTF load. QTFs. like wave load RAOs. Translational QTFs have units of force per unit length squared (F/L 2). See Vessel Theory: Wave Drift and Sum Frequency Loads for details of how OrcaFlex calculates second order loads. The View Wave Components button (on the Waves page of the environment data form) reports the wave frequencies that OrcaFlex will use to represent the spectrum. Sum frequency loads include high frequency components that can be important in systems with high frequency natural modes. OrcaFlex can import these data directly from the output files of some specific programs (AQWA and WAMIT) and from generic text files with OrcaFlex-specific markers added.φ) = a. Wave drift load can be used to model vessel slow drift and for this reason is often referred to as slow drift load. and rotational QTFs are moments per unit length squared (F. The QTF data for Newman's approximation are entered in a similar way to RAO data. so for example directions 270° and -90° are equivalent. but Newman's method requires much less QTF data. The second order wave load is calculated based on the wave conditions at the instantaneous low frequency primary motion position of this point. The Newman method cannot be applied for the sum frequency load: in this case. The QTF data will be interpolated on direction and period as required. the QTF data are entered in a single table. The QTF origin is specified relative to the OrcaFlex vessel axes (not the directions specified on the Conventions page). You should provide data for periods that (after allowing for Froude scaling if the vessel length differs from the vessel type length) cover the wave periods the vessel will experience. in which case the phase origin coordinates can be set to '~'. Each QTF table consists of data for a range of wave periods or frequencies (depending on the convention specified). To change the direction associated with a table. which allows calculation of the slowly varying part of the wave drift load. The next 2 columns specify either the periods τ1 and τ2. These are the mean wave drift QTFs. The phase origin is specified by giving its coordinates with respect to the OrcaFlex vessel axes (not the +ve directions specified on the Conventions page). QTF Origin The QTF origin is the point on the vessel to which the QTFs apply. The direction conventions apply to the QTFs. You must provide QTF tables for enough directions for OrcaFlex to have data (either user-specified or generated based on symmetry) for directions that cover the wave directions the vessel will experience. or the corresponding frequencies (in rad/s or Hz). QTF tables are specified for each of a number of wave directions. QTF data for Newman's Approximation Method When the Newman's approximation method is used. To insert a new table use the Insert Direction button and to delete a table select that table's page and then click the Delete Direction button. The rows in the table can be specified in any order. of the pair of wave components. the effect of which is that the off-diagonal QTFs are approximated by the geometric means of the diagonal QTFs for the two directions and periods involved. the user only specifies the diagonal terms of the full QTF matrix. 267 . and the data specified in each row is: The first 2 columns specify the vessel-relative directions β1 and β2 of a pair of wave components. select that table's page and then edit the Selected Direction value. governed by the 'Waves referred to' convention on the Conventions page of the form. in the same way as RAO data. The Newman method may also be much less computationally intensive. the full QTF data and calculation must always be used. The second order wave load is then applied at this point. The full QTF method is generally preferable. as follows: For each draught. If the vessel type has some symmetry (see the conventions page) then OrcaFlex automatically generates QTF tables for all the reflected directions implied by that symmetry. since it only requires the 'diagonal' QTF data that specify the mean wave drift load. OrcaFlex then uses Newman's approximation. meaning 'same as QTF origin'. For details see QTF data for Full QTF Method below. Vessels QTF Specification Method (wave drift only) For the wave drift load (but not for the sum frequency load) OrcaFlex supports two calculation methods: Newman's approximation and Full QTFs. Directions can be positive or negative. and on theoretical grounds they are real-valued. meaning that the practicality of using full QTFs needs to be assessed on a per simulation basis. It might often be at the same point as the QTF Origin. QTF data for Full QTF Method When the Full QTF method is used. such as by making use of the guidance notes detailed in Vessel Theory: Wave Drift and Sum Frequency Loads. The Newman approximation then extrapolates the mean wave drift QTFs to approximate the off-diagonal QTFs. and wave drift damping (if included) is calculated using the low frequency primary motion velocity of this point. Full QTF phases are specified relative to the time the wave passes this QTF phase origin. For details see Vessel Theory: Wave Drift Loads and Sum Frequency QTFs.w System Modelling: Data and Results. QTF Phase Origin This phase origin does not apply to wave drift QTFs specified using Newman's approximation. specified using the Orcina direction convention. pitch. The range of directions should therefore cover the range of wave component directions present in the sea state. τ1. so they have units of F/L2 (for surge. as follows: 268 . The phases must be given in accordance with the conventions for phase and positive directions on the Conventions page of the vessel type data. OrcaFlex will treat the QTF data as uni-directional if there are no data rows with β1 ≠ β2. This amount of data clearly cannot be typed in. You should provide data for directions and periods that (after allowing for Froude scaling if the vessel length differs from the vessel type length) cover the wave periods the vessel will experience. relative to the time that the wave crest. the amplitudes and phases of the QTF.262 = 97344 rows.nβ. But for any pair of wave components that have different directions. the number of data rows may often be less. In both cases. then the complete full QTF table would have 122. for details see Vessel Theory: Wave Drift Loads and Sum Frequency QTFs. and with a sufficiently small direction interval for the accuracy wanted. by using QTF = Q(βmean. where i=1.. since in the full circle of directions 180° lines half way between those directions. Q(β1. The resulting total QTF load is then applied at the QTF Origin (which can be different from the QTF Phase Origin. OrcaFlex allows you to enter QTF data of either type. such as Excel.w System Modelling: Data and Results. sway. 2: Vessel Type Symmetry specified in Conventions OrcaFlex will use any Symmetry specified on the vessel type Conventions. where i=1.nτ2 rows. Whether the phases are leads or lags. βi). Let: nβ = number of different directions specified βi = the directions specified. -30°.τ2). 1: Uni-directional or Bi-directional Full QTF data Some diffraction programs only output QTFs for pairs of wave components with the same direction. this reduces the number of directions nβ that need to be specified. whereas the output from other diffraction programs also includes QTFs for pairs of wave components with different directions. are all specified by the phase conventions on that Conventions Page. βmean. and automatically detects whether you specify uni-directional or bi-directional data. as follows: OrcaFlex will treat the QTF data as bi-directional if there are any rows in the full QTFs table with β1 ≠ β2. In this case the QTFs are being specified only for the nβ direction pairs (βi. The number of rows in the table can be altered by changing the Number of QTFs. 90°) then for direction 180° OrcaFlex will linearly interpolate between the QTFs given for directions 90° and -90°. 0°. if nβ=12 (30° intervals covering the full 360°) and nτ = 26 (1s intervals covering periods from 5s to 30s). The QTF phase values specify the phase timing of the peak +ve QTF load contribution in the +ve direction given by the direction conventions. 30°. OrcaFlex will use linear interpolation to obtain the QTFs for wave component directions not specified in the table. 60°. full QTF data when the sea state includes multiple wave directions. Specific rows can be removed by highlighting cells in the appropriate rows and pressing delete.nβ nτ = number of different periods specified τi = the periods specified. OrcaFlex will now have to approximate. crest.. yaw). The full QTF table will normally have a very large number of rows.nτ Then the complete full QTF data table for these directions and periods would have n β2.L/L2 (for roll. in degrees or radians. where βmean is the direction that is half way (modulo 360°) between β1 and β2. respectively. if needed). β 1 ≠ β2. that apply to a pair of wave components with those vessel-relative directions and periods. so for example if the directions specified are (-90°. β2. for one of the following 3 reasons.or up-crossing occurs at the low frequency primary motion position of the QTF Phase Origin. τ2) for that pair. i=1. trough or zero down. However. In this case you must specify data rows for all nβ2 combinations of directions.τ1) and (β2. It is therefore preferable to provide bi-directional.. The +ve directions are specified by the direction conventions on the Conventions page. τ2). so the number of rows in the full QTF table is reduced by a factor of 1/nβ. For uni-directional QTF data only. 60°. This interpolation includes wrapping through 360°. for each of the 6 degrees of freedom. So for example. heave) or F. (β1. relative to trough. We call these two types of QTF data uni-directional and bi-directional. It can either be imported (see Import QTFs) or else pasted into the table from a separate source. rather than uni-directional. The QTF amplitudes are the force or moment per unit wave component amplitude squared. Vessels The remaining columns specify. zero down-crossing or zero up-crossing. The QTFs for wave component pairs with other directions and periods are obtained using linear interpolation on period and direction. τ1. Lower triangle only: Enter QTF rows for all period combinations with τ2 ≤ τ1. τi. or 270° ≤ (β mod 360) ≤ 360° for all β. The full 360° range of directions must be supplied. that is. enter rows for all combinations of periods. Note that OrcaFlex tapers the cut off. τj.τi) ] QTF Cutoff Period The Full QTF method involves a double summation over all pairs of wave components in the sea state.βj. For the sum-frequency QTF load. If this applies to your model then you can reduce the amount of computation by specifying a Cutoff Period.τj) + Qs(βj.w System Modelling: Data and Results. Symmetry = Circular: In this case only one wave direction must be specified. τi. This can be very time-consuming. τi. That is. OrcaFlex allows you to take advantage of this symmetry. with bi-directional QTFs the user data must give the QTFs for all combinations of the directions specified.βj. If the whole matrix is specified then OrcaFlex will enforce the symmetry conditions by using: Qd(βi. 3: Entering Upper or Lower Triangle or Both QTF theory shows that the complete complex-value sum-frequency QTF matrix must be symmetric and the complete complex value wave drift (difference-frequency) QTF matrix must be conjugate-symmetric. The QTFs for all other directions will be derived using the symmetry condition. To include all the QTF load contributions set the cutoff period to Infinity. and the directions specified must cover the full 360° range of directions. vessel symmetry gives more complicated relationships in the QTF data. by entering any of the following combinations: Upper triangle only: Enter QTF rows for all period combinations with τ2 ≥ τ1. of course. Warning: If the vessel type symmetry defined in the Conventions includes a plane of symmetry. This is necessary since otherwise the QTF load would 269 .βj.βj.τi) where Qd is the wave drift QTF (subscript 'd' for drift or difference frequency). τj. τj. not both. the QTF data should obey the defined symmetry. The QTFs for the other quadrants will be derived using the symmetry condition. so OrcaFlex will suppress QTF load contributions whose periods are greater than the specified cutoff period. if you want. it is generally only the high frequency contributions that are significant.τi)* ] Qs(βi.βi. Because of this.τj) = ½ [ Qd(βi.βj. The QTFs for the other half plane will be derived using the symmetry condition. Vessels Symmetry = XZ plane: In this case the directions specified must all be on the same side of the XZ plane. or else 90° ≤ (β mod 360) ≤ 270° for all β. either 0° ≤ (β mod 360) ≤ 180° for all directions β.βi. τi. The QTFs for the other half plane will be derived using the symmetry condition. or else 180° ≤ (β mod 360) ≤ 360° for all β.j that require QTFs from the unspecified triangle. This will reduce the number of rows by almost a factor of 2.τj) = Qs(βj. That is. but no rows with τ2 < τ1. or 90° ≤ (β mod 360) ≤ 180° for all β. If only the upper or lower triangle is specified. and many of the resulting QTF load contributions might have frequencies that are not significant for the calculation wanted. OrcaFlex will then omit QTF load contributions that are beyond that cutoff period. or 180° ≤ (β mod 360) ≤ 270° for all β.τj) = Qd(βj. then when specifying bi-directional full QTFs it is not sufficient to only specify directions on one side of the symmetry plane. so OrcaFlex will suppress QTF load contributions whose periods are less than the specified cutoff period. For details of the definition of these complex value QTFs see Theory for Full QTFs.βi. That is.τj) + Qd(βj. τi. And. To include all the QTF load contributions set the cutoff period to zero. 0° ≤ (β mod 360) ≤ 90° for all β.τj) = ½ [ Qs(βi. then OrcaFlex will use the symmetry equations above for wave component pairs i. for any i. Both upper and lower triangles: Enter QTF data for the whole matrix.βj.βi. which do not lead to simple reductions in the QTF directions that need to be specified. it is generally only the low frequency contributions that are significant. Q s is the sum frequency QTF (subscript 's' for sum frequency) and superscript * denotes the complex conjugate. but no rows with τ2 > τ1. either -90° ≤ (β mod 360) ≤ 90° for all β. Symmetry = YZ plane: In this case the directions specified must all be on the same side of the YZ plane. by scaling down (instead of suppressing completely) contributions whose periods are only up to 10% beyond the specified cutoff period. τi. Symmetry = XZ and YZ planes: In this case the directions specified must all be in the same quadrant.j we have the following symmetry equations for the complex-valued QTFs: Qd(βi. τj. For bi-directional full QTFs. as follows: For the wave drift QTF load.τi)* Qs(βi. That is. If your RAO and QTF data are in different files and use different conventions you will therefore need to take account of this. Its disturbance effects can be applied to nearby 3D Buoys. wave period and direction. such as small buoys. and for Newman QTFs many other diffraction program output file formats can be imported if OrcaFlex-specific markers are first added to the file. and also of wave period. The following objects are able to experience the disturbed sea state generated by a disturbance vessel: 3D Buoys. 6D Buoys. line sections and line attachments (clumps. In reality. fluid velocity and acceleration in the disturbed sea state. which is the default value. Disturbed Objects As well as specifying the disturbance effects of a vessel using the sea state RAOs described above. for any object whose disturbance vessel is set to this vessel. however. This amplitude scaling would then be applied to all wave components. as a function of position and wave direction relative to the vessel. OrcaFlex can import such data from WAMIT output files. from which the OrcaFlex sea state RAO data can be derived. the presence of each of these objects will modify the undisturbed sea due to interactions between the objects and the passing waves (e. and at all positions. Warning: The settings on the conventions page apply to all draughts and they apply to both the vessel type's RAOs and to its wave drift and sum frequency QTFs. on the object's data form. Sea State Disturbance RAOs Introduction By default. wave radiation and diffraction). but large objects such as vessels can significantly disturb the sea state that is experienced by other objects nearby. You can also view the disturbed sea surface on a 3D view. 6D Buoys and lines (including line attachments) by specifying. relative to the incoming undisturbed wave components. You do this by specifying. and this could give step changes in the QTF load when wave drift damping is included. But it might also be useful in other situations where the presence of the vessel significantly affects the nearby sea state – for example to model the vessel-driven fluid motions experienced by an object that is very close to the vessel hull. where necessary. for example by specifying the different convention systems for each in the files from which they are imported. drag chains. 6D Buoys and stiffeners). For example you can model uniform scaling of all wave component amplitudes by entering a single sea state RAO amplitude. where objects in the lee of a large vessel experience smaller waves than they would otherwise be exposed to in clear water. will cause only minimal disturbance to the sea state. You cannot apply disturbance effects to other vessels in the model using this facility. the disturbance vessel that affects that object. Instead. you also need to tell OrcaFlex which objects are close enough to be significantly affected by that vessel's disturbance. ignoring the disturbance effects associated with the non-linear wave train). Relatively small objects. If an object's disturbance vessel is set to None. to model inter-vessel disturbance effects 270 . Vessels be a discontinuous function of the wave component frequencies. Warning: OrcaFlex's sea state disturbance model is not valid for non-linear wave theories. For more details see Disturbance RAO data below and Sea State Disturbance Theory. This leaves the component phases unchanged and ignores variation with position. a warning will be issued if a non-linear wave train has been included in the model (although the model will still run. The Sea State RAO data are velocity potential disturbance RAOs. then the undisturbed sea state is used. from which OrcaFlex can calculate the sea surface elevation. by specifying a disturbance vessel on that view window's view parameters form. Obtaining QTF data All of the above data can generally be obtained from the results of a diffraction program. You can model the disturbance effects of a vessel (or a multibody group of vessels) by specifying Sea State RAO data for the vessel type of the vessel. that the object is affected by this disturbance vessel. As an alternative you can enter very simple sea state RAO data manually. We call this vessel the disturbance vessel.w System Modelling: Data and Results. objects in OrcaFlex experience the undisturbed sea. or to model the sea state in a moonpool. This facility can be used to model effects such as wave shielding. on the object's data form. OrcaFlex can import these data directly from the output files of AQWA and WAMIT. as specified on the Environment form. to obtain the sea state disturbance RAO to use for any given wave component at any given position. Some vessel motion diffraction analysis programs can calculate sea state results at a grid of points near the vessel.g. Essentially they specify the amplitude scaling and phase shift of the velocity potential of the disturbed wave components. OrcaFlex will use interpolation. Sea State RAOs The sea state effects of a disturbance vessel are specified on the Sea State RAOs page of that vessel's Vessel Type data. etc. of the wave component to which the disturbance RAO data applies. Direction (θ): The heading of the wave component relative to the vessel. and set that intervening single-segment section's disturbance vessel to None. This drop-down list includes all vessels in the model for which you have specified some sea state RAOs. including both the nodes at the ends of that section. You can work around this restriction by breaking one of the sections into two sections.g.) will include the effects of any sea state disturbance if the associated object has a disturbance vessel associated with it. using interpolation if needed. y relative to vessel.w System Modelling: Data and Results. 271 . But you must not have two or more rows in the table that specify RAOs for the same wave direction and the same period/frequency and the same position (all three coordinates). Since the velocity potential of a wave component completely determines all properties of that component. these are the dependent variables. since that would give ambiguous data. The sea state results (e. the rows of which can be given in any order.Z) coordinates of position (x. these are the independent variables. Note: If the disturbance vessel specified for a line section is not None then all the nodes in that section. Line Attachments: It is not possible to independently specify the disturbance vessel for line attachments. Vessels you need to set up a multibody group of vessels. From these data. The disturbance RAO data are specified in a table. The table has the following columns. The remaining columns then specify the disturbance RAO data. two neighbouring sections of a line must not specify different disturbance vessels unless at least one of them specifies None. are subject to that vessel's disturbance. Instead the disturbance vessel of the attachment will be set to be the same as the disturbance vessel of the node to which that attachment is connected.y. on the Fluid Loads page of the line data form. sea surface elevation. If a disturbance vessel is selected then the waves shown in the 3D view will be calculated as if disturbed by the presence of this vessel. The disturbance vessel associated with a given object can be specified by selecting the name of the desired vessel from a drop-down list on the object's data form. Z relative to mean sea level). using the results of a multibody analysis from an external vessel response program. Sea State Disturbance RAO data The disturbance effects of a vessel (or a multibody group of vessels) are specified on the Sea State RAOs page of the vessel type data form. in a table of velocity potential disturbance RAOs. For an overview see the introduction above. Period (T) or Frequency: The period or frequency.g. Because of this. lines. The disturbance vessel is specified as follows: 3D and 6D Buoys: The disturbance vessel drop-down list is on the buoy data form. see Vessel Theory: Sea State Disturbance for details. since otherwise there would be ambiguity at the shared boundary node between the two sections. It is also possible to select a disturbance vessel when viewing environment results. and the position in the water. You then define the resulting intervening section to have just one segment. fluid velocity and acceleration. plus the reserved keyword None. as a function of five independent variables: the wave direction (relative to the vessel). the wave period/frequency and the (x. OrcaFlex calculates the disturbed velocity potential of each wave component at any point. This removes the ambiguity at the section boundaries and ensures that all nodes in these sections still experience disturbance from the intended vessels. OrcaFlex will internally analyse and sort the data before using it. The sea state disturbance RAO data specify the amplitude scaling and phase changes that the disturbance causes to the velocity potential of the undisturbed wave components. 6D Buoys. The first 5 columns specify the wave direction and period. This can be achieved by specifying a disturbance vessel for the 3D view on the view parameters window. Note that this is also true if you create a 6D Buoy line attachment. The value None means that the object experiences the undisturbed sea state (as specified on the Environment data form) without disturbance effects from any vessel. Visualising the Effects of Sea State Disturbance The sea state disturbance due to the presence of a vessel can be visualised in a 3D view. as specified by the vessel type's conventions. For points at mean water level (Z=0) these disturbance RAOs are also the disturbance RAOs for the surface elevation. OrcaFlex can then calculate the resulting disturbed sea surface elevation. even if the template 6D Buoy specifies a different disturbance vessel on its data form. Lines: The disturbance vessel is specified on a per line section basis. fluid velocity) associated with individual objects (e. w System Modelling: Data and Results. but entails greater computation costs than the latter. {xk. and the gradients will be estimated using finite-difference differentiation of the RAO data given in the previous columns. Z relative to mean water level): The position of the point at which the RAOs apply. Velocity Potential Disturbance RAO Ampl. you will need to provide amplitudes and phases for the x. as specified by the phase conventions specified on the Conventions page of the vessel types data form. relative to a right-handed frame of reference defined such that: The frame origin is at the mean sea surface.Z) points at which the disturbance RAO has been specified. This is a 2-dimensional (2D) interpolation. if needed. Calculation or Specification of RAO Gradients The spatial gradients of the disturbance RAO are required for the calculation of wave component properties from the disturbed velocity potential. Velocity Potential Disturbance RAO Gradients: OrcaFlex also needs to know the gradients (spatial rates of change) of the velocity potential RAOs described immediately above. The phase values must be specified as either leads or lags. i=1…nθ} and {Tj. However. {yl. this is a 5-dimensional (5D) interpolation. The conventions that do apply are whether Waves are referred to by period or frequency (in Hz or radians/sec). so they are the rates of change in the directions of the vessel low frequency heading axes (the Z-direction gradient is therefore the rate of change in the vertically upwards direction). Z directions as are used for the Position columns in the table.Z) of a given disturbed object will not in general match any of the positions specified in the disturbance RAO table. direction and period or 2D interpolation on Direction and period only. OrcaFlex therefore allows you to choose whether the disturbance RAO gradients are Calculated or Specified. and also requires that the positions specified in the disturbance RAOs table form a complete grid. y. then it is likely that choosing the gradients to be Specified will lead to a better representation of the disturbed wave field. j=1…nT}. These spatial rates of change use the same x.y. will not in general match any of the values {θi. So for best accuracy OrcaFlex needs to also interpolate the disturbance RAOs on position. The Z-axis points vertically upwards. in either degrees or radians. j=1…nT} given in the disturbance RAO table. The accuracy of this approximation will depend upon the resolution of the grid of (x. of direction θ (relative to the vessel) and period T. x positive in the vessel forwards direction and y positive to port. as well as on wave direction and period. and so are dimensionless. i=1…nθ}. the position (x. y and Z components of the gradient of the velocity potential disturbance RAO. θ. vertically above or below the low frequency position of the vessel origin. 272 . following the low frequency yaw of the vessel only. & Phase: The amplitude and phase of the velocity potential disturbance RAO at position p for this wave direction and period/frequency. and this will normally be more accurate than using the Calculated option. l=1…ny} and {Zm. Now consider a given wave component. See Vessel Theory: Sea State Disturbance for details. which involves significantly more computation. The former is generally preferable. {Tj. OrcaFlex will automatically import gradient data when importing sea state RAOs from WAMIT output files. k=1…nx} . such that -Z is the depth below the mean sea surface. Upon choosing Specified RAO gradients. Interpolation of Sea State Disturbance RAOs Let {θi. The other conventions on the vessel types conventions page do not apply to these data. Note: Some of the settings on the vessel type conventions page apply to sea state disturbance RAOs. OrcaFlex therefore provides the choice of whether to do 5D interpolation on Position. y and Z coordinates given for the five independent variables (the first five columns) in the table. and the period.y relative to vessel origin. This means that OrcaFlex will need to interpolate between the specified disturbance RAOs to obtain the disturbance RAO to use for each wave component in the sea state. T. OrcaFlex can estimate these gradients itself. and whether phases are specified as either leads or lags and in either degrees or radians. in the sea state that has been specified on the Waves page of the Environment data form. on wave direction and period. alongside the disturbance RAO amplitudes and phases in your input data. m=1…nz} be the sets of distinct directions. Vessels Position (x. The wave direction. but if you have data available then it is better to specify the gradients as well as the RAOs themselves. The RAO amplitudes are amplitude ratios. then the gradient columns are not shown in the RAOs table. A coarse grid with widely spaced positions will give greater approximation error. In addition. If these data are present.y. Gradient data can be derived from sea state results output by some vessel response diffraction programs. The x & y axes are horizontal. If you choose Calculated RAO gradients. distinct periods and distinct x. See also Treatment of Values Outside the Range Specified. x. Interpolation on θ uses linear circular interpolation. xk. The nearest specified point table must again be complete. This option therefore does not account for any change in disturbance RAO due to movement of the disturbed object relative to the vessel during the simulation. If this is not the case then OrcaFlex will report an error. period interpolation is linear Cartesian and direction interpolation is linear circular. x. Instead it will use the data specified for the lowest or highest period in the table. below. The disadvantage is the requirement of a complete five-dimensional grid and a possibly significant increase in simulation run time. interpolation on direction and period only will not be as accurate in cases where any disturbed objects move significantly relative to their disturbance vessel(s) during the simulation. Tj. Interpolation on direction and period only is. in general. T. direction and period described above. y and Z outside the ranges specified in the table are also treated in this same way. It treats the specified directions as being arranged around the full circle of possible directions (modulo 360°). It will then form an internal cut-down table of disturbance RAOs for that disturbed object. This means that there must be nθ. However. where complete here means that there must be a row in the table for each possible combination of the θi. OrcaFlex will then use this cut-down nearest specified point table to calculate the disturbance RAOs to use for that disturbed object. T. Interpolation on Direction and Period Only If this option is chosen then OrcaFlex will not interpolate on position. which only includes those rows from the user's data that are specified at that nearest specified position. As with the 5D interpolation on position. The number of rows in the cut-down table will therefore be nθ. faster than interpolating on position. If any of the values lie outside the given grid of specified values then OrcaFlex will not extrapolate – instead for that dimension OrcaFlex will truncate using the specified value for the nearest edge of the grid.nx. The interpolations on the independent variables. then OrcaFlex will not extrapolate the user's data. for each wave component (of period T and direction θ) in the sea state. yl. Instead. So the disturbance RAOs specified at the edges of the grid of positions specified will be used everywhere outside that grid.nT. Vessels Interpolation on Position. yl. so there are no lowest or highest direction values. Z that are defined by the first 5 columns of the disturbance RAO table. and linearly interpolates all values within that circle. Zm values that have been specified in the table. so the volume of data becomes large quite quickly. below. OrcaFlex will find the position (xk. y and Z. as appropriate. and at each disturbed object position p = (x. If 5D interpolation is being used. y.nz rows in the table. 273 . i=1…nθ} and periods {Tj. using 2D linear interpolation on the direction and period columns. otherwise OrcaFlex will report an error. See Treatment of Values Outside the Range Specified. This nearest specified point table does not include the position columns.y. j=1…nT} that it includes. then values of x. T. is outside the range of Tj specified in the table (the cut-down nearest specified point table in the case of 2D interpolation). To do this OrcaFlex requires that those 5 columns of the disturbance RAO table specify a complete grid in the five independent variables. the cut-down nearest specified point table must present rows for all combinations of all the directions {θi. since as explained above the direction interpolation is done using circular interpolation modulo 360°. Zm) specified in the disturbance RAOs table that is closest to the position of that disturbed object at the start of the simulation.w System Modelling: Data and Results. and there is no requirement that the (x k. Direction and Period If this option is chosen then.Z) at each time step. and requires less data to be entered in the table. yl. but this time the condition only applies to the directions and periods/frequencies specified. The disturbance RAOs specified at the lowest and highest specified periods will therefore be used for all wave components with periods outside the specified period range. Zm) positions specified in the table form a complete grid of positions.ny. use linear Cartesian interpolation. and so only two independent variable columns remain: direction and period. direction and period. OrcaFlex will calculate the disturbance RAO for that object using a 5D interpolation on the independent variables θ. with no interpolation on position. Treatment of Values Outside the Range Specified If a wave component period. That is.nT (where nθ and nT are now the numbers of distinct directions and periods in the cut-down table). Note that this treatment does not apply to the direction θ. The advantage of this interpolation scheme is that the disturbance experienced by an object will be updated as the object moves relative to the vessel. You then set the disturbance RAO amplitude to be the scaling factor that you want applied to the undisturbed wave field. Here are some typical examples of how these facilities can be used. direction and period when using disturbance RAOs derived from externally-calculated sea state data. on direction and period only. You could also apply a phase shift. and OrcaFlex can import the data directly from the output files produced by WAMIT. With this disturbance data OrcaFlex will simply apply the input scaling factor to all wave components when calculating fluid effects on any disturbed objects that specify this for their disturbance vessel. if wanted). Simple scaling. and of the fluid pressure and velocity. For example: Simple scaling. This would probably be best done programmatically. Centre of Buoyancy and Hydrostatic Stiffness matrix.y. But the velocity potential disturbance RAOs specified in OrcaFlex can be derived from the WAMIT results and OrcaFlex does this conversion automatically when importing sea state results from WAMIT output files. in which case you need to choose Specified disturbance RAO gradients. specified as coordinates with respect to the OrcaFlex vessel axes. and choose 2D interpolation. 2D interpolation. rather than Z relative to global axes. Vessels Sea State Disturbance Examples The facilities described above provide quite a lot of flexibility for modelling sea state disturbance. Using Estimated Sea State Data If externally-calculated sea state results are not available then estimated disturbance RAOs can be entered manually. However. Note that Z above mean water level is specified.w System Modelling: Data and Results. To use sea state data calculated by other programs it would be necessary to convert the sea state data into the disturbance RAOs that need to be specified in OrcaFlex. 274 . added mass and damping matrices all refer. OrcaFlex will use the disturbance RAOs specified on the row whose specified position is nearest to that disturbed object's position at the start of the simulation. and in that row specify any direction. independent of direction. Added Mass and Damping Reference Origin The origin to which the stiffness. but differing for different disturbed objects: If you have several objects near the disturbance vessel. then you can separately control the disturbance they see by having one row in the disturbance RAO table for each disturbed object. might also be useful if it results in faster simulations. You then specify (x. It will be more accurate to use full 5D interpolation on position. but that is less likely to be useful. For details see Sea State Disturbance Data for Multibody Groups. And it should be possible to derive both the disturbance RAOs and their gradients from the external data. on direction and period only. specify zero for the disturbance RAO phase. Notes: The sea state results output by WAMIT are not the velocity potential disturbance RAOs required by OrcaFlex – they are RAOs of the disturbed sea surface elevation.y. A disturbance RAO amplitude of 1 therefore corresponds to no disturbance: the object experiences the undisturbed wave. period and (x. One such program is WAMIT. For each disturbed object. and specify Calculated disturbance RAO gradients. Reference Origin Datum Position The Z height of the reference origin above the mean water level. then OrcaFlex will import sea state RAOs for each of the vessel types in the group. So you can expose the different disturbed objects to differing levels of sea state amplitude (and phase changes.Z) values. by specifying a non-zero disturbance RAO phase value. when the vessel is in the datum position that was used to calculate the Displaced Volume. If you import sea state RAOs for a multibody group of vessels. Using Sea State Data Calculated by an External Program Some vessel response diffraction analysis programs can calculate and output sea state results from which disturbance RAOs can be derived. so that the vessel type data are independent of mean water level and the choice of position of global origin. Stiffness.Z) values corresponding to where each of those objects are at the start of the simulation. period and position: You can just specify a single row in the disturbance RAOs table. and the heel and trim (relative to horizontal). see Vessel Theory: Stiffness.e. This is because the user's stiffness matrix linearises the effect of any shift in the moment arm between the centre of gravity and the centre of buoyancy. and the theory used. Note: The form of the buoyancy calculation in OrcaFlex depends upon whether the coordinates of the centre of buoyancy have been specified explicitly or not (i.~. see Vessel Theory: Stiffness. For details of the units. See Damping Effects on Vessel Slow Drift for further information. Free-Floating Equilibrium Datum Positions If the datum position is a free-floating equlibrium position of the vessel. then the net weight+buoyancy load for the datum position. 275 . where N is the number of vessels in the group). Hydrostatic Stiffness The hydrostatic stiffness matrix specifies how the net weight + buoyancy load varies with changes in position from the datum position. then the constant added mass matrix. The added mass and damping matrices are specified in all 6 degrees of freedom (or 6N degrees of freedom for a multibody group. whether or not the coordinates have been set to (~. Theses loads will only influence the motion of the vessel if the Primary Motion is set to one of the calculated modes.e. Added Mass and Damping. with respect to the directions specified on the conventions page of the vessel types form. Added Mass and Damping). For such cases the Displaced Volume and all three coordinates of the Centre of Buoyancy can either be specified explicitly or else they can all be set to '~'. Ld. And it only affects the vessel motion in a dynamic simulation if the vessel's Primary Motion is set to one of the 'Calculated' options. Added Mass and Damping. If the centre of buoyancy coordinates are all set to '~' then the centre of buoyancy will be taken to be on the same vertical line as the vessel type centre of gravity when the vessel is in its datum position (this is sufficient for OrcaFlex to calculate the datum buoyancy effects correctly). in a diffraction analysis) is a disturbed position in which the weight and buoyancy forces do not balance. OrcaFlex can eliminate this approximation if it knows the precise position of the centre of buoyancy.w System Modelling: Data and Results. i.e.e. when the vessel is in its specified datum position. For example. The matrices must be specified with respect to axes through the specified Reference Origin in the conventions directions. the datum position for a TLP is likely to be the pulleddown position due to its tethers. See Vessel Theory: Stiffness. will be used in order to calculate the manoeuvring load. and Added Mass and Damping is specified as an included effect on the vessel data form. The stiffness components are only specified for the heave. If manoeuvring load is specified as included on the vessel data form. For details of the units of the data and the theory used. Note: There are other sources of damping that can be important. Added Mass and Damping.~)). This would be necessary if the vessel position used when calculating the hydrostatic stiffness data (i. Added Mass and Damping for details. These data are used with the hydrostatic stiffness matrix to calculate the net weight+buoyancy load on the vessel. Added Mass and Damping The added mass & damping data specify the fluid loads on the vessel due to wave radiation effects. Non-Free-Floating Equilibrium Datum Positions Datum positions that are not free-floating equilibrium positions can be specified by setting the Displaced Volume and/or the Centre of Buoyancy coordinates explicitly (i. Further details can be found in Vessel Theory: Stiffness. The centre of buoyancy cannot be partially specified: '~' can only be specified for one of its coordinates if it is specified for all three coordinates. The hydrostatic stiffness matrix must be specified with respect to axes through the specified Reference Origin in the conventions directions. Vessels Displaced Volume and Centre of Buoyancy The volume of water displaced by the vessel.e. i. with respect to the directions specified on the conventions page of the vessel types form. will be zero (see Vessel Theory: Stiffness. the stiffness is zero for the other degrees of freedom. or the longest-period added mass matrix if frequency-dependent data are specified. and the position of the centre of buoyancy relative to vessel axes. roll and pitch degrees of freedom. not '~'). The hydrostatic stiffness only affects the vessel position in Static analysis if the vessel's Static Analysis is set to 6 DOF. For the latter case: If the displaced volume is set to '~' then it will be taken to equal the volume of water whose mass (using the specified sea density) equals the specified structural mass of the vessel type. the button is on the Vessel Types form. for slow drift simulations you can zoom in on the low frequency part of the damping curves to see the effect of cutoff on the low frequency radiation damping level that will be applied. The form shows graphs of: The Impulse Response Function (IRF). You can also look specifically at the frequencies of oscillation that are relevant to your simulations.) for the vessel degrees of freedom that you expect will be excited. Vessels Added Mass and Damping Method If you choose Constant for the Added Mass and Damping method. frequency independent) method. Damping page (assuming you have selected frequency-dependent added mass & damping). OrcaFlex allows you to specify the Cutoff Time as '~'. and although the errors become insignificant for large Cutoff Times this does require more calculation. and then specify a damping level approximation Cutoff Tolerance. Impulse Response. But fortunately the impulse response function involved in the integral decays to zero as the time lag τ goes to ∞. OrcaFlex will then automatically calculate the Cutoff Time that gives this level of approximation of the damping levels. and for a multibody group it is on the Multibody Groups form.) Obtaining the data All of the above data can generally be obtained from the results of a diffraction program. the added mass and damping data should be consistent in the sense that they obey the Kramers-Kronig relations – see Consistent Added Mass and Damping for details. a convolution integral that in theory should integrate right back to the start of the simulation. the frequency-dependent method is more appropriate and would be expected to give better results. These errors can be significant for small Cutoff Time values. and very large Cutoff Times can greatly slow down a long simulation. To calculate slow drift motion of the vessel it is normally appropriate to enter low frequency values. OrcaFlex can import these data directly from the output files of some specific programs (AQWA and WAMIT) and from generic text files with OrcaFlex-specific markers added. Stiffness. Added Mass and Damping Graphs This form is opened by clicking on the Show Graphs button: for a single vessel. Otherwise values corresponding to the dominant wave frequency are perhaps more appropriate. To help with this. If you use the Frequency Dependent method then you need to specify both the added mass and damping matrices. If you use the Constant (i. and setting the Cutoff Time to the value that sets the largest such error norm. and the other shows the damping values realised by truncating the convolution integral at the specified Cutoff Time (whether directly specified or automatically calculated). Truncating the convolution integral does introduce some approximation errors into the levels of damping and added mass that are applied. etc. alternatively. sway-sway. 276 . (At low frequencies the radiation damping might be very small anyway and other sources of damping might be more significant – see Damping Effects on Vessel Slow Drift. as a percentage error relative to the largest damping level specified in the user data. Whether you specify period or frequency values is determined by the Waves are referred to by setting on the Vessel Type Conventions page. OrcaFlex therefore truncates the convolution integral at a user-specified Cutoff Time. so there comes a point beyond which the rest of the integral can safely be neglected. the approximation error on the added mass will be similar. click the OK button to transfer the cutoff values to the original Vessel Type or Multibody Group and close the graph form. (This automatic calculation is done by calculating the Frobenius norm of the difference between the directly specified damping matrix and the effective damping matrix. over all frequencies. and for a range of frequencies. Added Mass & Damping page. This could cause long simulations to run slower and slower as the simulation time progresses. For example. When you are happy with the level of approximation. Added Mass. each pair corresponding to a particular given frequency or period. Cutoff Time When you use frequency-dependent added mass & damping OrcaFlex has to calculate. then you may specify a number of added mass and damping matrices. If you choose Frequency Dependent. if the vessel experiences a wide range of frequencies. then single-valued added mass and damping matrices will be used. The damping graphs show two curves: one shows the idealised (user-specified) damping values as a function of frequency. at each time step of the simulation. Also. click cancel to ignore any changes you have made on the graph form. Clearly. then you should specify values that are appropriate to the frequency of vessel motion you expect.e. Added Mass and Damping Graphs form.) You can judge the effect of the Cutoff Time by adjusting it on the Impulse Response.w System Modelling: Data and Results. Of course there are a lot of such damping graphs – one for each of the components of the damping matrix – but it will normally be sufficient to look at the diagonal components (surge-surge. to be near the specified tolerance percentage of the largest Frobenius norm of all the user-specified matrices. which are close to each other but far enough away from the first group that the hydrodynamic interactions between the two groups can be neglected. Each multibody group is given a user-specified group name. the added mass and damping matrices will be 6N×6N. In the case of vessels that belong to a multibody group. two extra drop-down lists are visible: Row Vessel and Column Vessel. We refer to a set of hydrodynamically interacting vessels as being a multibody group. The Damping graph displays two curves. the dashed line labelled Cutoff time of x represents the damping realised by OrcaFlex at the specified cutoff time: if this curve departs significantly from the idealised one representing the actual data then you should consider a longer cutoff time or smaller cutoff tolerance. added mass and damping) these vessel interaction effects can be calculated by diffraction/radiation programs. This could give quite poor modelling of the manoeuvring effects. Note that the added mass and damping data are matrix-valued quantities. in which case the fluid loads they experience are not influenced by the presence of other vessels. These will be 6×6 matrices for a solitary vessel. And you can have other vessels in the model that are not part of any group. Vessels The original frequency-dependent added mass data. pitch and yaw degrees of freedom (DOFs). sway. the Row DOF.w System Modelling: Data and Results. whether the vessels are in a multibody group or not. This is because it is possible for added mass and damping loads on one vessel to be induced by the motion of another vessel. but too short may mean significant IRF values are discarded and accuracy lost as a result. due to motion of the vessel in another degree of freedom. So long as the data are given to sufficiently high frequency. the rows and columns corresponding to the surge. where N is the number of interacting bodies in the group. This graph may be useful in judging the effect of this cutoff time: a shorter cutoff time will allow for faster calculation. for example if you have a second separate group of vessels. 277 . so that simulations can be performed which include the interaction effects. The idealised curve uses a fine timestep. The original frequency-dependent damping data. stiffness. except that the added mass matrix coefficients used will be those of that vessel's diagonal block in the multibody group's longest period added mass matrix. For an N-body multibody group there will therefore be 36N2 sets of graphs. To deal with this. while the model timestep curve indicates the actual IRF which will be realised by OrcaFlex with the timestep as currently set on the General Data form. You can define more than one multibody group if needed. the Column DOF. differing by the timestep with which the integral used to calculate the IRF is discretised. For the hydrostatic and potential theory loads (1st and 2nd order wave loads. in which case you should consider a shorter timestep to improve resolution and avoid losing accuracy in the IRF calculation. Note: A multibody group is only needed if you want to include the interaction effects on the fluid forces acting on the vessels. Interaction forces due to lines. since OrcaFlex does not allow this option in conjunction with frequency-dependent added mass and damping. The scale of the time lag axis for the IRF is determined by the cutoff time. The resulting data can be imported into OrcaFlex. The Added Mass graph has superimposed on it a horizontal intercept representing the calculated value of the "infinite-frequency" added mass. the second curve is shown but (at least until after the statics simulation) is labelled provisional. heave. Note that this second curve will not be shown if implicit integration with variable timestep has been selected. The added mass and damping graphs plot against frequency the values of the original data given on the Vessel Types or Multibody Groups data form. They will simply be calculated in the same way as for a vessel that is not in a multibody group. links or winches connected between two vessels are always included. For particularly long timesteps. This means that there will be one set of graphs for each pair of row and column DOFs (so 36 for a solitary vessel). If explicit integration with the Always Use Recommended Time Steps is selected. The graphs displayed will therefore correspond to the effect on the Row Vessel's Row DOF due to motion in the Column Vessel's Column DOF. this is an indicator of the consistency of the added mass and damping data. roll. Warning: Although you can include manoeuvring load on vessels in a multibody group. since OrcaFlex does not calculate what this recommended timestep should be until after the statics calculation. All combinations of Row DOF and Column DOF can be selected via the drop-down lists of the same name. you may find that the model timestep IRF curve departs significantly from the idealised one. The IRF graph shows two curves. Similarly to the IRF graph. Multibody Data Introduction The fluid loads on a vessel can be significantly affected by the presence of nearby vessels. An entry in a particular matrix represents the load generated in one degree of freedom. the manoeuvring load on the vessel will not take into account the motion of the other vessels in the group. displacement RAOs. direction and period. for interpolation of the sea state RAOs. since the disturbance will be calculated using the disturbed object's position relative to that vessel. The vessel that generates the most significant disturbance will generally depend on the position of the disturbed object. and those objects will then experience the disturbance effects of the whole group. since they each account for the combined disturbance of the whole group. you can then choose which vessel to use as the disturbance vessel for any given disturbed object. As described above. for each disturbed object. 2nd order QTFs. direction and period. Because this requires more data. See Setting up a Multibody Group below. However for the stiffness. which of those vessels is used as its disturbance vessel. added mass & damping effects. The vessel that is generating the most disturbance could therefore be different for different disturbed objects. the vessel interaction effects require the user to specify new data. If you import sea state RAO data. not just matrices for each vessel. 2nd order QTFs and added mass & damping data only need to be set up if those effects are included in the vessel's Included Effects. Because of this the vessel Length specified must either be '~' or be equal to the vessel type length.y position coordinates specified would differ between the vessel types. for each vessel type/draught in the group. by specifying sea state disturbance RAO data for more than one of the vessel types in the group. These separate sea state RAO tables (one for each vessel type in the group) all specify the same disturbance effects – those of the whole group – and they will only differ in that their x. Note: If. for details see interpolation on position. You then specify vessel type data for those types that includes the hydrodynamic interaction effects.y axes directions of the vessel of that type. added mass and damping matrices. These are all data of the vessel type/draughts of the vessels involved. And the 1st order wave load RAOs. You can allow for this. Other Data for Multibody Groups The following other data are also affected when using a multibody group: Froude scaling cannot be used with a vessel in a multibody group. 1st order wave load RAOs. All the vessels in a multibody group must use the same setting for whether added mass & damping is in their Included Effects. The best choice would normally be to specify the sea state disturbance RAOs for the vessel type of the vessel that will contribute the most significant disturbance. This requirement affects the positions at which you calculate the sea state RAO data to use. Sea State Disturbance Data for Multibody Groups The combined sea state disturbance of all the vessels in a multibody group can be modelled by specifying sea state disturbance RAO data for any of the vessel types in the group. For example the displacement RAOs only need to be set up if the vessel involved has its Superimposed Motion set to Displacement RAOs + Harmonic.y axes directions of the vessel of that type. and if the vessel axes of the vessels in the group are not parallel then it might also affect which vessel(s) you choose to specify sea state disturbance RAOs for. the x. So the vessels in a group must either all include or all exclude added mass & damping. Vessels Data for Multibody Groups The data that are affected by being in a multibody group are the displacement RAOs. This vessel can then be used as the disturbance vessel for any chosen disturbed objects. You can then choose.y position coordinates being specified relative to the origin and x. Of course data that are not in use do not need to be set up.y position coordinates will be relative to different origins and x. since any object is likely to be most affected by the vessel it is closest to. 1st order wave load RAOs and 2nd order QTFs that include the effects of the other vessel(s) in the group. and because of this the group is actually defined by specifying that the vessel type/draughts of the vessels involved are in a multibody group. there are no extra vessel type data involved in modelling the interaction effects – the interaction effects must be included by specifying. However. then OrcaFlex will automatically set up sea state disturbance RAOs for each of the vessel types in the group. for example from the output file of a multibody WAMIT analysis. added mass and damping matrices no longer appear on the vessel types data form – they are instead on a separate multibody data form. if you wish. you want to use interpolation on position.y axes directions (those of the vessel of each vessel type in the group). sea state disturbance RAOs and the stiffness. For all except the added mass and damping effects.w System Modelling: Data and Results. then you need to arrange that the disturbance RAOs are specified at positions that form a complete grid with respect to the vessel axes of the vessel type. since they must be relative to vessel origin and x. The disturbance that is specified would be consistent between each vessel type. Normally these data can be imported from the results of a multibody diffraction analysis. 278 . This is because the added mass and damping matrices must be specified for all pairs of vessels in the group. and have one vessel in the model for each vessel type/draught that is in the multibody group. when a multibody group is used the stiffness. with the x. The added mass and damping matrices for a multibody group are much larger than those a for a single separate vessel type. The Integration Method must be set to Implicit. as described below. Multibody Stiffness Data The buoyancy and hydrostatic stiffness data for each body in a multibody group are exactly the same as for a vessel type that is not in a multibody group – see Reference Origin datum position. the new draught will inherit all the data of the original. Vessels All the vessel type/draughts in a multibody group must use the same convention setting for how Waves are referred to. as described below. click the Multibody Data button. Cutoff Tolerance and the Periods or Frequencies setting for which the matrices are specified. The Stiffness page of the Multibody Groups data form then specifies the hydrostatic stiffness data for each body in the group. by clicking on its name on the Multibody Groups form. Then select the group you want to specify data for. And the Added Mass & Damping page specifies the added mass and damping matrices for the group. set up one vessel type/draught for each vessel in the group of vessels whose interactions you want to model. 279 . and the Stiffness. If you want to model interaction effects between two identical vessels with the same draught then you should set up all the other data for that draught. The exceptions are the Reference Origin datum positions (in some cases) and the added mass & damping Cutoff time and Cutoff Tolerance. specify how many vessel types/draughts are involved (one for each vessel in the group). Added Mass & Damping Reference Origin for each one. where the r. On the Interacting Bodies page. or in two different groups. Centre of Buoyancy and Stiffness. are shared by all the vessel type/draughts in the group. where N is the number of bodies in the group. and then specifying the components of that block of the whole matrix. specify the number of multibody groups you want to use (in many cases just one) and give a suitable name to each group. You specify the data by first selecting the Row and Column vessel types.c block M rc is a 6 x 6 matrix that specifies the effect of motion of the c'th body in the group on the fluid load on the r'th body in the group – r and c denote the block row and column numbers within the whole multibody matrix. Setting up a Multibody Group To set up a multibody group: On the Vessel Types data form. Multibody Added Mass & Damping Data The added mass & damping data are specified in the same way as for a vessel that is not in a multibody group – see Added Mass & Damping – except for the following differences: The added mass & damping data for a multibody group must be frequency-dependent data – the Constant Added Mass and Damping Method is not available for use with a multibody group. or all by frequencies in rad/s. so no vessel interaction effects are included in the stiffness data for a multibody group in OrcaFlex and such effects are not modelled. you need one (and only one) vessel object in your model that uses each vessel type/draught that you have included in the group. which vessel types/draughts they are. Note: The vessel type and draught combinations specified as the interacting bodies must be distinct – you cannot use the same type and draught combination twice in the same group. However OrcaFlex assumes that the vessels are in water whose surface area is far larger than the waterplane areas of the vessels. The Calculated (3DOF) option cannot be used for the Primary Motion of a vessel in a multibody group. Finally. On the Multibody Groups form. Each matrix is effectively an N x N block matrix. Normally almost all of these data can be imported from the results of a multibody diffraction analysis. On the Vessel Types data form. The Cutoff time. or all by frequencies in Hz. Displaced Volume. and then pressing the Insert key. so they must be the same for all of them. and then create a copy of that draught to use as the second interacting body. This opens the Multibody Groups data form. They are 6N x 6N matrices (that is. The Explicit integration method cannot be used if the model includes a multibody group. So they must all refer to waves by period.w System Modelling: Data and Results. You can create a copy by selecting the draught Name on the Vessel Types data form. Note: Vessel interaction effects can only influence the hydrostatic fluid loads on vessels if the multibody group is in an enclosed volume of water. have 6N rows and 6N columns). w System Modelling: Data and Results. so no coupling effects (surge-pitch. as a way to incorporate other sources of damping which do not fall into any of these categories. For a discussion of the various damping sources see Damping Effects on Vessel Slow Drift. The velocity used to calculate the drag loads is the relative low-frequency velocity of the fluid past the vessel. Viscous roll damping. Note that if the load origin is above the water surface then the current velocity used is that at the water surface. Other Damping is specified using the following data on the vessel type data form. This need not be at the vessel origin. 280 . In addition to these. If the length of the vessel differs from that of the vessel type then the vessel type data will be scaled accordingly. wave drift damping. The drag forces and moments due to any vessel rate of yaw are modelled using yaw rate drag load factors. It is specified by giving its coordinates relative to vessel axes. For details of how the loads are calculated. Vessels Other Damping There are various sources of drag or damping (the terms are often used interchangeably) on vessel motion. minus any velocity of the wind load origin due to low-frequency primary motion of the vessel. for example. OrcaFlex models most of these explicitly using data on the vessel type data form for each form of damping: current and wind loads. minus any velocity of the load origin due to low-frequency primary motion of the vessel. then the coefficients are used with a cross-flow drag model. Damping Coefficients Damping coefficients are specified for all six vessel degrees of freedom and are given relative to the vessel axes. etc. the quadratic coefficients are used with a drag model that treats each direction of motion independently. If the symmetry is set to Circular. with a vertical axis. Current and Wind Loads Current and wind drag loads on a vessel are loads due to the relative velocity of the fluid past the vessel. For details of the damping force model see Other Damping Theory. This includes any current or wind velocity and the vessel velocity due to any low-frequency primary motion. They can be modelled using the data on the Current Load and Wind Load pages on the vessel type data form. The relative velocity used to calculate the Other Damping load is the value at this reference origin. The Reference Origin should therefore be close to the overall centre of damping load. and the Other Damping load is applied at this point. since that is the height used by the OCIMF vessel wind load model (see Wind Speed for more details). all of which are automatically Froude scaled to the vessel length if it differs from that of the vessel type. one for linear damping and one for quadratic. see Vessel Theory: Current and Wind Loads. Reference Origin The point on the vessel to which the Damping Coefficients refer. Two sets of coefficents are available. The drag forces and moments due to translational motion are modelled using the standard OCIMF method. Load Origin The coordinates (relative to vessel axes) of the point on the vessel at which the current or wind drag loads are calculated and at which they will be applied. The details of how they are applied are given in Other Damping Theory. is a wave-frequency effect which is not covered by any of these specific damping forms and so would be modelled using Other Damping. where such coupling effects are small. Note that the wind velocity specified should be that at 10m above mean water level. These loads are an important source of damping when modelling vessel slow drift. Note: The vessel type Symmetry convention affects how the quadratic coefficients are used. It will only be calculated if Other Damping is specified as included on the vessel data form. Note: The Other Damping data only accepts coefficients for the diagonal terms of the damping matrix. The velocity used in the current drag load calculation is the current velocity at the load origin. The velocity used in the wind load calculation is the wind velocity (as specified by the speed and direction on the Wind page on the environment data form). sway-roll. and coupling effects will only be included due to the offset of the reference origin from the vessel origin. wave radiation damping. OrcaFlex also offers wave frequency Other Damping. Warning: The current and wind loads are based on theory for surface vessels and are not suitable for submerged vessels. For other symmetry settings.) are applied at the Reference Origin. based on vertices and representing the vessel type. If the edge diameter is '~' then that edge will be used to build a filled in shape. Areas and Area Moment The surge and sway areas and yaw area moment that will be used to calculate the current or wind loads. For details see Vessel Theory: Current and Wind Loads. Coefficients Load coefficients are specified for the vessel surge. sway and yaw directions. 281 . Note that you can use a mixture of edge diameters (some defined. Note: When the symmetry is XZ and YZ the yaw moments must be zero. filled-in shape based on the vertices and edges. due to low-frequency vessel yaw rate. otherwise that edge is drawn as a cylinder with the specified diameter. though of course the symmetry for current drag would normally be the same as that for RAOs. the vessel is drawn using a solid. OrcaFlex uses any symmetry specified to derive coefficients for other directions and then uses linear interpolation to derive coefficients for intermediate directions. then the surge and sway drag factors can usually be taken to be zero. you must specify coefficients for one direction only and OrcaFlex will use symmetry to derive coefficients for all other directions. You should specify sufficient directions to define the shape of the curve and to cover the range of directions that the vessel will experience. about the load origin. As an alternative you can use the vertices and edges to define a frame like structure. OrcaFlex will use the symmetry to derive load coefficients for extra directions generated by reflection in the specified vessel axes planes. Vessels Load Symmetry Specifies what symmetry the vessel type has below (for current load) or above (wind load) the water line. plus a wire frame representing vessel-specific features.w System Modelling: Data and Results. and the curve shows the interpolated coefficients that will be used for intermediate directions. See Drag Loads due to Yaw Rate for details. Yaw Rate Drag Factors The yaw rate drag factors only apply to the current load. For a slender ship. The View Coefficients button allows you to view the coefficients that will be used – the blobs on the graph show the coefficients you have specified plus any that OrcaFlex has derived using reflection. by default. and then yaw drag factor can be estimated based on the vessel length and draught. and if the load origin has been placed at the centre of the vessel. and any surge and sway drag forces. For circular symmetry. Drawing Drawing Data Each vessel of this type is drawn as a wire frame. For XZ and YZ symmetry. Edge diameter (used only for shaded drawing) For shaded graphics views. so OrcaFlex forces zero yaw coefficients in this case. See Drawing. wind drag and RAOs (see RAO Symmetry) need not be the same. Note: The symmetry for current drag. They model the yaw drag moment. not to the wind load. They depend on the direction of the current or wind. some set to '~') to combine both filled in and framework shapes. and are given relative to the low-frequency vessel heading using the OrcaFlex direction convention. diameters not equal to '~') are drawn as cylinders. The remaining edges are used to partition the vertices into sets of connected vertices. Two vertices are deemed to be connected if there exists a path of edges between the two vertices. vessels are drawn using the wire frame data. A value of '~' is used for the wire frame on the left and a value of 1m is used for the wire frame on the right. When drawn in wire frame mode they look the same. e. crane boom latticework. Shaded Drawing By default. Finally. the smallest convex hull enclosing the set is drawn. but in shaded mode they differ. 282 . The wire frame drawing data comprises vertices and edges.w System Modelling: Data and Results. OrcaFlex uses the following procedure to generate this surface from the wire frame vertices and edges.g. This algorithm does not always generate the shaded drawings that you might expect.e. for each set of connected vertices. First any edges with specified diameters (i. This allows you to use such edges to visualise parts of the structure that are not solid. but OrcaFlex needs a solid surface for the shaded graphics representation. for shaded 3D Views. Consider the following two wire frame vessels. These edges are now handled and are excluded from the remainder of the procedure. Vessels Figure: Wire frames with different edge diameter. in order to work it requires that the triangles defined in the . usually with the .x file will not display 283 . This results in two separate convex hulls and a better representation. The Use Culling option is normally selected since it can provide a useful performance benefit.x file have their outward facing directions defined correctly. Alternatively the object can be represented by an imported 3D model by specifying the Shaded Drawing File.x file extension. This results in a single convex hull for all vertices being drawn. However. In the red vessel. In the unusual situation where the outward facing directions are not defined correctly then the . Vessels Wire Frame and Shaded Drawing For the green vessel the superstructure and the hull share vertices and so all vertices are connected. The Browse button allows you to specify the Shaded Drawing File quickly and also provides quick access to the Orcina sample drawings via the Navigate to Orcina sample drawings button. the superstructure and hull do not share vertices and so there are two distinct sets of connected vertices. If you use a relative path then the path will be taken as relative to the folder containing the OrcaFlex file. This must be a Direct X format file.w Figure: System Modelling: Data and Results. almost always mean the rotational motions are relative to waves of unit amplitude.x file directly. Very rarely.g. 284 . imply rotational RAOs relative to waves of unit steepness or maximum slope. OrcaFlex will only accept RAO form. but you must find out how your data are defined. You also need to know what conventions apply to your data. RAO Data Checklist To derive vessel point motions. sway and heave directions. To what point on the vessel are the phases relative? This is the RAO phase origin and is usually. before entry to OrcaFlex. this should be obvious from the range of phase values. rotational RAO amplitudes are given per unit wave height (i. pitch in head or stern seas) should tend to 1 for RAOs relative to unit maximum slope. or to pi for RAOs relative to unit steepness. Vessel length scaling If the vessel length and the vessel type length are different then the shaded drawing is scaled accordingly. If these coordinates use a different length units system from your OrcaFlex model then you should specify the units used in the . In what form are the rotational roll. but some authors use heave positive downwards. heave positive up. radians/radian. This cuboid is aligned with the shaded drawing's local axes.x file). The Shaded Drawing Origin defines the origin of the shaded drawing with respect to the vessel type's local axis system.e.x file. these may be documented with the data. pitch and yaw? Often they are surge positive forward. pitch and yaw RAOs? Units such as degrees/metre or radians/metre (displacement RAOs). sway. If this happens then typically sections of the model will be missing when drawn by OrcaFlex. sway positive to port. In this case you will have to multiply the RAOs by 2 manually.w System Modelling: Data and Results. roll. Disabling the Use Culling option resolves this problem.m/m (wave load RAOs).e. Note: If you use a value of '~' for Draw Size then OrcaFlex uses the coordinates in the . Similarly Shaded Drawing Orientation allows you to reorient the shaded drawing to match the vessel type's axis system.x file by including an auxiliary file called AdditionalInformation. Examples of this can be found in the sample shaded drawings provided by Orcina. Units such as degrees/degree. Roll. Draw Size is provided to allow you to scale the drawing.m/radian (wave load RAOs). but not always. or kN. but you need to be sure. for unit wave amplitude) is the most common. This scaling is applied in addition to the scaling of the shaded drawing specified by the Draw Size. the same as the RAO origin. This longest side is calculated by first fitting the smallest possible cuboid around the vertices of the shaded drawing (these are defined in the . or kN. but sometimes you may have to deduce what they are. Then the length of the longest side of this cuboid is found. All directions are scaled equally to arrange that the longest side in the drawing is drawn to the specified Draw Size. but not all. Shaded Drawing Origin is provided because the shaded drawing and the vessel type may have different origins. you need to obtain data giving both RAO amplitudes and phases for the vessel for the relevant wave period. For long wave periods in deep water.txt. double amplitude) – check your data source. OrcaFlex allows complete generality in its data input. Most data sources use right-handed axes. What directions are positive for surge. If it is not specified check with your data supplier. or no units (displacement RAOs). Are the responses in dimensional or RAO form? RAO form (i. the rotational displacement RAOs in the wave plane (e. Vessels correctly. You should have answers to all the following questions: To what point on the vessel do the data apply? This is the RAO origin and is often the vessel centre of gravity. Are the phases in degrees or radians? Unless you only have a small amount of data. data giving dimensional form would have to also give the associated wave amplitudes/heights. pitch and yaw are usually positive when clockwise about the positive surge. heave. Specify a value of '~' to display the drawing using the absolute coordinates as specified in the . sway and heave. the RAO data for period 'Infinity' cannot (for technical reasons) be included in the curve. For roll. Complex Value Graphs The graphs initially show the RAOs for the currently selected draught and direction. but you need to check and tell OrcaFlex – see note on phase leads/lags below. cos(ωt + P') implies that phase P' is a lead. For the X axis you have the choice of plotting period. You can change the scale of the graphs (double click on the graph and change the ranges of the axes). You can switch to other draughts and directions. Commonly used ones are: A. so instead the other end of the curve is the RAO data for the largest finite period specified. A solid circle representing the expected long wave response limit for a freely floating vessel. pitch and yaw. it displays graphs (one for each vessel degree of freedom) showing how the RAO and phase vary with wave period. For surge. the other end of the curve is the 'long' wave RAO data specified for period 'Infinity'. trough. Checking RAOs The Check RAOs button on the vessel types form allows a visual check on the RAO data for either displacement RAOs or wave load RAOs. which should have zero or very small amplitude. Vessels To what phase time origin are the phases relative? OrcaFlex allows you to specify that the phases are relative to the time the wave crest. zero up-crossing or zero down-crossing passes the phase origin. For a given draught and wave direction. This is useful if the curve does not initially fit on the graph. The graph has two parts: A curve showing the RAO data specified by the user as a series of points joined in order of increasing period.P) or A. Are the phases leads or lags? Phase conventions are sometimes documented by giving the formula used to represent the harmonic motion. so the curve should start from near the origin. R 0 0 Figure: Complex Value RAO Graph for Amplitude (R) and phase (φ) The graph depicts the RAO data specified by the user for the specified RAO origin. 285 . either by using the navigation buttons at the bottom of the form to step through the data. There are 3 types of graph available: Complex Values Amplitude Phase Amplitude and Phase Graphs These graphs provide a straightforward graphical representation of the RAO data as input on the Vessel Types data form. Moving along the curve away from the origin corresponds to the wave period increasing from zero. See RAO Quality Checks for details of the expected long wave RAOs.w System Modelling: Data and Results.cos(ωt . Using sin rather than cos in the above formulae has no effect on whether the phases are leads or lags. The amplitude or phase is plotted on the Y axis of the graph.ωt) imply that phase P is a lag. The curve starts from the 'short' wave response. The passage of the crest past the RAO origin is the most common phase time origin. frequency in rad/s or frequency in Hz. else or by selecting from the drop-down lists.cos(P . There are two likely causes – it may be that the phase lead/lag convention data has been set wrongly (this would give a phase angle sign error) or 286 .5 1 1.5 -1 -0.5 0 0 0 -0.5 1 1.5 0 0. positive sway is to port. See How to Check RAO Data for details.w System Modelling: Data and Results. Vessels Warning: The expected long wave response limits calculated by OrcaFlex only apply to free-floating vessels. R is the rotational response normalised with respect to maximum wave slope – i.φ). but its phase differs by 180° from the expected long-wave value (represented by the circle). For roll. you should check that the curves on the Complex Value RAO graphs are reasonably smooth and approach the circle.5 0. Smooth graphs can only be expected if the data includes RAOs for reasonably closely spaced periods. Note that: The curve may not approach the expected long wave limit if the RAO data do not include values for any long waves. The circle on the yaw graph only applies to slender vessels (i. the second graph is clearly in error. For a freely floating vessel.5 0.5 0 0. R is found for both translation and rotation by normalising both the forces and moments applied to the vessel using wave amplitude.5 -0. well-behaved set of displacement RAO data – the curve is smooth and the long-wave limit agrees with the expected value marked by the circle. which is the expected long-wave limit for a free-floating vessel. sway and heave are the vessel translation amplitudes divided by the wave amplitude. How to Check RAOs For each draught and wave direction. where: R is the non-dimensional amplitude.5 -1.5 1. For example the heave displacement RAO amplitude of a tension leg platform will not approach the usual long wave limit of 1. As examples. The curve might also not approach the circle if the vessel is not free-floating.5 0 0. This polar coordinates way of representing RAOs is better than drawing separate graphs of amplitude and phase.e. the yaw response limit only applies to slender vessels that are long in their x-direction and narrow in their y-direction. The graph represents RAOs as points in polar coordinates (R.5 -1.5 1 1 1 0. consider the following three example graphs: 1. from the time the wave crest passes the user-specified phase origin until the maximum positive motion occurs.5 -1. whereas phase graphs frequently show phase jumps. long in the x-direction and narrow in the ydirection). So positive surge is forward. or 30 seconds for semisubmersibles. the non-dimensional values R for surge.5 -1 -0. Note: Solid circle limits are defined using the OrcaFlex conventions (not necessarily the same as the vessel type RAO conventions). The purpose of the graph is help you check your RAO data – the curve should normally be reasonably smooth and tend towards the expected limit shown by the solid circle. since the curve does not lead to the expected long wave limit. are considered to be sufficiently long for this purpose. φ is the phase lead. Also. it is vessel rotation amplitude divided by the maximum wave slope. positive pitch is bow down and positive yaw is bow to port.5 -1.e. pitch and yaw displacement RAOs.5 The first graph shows a typical.5 -1. positive heave is up. positive roll is starboard down.5 -1 -0. For wave load RAOs. since it presents all the information on a single graph and also the resulting curves are smooth.5 1.5 -1 -1 -1 -1.5 1 1. Wave periods over 20 seconds for ships.5 -0. The RAO data for long waves (represented by the end of the curve) has the correct amplitude. Non-dimensional Amplitudes For displacement RAOs. rather than the direction it is progressing towards (which is the OrcaFlex convention). But beware that several common problems have very similar symptoms. The effect would be a 180° shift in the sway. OrcaFlex can import directly data which have been output by AQWA and WAMIT. seastate RAOs). Below are some common problems and their symptoms. Vessels else that the convention data for the direction of positive motion has been set wrongly (this would give a phase error of 180°). The phases may be leads instead of lags (OrcaFlex will accept either – see RAO Phase Conventions). This suggests that the RAO data for period 'Infinity' has not been set correctly and is zero. after the addition of some markup text.4 Importing Hydrodynamic Data The Import button on the vessel types form enables the import of data. but then suddenly goes to zero. load RAOs. hydrostatic stiffness. When you do so. The effect would be to negate all the phase values. rather than anticlockwise (which is the OrcaFlex convention). so it is not possible to be sure what the problem is unless you are sure about most of the data's conventions and only unsure about one. The quoted wave direction might be measured clockwise (viewed from above) from the x-direction. It is therefore important to get as much information as possible from the original RAO data supplier. or generic). The quoted wave direction may be the direction the wave is coming from. Pressing the Import button prompts you to select a file for import. The effect of an error here would be to negate all the phase values. in the form of results from common ship response calculation packages. WAMIT. Common Problems It is not unusual to be given RAO data for a vessel but not be given all the conventions that apply to the data. mass and inertia. Hydrostar/ARIANE and Wadam output files. OrcaFlex will open the file and analyse its content to determine: what type of file it is (AQWA. other damping. 6. Presently. By default. OrcaFlex can also import data from MOSES.7. added mass and damping. into OrcaFlex. all data types which are present in the file and eligible for import are selected for import at this point: simply deselect any which you do not 287 . what bodies/structures it has data for. which is where you can choose the destination Vessel Types and/or Draughts for the data to be imported and check or set reference origins (see below for AQWA/WAMIT and for generic text files). and what data it contains which OrcaFlex is capable of importing (any or all of: displacement RAOs.w System Modelling: Data and Results. You will then see the Import Vessel Data form. roll and yaw phases. QTFs. The curve on the third graph approaches the expected long wave limit. and select from a list which data you wish to import from the file: Figure: Selecting data for import Data types in this list which are disabled (greyed out) are so because either they are not present in the file or their import from this type of file has not been implemented in OrcaFlex (or both). as well as others. click on the Import button to begin the actual import procedure. are hidden for a Vessel Type/Draught in a multibody group. You should take careful note of these. checked or set up origins. the independent data become visible. on the Vessel Types form. are the coordinates of the Centre of Gravity of the OrcaFlex Vessel Type/Draught. see the specific topics on importing AQWA data and importing WAMIT data. These independent data. Multibody Data If the AQWA or WAMIT file contains multibody data. For more details on the import procedure. When you import multibody data.w System Modelling: Data and Results. Vessels wish to import. Usually there will be only one. Importing data from AQWA and WAMIT The Sources & Destinations page has the same form for both AQWA and WAMIT files. Also given. and selected the data types you wish to import. The remaining OrcaFlex Vessel Type data are not typically calculated by diffraction programs. it will be emptied before the new data are imported into it. a Messages page will be created. Having chosen your destination Vessel Types/Draughts. you must select a Vessel Type and Draught destination to where the data for that structure will be imported: each Vessel Type/Draught combination in the table must be unique. since they will have an impact on how the imported data have been interpreted by OrcaFlex. Any OrcaFlex data for which there are not any corresponding data in the imported file will not be changed. then you must also specify a destination Multibody Group which will contain all the Vessel Type/Draught destinations in the list. For each source. these data are the same stiffness and buoyancy data and the diagonal 6×6 blocks of the whole group added mass and damping matrices. If you use an already-existing one. the original Vessel Type data will be retained) and will list any errors or warnings raised during the process. OrcaFlex will create a new one. This multibody group does not need to exist beforehand: by default. the corresponding independent (ie non-multibody) data are also assigned as part of the import process. Multibody stiffness and added mass and damping data are imported for the members of the group. the only difference being in the naming of the data sources: AQWA refers to Structures and WAMIT to Bodies. if you delete a Vessel Type/Draught from a multibody group. which will indicate whether or not the import was successful (if not. Specifically. Figure: AQWA/WAMIT Sources and Destinations The table on this page will contain one row for each Structure/Body source in the import file. though not editable here. 288 . so will need to be obtained from another source. The imported data are converted to match the prevailing vessel type conventions and scaled to match the units of the OrcaFlex model. Following the import. but OrcaFlex is able to import multibody data where it is given. as a reminder that these data must be correct before import – this is so that the relation between the OrcaFlex vessel origin and AQWA/WAMIT origins can be determined and the reference origins set appropriately. QTF origin. likewise. Importing data from generic text files We use the term generic text files to refer to output from other diffraction software packages which has been marked up with specific text that enables OrcaFlex to import the data. The following data may be imported from such files: Displacement RAOs. If this is successful. Reference origins All of the AQWA data have their reference origin at the vessel centre of gravity. you must instead enter at the time of import the reference origins and phase origins. are at the vessel centre of gravity. Multibody data can not be imported from these files. Units OrcaFlex first attempts to determine the units in use in the file. You will need to ensure that this value is appropriate before importing the AQWA data. though multiple draughts are allowed. or if they are a mixture of SI and US. OrcaFlex will be unable to convert the data in this way: in this case. from the values of g (acceleration due to gravity) and ρ (water density). and the knowledge that the unit of time is the second. AQWA AQWA results are output in dimensional form. Vessels If the import file contains data for a single body only. in OrcaFlex units and with respect to OrcaFlex Vessel axes: Figure: Generic Sources and Destinations The values of these reference origins will be assigned to the reference origins for the imported RAO. Load RAOs. So OrcaFlex sets the RAO origins. 289 . the raw data will be imported from the file unscaled and a warning will be issued. then the Destination Multibody Group will not be visible and no multibody data will be imported. Newman QTFs. relative to the selected Vessel Type origin. then OrcaFlex will scale the data (if necessary) from the units in use in the file to the units of the OrcaFlex model. added mass & damping to the value of the centre of gravity given on the vessel types Structure page. and reference origin for stiffness. Also. Frequency dependent added mass and damping matrices. interacting vessel data are not imported. If the units cannot be determined. RAO phase origins. to a text file with a . since OrcaFlex cannot determine the origin of vessel data in these files as it can for AQWA and WAMIT. QTF and added mass & damping data. so are set appropriately by OrcaFlex.w System Modelling: Data and Results. Hence only a single Vessel Type may be selected as the destination for these data and.lis extension. OrcaFlex will automatically import the QTF data it contains. though the harmonic data in the . Again. Multibody data If the file contains data for more than one structure. under the hydrostatic and hydrodynamic headings. these values are set to zero: if necessary. You will receive a warning if any of these matrices. Note: AQWA may output the stiffness matrix twice. If so. Newman QTFs. OrcaFlex allows for this when importing .out extension and OrcaFlex can import data from such a file. since OrcaFlex is unable to handle this. g. The Requested data page of the Import Vessel Data form allows you to choose between the methods that are available in the . and a warning is issued if the AQWA data are non-symmetric. The value of displaced volume is taken from the figure given by AQWA for "mesh-based displacement". The Z-component of the reference origin datum position is imported.lis file. Stiffness. since those are the only values OrcaFlex allows for.out file you have selected. Vessels RAOs Displacement RAOs are imported in a straightforward way. OrcaFlex interprets this as other damping having a linear damping effect on the wave-frequency motion of the vessel. Seastate RAOs AQWA does not output seastate RAOs. a warning will be given and the 'hydrostatic' form will be imported.qtf files. Other damping Later versions of AQWA output what is labelled "additional damping (frequency independent)" as a 6×6 matrix. RAO directions are read in directly and require no adjustment. and if the two matrices are not the same. added mass and damping AQWA outputs the whole 6×6 matrices for added mass and damping. Since AQWA does not give the heel and trim values at the reference origin datum position. WAMIT WAMIT outputs its results to a text file with an . but OrcaFlex uses only the upper right triangle of each. the latter from the diagonal elements of the inertia matrix output by AQWA. AQWA writes full QTFs to a separate text file with the same name as the . roll and pitch components of the hydrostatic stiffness matrix are imported.w System Modelling: Data and Results. which is used to non-dimensionalise the data. as with RAOs.qtf file is present in the same folder as the . so this data item is not selectable for AQWA files. in the imported file. QTFs Wave drift QTFs are imported and. Only the diagonal values of the matrix are imported. no adjustment is necessary for directions.qtf extension: if this . the main exceptions to this being acceleration due to gravity. Note: AQWA appears to write the full QTFs with the convention that the argument of their complex value is a phase lead. are significantly non-symmetric. you should edit these values yourself. Full QTFs) WAMIT may offer results from various different calculation methods. as illustrated in the following figure: 290 .lis file but a . The data are almost all non-dimensional. only the upper right triangle is used. In general these data are likely to be zero.lis file. The heave. OrcaFlex will treat all the structures as being members of a Multibody Group and import the multibody data accordingly. Choice of Calculation Methods For some types of data (Load RAOs. Since AQWA and OrcaFlex use the same conventions for vessel headings. and WAMIT's length scale L. Centre of Buoyancy is read in if given in the AQWA file. Mass and inertia Mass and moments of inertia are imported if requested. and assumes that the same reference origin and direction conventions as for frequency-dependent damping apply to these data. Load RAOs are imported including the Froude-Krylov contribution.lis file use the convention that phase is a lag. Newman QTFs are imported directly from the . with the exception of the roll-roll term. e. OrcaFlex determines this by (i) expressing the WAMIT global origin relative to the WAMIT vessel origin (i.out file. the phase origin is at the global origin. if possible. But in this particular example file the Newman QTF results are present for the Pressure Integration method only. Note: In some cases. If this is successful. 291 . OrcaFlex deduces the position of this WAMIT vessel origin. Units The length unit in use in the file will be determined. from the difference between the centre of gravity coordinates in the .out file is imported (which are relative to the OrcaFlex vessel origin). WAMIT does not output the horizontal position of the centre of gravity. Vessels WAMIT Calculation methods In this example. using WAMIT's length scale (converted to the length unit of the OrcaFlex model) and the current OrcaFlex values of g (acceleration due to gravity) and ρ (nominal water density). and you will need to set these reference origins yourself. Vessel Axes and Reference origins The vessel axes directions you use in your OrcaFlex model must match the vessel axes directions used in the WAMIT analysis and . using the scaling factors defined in the WAMIT user manual. so the OrcaFlex RAO phase origins are represented by the coordinates of the WAMIT global origin relative to the OrcaFlex vessel origin. using the difference between the centres of gravity coordinates specified in WAMIT and in OrcaFlex. In WAMIT. YBODY. OrcaFlex then sets the vessel type's RAO origins. If so. QTF origin. and added mass & damping origin to be the coordinates of the WAMIT reference origin relative to the OrcaFlex vessel origin.w Figure: System Modelling: Data and Results. using the values of XBODY. from the value of g and the knowledge that the unit of time is the second. then OrcaFlex will convert the data from non-dimensional to the units of the OrcaFlex model. then the coordinates of the centres of gravity in WAMIT and OrcaFlex will also coincide and the reference origins will all be zero. Almost all of the WAMIT data (with only one exception) have their reference origin at WAMIT's vessel origin. If the length unit cannot be determined then the raw data will be imported from the file unscaled and a warning will be issued. so the Control Surface and Momentum Conservation method options are disabled and may not be selected in this case.out file (which are relative to the WAMIT vessel origin) and the centre of gravity coordinates specified in the OraFlex vessel type data at the time the . You must therefore ensure that the vessel type centre of gravity coordinates are set appropriately in OrcaFlex before importing WAMIT data. then OrcaFlex will warn you of this. ZBODY and PHIBODY in the WAMIT output file. relative to OrcaFlex's vessel origin. in body-fixed axes). a choice may be made between the different calculation methods employed by WAMIT for the Load RAOs and the Full QTFs. So in the simple case where the OrcaFlex vessel origin coincides with the WAMIT vessel origin. and (ii) translating this value to be relative to the OrcaFlex vessel origin. 2. The heave.B respectively) according to the formulae Aij = ρLkaij Bij = ρLkωbij where k = 3 for i. OrcaFlex takes account of this during the import and sets the QTF origin accordingly. so you should edit this value yourself.2. where k = 1 for i=1.j=4. j=1. and OrcaFlex enforces this symmetry. The displaced volume is taken as the median of the three estimates given by WAMIT. OrcaFlex allows only uni-directional Newman QTFs.5. WAMIT outputs components for the whole matrix.3. on theoretical grounds.3. added mass and damping WAMIT outputs added mass and damping as a list of (i. The reference origin datum position is not specified by WAMIT. If both are given.5. so OrcaFlex imports only the upper right triangle of each matrix and sets the lower left triangle values to match. k = 3 for i=4.6 and ω is the frequency in rad/s. you will have to make this choice for each. They are re-dimensionalised by multiplying by the factor Lk. Components for which an (i. You will receive a warning if any of these matrices. then you will be prompted to choose one of them.3. Mass and inertia Mass and moments of inertia may be imported if available. OrcaFlex will calculate the inertia matrix from the radii of gyration and displaced mass (= structural mass. if data from more than one of the methods are present. which are given in WAMIT with respect to global axes.5. Stiffness.2.j) value is not given are assumed to be zero. Vessels RAOs Displacement RAOs are imported in a straightforward way. The re-dimensionalising factor for load RAOs is ρgLk. using the formula given in the WAMIT user manual.2. 292 .2. in which case these data will be imported directly. if both difference-frequency and sum-frequency QTFs are present. WAMIT may calculate load RAOs in one of two ways.j) components. are significantly non-symmetric. k = 4 for i=1.6. Similarly full QTFs (if included) can be calculated by WAMIT in two different ways: a Direct and an Indirect method.3.6.out file. k = -1 for i = 4. Directions are adjusted in the same way as for RAOs. in the imported file. k = 2 for i=4. but in fact the matrix must be symmetric. where k = 0 for i = 1. Depending on the options chosen at the time of the WAMIT analysis.6.6 or i=4. Radii of gyration. j=4. In this case.3. The RAO directions in OrcaFlex are relative to the vessel x-axis direction. QTFs Wave drift QTFs are re-dimensionalised with the factor ρgLk. and data from either or both methods (labelled "Haskind" and "Diffraction") may be present in the file. If data from both of these methods are present in the .5. The non-dimensional WAMIT values for added mass (a) and damping (b) are scaled to dimensional values (A. roll and pitch components of the hydrostatic stiffness matrix are imported.5. This restriction does not apply to full QTFs. WAMIT results for Newman QTFs obtained using the Momentum Conservation calculation method are referred to WAMIT's global origin.w System Modelling: Data and Results. Control Surface and Momentum Conservation.3. these may take one of two forms in the WAMIT output file An explicit 6×6 inertia matrix.6. you may choose either method and OrcaFlex will import the data for that method only.5.j=1. WAMIT may calculate Newman QTFs in a number of different ways: Pressure Integration.2. Notes: WAMIT outputs Newman QTFs for pairs of wave headings. since the vessel is free-floating) that are given in the WAMIT file. then you will be given the choice of which to import. As with load RAOs. in the case of a free-floating vessel. Centre of Buoyancy is read in if it is given in the WAMIT file. k = 5 for i. so imports only the data for which the two headings coincide. where k = 2 for i=1. and are determined by subtracting the value of PHIBODY in the WAMIT input file (the vessel heading at rest) from each of the values of wave heading. pressure and fluid velocity.1'. OrcaFlex can import these data.out file which do not include interaction effects. Vessels Having determined the full 6×6 inertia matrix by one of these two means. If the group has only a single body (i. if your text file contains only displacement RAO data. a ship response calculation program other than AQWA or WAMIT.out file. If the draught already exists. So. If any of these draughts does not already exist for the selected vessel type. then importing these data will not have any effect on load RAOs. The file must contain data for one or more named draughts. WAMIT also outputs interacting hydrostatic stiffness matrices.out file but the suffix '. Data of other types for these draughts will not be affected. QTFs. but OrcaFlex does not allow for this interaction. This means that for each draught you import. but you can choose to put the displacement RAOs for all draughts in a single file or have separate files for separate draughts. OrcaFlex requires velocity potential disturbance RAOs that are measured relative to the undisturbed wave. then OrcaFlex will convert the imported data from the declared source conventions/units to the model conventions/units as part of the import process. OrcaFlex will then transform this matrix according to the difference (if any) between the WAMIT and OrcaFlex vessel origins and extract the mass and moments of inertia from the transformed matrix.w System Modelling: Data and Results. then the data other than displacement RAOs will remain unchanged. Seastate RAOs WAMIT seastate RAO data take the form of absolute values of sea surface elevation. For details see Sea State Disturbance Data for Multibody Groups. for example. or the units do not match those prevailing in the OrcaFlex model. with the same name as the . but for a multibody WAMIT analysis OrcaFlex is unable to import these collective Momentum Conservation QTF data. The hydrostatic stiffness data imported are those in the . then any data it contains of the same type as that given in the text file will be deleted. then OrcaFlex will import sea state RAOs for each of the vessel types in the group. for example. Note: WAMIT results for Newman QTFs obtained using the Momentum Conservation calculation method are for the ensemble slow drift motion of a multibody group as a whole.out file. The types of data which can be imported in this way are Displacement and Load RAOs Newman QTFs Frequency dependent added mass and damping matrices Specifying conventions and units You can add markup to the file to define the conventions and units of the data contained in the file. Multibody data WAMIT writes interacting multibody added mass and damping data to a separate file. or any other data for that draught. If this file is present in the same folder as the . OrcaFlex will import the data it contains and re-dimensionalise them in the same way as the independent added mass and damping (described above). making it easier to enter data manually and giving better-behaved interpolation. if it does not exist. the analysis is for a single vessel). then the data other than displacement RAOs will take the values of the default OrcaFlex Vessel Type. so long as the data in the file are in tabular form and you add the appropriate markers to the file to indicate the data to OrcaFlex. using the scaling factors and units as determined from the . If any of these conventions do not match those for the selected Vessel Type. all the displacement RAOs (for example) for that draught must be in a single file.e. or from model test results. Generic Text Files You can use generic text files to import data from. If you import sea state RAOs for a multibody group of vessels. OrcaFlex will therefore convert the WAMIT data into disturbance RAOs of the required form as part of the import process. it will be created at the time of import with the default OrcaFlex Vessel Type data. A typical markup block for conventions is *** OrcaFlex Conventions Start *** RAOResponseUnits = degrees RAOWaveUnit = amplitude RAOPhaseConvention = lags RAOPhaseUnitsConvention = degrees RAOPhaseRelativeToConvention = crest SurgePositive = forward SwayPositive = port HeavePositive = up RollPositiveStarboard = down 293 . If any named draught does already exist. one for each header in the headers line.w System Modelling: Data and Results. There must not be any blank lines between these two marker lines. Note that the waves are referred to by convention is not allowed because the WP. N/A or ~). in degrees. If some units settings are omitted then OrcaFlex uses the corresponding value from the OrcaFlex model. Note: The reference origins are not read in from the file. The line specifying the draught must be of the form Draught DraughtName. Columns with unrecognised header strings not in this list are ignored. or scale the data yourself. If the block is omitted altogether then a warning is issued and no conventions conversion is performed. It is usually easy to create a suitable file by adding a few lines to your original response data file – see the examples below for specific program output.g. since OrcaFlex will not accept two columns specifying what is effectively the same information. Importing RAOs A text RAO file must contain the RAO data in the following form. Please note that it is the order of the columns that matters. each table must be preceded by a line containing the string OrcaFlex Displacement RAO Start and immediately followed by a line containing the string OrcaFlex Displacement RAO End. So Direction 0 means waves coming from astern and Direction 90 means waves coming from the starboard side. If you want OrcaFlex to ignore a column. Not all of these conventions are relevant to all of the imported data: Newman QTFs and added mass & damping require only the direction conventions. Immediately following the line containing the RAO Start string there must be two lines (in either order) specifying the draught and direction that apply to that table. then DraughtName must be enclosed in quotes. If some conventions are omitted then OrcaFlex uses the corresponding value from the selected Vessel Type conventions. separated by tabs and/or spaces. In addition the symmetry convention should not be specified in this block: instead you should simply set it to the appropiate value in the OrcaFlex model. since their scaling is rather more complicated. (e. This list contains all possible conventions settings that can be included in the block. The line specifying the direction must be of the form Direction n. then insert an unrecognised header string. not their actual position across 294 . For load RAOs and QTFs both length and force units should be specified. Warning: This units setting does not apply to added mass and damping matrices. For load RAOs these strings should be OrcaFlex Load RAO Start and OrcaFlex Load RAO End. where DraughtName is the name of the draught. Vessels PitchPositiveBow = down YawPositiveBow = port *** OrcaFlex Conventions End *** The block begins with a line containing the string OrcaFlex Conventions Start and ends with a line containing OrcaFlex Conventions End. The remaining lines in the table must contain numbers. The units of the data contained in the file are specified in a similar way: *** OrcaFlex Units Start *** LengthUnits = m ForceUnits = kN *** OrcaFlex Units End *** This list contains all possible units settings that can be included in the block. They should be set on the Import Vessel Data form. These are not converted automatically to OrcaFlex model units. The strings indicate the contents of the columns – see RAO Table Headers. If the block is omitted altogether then a warning is issued and no units scaling is performed. if the table contains both wave period and frequency you must indicate that one of these is to be ignored. separated by spaces. This headers line consists of a number of character strings. The RAO data must appear in the file in one or more tables. In particular. each table being for one draught and direction. the first line of the table must be a set of headers defining the subsequent columns. for example because it contains irrelevant or superfluous data. The lines in between specify the conventions using the standard OrcaFlex data names and values. measured positive from forward towards the port side. Following these two lines. If the name contains spaces. You must ensure that either their units are consistent with the OrcaFlex model. For displacement RAOs the length unit is the only one which is used and consequently the force units can be omitted. For displacement RAOs. WFH or WFR header string identifies the period/frequency convention. where n is a number specifying the direction the wave is progressing. Newman QTFs are imported from both of these. roll. Immediately following the Start line should be a line nominating the draught into which to import the data. Hence. The format of the markup for QTFs differs from that of RAOs in the following ways: The identifier lines are OrcaFlex QTF Start/End rather than OrcaFlex Displacement RAO Start/End or OrcaFlex Load RAO Start/End. followed by a line defining the period ("WP x" for x seconds) or frequency ("WFR x" or "WFH x" for x rad/sec or Hz respectively). Hence. RY and RZ respectively.w System Modelling: Data and Results. Phase data are not specified. OrcaFlex will ignore them and will not treat them as actual data values. frequency-dependent added mass & damping may be imported from generic text files with the addition of suitable markup. do not apply to the added mass and damping data import. heave. pitch and yaw instead of X. etc) of the convention settings apply to these data. say. which may be in use for RAO or QTF import. and all QTFs are assumed to be given relative to waves of unit amplitude. you may define different scaling factors for each 3×3 added mass submatrix and each 3×3 damping submatrix. only the direction conventions (SurgePositive.6 as row and column headers to each matrix: if these are present. This only applies to independent vessel data: multibody data cannot be imported in this way. and may also be imported from generic text files in much the same way as RAOs. Draught DraughtName. Note that the scaling factors may be entered multiple times and will be updated each time they are encountered. so long as they are presented in the usual 6×6 matrix form.2. The column headers are surge. Only the direction conventions (SurgePositive. RX.. Y. The unit settings. as for RAO import. Both the length and force unit settings apply. so the RAOWaveUnit convention is implicitly set to be "amplitude". since added mass & damping are not directional data. as shown in this MOSES example in which all the added mass and damping data are scaled by the vessel structural mass. Each 6×6 matrix is delineated by the identifiers OrcaFlex Added Mass Matrix Start and OrcaFlex Added Mass Matrix End. but will not be otherwise scaled or have any units conversion applied. Instead. Some packages output the digits 1. they depend on frequency. as in this WADAM example.. The scaling factor(s) may take one of a number of forms: It may be completely absent. sway. etc) apply to QTFs. There is no corresponding Direction. Importing QTFs Full QTFs are at present only imported from AQWA and WAMIT results files. if given. of the convention settings. Vessels the page. in which case the data must be unscaled and in the same units as the OrcaFlex model. Z. The data will be converted to account for any differences in direction conventions. More generally. This form will also be necessary if your added mass & damping data are in different units to your OrcaFlex model: you will need to determine the appropriate scaling factors to convert between the two sets of units. in view of the wide variety of ways in which these data are presented by diffraction analysis packages. Examples Examples are given in the help file of the markup required for the output from three commonly-encountered analysis packages: MOSES Hydrostar WADAM 295 . this is not in fact necessary. It may be given as a single value which multiplies each of the imported data. Importing Added Mass and Damping Similarly to RAOs and QTF data. This may be useful if. you are required to define a scaling factor or factors with which to reinstate the data to their full dimensional form. although it is natural to align the headers above the columns of numbers. or OrcaFlex Damping Matrix Start and OrcaFlex Damping Matrix End as appropriate.. Since QTFs contain no phase information the conventions relating to phase have no relevance. This will be necessary for data which are fully non-dimensional since these submatrices have different dimensions. com/SoftwareProducts/OrcaFlex/Documentation/. The path's trajectory from the support path origin is then defined by specifying the length and bend radius of individual path sections. e.g. This method allows for the generation of detailed support models in an arbitrary arrangement.5 Supports Data Supports are sets of cylinders which are rigidly fixed to either a Vessel or a 6D Buoy. 296 . it is applicable to both Vessels and 6D Buoys. which is available on any machine on which OrcaFlex has been installed or can be obtained from our web site at http://www. The Vessel or 6D Buoy is referred to as the owner in the documentation for supports. RAO Table Headers When importing RAOs from a text file.w System Modelling: Data and Results. They can be found in the help file. The functionality of supports is identical for both types of owner and although the documentation is located here in the Vessels topics. the following strings can be used in the header line. A denotes amplitude. specified on the Support Coordinates page. so do not appear here. Vessels Note: These examples are rather too lengthy and space-inefficient to include in the printed manual. you should be able to import any such data. The supports data are primarily used to identify which support types are to be used and specify the geometry of the support arrangement. where the rollers boxes are on a stinger. P denotes phase and R rotation about the given axis. OrcaFlex can import data produced by other programs (or any other means) so long as they are in the format described above. There are two options available: Simple: A support path is defined by first specifying a support path origin.7. For information on modelling with supports see Supports: Modelling. 6. Supported Lines The set of lines that the owner's supports will interact with. Geometry Specification Specifies how the supports geometry is defined. Explicit: Individual support positions and orientations are explicitly specified in user defined coordinate systems. The supports data is specified on the Supports page of the owner's data form. If the geometry specification is set to be explicit. By following these examples. The method is primarily aimed at the efficient generation of simple stinger models. Header string Column contains WP Wave period in seconds WFH Wave frequency in Hertz WFR Angular wave frequency in radians/second XA Surge amplitude XP Surge phase YA Sway amplitude YP Sway phase ZA Heave amplitude ZP Heave phase RXA Roll amplitude RXP Roll phase RYA Pitch amplitude RYP Pitch phase RZA Yaw amplitude RZP Yaw phase In these header strings X.orcina. Supports are placed along the path by specifying their arc length and offset. Y and Z represent the vessel axes. then additional data are required. A value of Infinity is used for the Bend Radius to specify a straight path section. Support path drawing If the Draw Support Path check box is checked the support path will be drawn as a line in the wire frame drawing with the chosen pen. the support path is considered to be straight before the support path origin. The coordinate system Position defines the position of the coordinate system relative to the owner's origin and with respect to the owner axes. If using the explicit geometry specification the data are only reported relative to the owner axes. Each row of the table defines an individual support path section. If a value less than zero is specified for the Arc Length then the support path is linearly extrapolated in the negative support path origin x-axis direction. 297 . as specified in the support path table. Supports Table These data items are used to specify the positions and Support Types of the supports relative to the support path. Data for the explicit geometry specification Coordinate System Table These data items are used to specify the positions and orientations of coordinate systems which are used when specifying the positions and orientations of supports. Data for the simple geometry specification Support Path origin Position and Orientation The support path origin position defines the position of the support path origin relative to the owner's origin and with respect to the owner axes. The orientation is defined by specifying the azimuth and declination of the support z-axis with respect to the coordinate system and the gamma angle which defines a rotation of the support axes about its z-axis.w System Modelling: Data and Results. The support path origin orientation defines the support path origin orientation with respect to the owner axes. The support coordinates Position defines the position of the support relative to the coordinate system position and with respect to the coordinate system axes.e. The z offset is the offset of the support position from the support path in the support path z-axis direction at the support's arc length. Each row of the table defines an individual support. the support path is considered to be straight beyond the total specified cumulative length. If using the simple geometry specification the data are reported on two sheets: relative to the owner axes and relative the support path origin axes. If unchecked the support path will not be drawn. For each support path section its Length and Bend Radius must be specified. The support path is never drawn in the shaded drawing. then the support path is linearly extrapolated in the direction of the support path at the total specified cumulative length. The orientation is defined by specifying the azimuth and declination of the coordinate system z-axis with respect to the owner axes and the gamma angle which defines a rotation of the coordinate system axes about its z-axis. i. must be specified. At the support path origin the support path is directed along the support path origin xaxis. relative to which the support coordinate position and orientation are defined. Vessels Support Geometry Table The support geometry table button outputs a spreadsheet of the positions and orientations of the owner's supports. A Coordinate System. The coordinate system Orientation defines the orientation of the coordinate system with respect to the owner axes. the offset is in the direction normal to the support path at the support's arc length. Support Coordinates Table These data items are used to specify the positions. Support Type Data The support type data is specified on the support type data form. The support coordinates Orientation defines the orientation of the support axes with respect to the coordinate system axes. orientations and Support Types of the individual supports. Each row of the table defines an individual support. The orientation is defined by specifying the azimuth and declination of the support path origin z-axis with respect to the owner axes and the gamma angle which defines a rotation of the support path origin axes about its z-axis. Support Path Sections Table These data items are used to specify the geometry of the support path. i. The support type data are used to specify the geometry and physical properties of the support cylinders.e.e. The Name is used to refer to the coordinate system. If the specified Arc Length is greater than the total cumulative length of the support path. i. The Arc Length is the support position along the support path measured from the support path origin. Circles of this diameter will be drawn at cylinder ends if the "Draw Ends in Wire Frame view" check box is filled. with a single support cylinder along the support y-axis direction and two support cylinders along the support z-axis direction. U shaped: Three support cylinders in a "U" shape. The following figures illustrate the possible support geometry options. The support cylinder positions are defined by specifying individual cylinder lengths and the angle change between consecutive cylinders. per unit depth of penetration. Figure: An example flat support.w System Modelling: Data and Results. Vessels Contact Stiffness The reaction force. User specified: An arbitrary number of support cylinders. generated by contact between the supported line and the support cylinders. Geometry Defines how the support cylinder geometry is defined. V shaped: Two support cylinders in a "V" shape defined by the angle the support cylinders make with the support y-axis direction. There are four possible geometries: Flat: A single support cylinder along the support y-axis direction. Diameter The contact diameter of the support cylinders. 298 . Vessels 299 .w Figure: An example V shaped support. Figure: An example U shaped support. System Modelling: Data and Results. If a support segment length of zero is specified then support cylinders are not generated for that segment. from one segment to the next. For the second support segment onwards. User specified Support Segments Table For the first row in the support segments table a single horizontal support cylinder is generated in the support yaxis direction. Flat data Length The length of the support cylinder. 300 . This defines the separation. in the support y-axis direction. Angle The angle between the support cylinders' axes and the support y-axis. in the support yz-plane. The length specifies the length of the cylinder and the point at which the next segment will start. U shaped data Horizontal Length The length of the horizontal support cylinder in the support y-axis direction. If you do not want a horizontal support as the base of your support shape then the length of the first support segment should be set to zero. between the z-axes of the two vertical cylinders. Vertical Length The length of the vertical support cylinders in the support z-axis direction.w System Modelling: Data and Results. The angle specifies the change in direction. V shaped data Length The length of the support cylinders. two support cylinders are generated per segment and placed symmetrically about the support z-axis. Vessels Figure: An example user specified support. the convergence of the model to the desired equilibrium becomes very robust and efficient. but for the purpose of contact they are treated as having an infinite extent in the cylinder's axial dimension. used by the line contact model. Like the line contact model the contact surface of the splined line interacts with a penetrator object. but in the supports contact model it is an infinitely long cylindrical penetrator called a support cylinder. Support cylinders are drawn with a finite length. rather than contact between lines. fixed to Vessels or 6D Buoys. Vessels Modelling The supports facility enables you to model contact between lines and sets of rigid cylinders. The similarity is that to model the contact surface of a supported line a smooth spline curve is fitted between the line nodes. Supports and support cylinders A support is composed of one or more support cylinders. Figure: An example of a V-shaped support. OrcaFlex does not treat the support cylinders as simple cylinders. continuous. The number. in conjunction with the support cylinder desired side property. The major difference is that the supports contact model is used to model contact between rigid support cylinders and supported lines. The spline allows OrcaFlex to represent the line as a smooth. rather than the spherical penetrators.w System Modelling: Data and Results. called supports. The z-axis of a support cylinder is parallel with the cylinder's axis and is always in the support axes zy-plane. Support cylinder desired side For the purposes of calculating contact penetration. The support cylinder geometry is always symmetric about the support's z-axis. Primarily the supports feature has been designed to facilitate the efficient modelling of pipe lay stingers. Instead the support cylinder has a desired side associated with it. Support cylinders are given infinite contact length because. Supports contact model Similarities with the line contact model Conceptually the supports contact model shares many similarities with the line contact model. The figure below shows an example of a support. The desired side is the region of space 301 . whose support type uses a V-shaped geometry. The support cylinder z-axis orientation in the support axes zy-plane is defined by the the support type. geometry and physical properties of the support cylinders associated with a particular support. The x-axis of a support cylinder is always parallel to the support's x-axis. as specified in the support type data. but it is also useful in modelling many other applications where contact is important. are defined by the support type. attached to another line's nodes. Contact occurs when a support cylinder is deemed to have penetrated into one or more of the Vessel's supported lines. deformable elastic solid tube. described in more detail below. The Support Off End Contact Distance and Max Support Off End Contact Distance result variables can be used to check if the supported line is in contact with support cylinders beyond the length specified in the support type data. However. OrcaFlex calculates the closest approach between the supported line spline and the support cylinder axis. a spline is associated with the supported line. If the point of closest approach on the spline is on the support cylinder's desired side then the contact is handled as if the support cylinder was a simple cylinder. as shown in the below figure: 302 .w System Modelling: Data and Results. as shown in the below figure: Figure: Supported line contact with support cylinder. where point of closest approach on the spline is on the support cylinder's desired side. Vessels above the support cylinder axes xz-plane in the positive support cylinder y-axis direction. To calculate the contact penetration between a supported line and a support cylinder. in the same way that splines are used in Line Contact. if the point of closest approach on the spline is not on the support cylinder's desired side then the splined line is assumed to have penetrated to its position through the support cylinder. The support cylinder's desired side is a very useful property. then the contact force is linearly scaled from zero up to the full value over this off-end distance. Using the simple geometry specification The simple geometry specification is a quick way to set up a simple stinger model. with the supports positioned along a user-specified support path. even though it appears that the line is not in contact with the support cylinder. and the contact stiffness is not zero. The supports and support cylinders should therefore be arranged such that the support cylinder y-axes point in the direction of the expected reaction forces between the supported line and the support cylinders. 303 . the line will feel a reaction force equal to the penetration depth multiplied by the contact stiffness. the supported line will feel a reaction force along the line of penetration. i. Vessels Supported line contact with support cylinder. where point of closest approach on the spline is not on the support cylinder's desired side. with respect to the support. Defining support geometry The support cylinder geometry is defined. If the point of closest approach on the spline is outside the supported line length by more than one support cylinder radius. by the support type. the supported line can not be doubled back and laid over a support cylinder multiple times. OrcaFlex will calculate only a single point of closest approach. The support arrangements that can be modelled using the simple method are limited because individual support orientations can not be independently specified and the support positions are restricted to the plane of the support path. If the point of closest approach on the spline is outside the supported line length by less than one support cylinder radius. Calculating contact force For each support cylinder and supported line pair. The position of the supports is defined using the supports data specified on the Vessel or 6D Buoy data form. If the point of closest approach on the spline is within the supported line's length.e. This means that if the point of closest approach on the spline is not on the support cylinder's desired side. This directs static convergence towards the user's desired equilibrium position. It allows the user to define the side of the support cylinder on which the supported line should rest. This means that a supported line can only contact each support cylinder once. Such a case is depicted in the above figure. Beyond the supported line's end nodes the spline is extrapolated as a straight line with infinite extent in the end nodes' z-axis directions. The supports data are input using either the simple or explicit geometry specification method. then the support cylinder and supported line are not in contact and the contact force is zero.w Figure: System Modelling: Data and Results. Supports are added using the support coordinates table. User specified coordinate systems are specified with respect to the Vessel or 6D Buoy axes using the coordinate system table. The support path x and z directions are initially aligned with the support path origin axes and track with the path curvature. in the order they appear in the table. Vessels To generate a supports model using the simple geometry specification. Each row of the table represents a section of the support path defined by its length and bend radius. The positions and orientations of the supports are defined with respect to user specified coordinate systems. The figure below shows how the simple geometry specification data are used to define support geometry. allowing for simple grouping of supports into frames which can be moved or rotated. The path sections defined in the table are added to the path. Using the explicit geometry specification The explicit geometry specification allows full control of the positions and orientations of individual supports. The support path origin is defined with respect to the Vessel or 6D Buoy axes. The figure below shows how the explicit geometry specification data are used to define support positions 304 . For each new support a coordinate system should be nominated and then the support position and orientation specified with respect to this coordinate system. The supports are placed using the supports table by specifying their arc length along the path and their z offset in the path z direction. Its position defines the start of the user specified support path. Next the support path is specified using the support path sections table. starting from the support path origin. Multiple supports can be associated with a single coordinate systems. Figure: Support placement using the simple geometry specification. first a support path origin must be defined. The support path origin's x-axis defines the initial direction of the support path. For results purposes the supports are given an index defined by their position in the supports table.w System Modelling: Data and Results. The OrcaFlex simulation will then calculate the vessel's resulting dynamic motion. Optionally. The OrcaFlex static analysis will then calculate the equilibrium position allowing for the mean wave drift load. First. select 6 DOF for the static analysis. 6. One common situation where the wave drift loads can matter is with a moored vessel. And include Added Mass and Damping in the vessel's Included Effects. added mass and damping matrices and the reference origin to which they apply. mass and moments of inertia data for the appropriate draught. Alternatively OrcaFlex can calculate and apply the slow drift motion for you.7. Wave frequency motion can also then be superimposed on top of that slow drift motion. Vessels Support placement using the explicit geometry specification. This tells OrcaFlex to apply the mean wave drift load to the vessel during the static analysis. On the Structure page on the vessel type form. Options for Modelling Slow Drift In OrcaFlex you can model slow drift motion in broadly 2 ways. by using displacement RAOs or a time history superimposed motion. To do this you need to do the following: On the vessel form. The second order terms are much smaller but they include loads with a much lower frequency (see the Wave Drift theory section for more details). The vessel's natural frequencies in surge. and then in the dynamic analysis to apply the mean and time-varying wave drift load. 305 .w Figure: System Modelling: Data and Results. sway and yaw are typically quite low and so the low frequency wave drift loads can generate large slow drift excursions in these directions.6 Modelling Vessel Slow Drift When a vessel is exposed to waves it experiences wave loads that can be split into first order and second order terms. This can either be done using time history or externally-calculated options for primary motion. specify the stiffness and reference origin datum position. These low frequency terms are called the wave drift loads and they can cause significant slow drift motions of the vessel if their frequencies are close to a natural frequency of the vessel. And set the primary motion to Calculated (6 DOF). or done using the time history or harmonic motion options for superimposed motion.) Specify QTF data on the wave drift page of the vessel type form (the wave drift loads are calculated based on these data). include wave drift damping in the vessel's Included Effects. (The hydrostatic stiffness is always included. and include Wave Drift Load (2nd Order) in the vessel's Included Effects. Added Mass and Damping page. OrcaFlex will then include the damping effect due to the way the wave drift load varies with vessel low frequency velocity and with current. you can calculate the vessel slow drift motion outside OrcaFlex and then impose that motion on the vessel. specify the vessel centre of gravity. And on the Stiffness. The first order terms generate motion at wave frequency and this is modelled in OrcaFlex using RAOs to specify either the displacement or the load. For details of the theory see Vessel Theory: Current and Wind Loads. But if all the motion is being modelled as primary motion. See the Current Load data on the vessel type data form. In addition to the usual contribution of the product of added mass and acceleration. include Applied Load in the vessel's Included Effects and specify appropriate applied load data. Damping Effects on Vessel Slow Drift Drag and damping loads have an important effect on vessel slow drift motions. For details of the theory see Vessel Theory: Current and Wind Loads. include Current Load in the vessel's Included Effects and specify appropriate data for current load and yaw rate drag. Note also that this combination of calculated and superimposed motion is not compatible with implicit integration: in this case you will have to use explicit integration. And then specify the wind data on the environment data form. Then set the vessel superimposed motion to None. OrcaFlex gives you the option to include this additional load.g. which can be significant. then you should not include Wave Load (1st order) in the vessel's Included Effects. This will superimpose the wavefrequency motion. This is modelled in OrcaFlex using a combination of the OCIMF approach and a yaw drag moment proportional to (low-frequency yaw velocity)2. so that the first order vessel motion is fully calculated and takes into account coupling effects between the wave frequency and low frequency response. then we recommend that you specify those data in the vessel type's Load RAOs and include Wave Load (1st order) in the vessel's Included Effects. It is modelled in OrcaFlex based on the OCIMF approach. This method will not include coupling effects between the two parts of the motion. and you can instead instead model the wave frequency response using displacement RAOs. for example to model viscous roll damping. Optionally (usually needed).w System Modelling: Data and Results. and wind load data on the vessel type data form. wave frequency viscous damping (both linear and quadratic) can be included in the Other damping data. If you have wave load RAO data available. The former is appropriate if you are using superimposed displacement RAOs to model the wave frequency motion. OrcaFlex will automatically include loads from any lines or other objects that are connected to the vessel. See the Wind Load data on the vessel type data form. Wind drag on the vessel hull. defined by the displacement RAOs. This is modelled in OrcaFlex by the drag force part of the Morison force on the lines that model the risers/moorings. you should set Primary Motion is Treated As to either Low frequency or to Both low and wave frequency. OrcaFlex will then include the low frequency 2nd order potential theory manoeuvring load in the analysis. include Manoeuvring Load in the vessel's Included Effects. Wave drift damping. on top of the calculated low-frequency primary motion. Material damping in the risers/moorings. See Wave Drift Damping Theory for further details. This is the aerodynamic drag due to wind and any vessel velocity. If you do not have the wave load RAO data. Wave radiation damping. Optionally (e.g. See CMPT (1998) section 3. If wanted. See Vessel Modelling Overview for further information. Optionally. Manoeuvring load.12. the vessel velocity gives rise to an additional 2nd order low frequency manoeuvring load. Hydrodynamic drag on the risers/moorings. There are no further data required. by setting the vessel's superimposed motion to Displacement RAOs + Harmonic Motion but with no harmonic motion specified (on the Superimposed Motion page of the vessel data form). It can be modelled in OrcaFlex by simply including it in the vessel's Included Effects. Should you be using the explicit integration scheme. include wind load on vessels (on Wind page of the environment data form) and include Wind Load in this vessel's Included Effects. This arises because the wave drift loads vary with vessel velocity. Finally. This is not usually very significant at low frequencies. material damping may be 306 . to model thruster loads). 1979. Hydrodynamic drag and skin friction on the vessel hull. because the asymptotic limit of the wave frequency damping is zero. This is the structural damping in the material of the risers and mooring lines. using wave load RAOs as the excitation for this motion. then you should treat the primary motion as Both low and wave frequency and specify a suitable Dividing Period for OrcaFlex to use to filter the primary motion into its low and wave frequency parts. e. It can be modelled in OrcaFlex using either constant or frequencydependent damping on the vessel type form. OrcaFlex provides Rayleigh Damping to model material damping in lines when the implicit integration scheme is in use. Vessels Optionally. Note that OrcaFlex does not yet have the dependency of yaw drag on sway velocity proposed by Wichers. The following discussion documents the various damping effects and how they are modelled in OrcaFlex. This affects the periods at which the RAOs are reported. Theses results are accurate for small-angle rotational motion. The rotational RAO amplitudes do not depend on the position of the output point. Directions and Output Points You specify one or more vessel-relative wave directions. as specified in the vessel type RAO conventions) passes the RAO phase origin specified on the vessel type form. The reported RAOs allow for the following effects: They allow for the position of the output point relative to the RAO origin to which the vessel type RAOs apply. It is modelled in OrcaFlex by the friction between the seabed and the line used to model the mooring/riser. Note: The reported RAOs are first order RAOs calculated using small-angle theory to transform the RAOs from the vessel RAO origin to the points specified on the Vessel Response form. They give the RAOs for the specified wave direction. In this case the necessary phase shift will be calculated using deep water wavelengths. and one or more points on the vessel. However Triantafyllou et al (1994) concluded that material damping effects are negligible. which uses large angle theory. Conventions You can choose for the RAOs to be reported either using the same RAO conventions as specified for this vessel's type or using Orcina standard conventions. If there is more than one wave train then the direction of the first wave train is used. The phases will then be reported relative to the time that the given point on the wave (crest / trough / zero up. containing the RAOs for each of the specified output points. If this is not one of the directions for which RAOs are specified. 307 . From this form you may report displacement RAOs and report spectral values of the vessel's response to waves. Seabed soil friction on the risers/moorings. This arises from the frictional force acting on the part of a mooring/riser that is lifting off and touching down on the seabed. velocity and acceleration of the output points. However Triantafyllou et al (1994) concluded that its effect is negligible. Vessels modelled using the line target damping values. pitch and yaw of a vessel are the same everywhere on it. They allow for Froude scaling if there is a difference between the vessel type length and the vessel length.or down-crossing. More accurate results can be obtained in this case by running a simulation. RAOs are given for the position. based on its vessel type's displacement RAOs. The RAO report covers the wave periods specified on the vessel type data form. Phase Origin You can choose the Phase Origin to use for reporting phases.w System Modelling: Data and Results. relative to the vessel. The rotational RAO phases depend on the position of the output point only if you specify the Phase Origin to be Each Point. The translational RAOs depend on the position of the output point. Generation of vessel response reports can also be automated through the batch script. for which the RAOs and spectral response will be reported. or from the OrcaFlex programming interface. If you specify a direction of '~' then the direction of the wave relative to the vessel is used. but if the vessel undergoes large-angle rotational motion it will exhibit a non-linear higher-order response that can only be approximated by RAOs. the options being: RAO Phase Origin.or down-crossing. The phases will then be reported relative to the time the given point on the wave (crest / trough / zero up. Each Point. as specified in the vessel type RAO conventions) passes that particular output point. and this can often be done very quickly by removing from the model all other objects that do not affect the motion of the vessel. 6. Report RAOs The RAO report gives a separate worksheet for each specified direction. then the RAOs are derived by interpolation on direction.7. derived from the displacement RAOs of its vessel type. The output points are specified by giving their coordinates relative to vessel axes.7 Vessel Response Reports The vessel response form can be opened using the Results Menu or using the Report Vessel Response button on the vessel data form. since the roll. plus (if appropriate) the regular wave period specified on the environment data form. for all 6 degrees of freedom and for Z Above Wave. Z indicate components in the global axes directions. Faltinsen. Notes: For Z Above Wave. no spectral values can be reported for acceleration and only the significant amplitude can be reported for velocity.Y. The average period of the response. The following spectral values are reported. velocity and acceleration. Warnings: Wave directional spreading spectra are not taken into account. to obtain the response spectrum for each degree of freedom. and that the extremes are Rayleigh distributed. Warning: Z Above Wave does not take account of wave surface disturbance due to the presence of the vessel. is assumed to remain constant over this duration. 6.8 Vessel Results For details on how to select results variables see Selecting Variables. For velocity of Z Above Wave you could perhaps estimate the expected maximum amplitude by assuming that the ratio of maximum amplitude to significant amplitude is roughly the same for velocity as for position. or Ochi. since the sea-state. Report Spectral Response The spectral response report contains a separate worksheet for each specified direction and each random wave train specified on the Environment data form. whereas upper case letters X. as represented by (Hs. All these reports are based on the vessel type displacement RAOs. for example. Vessels Z Above Wave Z Above Wave reports the amplitude of the heave motion of the vessel relative to the water surface. Any wave load RAO data are ignored. for all 6 degrees of freedom and for Z Above Wave. ie of the order of hours rather than days or years. D is the specified Duration (in hours) and Tave is the average period (in seconds). Note: The spectral response report is not available if no random wave trains are specified. The most probable maximum amplitude for a period of the specified Storm Duration.7. See. This requires that the zero period RAO is present and has zero amplitude . The storm duration should be short-term. They are also based purely on small amplitude linear theory. so some of the integrals for the spectral moments do not converge. This is because the RAO of Z Above Wave does not decay to zero as wave period goes to zero.Tz). and the spectral values are then given by: Significant Amplitude = As = 2m0½ Average Period = Tave = (m0/m2)½ Max Amplitude = As(½ln(D*60*60/Tave))½ where As is the significant amplitude. Separate tables are given for each of the specified output points. Note: The significant and maximum values are reported as single amplitudes. 308 . of the response spectrum are calculated. This is the mean period between zero up-crossings. the motion is +/. i. The worksheet contains tables of spectral values for position. pages 151-152. This can be useful when evaluating whether an object at some point on the vessel will contact the water surface and if so with what relative velocity. The standard formulae used to calculate the spectral values (see below) are based on the further assumptions that the spectrum is narrow-banded and Gaussian. pages 24-27.e. The significant amplitude.y. The zeroth and second spectral moments.z indicate components in the vessel axes directions. m0 and m2. Note that in the names of the vessel results we use the convention that lower case letters x.w System Modelling: Data and Results. The calculation assumes that all the spectral energy is in the specified direction for each wavetrain. linearly interpolated as necessary.OrcaFlex will override the given values if this is not the case.the value reported. These spectral values are calculated as follows: The spectrum of the wave train is combined with the vessel response specified by its RAOs. g. a. 2. Vessel motion can include both primary and superimposed motions. The position and orientation results are available for each of these contributions separately. 3 report the primary motion of the point P. relative to the vessel primary motion position and orientation. relative to its low frequency position and orientation. x-Acceleration rel. of the acceleration vector. These results report the components in the directions of the vessel axes after only the primary motion has been applied. due to the total combined primary and superimposed motion. relative to earth. Total Position and Motion Results X. GY-Velocity. Rotation 1. 309 . Rotation 3 report the total combined motion of the point P. Range jump suppression is applied to the Rotation 1 and Rotation 3 angles. Y. due to the total combined primary and superimposed motion of the vessel. Yaw report the wave frequency part of the primary motion of the point P. due to both primary and superimposed motion. of the angular velocity of the vessel. Rotation 2. GZ-Velocity The magnitude and components. unlike line velocity results. z-Acceleration rel. Primary WF Surge. of the acceleration of the user-specified point P on the vessel. Y. GX-Velocity. g The magnitude and components. relative to global axes. in vessel axes directions. due to the total combined primary and superimposed motion.w System Modelling: Data and Results. 2 and 3 define the orientation of the vessel. Z and Primary LF Rotation 1. relative to global axes.0) then the results reported are for the vessel origin. The velocity. in vessel axes directions. z-Angular Velocity The magnitude and components. Rotation 2 is in the range -90° to +90°. acceleration and other results are only available for the total combined motion of the point P. Rotation 1. X. Heave. due to the total combined primary and superimposed motion. GY-Acceleration. Pitch. Y. Roll. Sea Surface Z The global Z coordinate of the sea surface directly above or below the user-specified point P on the vessel. Rotation 3 X. so if Position = (0. of the user-specified point P on the vessel. g. So. due to both primary and superimposed motion. Z. Vessels Position and Motion Results All the position and motion results (see the headings below) report the motion at a user-specified point P on the vessel whose Position is specified on the results form. The acceleration vector reported. Sway. GX-Acceleration. y-Angular Velocity. relative to global axes. is the acceleration of the point P. A positive value indicates the point P is above the sea surface. so values outside the range -360° to +360° might be reported. Sway. The velocity and acceleration results are obtained from logged values of the velocity and acceleration of the vessel. in the global axes directions. Angular Velocity. relative to earth. relative to the vertically downwards acceleration due to gravity. due to the total combined primary and superimposed motion. Z and Primary Rotation 1. Acceleration. the vessel velocity and acceleration results do not have possible inaccuracy due to numerical differentiation of logged position values.0. g. Heave. The three rotations (called Euler angles) are 3 successive rotations that take the global axes directions to the vessel axes directions. x-Angular Velocity. The position of P is specified by giving its vessel local axes coordinates relative to the vessel origin V. Primary X. Acceleration rel. Sea Surface Clearance The vertical clearance of the user-specified vessel point P above the instantaneous sea surface. 3 report the low frequency part of the primary motion of the point P. Yaw report the superimposed motion of the point P. if the vessel primary motion is treated as being both low frequency and wave frequency then Orcaflex also makes available the separate low frequency (LF) and wave frequency (WF) parts of the primary motion: Primary LF X. Y. Surge. relative to global axes. Roll. Additionally. Pitch. due to the total combined primary and superimposed motion. as well as for the total combined vessel motion. 2. a. of the velocity of the vessel at the user-specified point P. Z. These results report the components in the directions of the vessel axes after only the low frequency part of the primary motion has been applied. GZ-Acceleration The magnitude and components. g. Velocity. Y. Rotation 1. in the global axes directions. y-Acceleration rel. For details see Vessel Rotations. Rotation 2. Z are the global axes coordinates of the position of the user-specified point P on the vessel. Primary Rotation 2 and Primary Rotation 3 are the rotation angles of the orientation of the vessel relative to global axes. z-Angular Acceleration The magnitude and components. Y. In addition. relative to its position and orientation after only the low frequency part of the primary motion has been applied.Lz) and global axes directions (GX. Vessels The acceleration vector. Primary WF Pitch is in the range -90° to +90°. 3 results described above. Primary LF X. y-Angular Acceleration. For each of these loads the results available are the magnitudes of the force and moment vectors. in the primary vessel axes directions. Range jump suppression is applied to Primary Rotation 1 and Primary Rotation 3. Primary WF Heave. And the values reported are the components in the directions of the vessel axes after only the low frequency part of the primary motion has been applied. This is the acceleration that would be reported by an accelerometer attached at the point P (since an accelerometer reading of zero corresponds to free-falling). due to the vessel primary motion only. of the user-specified point P on the vessel.g. so values outside the range -360° to +360° might be reported. Angular Acceleration. They therefore report the total primary motion position and orientation of the point P. Primary Rotation 1.GY. but for only the low frequency part of the vessel primary motion. Primary LF Z. Total Load The magnitude and components (in vessel axes directions) of the sum of the constituent loads on the vessel which are included in the calculation. For details see Vessel Rotations. Sway and Heave are the superimposed translational displacement components. Surge. Force and Moment Results Force and moment results are available for the Total Load on the vessel. a. relative to the primary position of the vessel. so values outside the range -360° to +360° might be reported. in vessel axes directions. This relative acceleration can be thought of as the acceleration of the point P relative to the free-falling state. Primary Y. If a load is not included then it will not be calculated and will not appear in the list of available results.e. Roll. Sway. For details see Vessel Rotations. i. Primary Z. Primary WF Pitch and Primary WF Yaw These results are the wave frequency part of the primary motion of the user-specified point P on the vessel. and will not be included in the Total Load results. relative to its primary motion position.GZ). Superimposed Motion Results Surge.Lz) of those vectors in the vessel axes directions. Pitch and Yaw are the superimposed angles of rotation. These results report the acceleration relative to the (downwards) acceleration due to gravity. Heave. Roll. Range jump suppression is applied to the Roll and Yaw angles. x-Angular Acceleration.w System Modelling: Data and Results. They report the components in the global axes directions of the position of point P due to only the low frequency primary motion. is the acceleration of the point P due to the combination of both primary and superimposed motion of the vessel. due to the superimposed motion. Pitch and Yaw The position and orientation of the vessel due to superimposed motion.Ly. In all cases the moments given are moments about the vessel origin. Primary WF Roll. These are typically the wave-generated part of the motion. a . Primary Rotation 1. and also separately for the various individual loads on the vessel that are in the vessel's Included Effects. Primary Rotation 2 and Primary Rotation 3 Primary X. Primary LF Y. of the angular acceleration of the vessel. Primary LF Rotation 1. and the components (Lx. if there are other objects connected to the vessel then the sum of the loads from all attached objects is also available. Range jump suppression is applied to Primary WF Roll and Primary WF Yaw. Primary Rotation 2 is in the range -90° to +90°. Primary WF Surge. 310 . due to the vessel primary motion only. Primary Motion Results Primary X. Primary WF Sway.Ly. And the force and moment components of this Connections Load are available in both vessel axes directions (Lx. Primary Y and Primary Z are the global axes coordinates of the user-specified point P on the vessel. Z and Primary Rotation 1. Primary LF Rotation 2 and Primary LF Rotation 3 These results are analogous to the Primary X. so values outside the range -360° to +360° might be reported. Pitch is in the range -90° to +90°. 2. relative to the primary vessel axes directions. due to the total combined primary and superimposed motion. with its measurement directions aligned with the vessel local axes directions. Wave Drift Load (2nd order) The wave drift force and moment exerted on the vessel. The Support Contact Clearance . Available only if Wave Load (1st Order) is in the vessel's Included Effects. Available only if Wind Load is in the vessel's Included Effects and Include Wind Loads on Vessels is checked on the Wind data page of the Environment data form. Available only if Other Damping is in the vessel's Included Effects. Wave Load (1st order) The force and moment on the vessel due to the wave load RAOs. Current Load The current drag force and moment on the vessel. Supports Force The magnitude and components (in vessel axes directions) of the sum of reaction loads on the vessel's supports. alternatively (all supported lines) can be specified and then the result is taken across all lines supported by the vessel. Hydrostatic Stiffness Load The Hydrostatic stiffness force and moment on the vessel. but these load results are reported with respect to vessel axes. Available only if Current Load is in the vessel's Included Effects. Supports Moment The magnitude and components (at the vessel's origin and in vessel axes directions) of the sum of moments due to the reaction loads on the vessel's supports. 311 . Note that the connections loads reported include the structural inertia loads and added inertia loads on the objects connected to the vessel. but large values of Primary Rotations 1&2 may have a significant effect on these results. shapes. Available only if Manoeuvring Load is in the vessel's Included Effects. Available only if Applied Loads is in the vessel's Included Effects. winches. Applied Load The sum of all the local and global applied loads. Wind Load The wind drag force and moment on the vessel. links. Note: The first order wave RAO load. Available only if Added Mass and Damping is in the vessel's Included Effects. Added Mass and Damping Load The sum of the forces and moments on the vessel due to Added Mass and Damping. due to the translational and rotational acceleration of their points of connection. These results are available only if Wave Drift Load (2nd order) is in the vessel's Included Effects. For convenience. Vessels Connections Load The sum of the loads from all attached lines. Details of the loads exerted by each individual object are available as results tables.w System Modelling: Data and Results. in which case the result is specific to that supported line.GY. Support Lift Out and Support Off End Contact Distance results allow a supported line to be specified. etc.GZ). These are available only for vessels with at least one such object attached. Manoeuvring Load The Manoeuvring Load on the vessel. the components of Connection Force and Moment are also available in Global axes directions (GX. and can also be found under the results for each object itself. If Wave Drift Damping is also included. second order wave drift load and sum frequency load are calculated and applied with respect to primary heading axes. In most cases there will be little difference between the two frames of reference. plus any load from low frequency yaw rate drag. Support Results Support results are available for the vessel if it has one or more supports. then its effect will be included in this Wave Drift Load (2nd order) result. Other Damping Load The force and moment due to the specified Other Damping on the vessel. These results are available only if Sum Frequency Load (2nd order) is in the vessel's Included Effects. Sum Frequency Load (2nd order) The sum frequency wave force and moment exerted on the vessel. Multiple Static Results For multiple statics calculations the results variables available are as follows.w System Modelling: Data and Results. Support Lift Out The maximum distance. including those from current. Lines are represented in OrcaFlex using a lumped mass model. about the vertical. in the support z direction. If the point(s) of closest approach on the supported line spline are outside the supported line's length by more than one support cylinder radius. then the result is reported as zero. Support Contact Clearance The minimum distance between the support cylinders and the supported line contact surface. The result allows you to check for potential escape of the specified supported line(s) from the specified support. GZ-Moment The total moment. Each segment represents a short piece of the line. Essentially this result is the distance that the supported line spline has lifted away from the support position in the support z-axis direction. wind. hoses. Max Support Off End Contact Distance The maximum Support Off End Contact Distance across all of the vessel's supports. buoyancy. If the point(s) of closest approach on the supported line spline are outside the supported line's length by more than one support cylinder radius. Note that this force is not necessarily in the offset direction. If (all supported lines) is specified then the maximum Lift Out across all supported lines is reported. the line is modelled as a series of lumps of mass joined together by massless springs. whose properties (mass. If the support has multiple cylinders in contact with the supported line then the maximum Support Off End Contact Distance across these cylinders is reported. drag etc. then there is no contact and the result is not available. the support cylinders are drawn with finite length but for the purpose of contact they are assumed to have infinite axial extent and so it is possible that the supported line is being contained within the support by part of the support that is not present in the real physical system being represented. for modelling purposes. then there is no contact and the result is not available. Lines Support Reaction Force The magnitude and components (in support axes directions) of the reaction load on the support. applied to the vessel. or all the points of contact on the support cylinders are within the length of the support cylinders.8 LINES Lines are flexible linear elements used to model cables. If (all supported lines) is specified then the minimum contact clearance across all supported lines is reported. applied loads and attached lines and other objects. at the nodes at its ends. The loads reported are the total loads. See the figure below. The lumps of mass are called nodes and the springs joining them are called segments. chains or other similar items. That is.) have been lumped. Restoring Force The magnitude of the horizontal component of the total force applied to the vessel. Vertical Force The vertically downwards component of the total force applied to the vessel. 6. rather like beads on a necklace. If (all supported lines) is specified then the maximum Support Off End Contact Distance across all supported lines is reported. Max Support Lift Out The maximum Support Lift Out across all of the vessel's supports. Worst Tension The largest tension in any segment of any Line connected to the Vessel. If none of the support cylinders and specified supported line(s) are in contact. 312 . from the support position to the point(s) of closest approach on the supported line's spline. If the result is negative it means one or more of the supported lines have penetrated one or more of the support cylinders and the result is equal to the deepest penetration. which shows an example line spanning from a Vessel to a Buoy. Support Off End Contact Distance If the specified supported line is in contact with a support cylinder at a point beyond the support cylinder's ends this result reports the distance from the end of the support cylinder to the point on the support cylinder axis making closest approach with the supported line. The Line Types are defined separately. etc. A Line Type is simply a set of properties (for example the diameter. z y End A z V B x y x End B section 1 (3 segments) section 3 (9 segments) Clump section 2 (7 segments) Figure: Line Model The properties of a Line are specified by dividing it up into a number of consecutive sections that are chosen by the user. ropes. Lines End positions and no-moment directions are defined relative to the objects to which the ends are connected and move with those objects. In addition. drag chains or buoyancy bags attached to the line. a number of attachments may be specified. 313 . This allows the same set of line properties to be used for a number of different sections of the line. For each section you must define its length. the Line Type of which it is made and the number of segments into which it should be divided for modelling purposes. There is also a Line Type Wizard tool that helps you set up Line Types representing common structures like chains. For example. mass per unit length and bend stiffness) given a name so that they can be called by that name. attachments may be used to model clump weights. to represent items that are connected to the Line.w System Modelling: Data and Results. or for different lines. Two types of attachment are available – clumps (buoyancy or heavy) and drag chains. on the Line Types data form. Various calculations performed by the program need to know which end of the line (End A or End B) is at the top. On the other hand. Anchored or else connected to a Vessel or Buoy. The properties themselves are then given separately. P-y Model Optionally specifies the P-y model used to define horizontal soil loads for a vertical line that extends beneath the seabed.1 Line Data For every line in the system there is a data form defining its structure and interconnection. if you wish to measure arc length from the seabed then you should connect End B to the vessel. Include Torsion Torsional effects can be included or ignored. You specify which end is at the top. If the Line is not in contact with the seabed then Top and Bottom End designations are somewhat arbitrary. you must specify the torsional orientation at each end of the line. If torsion is included for a line. measured from End A. If you wish to measure arc length from the vessel then you should connect End A to the vessel. Top End This data item is used to give OrcaFlex information about the sense of the Line. You are free to make whatever choice suits your model. Name Used to refer to the Line. for each line in the model. The setting of the Top and Bottom Ends is used by the program as follows: The Lay Azimuth data defines a lay direction starting from the Bottom End and moving towards the Top End. make End B anchored and set Top End to End A. The Gamma angle determines the torsional position of the line end – for details see Line End Orientation. The Line Setup Wizard uses the bottom end when calculating anchor positions and also for the layback calculation. See Torsional Stiffness. To see the line orientation visually on the 3D views. Suppose you have a line with the top end connected to a vessel. at which it should be attached. and the program assumes that the other end is at the bottom. This is done by setting the Gamma angle of the end connections on the line data form. It is on these data forms that the system is built up by connecting lines between the objects that have been defined. This allows the same set of attachment properties to be used for a number of different attachments. We recommend that the Full Statics option is selected because this is the only statics option in OrcaFlex that includes the effects of torsion. If torsion is included for a line. 6. but remember that the contents pressure will be referenced from the Top End. the static analysis should also include the effects of torsion – otherwise the simulation will start from a position that is not in torsional equilibrium and an unstable simulation may result. The two ends of a Line are referred to as End A and End B and each end can be Free. and which end is at the bottom. Notes: The node axes are drawn using the node pen. Fixed. make End A anchored and set Top End to End B.8. 314 . The Contents Pressure Reference Z level can be set to '~' (indeed this is the default value) which OrcaFlex interprets as the Z level of the Top End in the reset state. select Draw Node Axes on the View menu. If the entire Line is in contact with the seabed then again you are free to make whatever choice of Top and Bottom Ends suits your model. If torsion is included then the line type torsional properties must be specified. Lines Each attachment attached to the Line is specified by giving the Attachment Type and the arc length. specified on the line data form. OrcaFlex then draws the node axes Nxyz at each node. on the Attachment Types data form. To check visually that you have the orientation you expect. The two ends of a line are treated in essentially the same way. In particular the numbering of parts of a Line is always done starting at End A. and the bottom end anchored to the seabed. The attachment is then attached to the nearest node to that arc length. but some aspects of the line are dependent on which end is which.w System Modelling: Data and Results. The Touchdown results point is determined by starting at the Top End and then moving towards the Bottom End until the first node in contact with the seabed is found. Attachment Types are similar to Line Types – they are simply named sets of attachment properties. select Draw Node Axes on the View menu. and these axes allow you to see how the line is behaving torsionally. If the seabed is not horizontal then the mathematics is slightly more complicated as it has to take into account the slope of the seabed.g. when the end segment is aligned with Ez then no bending moment is applied by the joint. at the end. it is connected into an end fitting that is rigidly attached to that object and you specify the orientation of this connection by giving its Azimuth. and whether the end is released during the simulation. however. Declination and Gamma define the end fitting orientation by specifying the directions of the axes (Ex.e. And if the line has torsion included and the joint twisting stiffness is non-zero. The connection at a line end is modelled as a ball-joint with this orientation being the preferred no-moment orientation.Y) position. See Line End Orientation. The node sits just in contact with the seabed and the above problems are removed. These angles define the end fitting orientation relative to the object. Or you can view and edit the connection data for all the lines together on the All Objects Data Form. Because it is anchored this force cannot displace the end node. Connect to Object The line spans from End A to End B and each end may be connected to another object in the model. 315 . The Ex and Ey directions are used for reporting results (e. The direction of Ez is defined by specifying its Azimuth and Declination angles. where E is the end fitting origin – the point to which the line end is connected. If the end is Fixed this defines the coordinates of that point relative to global axes. You can view and edit an individual line's connection data on the line's data form.w System Modelling: Data and Results. a line end anchored to a flat horizontal seabed. End Orientation When a line is connected to an object. the position. for simplicity. Ez is the end fitting axial direction. you set Height above seabed to 0 then the end node centreline will have a z coordinate of ½D. the recommendation of setting Height above seabed to 0 remains valid. such as a buoy or vessel. relative to the seabed. so Ez is sometimes called the no-moment direction. vessels and 6D Buoys) the fitting rotates with the object. where D is the contact diameter. Declination and Gamma angles. or else Fixed. i. If the end is connected to another object this defines the coordinates of the connection point relative to that other object's local axes. This value is coupled to the Object Relative z coordinate – changing either one results in the other being changed to match. Ez is into the line at End A. which is a rotation about Ez. Note that Ez must be specified using the End A to End B convention. If the end is Free then this defines the coordinates of the estimated equilibrium position of the line end. plus the Zcoordinate relative to the seabed level at that (X. but out of the line at End B. However. The net result of this is that the end node is 'buried' in the seabed and receives a large seabed reaction force. The Object Relative z coordinate specifies the position of the centreline.g. Ez) of its frame of reference. but the adjacent node is free to move and it will try to take up a position sitting on top of the seabed. Azimuth. Ey. Object Relative Position Defines the position of the centre of the node at the line end. For Fixed or Anchored ends the end orientation is defined relative to global axes. Height above seabed This data item is only available for Anchored connections and specifies the vertical height above the seabed of the pipe underside. the orientation of the line end that gives rise to no moment from any rotational stiffness of the connection. This in turn will lead to unrealistic values of curvature. bend moment etc. so for objects that rotate (e. If.e. Anchored or left Free. then Ex and Ey also define the line end orientation at which no torsional moment is applied by the joint. Lines Connections The line end connection data specifies whether the line ends are connected to other objects. the 2 components of shear force). For Free ends the end orientation is not used. i. To understand how this data item should be used consider. If it is set to 0 then the end node will penetrate the seabed by a distance of ½D. If the end is Anchored this defines the X and Y coordinates of the anchor relative to global axes. Ex and Ey are perpendicular to Ez and they are defined by specifying the Gamma angle. relative to global axes. angle and stiffness of the connection. finite: can rotate but with resistance. The x bending and y bending behaviour can either be linear or non-linear.w System Modelling: Data and Results. and ω is the angular velocity of the end fitting relative to the angular velocity of the line. The restoring moments applied by the joint depend on the deflection angle. for example due to thermal expansion or contraction. shear and bend moment components. respectively. If no release is wanted then set this item to "~". Section Length The unstretched length of the section.g.) that depend on the local axes directions. 316 . The Twisting Stiffness value is only relevant if torsion is included for the line.e. If the line type is profiled then the section length is determined by the profile data and so cannot be edited here. stress components. meaning 'same as x-value'. OrcaFlex uses linear interpolation for angles between those specified in the table. as follows: For a simple linear behaviour. Connection Damping If torsion is included then connection damping can be specified. e. The end orientation is therefore the orientation of the line that corresponds to zero moment being applied by the joint. in this case the line must include torsion. A flex joint can be modelled by setting the stiffness values to be non-zero and finite. For the twisting stiffness this variation is always modelled as linear so the twisting stiffness you specify should be the slope of the linear angle-moment curve. Lines If all of the end connection stiffness values are zero. Non-zero. The bending and twisting connection stiffnesses can be set to: Zero: free to rotate with no resistance. For an isotropic ball-joint the two values must be equal. y and z-directions that are used to define results (e. Length changes due to external and internal pressure. Infinity: a rigid connection. meaning "not applicable". For a non-linear behaviour. The damping moment is given by -Cω where C is the specified value of connection damping. The restoring bend moment must be zero at zero angle. then the end orientation angles have no effect on the line behaviour. which is the difference between the end fitting orientation and the orientation of the line.g. Connection Stiffness The connection at a line end is modelled as a joint with the specified rotational stiffness. this can conveniently be specified by setting the y-bending value to '~'. to model a ball-joint that is completely free to rotate. This is the unstressed length (i. the sections being defined in sequence from End A to End B. Warning: To define a rigid connection use Infinity rather than a large stiffness value. etc. specify the bending stiffness to be the constant slope of the curve of restoring moment against deflection angle. A non-isotropic ball-joint can be modelled by giving different x and y bending values. Line Type This determines the properties of the section. are calculated and allowed for by OrcaFlex. since the latter can lead to numerical instability. It specifies the rotational stiffness about the end Ez direction. Structure Each line can be made up of up a number of sections with different properties. Expansion Factor The expansion factor allows you to model time-varying changes in unstretched length. and linear extrapolation for angles beyond those specified in the table. measured in deg/s. use variable data to specify a table of restoring moment against deflection angle. The angles then only serve to define the local x. The connection stiffness is the slope of the curve of restoring moment against deflection angle. Variable: non-linear (for bending connection stiffness only). and allowing for the Poisson ratio effect. The x bending and y bending values specify the connection bending behaviour for rotation about the end Ex and Ey directions. zero wall tension) at atmospheric pressure inside and out. Release at Start of Stage If desired each line end can be disconnected at the start of a given stage of the simulation. If it is set to No then the section will be ignored for clashing purposes. Each attachment can either be of a specified Attachment Type or else be a clone of a specified 6D Buoy. Alternatively the expansion factor can be a variable data source which specifies a table of expansion factor against simulation time. Otherwise. Attachments A number of attachments may be added to each line. Cumulative Length. Cumulative Segments These columns report the cumulative length and cumulative number of segments counted from the first section. For lines which are straight when unstressed then pre-bend should be specified to be zero – which is the default setting. The 6D Buoy from which the attachment is cloned cannot be deleted. Other positive values can be used. Notes: Line clashing is not modelled during statics. for example. Note: When pre-bend is modelled curvature and bend radius results are reported relative to the pre-bent curvature. Warning: Pre-bend breaks the assumptions of the stress results and fatigue analysis. Pre-bend is provided for modelling lines which are not straight when unstressed. a Stiffener Type or an existing 6D Buoy. a Drag Chain Type. spool pieces. Clash checking is quite time-consuming. It has no effect on mass. The pre-bend is defined for each section by specifying the pre-bent curvature (in radians per unit length) of the section. However. The values are for reporting purposes only and cannot be edited. in which case the unstretched length remains constant throughout the simulation. Note: Expansion factor is only used in the calculation of strain. This allows you to alter section lengths without altering segment length. Clash Check Clash modelling is included when this data item is set to Yes. without first deleting all the attachments that are clones of it. Number of Segments These data items determine the segmentation of the section. Attachment Type Can be a Clump Type. Pre-bend Pre-bend is only available when torsion is modelled.g.w System Modelling: Data and Results. This is especially useful to check that stress joint and bend stiffener data has been correctly input. drag. Lines A value of '~' means that no expansion factor is applied – this is equivalent to a value of 1. so you should only set this item to Yes for those sections for which you need clash modelling to be included. If you specify a 6D Buoy as the attachment type then the attachment is a clone of that 6D Buoy and changing the properties of the 6D Buoy also changes the properties of the attachment. first create the first buoy separately from the line and then connect it to the 317 . e. Note: It is usually preferable to determine segmentation by specifying Target Segment Length. buoyancy. Target Segment Length. If Target Segment Length is set to ~ then the number of segments in the section is set by Number of Segments. added mass etc. the segmentation is chosen based on Target Segment Length. See Line Clashing. The Number of Segments is not editable and reports the actual number of segments used which is given by the formula: Number of Segments = Round(Section Length / Target Segment Length) where Round is the function that rounds a floating point value to the nearest integer. To attach 20 identical buoys to a line. Profile Graph The profile graph plots the inner and outer radii of the line as they vary with arc length. to simplify data preparation and interpretation of results we recommend that you arrange the line's local axes such that the pre-bend is entirely in either the local x or local y direction. Pre-bend can be specified in both the line local x and y directions. 6D Buoy attachments are useful when you want a number of identical 6D Buoys attached to a line. The pre-bent curvature is the curvature of the pipe in its unstressed state. It specifies a multiplicative factor which is applied to the unstretched length when calculating axial strain which in turn is used to calculate effective tension (see Line Theory: Calculation Stages). a Flex Joint Type. specify 19 attachments and set their attachment type to be the first 6D Buoy. Note: If the attachment is a clump then it is also offset vertically from the node by the offset distance specified in the clump type data. on the line data form. y and z coordinates specify the position of the attachment relative to the line. For Stiffeners the z coordinate specifies the arc length of the stiffener connection point. Drag Chains. This first buoy acts as the master from which all the other attachment buoys are cloned. the static pressure head is calculated using the mean contents density in the line. Position The x. The lateral components of contents inertia. These attachments are connected at the node nearest to this arc length. y. For 6D Buoy attachments the z coordinate specifies the arc length at which the buoy should be connected to the line. The free-flooding option results in the line being filled with sea water. See 6D Buoy Initial Position for more details. Orientation For 6D Buoy attachments only. Name For 6D Buoy and Drag Chain attachments only.w System Modelling: Data and Results. This is the name of the attached object and is used to select results for that object. Beware that the sign convention for this offset varies depending on whether the clump is net buoyant (positive offset is upwards) or heavy (positive offset is downwards). For Clumps. as outlined below: If uniform is selected then the entire line is assumed to be filled with contents of a uniform density. The buoy will be connected with an offset (relative to that node's axes) that is given by (x. But the contents axial translational inertia would be excluded from an analysis of a line with free-flooding contents. they are relative to atmospheric pressure and so can be as low as -1 atmosphere (-101. up to the instantaneous water surface. Rotation 1. for example a drilling riser in emergency disconnect mode. The internal pressure at other levels is calculated allowing for the static pressure head due to differences in Z level. 318 . The z coordinate specifies the arc length at which the attachment is connected and this arc length may be measured relative to either End A or End B as specified by the user. The internal pressure at this Z level is assumed to remain constant throughout the simulation.3 kPa). Contents Pressure and Reference Z level The contents pressure specifies the internal pressure in the line at a specified fixed reference Z level (specified relative to global axes). The buoy will be connected to the nearest node to that arc length. Note: 6D Buoy attachments can only be used when the Line includes torsion. since the contents are assumed to not have to follow any twisting motion of the line. The reference Z level can be set to '~' and this is taken to mean the Z level of the Top End of the line in the reset state. Contents Contents Method Three methods of modelling contents are available. Lines line by setting its connection data item on the buoy data form. are always included. Rotation 2 and Rotation 3 determine the Initial Attitude of the attached buoy. All pressures in OrcaFlex are gauge pressures. That is. Typically the contents axial translational inertia should be included for a line with capped ends. The contents flow velocity can also vary with time. The slug flow method allows for spatial and temporal variation of contents. 0). including its axial motion. See Line Pressure Effects for details of contents pressure modelling. Flex Joints and Stiffeners the x and y coordinates must be zero and the z coordinate is the arc length. Include axial contents inertia This data item allows the axial component of translational inertia due to contents to be omitted from the analysis. For slug flow. for example. both translational and rotational. since then the contents must follow all translational motion of the line. The axial component of rotational inertia of the contents are always excluded. Then. not absolute pressures. A value of zero can be used to specify spatial contents variation with no temporal variation. If the flow velocity is zero then the previous definition is meaningless. Applied Moment The components of the applied loads. Load Type The loads are applied either with respect to global axes. the contents pattern. The z coordinate specifies the arc length at which the load is applied. Flow Rate The rate of flow of mass through the line. Lines Uniform contents data Contents Density Each section of the line is assumed to be full of contents of this density and the mass of the section is increased accordingly. Simple repeating patterns of slugs can easily be modelled using a single row in the table. Therefore. Applied Loads Applied loads can be specified at multiple points along the line. as specified by the user. weight and centrifugal and Coriolis forces. Each row of the table allows you to define a number or group of identical slugs specified by their density and length together with the distance between slugs. if you wish to model a constant flow rate. Slug flow contents pattern The spatial variation of contents density. for example. is specified in a table. i. Position The x. This pattern of contents can also progress along the line over time. For irregular patterns of slug you can model each slug as a single row in the table. The program accounts for the resulting variations of mass.e. Note: There is no need to ramp flow velocity at the beginning of dynamics – in fact it is better to include the fluid flow in the static calculation because this removes undesirable transients during the dynamic analysis. In addition you specify a reference point. In this case we adopt the convention that the group of slugs covers arc lengths (measured from End A) greater than the reference point. or can vary as simulation time varies. Slug flow data The slug flow data allows you to specify variation of contents density along the arc length of the line. Applied Force. Positive values mean flow from End A towards End B and vice versa. Density between slugs The contents density for sections of the line that fall in between slugs. Positive values mean flow from End A towards End B and vice versa. volume flow rate and flow velocity use the following simple formulae: Volume flow rate = Mass flow rate / ρ Flow velocity = Volume flow rate / A where ρ is the contents density and A is the internal cross sectional area. or with respect to local node axes. When torsion is not included. To convert between mass flow rate. This arc length may be measured relative to either End A or End B. and the simulation time at which the first slug in the group reaches that reference point. Flow velocity The velocity at which the contents pattern flows along the line. the x and y coordinates must be zero and the load is applied at the node nearest to the specified arc length. the flow of contents out of a drilling riser in emergency disconnect mode. A variable flow velocity can be used to model. vary with simulation time or be given by an external function. For example. These components can be constant. an arc length which can be relative to either end of the line. 319 . if the flow velocity is zero and you have a single slug with length L and reference point at End A then the slug will stretch between arc lengths 0 and L. Range graphs of contents density can be used to confirm that your data corresponds to your desired pattern of slugs. as specified. If it is non-zero then it is used to calculate the centrifugal and Coriolis forces due to flow of fluid in the line. you should set the flow velocity to be this constant value. This value can be constant.w System Modelling: Data and Results. y and z coordinates specify the position of the attachment relative to the line. Statics The line static calculation is performed in 2 steps as described in Statics of Lines. but not allowing for bend stiffness or interaction with shapes. we therefore need to make some assumptions about how the line was originally laid and friction is then assumed to act towards this position. Here the user specifies the starting position of the line as a sequence of straight line or curved sections on the seabed. If the Step 1 Statics Method is Prescribed. When Statics Method is not Prescribed. bend stiffness and interaction with shapes are included. See Spline Data and Spline Statics. The normal setting is Catenary. and it uses the Step 1 Statics Method to obtain this. in which case the static analysis finds the equilibrium catenary position of the line. In this situation you could exclude all other lines from statics (this is easiest from the All Objects Data Form). It then defines the position in which the line is assumed to have been originally laid. Full statics needs a starting shape for the line. For pull-in analysis the Prescribed option has been provided. with the specified As Laid Tension. the 'originally laid' position is defined by specifying the Lay Azimuth and As Laid Tension values. a unique static position for the line. leading away from the Bottom End position and with the specified As Laid Tension. In order to model the response to applied moments. such as those with slack or neutrally buoyant lines. it then finds the equilibrium position from there. The line was originally laid. in which case the line is instead set to a 3D spline curve based on spline control points specified by the user. See Catenary Statics. No calculation is performed. since the position it adopts depends on how it was originally laid and its history since then. Lines When torsion is not included. Included in Statics This switch allows you to exclude certain lines from the statics calculation. The Quick method leaves the line in the rough catenary shape used in the Reset state. See Quick Statics. Step 2 Statics Method (Full Statics) This can be either None or Full Statics. The Full Statics calculation finds a full equilibrium position for the model. 2. Unlike the Step 1 Catenary method. Note: Results are not available for such lines and dynamics is disabled if you have any lines which are excluded from statics. and so any applied moments are ignored in this scenario. in general. 320 . See User Specified Starting Shape and User Specified Statics. buoyancy. can be troublesome. the line cannot respond to applied moments. This would allow you to experiment with different statics convergence parameters for the problematic line without having to wait for all the other lines to converge each time you tried a new set of convergence parameters. Otherwise. See Full Statics. For such lines you can instead specify Spline. The Catenary solution has some limitations and some systems. starting with the Bottom End at its specified position (or at the point on the seabed directly below. Include Friction Friction can be included in the static analysis only if the Step 1 Statics Method is Catenary or if Full Statics is used for the Step 2 Statics Method. allowing for weight. The User Specified option allows you to specify the position for each node on the line. it is assumed that: 1. In order to define a unique solution. See Prescribed Starting Shape. The line was then laid in the Lay Azimuth direction. if the Bottom End is not on the seabed). then this 'originally laid' position is assumed to be the position defined by the Prescribed track. Lay Azimuth This value is only used when seabed friction is included in the static analysis and the Step 1 Statics Method is not Prescribed. Lines which are excluded from statics have no influence on other objects in the model. and friction is then assumed to act towards this position. Prescribed or User Specified. drag. the nodes are merely placed at the specified positions. Step 1 Statics Method This can be either Catenary. This is mainly useful when building a model and a particular line is not converging. Quick. With seabed friction present there is not. Spline. torsion must be included.w System Modelling: Data and Results. For more details of the Statics Calculation see Statics Analysis. You should therefore set the Step 1 Statics Method to give a reasonable starting shape. If None is selected then the position obtained by the Step 1 Statics Method is used. based on their current positions. Increasing this value can sometimes help. If this happens. but the calculation will then usually require more iterations. Catenary Convergence If the Catenary statics method is chosen. The catenary calculation cannot handle lines with slack segments – try increasing the number of segments in the relevant section of the line. either deliberately or by mistake. The minimum damping should not be set to less than 1. The catenary calculation has problems with floating lines – you may need to use the Spline statics method instead.0. The Top End was then moved slowly from that original position to its specified position. Change These parameters control the maximum size of the change. Mag. Max Iterations The maximum number of iterations that OrcaFlex will make before treating the calculation as having failed to converge. as outlined below. Convergence can sometimes be achieved by increasing this parameter to a value greater than 1 – try values in the range 1. first check your data for errors and check for the following common causes of convergence failure: Does the solution have a slack segment? This can happen in lines that touch down on the seabed almost at right angles or in lines that hang in a very narrow U shape. of Std. Full Statics Convergence The numerical method used to solve for the static position is an iterative process in which the program tries to converge on the solution in a series of steps. For example. 321 . if we have a line top at X=0. The line was laid following the profile of the seabed. This button sets the Lay Azimuth value to be the direction from the Bottom End towards the Top End. OrcaFlex uses this to determine the as-laid node positions. Does the line have a surface-piercing buoyant clump attached? If the clump is short then the catenary calculation is more difficult. in the estimated solution. The Line Setup Wizard also uses the Lay Azimuth direction. For further information contact Orcina.w System Modelling: Data and Results. However sometimes the calculation can fail to converge. Is the line buoyant. Lines 3. is the Lay Azimuth value specified correctly? It is the azimuth direction leading away from End B and it is easy to get it wrong by 180°. before the calculation is treated as having converged. then this value is used as described in the Lay Azimuth section above. As Laid Tension This data item specifies the effective tension with which the line was originally laid. we would expect trouble for a Lay Direction of 90°. we would expect the statics convergence routine to have increasing difficulty in finding a solution as the angle between the Lay Azimuth direction and the vertical plane through the line ends increases. This process is controlled by a number of convergence parameters. This calculation is controlled by a number of convergence parameters which can normally be left at their default values. there is a button on the form marked Set Lay Azimuth. If the Step 1 Statics Method is not Prescribed. If the calculation still fails to converge. which are used as the friction target positions towards which friction acts in the static analysis. found on the Line data form. and anchor at X=100. this is allowed in a single step. Notes: Whilst the program will accept any Lay Azimuth. then the statics friction target positions are laid out along the prescribed shape with a strain determined by the axial stiffness and this As Laid Effective Tension value. Error. To help set this data item. then an iterative catenary calculation is used to determine the static position of the line. Tolerance The non-dimensional accuracy to which the calculation is done. of Std. Y=0. This value is therefore only used if friction is included in statics. The remaining parameters should not normally be changed. then it is sometimes possible to obtain convergence by changing one or more of the convergence parameters. Increasing the tolerance increases the chances of convergence but reduces the accuracy. Reducing these values can sometimes help. 4. For lines that touch down on the seabed. If the Step 1 Statics Method is set to Prescribed starting shape. Min Damping The minimum damping factor to be used in the calculation. Mag.1 to 2. Y=0. For a line with a Fixed end. of Std. Error. but it may be necessary in order to achieve convergence! Spline Starting Shape The following data are only used if the Spline statics method is specified. since the computer has limited numerical precision. Min Damping. Tolerance This controls the accuracy of the solution. of Std. We recommend using the default value. contact diameter. say values in the range 1 to 10. The first and last control points are automatically placed at the line ends A and B respectively and OrcaFlex generates a smooth curve between the first and last control points and passing near to the intermediate control points.g. of Std. For cases that appear to make the convergence unstable (e. If a higher order is chosen. Order This sets the smoothness of the spline shape. but will take more iterations. reducing) the step taken at each stage. giving very bad line positions on the screen) try increasing the Min Damping factor to a value greater than 1. For some difficult cases simply increasing this limit may be enough. When torsion is included the static equilibrium position must also satisfy the condition that the largest out of balance moment component on any node is less than Tolerance * total weight in air * ODmax where ODmax is the maximum diameter. You can also try increasing the Max Damping factor. Mag. Change These parameters are only available when the Mag of Std. stress diameter or normal drag diameter over the entire line. Note: Convergence will be slower with larger damping values so you should use the smallest values that result in statics converging. Error / Change may succeed. Line Search. but the user can set the minimum damping and maximum damping factors that are used. Max Iterations The calculation is abandoned if convergence has not been achieved after this number of steps. Lines Convergence Control Method Either Line Search or Mag. of Std. An error is reported if this process fails. but if this fails then the alternative Mag. Normally the default values will suffice but for difficult cases the default values can be altered. Reducing the Tolerance value will give a more accurate static equilibrium position.e. The program includes an automatic damping system that chooses a suitable damping factor for each iteration.w System Modelling: Data and Results. The line is stretched to the specified As Laid Tension and laid out following the spline curve starting at End A and working towards End B. Max Damping For some cases it is necessary to control the convergence process by damping down (i. Anchor or attached to some object the curve is automatically expanded or contracted to allow the end to lie at the specified end position. These intermediate control points may be adjusted to 'pull' the curve into the desired shape. used to calculate the Jacobian matrix for the problem. For a line with a Free end the line is laid out along the curve until End B is reached. a smoother curve results. Mag. Delta should always be less than the tolerance specified. Error / Change convergence control method is selected. Control Points The line shape is specified by a number of Control Points. Delta This is a perturbation size. The first and last control points correspond to line ends A and B respectively. 322 . generally order 3 is reasonable. Doing so is likely to slow down the convergence. The program accepts the line position as a static equilibrium position if the largest out of balance force component on any node is less than Tolerance * total weight in air. say to values in the range 10 to 100. OrcaFlex may not be able to achieve the Tolerance specified if it is too small. The order cannot exceed the number of spline points. Error / Change. Note: This parameter is only used when torsion is included. For some cases it may be necessary to reduce one or both of these values from their defaults. If the length around the curve is not equal to the stretched line length then the end will either fall short of the end Estimated Position or lie beyond it (along the continuation of the curve along its 'final' direction). Section X and Y The global X and Y coordinates of the end of this track section.e. Section Turn The amount by which the track azimuth increases over this section. and the X and Y coordinates for subsequent sections. not an editable data item. By editing the X and Y coordinates of the ends of a track section on the line data form. The individual data items (see Figure: Plan View of Example Track) are as follows: End A Azimuth The initial direction of the track. on the line data form. You can switch between the options of drawing the track in the chosen pen and not drawing it at all. or else by dragging the end point on a 3D view.w System Modelling: Data and Results. OrcaFlex then creates the (unique) circular arc (or straight line) that is a smooth continuation of the previous section and passes through the new (X. when viewed from above.Y) point. 323 . Section Arc Length The total arc length to the end of the section. and is hence always shown in grey. and a negative value denotes a turn to the right. Notes: This is a reported value. and is hence always shown in grey. and all subsequent sections. For straight sections (i. not an editable data item. If you edit X or Y then OrcaFlex fits a circular arc (starting at the previous section's end point) through the new end point and the Section Length and Section Turn are automatically updated to match this new arc. and is hence always shown in grey. and is hence always shown in grey. Section Azimuth The azimuth direction at the end of the section. This is a reported value. A positive value denotes a turn to the left. Section Z The global Z coordinate of the section end point on the seabed. in degrees. By dragging the end points of the track sections on a 3D view using the mouse. are then automatically adjusted to match. if Section Turn = 0) the radius is reported as Infinity. This is a reported value. It can be found in the Prescribed Starting Shape page on the line data form and can be edited in several ways: By editing the Length and Turn values of a track section on the line data form. not an editable data item. With a profiled or sloping seabed the actual track on the seabed will have a slightly different radius of curvature – see Laying out the Line. Track Pen This controls how the track is drawn. The Length and Turn values for this section. The radius equals (180L)/(πT). A value of zero can be entered to specify a straight track section. Section Length The length of the circular arc (or straight line if Section Turn = 0). The track and the track section end points are drawn on the 3D views. where L is the section length and T is the absolute value of section turn. not an editable data item. Track Sections The number of sections used to define the track. and the X and Y coordinates of the end of this section. Dragging a track section end point is equivalent to editing its X and Y values. are automatically adjusted to match. You can either edit these X and Y coordinates explicitly. This is a reported value. Lines Prescribed Starting Shape These data are only used if the Prescribed method is used for Step 1 statics. Section Radius The radius of curvature of the circular arc. OrcaFlex then creates an arc of the specified Length and Turn. as described above. reaching the seabed at the end of the first track section. Fluid Loads Drag Formulation A number of authors have proposed formulae to model how the drag force on a line varies with the incidence angle. But with a sloping seabed the vertical projection does not preserve distances and this causes some effects that users should note: The section lengths and arc lengths that appear in the prescribed starting shape data table are lengths in the horizontal plane. User Specified Starting Shape Starting Shape The User Specified Starting Shape statics method places each node at the position specified in this table. you need to model the catenary as two lines. 324 .e. Note: Wake modelling does not include the wake effect of one part of a line on another part of the same line – it only includes wake effects on other lines. The size of this discrepancy reduces as more segments are used. Pode or Eames formulations. Sloping and profiled seabeds The track on the seabed is obtained by projecting the specified circular arcs or straight sections vertically down onto the seabed. OrcaFlex therefore only attempts to model the steady wake effects. For details of the formulations see the Line Theory section. but also generates its own wake that further downstream sections might react to). To model the wake effect of one part of a catenary on another part beyond the sag bend. i.w System Modelling: Data and Results. then the rest of the line is laid out in a straight line in the direction of the end of the track. See the Wake Models button on the Line data form. by either being included as a wake generator (an upstream section) or as a section that reacts to wake (a downstream section). The actual arc lengths can be obtained by running the static analysis and looking at the Full Results table for the line. Because the line is modelled as a series of straight segments. before projection down onto the seabed. How Wake Effects Are Modelled The wake models are steady state models of wake effects. allowing for any As Laid Tension specified by the user on the line data form. OrcaFlex offers the choice of the Standard. All of these use drag coefficients that are specified on the Line Types data form. Also OrcaFlex does not model the effect that wake takes time to convect downstream. With a horizontal seabed this vertical projection has no effect on the shape of the track. i. joined with a dummy 6D Buoy at the sag bend. The program then lays the line out along the track. With a sloping seabed the true section and arc lengths on the seabed will differ. the difference depending on the slope of the seabed. For details see the Line Wake Interference Data on the Drag & Wake page of the Line Data Form. If torsion is modelled then node orientations can also be specified. which are then projected vertically onto the seabed to define the track itself. You must then specify which line sections to include in wake modelling. The actual radii of curvature can be obtained by running the static analysis and looking at the Full Results table for the line. when the line is laid out along a curved track it will repeatedly 'cut corners' and so the length of line laid along a given curved track section will be slightly shorter than the length of that section. before projection down onto the seabed. or both (a downstream section that reacts to wake generated further upstream. If the end of the last track section is reached before all the line has been laid out. The section radius reported in the prescribed starting shape data table is that of the circular arc in the horizontal plane. If End A is above the seabed then the height above the seabed varies linearly between End A and the first track section point. so again the actual radius of curvature will differ. When the circular arc is projected down onto a sloping seabed the resulting track section is slightly elliptical rather than circular. Line Wake Interference To include wake interference modelling you must first define one or more wake interference models. Lines Laying out the Line The track data defines a sequence of straight lines and circular arcs in the horizontal plane.e. Disturbance Vessel Determines whether a line section will experience sea state disturbance generated by a particular vessel. by specifying which line sections generate modelled wake (the upstream sections) and which line sections react to modelled wake (the downstream sections). The strength of a given node's wake decays with distance downstream and also with distance in the transverse direction. And the wake effect will be based on the undisturbed steady relative flow velocity. as specified by the wake model. strongest at that downstream position) from any upstream nodes (on other lines) that generate modelled wake. The following two data items specify which sections generate and/or react to wake: Wake Generated This can be set to one of the defined wake models. However the wake effects of such a section will only affect other lines in the model. for example. in which case OrcaFlex will not model wake generated by that line section. The Blevins model is an analytic model that models the both the drag reduction and the wake lift force that tends to draw the downstream object into the centre of the wake. or of any changes in upstream cylinder velocity during a simulation.e. as if the other upstream nodes were absent. 325 . So if you are modelling riser arrays.w System Modelling: Data and Results.e. not the line generating the wake. so that the strongest wake selected comes from the upstream node that is axially closest to the downstream node. i. in which case OrcaFlex will model wake generated by that line section acting as an upstream line. then the wake effects at any given point are modelled as if they came from the upstream wake-generating node that gives largest wake effect in isolation. Or it can be set to None. Reacts to Wake If Reacts to Wake is turned on then each node in the section will act as a downstream cylinder in the wake modelling. due to modelled wake from upstream nodes in sections of other lines that have Wake Generated set to a wake model. but does not model the wake lift effect. More details are given in the paper by Wu et al. then OrcaFlex chooses to apply the wake effects of the upstream node that gives the strongest wake effect at that downstream position when the wake effects from other upstream nodes (which give weaker wake effects at that point) are ignored. generate modelled wake that further downstream line sections can react to. The User Specified model allows you to model both the drag reduction and wake lift effect using your own data. Those nodes will then be subject to the strongest wake effects (i. so the wake effects of this wake-generating section will not take into account any velocity reduction due to it in turn being in the wake of another wakegenerating section further upstream. Note: A line section is allowed to be both a downstream section.[any steady starting velocity specified for the model] The wake effects therefore do not include any effects of wave motion. See the Wake Models section for details. i. Three types of wake model are available.e. This is done on the Drag & Wake page of the line data form. so both fluid motion and upstream cylinder motion can contribute to the wake. Note: OrcaFlex does not model combined wake effects. so to avoid slowing simulations unnecessarily OrcaFlex enables you to only include wake modelling for sections of line where you think wake effects might be significant. Lines Wake is generated when there is fluid velocity relative to the upstream cylinder. So to summarise. If a given downstream node is in the modelled wake of more than one upstream node. by specifying the drag and wake lift coefficients as a function of the position of the downstream object relative to the wake of the upstream object. The Huse model is an analytic wake model that models the velocity reduction and hence drag reduction on the downstream object.e. and at the same time also act as an upstream section. The fluid forces applied to sections that react to modelled wake will include the strongest wake effect from the sections that generate modelled wake. Sections with Reacts to Wake turned off will ignore any modelled wake generated by upstream sections. Therefore the velocity OrcaFlex uses as the input to the wake model is the steady relative velocity Vs given by Vs = [undisturbed current velocity vector at upstream cylinder centre] . Reacts to Wake is turned on. the wake modelling will include the strongest wake effects on downstream sections that have Reacts to Wake turned on. i. But in addition OrcaFlex also makes the wake strength decay in the axial direction of the upstream line. Line Wake Interference Data Wake modelling requires significant computation. as described below. Changing these model parameters from their default values will give a variant of the Blevins model. Du. a2. The wake frame x-axis is in the direction of the steady relative fluid velocity vector Vs. Wake frame of reference The wake modelling is done relative to a wake frame of reference that is based on the steady relative fluid velocity vector Vs at the upstream cylinder. Vu0 is the undisturbed fluid velocity at the upstream cylinder centre.and y-directions then the wake modelling uses the mean of the two values. ignoring any wake effects.e. Lines Wake Models The Wake Model Data form enables you to define one or more models of wake interference.y) is the undisturbed fluid velocity vector at position (x. See the Appendix of Blevins OMAE 2005 paper for the theory of the model.k2Vu0[CduDu/xs]½exp[-k3(y/b)2] where xs = x + 4Du/Cdu b = k1[CduDuxs]½ and the other terms are defined above.y). and subscript '0' denotes undisturbed. In the Huse model the wake fluid flow velocity Vd(x.y) in the wake is given by: Vd(x.z. It is therefore normal to the plane formed by Vs and the cylinder axial direction. for example if you want to use different wake models to model the wake generation by different lines. but does not give any wake lift force. And each model can be one of three types: Huse model. lower case subscripts 'u' and 'd' denote upstream and downstream. allowing for wake effects. Dd and CDu0. a3 that are user-editable. The wake frame y-axis is the direction that completes the orthogonal right-hand triad of wake axes x. so you can define wake models and then decide later which (if any) to use to model wake generation.w System Modelling: Data and Results. and hence drag reduction.y) relative to the upstream cylinder wake. The wake model theory below uses the following key variables. If different drag coefficients have been specified for the line x. The model has 3 non-dimensional model parameters a1. Huse Model This is an analytic model proposed by Huse (1993). You can define more than one wake model.y.y) at a given position (x. They should normally be left as the default values. since these give the original Huse model.y) is the disturbed fluid velocity vector at downstream position (x. (Note that the parameter k 3 is mis-printed in Huse.639 and was corrected in a later paper to 0. and is given by: The wake frame origin is at the upstream cylinder centre.y) . CDd0 are the normal drag diameter and undisturbed drag coefficient of the upstream and downstream cylinders.y) position of the downstream cylinder centre relative to the wake frame of reference of the upstream cylinder.693. The wake interference model specified determines how the flow velocity. i. Blevins model The Blevins model is an analytic model that models velocity and drag reduction. k1.y) = Vd0(x. 326 . Vd0(x. respectively. They should normally be left as the default values. as specified on the line type data form.) Changing these model parameters from their default values will give a variant of the Huse model. Upper case subscript 'D' denotes drag. Note that the wake modelling does not allow for any non-isotropic aspects of the drag coefficients. k2 and k3 are user-editable non-dimensional model parameters. Blevins model or User-Specified model. since these are the values given by Blevins. It is therefore the direction normal to Vs and in the plane formed by the Vs and the cylinder axial direction. Vd(x. Wake Model Data Each wake model is given a user-specified Name. The +ve wake z-direction is towards end B of the upstream line. and also models the wake lift force that tends to draw the downstream object into the centre of the wake. wake drag reduction and wake lift force on a downstream cylinder varies as a function of the (x. It models the wake velocity reduction. A wake model that isn't used by any line in the model will be ignored. The wake frame z-direction is the direction obtained by projecting the upstream cylinder axial direction normal to Vs. 1993 as 0. If this option is unchecked then no simulation results are available for this Line. Arc length axis. and indeed the Blevins model can give flow reversal just behind the upstream cylinder. as follows. Other results variables which have not been logged are then derived when the results are requested. Note: Data reflection will not in general give perfectly symmetric response characteristics.e. since wake lift effects are normally towards the centre line of the wake. OrcaFlex will then automatically reflect all your data points that are not on the wake centre line. and wake lift effects anti-symmetric. and will then interpolate over that new specified+reflected data set. In this case you must only specify table rows for one half of the wake plane. which now covers both sides of the wake centre line. The Coefficient Factor columns of the table define the wake effects at the given (L/D u. as specified on the line type data form. where Du is the normal drag diameter of the upstream cylinder.w System Modelling: Data and Results. by specifying drag and lift coefficient factors.more closely spaced data points will give closer to perfect symmetry. not the drag and lift coefficients themselves. However the drag factors must not be greater than 1. or for T/Du ≤ 0 only. The lift coefficient factors are signed scaling factors that are applied to the Reference Wake Lift Coefficient CLd0. in non-dimensional form. This can happen. However any lack of symmetry will be proportional to the spacing of the points you specify in the data . Normally the axes on an OrcaFlex graph display increasing values to the right (for a horizontal axis) or upwards (for a vertical axis). 327 . only logging a minimal set of variables to the simulation file. Lines User Specified model This option allows you to define a model (of both wake drag reduction and wake lift effect) by specifying drag and lift coefficient factors as a function of the position of the downstream object relative to the wake of the upstream object. The Position columns of the table define. and that triangulation might not be symmetric either side of the wake centre line. The Arc length axis setting allows you to control whether the arc length axis is horizontal or vertical. OrcaFlex stores simulation results in an efficient way. Usually this means that simulation files are a reasonable size and we recommend that this value is checked. in which case they represent flow reversal at that position in the wake. OrcaFlex uses linear triangular interpolation to obtain the drag and lift coefficient factors to use for wake frame positions between those specified in the table. which is specified on the wake models data form. either side of the wake centre line. A +ve lift coefficient factor means a lift force in the +ve wake frame y-direction. This is because the interpolation involves triangulation of the data. so flow enhancement cannot be modelled. So to avoid the need to specify in the table both +ve and -ve values of T/Du you can tell OrcaFlex to Reflect Data. either for T/D u ≥ 0 only. Again this would typically be used for vertical risers to arrange that up and down on the arc length axis of the graph matched up and down in the physical system being modelled. Wake drag effects are normally symmetric. so the lift coefficient factor at a given T/Du position will normally have the opposite sign to the T/Du value. a number of downstream cylinder centre positions relative to the upstream cylinder wake frame of reference. See above for notation. This is done by specifying nondimensionalised distances L/Du (downstream) and T/Du (transverse) from the upstream cylinder centre to the downstream cylinder centre. by internally duplicating them and negating T/Du and the lift coefficient. Value axis inverted These data items allow you customise the way range graphs are displayed. T/Du) positions. The wake effects are specified by giving a table of wake drag and lift coefficient factors for the downstream cylinder. The axis inverted options allow you to reverse the axes. Results Log Results This option is checked by default and this means that simulation results at all points on the Line are available. Arc length axis inverted. i. Should you need to reduce the size of simulation files then this option can be unchecked for those lines for which you do not need results. The drag factors are scaling factors that are applied to the reference drag coefficient CDd0 of the downstream cylinder. The latter option would typically be used for vertical risers. as a function of the downstream cylinder position relative to the upstream cylinder wake. Note that these data are scaling factors. Note: The drag coefficient factors can be negative. z) can be given individual colours. End Node Shaded Drawing Determines how the two line ends are drawn for shaded graphics. 328 . VIV Drawing The VIV Drawing page is visible when a time domain VIV model is used. line style and thickness of the pens used for drawing the nodes and sections of the line. Lines Since changes to these settings are usually motivated by the physical layout of the line in question. Should you wish you can choose to disable the contact drawing. Segments There is a choice for which pen is used to draw the segments. This allows you to use different pens to distinguish sections of different line types. Alternatively. either as a hemisphere or not at all. The node axes directions are drawn optionally and can be controlled by the Draw Node Axes preference or by pressing CTRL+ALT+Y.Total line displacement. Total weight in air (excluding contents). Node axes Node axis directions (x. Contact You can define a contact pen which is used when drawing nodes and segments which are in contact with the seabed. See How Objects Are Drawn. Drawing Nodes You can define the colour. Total wet weight (including contents) Equals Total weight in air (including contents) . Properties Report The Line properties report is available from the popup menu on the data form.w System Modelling: Data and Results. in which case it will be used for all segments of that line. Summary page Total length The sum of all the section lengths. You can switch between the options of drawing the track in the chosen pen and not drawing it at all. These data items can also be set on the results form. Total displacement The weight of water displaced by the entire line's volume. The displacement of any attachments is excluded. The weight of any attachments is excluded. a free form multi-line text field which is passed to any external function used by the line object. You may either specify the pen explicitly on the Line Data form. For details see the VIV Drawing topic. Prescribed Statics Method (Track) For Lines with Prescribed Statics Method you can control how the track is drawn. Total weight in air (including contents) The force due to gravity of the entire line. elastic solids and other lines. The reported value uses the water density at the sea surface. External Functions Parameters This data item specifies the External Function Parameters. each line in an OrcaFlex model has its own copies of these settings. Spline Starting Shape For the Spline Starting Shape you can switch between the options of drawing the unscaled spline in the chosen pen and not drawing it at all. You can also choose to draw nodes as circular discs with diameter equal to the contact diameter. This allows you to use different pens to distinguish between different lines. This helps distinguish between x and y directions thus making component results easier to interpret. y. you can choose to have the segments drawn using the appropriate Line Type Pen defined on the Line Types form. The value of Tolerance is the General Data Statics Tolerance. 6. The line typical moment is defined to be [total weight in air] * [total length].) of a number of different line types. or when modelling stress joints and bend stiffeners. Properties for each section of the line. All mode shows all the line types. This table includes details of segmentation. The line types form must include all the line types referred to on all of the Lines forms. Equivalent Line The Equivalent Line category is intended for simple modelling of pipe-in-pipe and pipe-on-pipe lines.2 Line Types Data The Line Types form defines the properties of a number of named line types. since the computer has limited numerical precision. Statics moment accuracy (only reported if torsion is included) Static analysis finds an equilibrium configuration – that is a set of node positions for which the resultant force and moment on each node is zero. OrcaFlex accepts a position as a static equilibrium position if the largest out of balance load component is less than the statics accuracy. material density and pipe diameters. stiffness etc. The Line Type Wizard is available to help set up line type data to represent commonly used structures such as chains. which can then be used to specify the structure of the Lines used in the model. 329 . The Statics force accuracy equals Tolerance * [line typical force] and the Statics moment accuracy equals Tolerance * [line typical moment]. Properties for each line type used by the line: weight in air. but will take more iterations. but shows you all its properties.w System Modelling: Data and Results. structure. This allows you to build up a library of standard line types which can then be easily used when building Lines. OrcaFlex may not be able to achieve the Tolerance specified if it is too small. The program calculates combined line type properties (geometry. Homogeneous Pipe The Homogeneous Pipe category is appropriate for a pipe constructed from a single homogeneous material. We refer to the resultant force and moment as the out of balance load. displacement etc. as described above. If the line uses a P-y model then a page of detailed output is included which describes how the P-y model data has been interpreted. External Function Parameters mode shows the data used by any external functions referenced by the Line Type. hydrodynamics. Reducing the Tolerance value will give a more accurate static equilibrium position. for example a metal riser. Details page This contains a spreadsheet with the following information: The values reported on the Summary page. Lines Statics force accuracy. Because computers have finite numerical precision the static analysis cannot always find a configuration where the out of balance load is exactly zero. ropes etc. mass. so OrcaFlex offers different view modes: Individual mode shows one line type at a time. There is not enough room on the screen to show all the properties of all the line types. The line typical force is defined to be the total weight in air. Note that the data for equivalent line types can only be modified when using the Individual view mode. Line Type Name Used to refer to the Line Type. When modelling stress joints and bend stiffeners the outer diameter can be specified as varying with arc length. but different types of properties are shown in different tables. When the section's line type uses a profiled diameter the properties are reported for each segment in that section. The pipe's structural properties are defined by specifying Young's modulus. contact and friction. weight in water. Category Can be one of the following options.8. but it can also include other line types that are not currently in use in the model. then the Bulk Modulus can be set to Infinity. excluding contents. however. weight and displacement and also modify the pipe's inner and outer diameters. These data can also be used for other purposes as follows: If the Stress Diameters are set to '~' then these diameters are used for wall tension and stress results calculations. to calculate the additional mass and weight of the coating or lining. 330 . wires. Similarly the mass is specified as mass per unit length as opposed to being calculated from a material density. ropes. and so on. Similarly the pipe's inner diameter is reduced by twice the lining thickness which has the effect of reducing the contents mass and weight. they contribute no additional structural strength and are assumed not to be load bearing. Material Density (homogeneous pipe only) The density of the material. which means incompressible. plastic linings etc. Bulk Modulus Specifies the compressibility of the line type. The axial. Multiple layers The data on the Line Type data form only allow single coating or lining layers to be specified. Geometry & Mass Data Outer and Inner Diameter Used to define buoyancy and mass of contents per unit length respectively. These data items are only used when torsion is being modelled. mooring chains. If the Drag / Lift Diameters are set to '~' then the outer diameter is used. Mass per Unit Length The mass of the line or pipe structure. together with the thickness. For homogeneous pipes the material density is used to calculate the structural mass and therefore the mass per unit length data item cannot be edited. per unit length. The layers are listed in the order of application. power cables. also possible to specify multiple layers of coatings or linings. umbilicals. They are typically used with steel pipes to model the additional mass and displacement of concrete coatings. the second layer is next to the first layer. If the Contact Diameter is set to '~' then the outer diameter is used for contact calculations. This feature is used when modelling stress joints and bend stiffeners. contact diameter and drag diameters are all increased by twice the coating thickness. Arc length is defined relative to the start of the line section which uses this line type and increases from End A towards End B. bundles. To do this you define Coatings or Linings variable data sources which are then referenced by the thickness data on the Line Type data form. They contribute mass. Note that if the line has contents then the contents CG is assumed to be at the centreline and is not affected by this CG Offset. The material density is used. seismic arrays. These data sources specify a list of layers defined by thickness and material density. However. It is. If the line type is not significantly compressible. To do this you first specify the profile in a Line Type Outer Diameter variable data source which is then referenced by the outer diameter data of the line type. CG Offset The x and y coordinates of the centre of gravity (CG) relative to the centreline. bending and torsional stiffnesses are directly input instead of being calculated from E. Stress results are calculated based on stress diameters equal to the underlying pipe diameters.w System Modelling: Data and Results. Profiled line types (homogeneous pipe only) For homogeneous pipes the outer diameter can vary with arc length. For a coating the buoyancy diameter. In other words the first layer is immediately adjacent to the pipe. Lines General The General category is used in all other situations. nets etc. Coatings & Linings Data Coatings and Linings are available for homogeneous pipe only. See Buoyancy Variation. This approach allows analysis of flexible risers. hoses. Thickness and Material Density The thickness specifies the physical dimension of the coating or lining. To see the "allowable" curve in this case you will need to modify the graph to increase the range of values covered. See Line Compression and Modelling Compression in Flexibles for details. These stiffness data items are reported on the data form. They do not limit the bend radius of the line. For a line with non-zero bend stiffness the Euler load warning is effectively a warning that the segments at that point are too long to accurately model the bending that is occurring.w System Modelling: Data and Results. which cannot support any compression. This is a better model for cases where the bend stiffness is insignificant. Allowable Tension The maximum permitted tension for this type of line. A variable data item specifies a non-linear stress-strain relationship which results in a bending stiffness with non-linear elastic behaviour. In this case Compression is Limited should be set to "Yes" – this correctly models a chain or very flexible rope. use sufficiently short segments that the resulting segment Euler load is not reached. The segment Euler load warning is then simply a warning that the line has gone slack. and also (if the x and y-minimum radii are equal) on the Curvature range graph. Lines Limits Data Compression is Limited The program has two modes for handling slack segments. when the distance between two adjacent nodes becomes less than the original unstretched segment length: No means that the segment is treated as a strut which can support unlimited compression. A typical example of this would be a steel core umbilical. The segment Euler load is given by π2EI/L02 where EI is the bending stiffness of the pipe and L0 is the unstretched length of the segment. In all cases. such as for chains and soft ropes. 331 . i. For items such as mooring chain. If no limit curve is wanted then you may input "~". In addition. Using shorter segments in that area will give a larger segment Euler load. Minimum Bend Radii (MBR) You can specify the minimum permitted radii of curvature for bending about the x and y-directions. This value is used to draw a limit curve on Tension Range Graphs and to calculate the Normalised Tension. the bending stiffness is zero. Notes: MBR can be specified as a variable data item defined as a table relating MBR to tension – either wall tension or effective tension can be used. The "allowable" curve may not be visible on the range graph. It does not limit the tension achieved in the line. If you do not want these curves then set the x-radius to "~" (meaning "not applicable") and the y-value to "~" (meaning "same as x-value"). they are used (together with the specified bend stiffness) to derive "allowable bend moment" curves which are drawn on the x and y-Bend Moment range graphs. and the segment Euler load is also zero. and also (if the x and y-values are equal) on the Bend Moment range graph. ideally. since it may be outside the range covered by the graph. The specified values are used to draw "allowable curvature" curves on the x and y-Curvature range graphs. and to obtain an accurate solution you should. then a warning of this is given on the results form and in the statistics table. bending is occurring at a scale that is less than the segment length. Often the radii for the x and y-directions are equal and this can be specified by setting the y-radius to "~" which means "same as x-radius". so shorter segments are needed to model it accurately. This is the preferred model except where bend stiffness is insignificant. whenever a segment has been compressed to or beyond the segment Euler load.e. Structure Data Young's Modulus (homogeneous pipe only) The Young's modulus of the material which can be constant or variable. although they cannot be edited. A variable MBR is used solely in the calculation of Normalised Curvature. For homogeneous pipes the Young's modulus determines the axial. A constant value results in linear material properties. These values are optional – they are only used to draw "allowable" curves on range graphs and in the calculation of Normalised Curvature results. Effectively. Note however that the axial and torsional stiffnesses are still assumed to be linear. Yes means that the segment is treated as an elastic Euler strut – the compression is limited to the segment Euler load. The MBR is also used to calculate Normalised Curvature. bending and torsional stiffnesses. Warning: You must check that the hysteretic model is suitable for the line type being modelled. Non-hysteretic means that the non-linear stiffness is elastic. This option therefore behaves identically to the non-linear elastic model during statics. This slope is the equivalent EI value for the line. The bend stiffness equals the bend moment required to bend the line to a curvature of 1 radian per unit length. The bend stiffness specified may be zero. under bending. In addition hysteretic bend stiffness usually requires shorter time steps than non-hysteretic modelling. For homogeneous pipes the Plasticity Wizard may be useful to help set up the table. It is intended for modelling hysteresis due to persisting effects such as yield of material or slippage of one part of a composite line structure relative to another part. If the bend stiffness is not hysteretic then the mid-segment curvature reported is the curvature that corresponds to the midsegment bend moment (which is the mean of the bend moments at either end of the segment). Once the dynamic simulation starts. OrcaFlex uses linear interpolation for curvatures between those specified in the table. Linear Bend Stiffness For normal simple linear behaviour. Lines Bend Stiffness The bend stiffness is the slope of the bend moment-curvature curve. Note: If you are using non-linear bend stiffness. It can also be very large values. hysteretic non-linear or externally calculated. When the riser is pressurised. As the riser is bent. the line is assumed to be pressurised and the hysteric model is applied. and linear extrapolation for curvatures beyond those specified in the table. elastic non-linear. Depressurised: The bend stiffness is linear with stiffness determined by the slope of the final two rows of the bend stiffness table. for example for chains. This can be achieved by setting the y-bend stiffness to '~' which means 'same as x-bend stiffness'. With non-linear bend stiffness you must also specify whether the hysteretic bending model should be used. Also note that if the hysteretic model is used then the line must include torsion effects. No hysteresis effects are included and the bend moment magnitude is simply the specified function of the current curvature magnitude. non-linear stiffness in dynamics. Eventually. The program enforces continuity in the transition from linear stiffness in statics to hysteretic. without significantly affecting accuracy. To understand better the rationale behind this option consider the example of a flexible riser. where E is Young's modulus and I is the moment of area of the cross section. but this will often result in short natural periods in the model and hence require short simulation time steps. You can specify separate values for bending about the x and y-directions. You might be able to speed up the simulation. then the mid-segment curvature results reported depend on whether the bend stiffness is specified to be hysteretic or not. There are two options: Pressurised: The bend moment is calculated from the curvature by simple interpolation of the bend stiffness table. this friction has the effect of increasing the apparent bend stiffness of the riser. It is not suitable for modelling rate-dependent effects. A flexible riser is constructed using layers. This difference may be significant if the bend stiffness is significantly non-linear over the range of curvatures involved. If the bend stiffness is hysteretic then the mid-segment curvature cannot be derived in this way (because of possible hysteresis effects) so the mid-segment curvature reported is the mean of the curvatures at the ends of the segment. the friction reaches a limit and the 332 . by removing superfluous points in areas where the curve is very close to linear. The bend moment must be zero at zero curvature. when using implicit integration. so that the bend moment depends on the history of curvature applied as well as on the current curvature. Non-Linear Bend Stiffness For non-linear behaviour. Hysteretic means the bend moment includes hysteresis effects. See Inner and Outer Time Steps. See Calculating Bend Moments for further details of the bending model used. specify the bend stiffness to be the constant slope of the bend momentcurvature relationship. The Statics Model option controls how the non-linear bend stiffness table is interpreted during the statics calculation. for example for steel pipes. as follows. If you use the hysteretic bending model then the simulation speed may be significantly slowed if there are a large number of points specified in the table of bend moment against curvature. use variable data to specify a table of bend moment magnitude against curvature magnitude. When the riser is not pressurised.w System Modelling: Data and Results. but often these are equal. these layers are free to slide over each other. You can specify the bend stiffness to be linear. this leads to friction between the layers. OrcaFlex uses linear interpolation for strains between those specified in the table. See Calculating Tension Forces for details of the tension model used. including the Poisson ratio effect. We recommend that artificially low axial stiffness values are specified. Pressure effects. Axial Stiffness The axial stiffness is the slope of the curve relating wall tension to strain. i. are then allowed for by OrcaFlex. However. the dynamic bending stiffness is higher due to the inter-layer friction. post-slip stiffness. and this in turn requires very small simulation time steps when using explicit integration. The data specifies the behaviour in the unpressured state. use variable data to specify a table of wall tension against axial strain. Most materials have Poisson ratio between 0. For the depressurised option the program is assuming that the post-slip stiffness is the same as the depressurised stiffness. and is given by the final two rows of the data table. and linear extrapolation for strains beyond those specified in the table. Externally Calculated Bend Moment This option allows the bend moment to be calculated by an external function. Note: Axial strain is defined to equal (L . Warning: Non-linear behaviour breaks the assumptions of the stress results and fatigue analysis. A Poisson ratio of zero means no such length changes. (In practice. atmospheric pressure inside and out. Warning: Non-linear behaviour breaks the assumptions of the stress results and fatigue analysis in OrcaFlex. assuming perfectly linear elastic behaviour. For further details see non-linear bend stiffness theory. 333 . This is because very large axial stiffness values lead to very small natural periods for the nodes.g. When a pipe is pressured its tension at this 'unstretched' length is often not zero because of strains due to pressure effects. It is therefore normally quite acceptable to specify a much smaller axial stiffness value than applies to the real line. It equals the force required to double the length of any given piece of line.4. Here 'unstretched' means the length when unpressured and unstressed. It is used to model any length changes due to the radial and circumferential stresses caused by contents pressure and external pressure. as follows: For a simple linear behaviour. so enabling much faster simulations. The exception to this is where snatch loads occur. once the riser is pressurised.0 and 0. You should therefore not use these facilities when there are significant non-linear effects. The effect of this can easily be investigated later by re-running a selection of important simulations with the actual axial stiffness value. Lines layers are then able to slip over each other. since the axial stiffness directly affects the peak tension that results. where E is Young's modulus and A is the cross section area. Typically the riser will be installed without internal pressure and so its geometry will be determined by the much lower.5.3 and for polyethylene about 0.L0) / L0. If this option is used then the line must include torsion effects. The external function can be written by the user or other software writers. This inter-layer friction is what gives rise to the hysteretic behaviour of a flexible riser. the value of axial stiffness used is often not very important. specify the axial stiffness to be the constant slope of the line relating wall tension to strain. For metals such as steel or titanium the Poisson ratio is about 0. For a non-homogeneous pipe (e. particularly for early investigative simulations. Poisson Ratio This specifies the Poisson ratio of the material that makes up the wall of the line type. So the depressurised option is to be used for scenarios where the static analysis models the riser before it has been pressurised.) For a non-linear behaviour. The wall tension is allowed to be non-zero at zero strain. The External results option allows you to specify an external function that can be used to track the bend stiffness calculation and provide user-defined results variables. Note: If you use explicit integration for dynamic simulation then the axial stiffness specified here will have a major effect on how long the dynamic simulation will take. providing it is large enough that the axial strains produced are small. lines would yield before such a tension was reached. of course.w System Modelling: Data and Results.e. See Inner and Outer Time Steps. a flexible) the Poisson ratio may not be able to capture the pressure effects. Fortunately. For details see the OrcaFlex programming interface (OrcFxAPI) and the OrcFxAPI documentation. You can either specify linear or non-linear behaviour. For a homogeneous pipe this can be modelled by specifying the Poisson ratio. where L and L0 are the stretched and unstretched length of a given piece of pipe. This slope is the equivalent EA value for the line. See Calculating Torsion Moments for details on how this value is used. A value that varies with Height above Seabed. Lift & Added Mass Data Drag Coefficients The drag coefficients for the normal (x and y) directions and axial (z) direction are specified on the line type data form.2 and is independent of surface roughness. Consequently. Results for Reynolds number and drag coefficient are available as time history results. For values of Re between 2E4 and 3E5 the drag coefficient takes the value 1. For rough cylinders the effect is less marked. the drag coefficient is strongly dependent on both Re and surface roughness. Values below this range are unlikely to occur in practice. However for such cases an effective Poisson ratio could be specified as an approximation. specify the torsional stiffness to be the constant slope of the torsional momenttwist per unit length relationship. where G is the shear modulus and J is the polar moment of inertia. It is not really applicable to complex structures such as flexibles. OrcaFlex also offers a choice (on the line data form) of different formulations for how the drag force components vary with the incidence angle. For the x and y directions the drag coefficients can be one of the following options: A fixed constant value. Lines Note: The Poisson ratio effect is calculated assuming that the line type is a pipe made from a homogeneous material. the drag coefficient for normal flow depends on Reynolds number Re and surface finish. but remains significant. such as ESDU 80025. Often the coefficients for the x and y-directions are equal and this can be specified by setting the y-coefficient to "~". 334 . This slope is the equivalent GJ value for the line. If the behaviour is mirrored for positive and negative twist then you must specify the full relationship – OrcaFlex does not automatically reflect the data for you. Typical drag coefficient values For circular cylinders.w System Modelling: Data and Results. care is needed to ensure that the data are presented in a form that is consistent with the definition of Reynolds number used by OrcaFlex. In view of this behaviour. Note: When defining non-linear torsional stiffness you should specify values for both positive and negative twist per unit length. This allows you. Torsional Stiffness The torsional stiffness is used only if torsion is included on the line data form. You can specify linear or non-linear behaviour. Drag. the use of variable data for normal drag coefficients is strongly recommended. The torque must be zero at zero twist. as follows: For a simple linear behaviour. It equals the torque which arises if the line is given a twist of 1 radian per unit length. A value that varies with both Reynolds number and Height above Seabed. OrcaFlex uses linear interpolation for curvatures between those specified in the table. A value that varies with Reynolds number.28 at a Re of about 6E5 before recovering to a value of 0. for example. For a non-linear behaviour. OrcaFlex will then use the value of drag appropriate to the instantaneous local value of Reynolds number throughout the simulation.5 for Re values above 2E6. The torsional stiffness specifies the relationship between twist and torsional moment (torque). If wake interference effects are being modelled for a given line. For further details see the Line Theory section. For very smooth cylinders the drag coefficient falls rapidly to 0. whose length changes due to pressure are more complex. Warning: Non-linear behaviour breaks the assumptions of the stress results and fatigue analysis. For Reynolds numbers greater than 3E5. which means "same as x-coefficient". then these normal drag coefficients on the line type data form specify the undisturbed drag coefficient. to have different stiffnesses for positive and negative twisting. Note that some of these sources take account of the effect of the amount of turbulence in the incoming flow by defining an effective Reynolds number. And the drag force will be calculated using a drag coefficient that is modified from this value according to the wake model used. use variable data to specify a table of torque against twist per unit length. The functional form of the dependence is well documented in the open literature and also in proprietary data sources. and linear extrapolation for values outside those specified in the table. In subcritical flow (Re < 3. A value that varies with both Reynolds number and Height above seabed. i. See Line Clashing. For simple cases.011 for a rough cylinder. which are based on the assumption that the loads in the line are taken by a simple homogeneous cylinder.e. Da is the axial drag diameter and L is the element length. This value specifies the diameter to be used. For more complex cases. For line clashing. Contact Data Contact Diameter Contact between lines and the seabed. Drag / Lift Diameters These are used when calculating drag area and lift area. in which case they will be taken to be the same as the pipe diameters. C t. See Added Mass for details. See Added Mass for details. A value that varies with Reynolds number. Added Mass Coefficients (Ca) The added mass coefficients Ca for normal (x and y-directions) and axial (z-direction) flow. for example where the pipe outside diameter 335 . At higher Re. ESDU suggest that skin friction may be neglected. the contact diameter is chosen to be the larger of the contact diameters of the line types either side of the node. Stress Data Stress Outer and Inner Diameter The stress diameters are the inside and outside diameters of the load-bearing cylinder. Note that different programs handle these calculations in different ways. Axial drag results from skin friction only. Clash Stiffness and Clash Damping The stiffness and damping values used by the clashing algorithm. In practice. Ct = 0.008 for a smooth cylinder and 0. A value of "~" is equivalent to setting the coefficient to 1+Ca. For example it is common for programs to use a single drag / lift area for both normal and axial flow and in addition some programs do not include the factor of π in the axial drag area. If a value of '~' is specified then the line outer diameter is used. Because of these differences you must be careful when comparing or transferring data between different programs. For further details see the Line Theory section. Lift Coefficient The lift coefficient is used to specify a lift force which acts in the direction normal to the line axis and in the plane of that axis and the seabed normal. a more detailed VIV analysis should be carried out.w System Modelling: Data and Results. If this is the case. is 0. Damping is always zero when using the implicit integration scheme. then drag coefficients may be increased significantly. and for VIV modelling if the VIV diameter is set to '~'. A drag diameter of '~' results in the outer diameter being used. the drag coefficient for axial flow. elastic solids or other lines accounts for the diameter of the line. This value is also used in the calculation of Line Contact Clearance results and as the drawing diameter for shaded graphics views. contact is modelled between two segments and so the line type contact diameter is used directly. Note: For contact between lines and the seabed or elastic solids contact is modelled between a node and the contact surface. They are also used for any wake interference modelling. For a node at a line section boundary. They are used in the wall tension and stress results calculations. Inertia Coefficients (Cm) The inertia coefficients Cm for normal (x and y-directions) and axial (z-direction) flow. A value of "~" for the ycoefficient is equivalent to setting it equal to the x-coefficient. Note: Inertia coefficients are not specified for homogeneous pipe and are internally set to 1+C a. Lines The above values apply where vortex-induced vibration (VIV) is expected to be negligible.8E5). axial drag is often negligible and Ct = 0 is often acceptable. A value that varies with Height above seabed. the stress diameters can be set to '~'. It can be one of the following options: A fixed constant value. If significant VIV is anticipated. based on ESDU data. Note: OrcaFlex calculates the normal drag / lift area to be DnL and the axial drag area to be πD aL where Dn is the normal drag / lift diameter. (PiAi . You might estimate that the main pipe takes all of the tensile and torsional loads. lateral) and axial to the line. bend moment. wall tension. values less than 1 may be suitable. Transverse values will be greater. Stress Loading Factors These are used to specify what proportion of the loads (wall tension. T w: C1Tw . See Line Results – Forces. Note: The Stress Loading Factors only affect the wall tension results. The friction force applied never exceeds μR where R is the seabed reaction force and μ is the friction coefficient. it does not limit the stress achieved in the line. shear force and torque are multiplied by the appropriate stress loading factor when they are used to calculate stress results and code check results.PoAo) where C1 is the tensile stress loading factor. For example. In most cases. See Friction Theory for further details of the friction model used. The effective tension used in the code checks is calculated from the total. In some cases. consider a case where the line models a composite structure that consists of a main carrier pipe and an external piggyback pipe. Some information is given in Puech (1984) and Taylor and Valent(1984). but only carries 70% of the bending loads. These results are derived after the simulation has run. For intermediate directions of motion OrcaFlex interpolates between these two values to obtain the friction coefficient μ to use. perhaps by 50% to 100%. The Wall Tension results variable is scaled by the tensile stress loading factor. unscaled. fatigue analyses and code check results. Allowable Stress The maximum allowable stress for this type of line. If no limit curve is wanted then you may input the tilde character "~" (meaning not applicable) instead of a number. Note: The friction coefficient for contact with elastic solids is specified on the Solid Friction Coefficients data form.90 0. the sliding friction coefficient should be used. you can specify different friction coefficients μ for motion normal (i.7.e. This value is only used to draw a limit curve on Stress Range Graphs. the other 30% being taken by the piggyback pipe. This provides a convenient way of using the same friction coefficient for all directions of motion. the default value. If the axial friction coefficient is set to '~' then the normal friction coefficient is used for μ for all directions of motion. for instance when modelling a simple homogeneous pipe that carries all the loads. and because of this OrcaFlex allows these data items to be modified after a simulation has been run.w System Modelling: Data and Results.69 Mud/clay 0.74 Mud with sand 0. Both references are written in the context of the contribution of chains and cables to anchor holding power. bend moment. For many cases. The stress factors also influence the effective tension used when calculating the code check results. Lines lying on the seabed often move axially more readily than they move laterally. The values given below are recommendations from Taylor and Valent. shear and torque) are to be used when calculating stress results and code check results. Line type Seabed Type Starting Friction Sliding Friction Coefficient Coefficient Chain Sand 0. The wall tension. Lines allows for added buoyancy modules that are not load bearing. Typical values Published data are sparse. the stress diameters can be set separately.56 336 . these load factors should be set to 1. To enable this effect to be modelled. so we assume the friction values given are axial. this will usually be conservative.92 0. stress results. Both references distinguish between sliding friction and starting friction: starting friction is greater to represent the "breakout" force. OrcaFlex does not draw this distinction.98 0. Friction Data Seabed Friction Coefficients OrcaFlex applies Coulomb friction between the line and the seabed. Then to obtain stress estimates for the main pipe you could set the Stress Outer and Inner Diameters to '~' and set the bending and shear stress loading factors to 0. ODe c indicates properties of the carrier line. e. This data item can be set to "(no damping)". in which case no Rayleigh damping will be applied for this Line Type. lift. The carrier line. The axial. Not all equivalent line data can be derived by the program. Lines 0. etc.g. ODext[i] Geometry ODe is calculated to give a displacement equal to the displacement of the carrier line together with all the external lines: ODe = √(ODc2 + Σ ODext[i]2) 337 . For example.g. stiffnesses.25 Mud with sand 0. Other Data Drag/lift coefficients. A carrier line type. drag/lift diameters. bending and torsional stiffnesses of each secondary line can be specified as contributing or not contributing to the equivalent line's stiffness.23 Mud/clay 0. e. together with the internal secondary lines. For each secondary line. One or more secondary lines. etc.g. Equivalent Line Data The properties of an equivalent line type are calculated from properties of other line types. added mass/inertia coefficients. 2. These secondary lines are also defined by referencing existing line types. consider a pipe-in-pipe system.69 0. This item is only available when using the implicit integration scheme. One of these line types is decreed to be the carrier line and is treated differently from the other secondary lines in the following ways: Any internal secondary lines are deemed to be inside the bore of the carrier line. Secondary lines can be either internal or external. ODc int[i] indicates properties of the ith internal secondary line. Multiple secondary lines can be defined.g. 3. e. Single representative values for mass. Carrier Line The equivalent line properties are made by combining properties from a number of other line types. Other data. These are often modelled by combining the properties of both external and internal lines into a single representative line type. or alternatively from the Line Type properties report. the contents density must also be specified. determines the cross sectional area associated with the line contents data specified on the Line data form. This is a reference to an existing line type defined in the model. e. e. This contents density is associated with the bore of the secondary line. The values can be viewed using the All view mode. ODint[i] ext[i] indicates properties of the ith external secondary line. We will use subscript notation as follows: e indicates properties of the equivalent line. Stress results are reported for the carrier line. Secondary Lines Secondary lines are used to specify lines either internal or external to the carrier line. drag. CG Offset and Allowable Tension are all specified explicitly for an equivalent line. In order to express the equivalent line property derivations we need to establish notation that distinguishes between the various different line types involved. Such data are provided by the user. Modelling Details The program derives equivalent values for the line type as described in the subsequent sections.45 0. must be calculated and the equivalent line type category is designed to perform those calculations. added mass.w Wire rope Sand System Modelling: Data and Results. diameters.g. The input data for an equivalent line type comprises the following: 1.18 Structural Damping Data Rayleigh Damping Coefficients A named Rayleigh Damping Coefficient data set.98 0. fluid inertia. C2e. the shear stress loading factor. the torsional stress loading factor C4 e is defined to be: C4e = C4c(GJc/GJe) The bending stress loading factor. Data which are automatically set to the value of the carrier line: bulk modulus. EIx and EIy.Σ ODint[i]2) Mass Mass per unit length. for sake of completeness the program handles this issue as follows: C2e = C2c. Plasticity Wizard OrcaFlex allows you to specify non-linear bend stiffness for Line Types. Lines IDe is calculated to give an internal cross sectional area equal to that of the carrier line minus the external cross sectional area of all the internal lines: IDe = √(IDc2 . Stress The stress data are set so that stress results are reported for the carrier line.max(EIxc/EIxe. Once you have entered the appropriate data as described below. However. minimum bend radius. See How Objects Are Drawn. line style and thickness of the pen used for drawing this line type. To achieve this the stress diameters and the allowable stress for the equivalent line are set to be the corresponding values for the carrier line. compression is limited. This is not a practical limitation since the stress results derivation is predicated on the material being isotropic. a free form multi-line text field which is passed to any external function used by the Line Type. Analogous formulae are used for bending stiffness and torsional stiffness. For each line there is a choice. friction coefficients and Rayleigh damping coefficients.w System Modelling: Data and Results. The tensile stress loading factor. is the sum of the mass per unit length for the carrier line and all secondary lines: Me = Mc + Σ Mint[i] + Σ Mext[i] Structure Axial stiffness. The Plasticity Wizard is opened by clicking the "Plasticity Wizard" button on the Variable Data form. If you are modelling a uniform. of whether to draw the sections of the line using these Line Types pens. Other data The remaining line type data falls into two categories: Data which must be set explicitly. Poisson ratio. Note: Before you can open the Plasticity Wizard you must have created and selected a Bend Stiffness variable data source. EIyc/EIye) Finally. External Functions Parameters This data item specifies the External Function Parameters. C3 e. homogeneous pipe you can use the Plasticity Wizard to create this table. The data are given as a table of bend moment against curvature. Drawing Data Pen Defines the colour. on the Line Data form. The Bend Stiffness variable data source that is created is initialised to be hysteretic. EAe. 338 . or whether to define a specific pen to use for all the sections of the line. click the Calculate button and the curvature / bend moment relationship is generated. contact diameter. as described above. is defined similarly but with the minor complication that there is only a single value despite there being separate stiffness values for x and y. Me. is simply set equal to C2e. is the sum of the EA for the carrier line and all secondary lines that contribute to axial stiffness: EAe = EAc + Σcontributes EAint[i] + Σcontributes EAext[i] Here the notation Σcontributes means that the summation is performed only for those secondary lines that contribute to axial stiffness. C1e. is defined as follows: C1e = C1c(EAc/EAe) Likewise. clashing stiffness/damping. Contents Density The names and contents densities of each line that uses that line type. This calculation requires a direct tensile strain to be specified – this data item serves that purpose. Strain (Stress-Strain table only) This table directly specifies the relationship between stress and strain. Weight in water Equals Weight in air .05. K. Note that there is an alternative parameterisation of the Ramberg-Osgood equation. It is straightforward to convert between the two forms of the equation but please take care to ensure that the data you input correspond to the parameterisation used by OrcaFlex. Displacement The weight of water displaced by the line type's volume. Diam/Wt Ratio Equals Outer Diameter / Weight in water. The outer fibre strain corresponding to Cmax is denoted εmax and is defined as follows: For a Ramberg-Osgood curve εmax = max{0. and its length. which is why it is denoted σ y here. Reference Stress (σy). Material E. ε(σ) = -ε(-σ) for σ < 0. So the value used for εmax will be 5 times the strain corresponding to the reference stress or 5%. The reference stress parameter is usually taken to be the yield stress. 5ε(σy)}. n (Ramberg-Osgood curve only) These data define the relationship between stress (σ) and strain (ε) in terms of a Ramberg-Osgood curve as follows: ε(σ) = σ/E + K(σ/σy)n for σ ≥ 0. Stress. 339 . The reported value uses the water density at the sea surface. Profile length (only reported for profiled line types) The name of the variable data item that defines the profile. The table is interpolated linearly and for values of strain outside the table linear extrapolation will be used. Note: For Line Types that have a non-zero bore you must specify the contents density to be used in the calculation of the above properties. Values for positive strain must be entered and the relationship for negative strain is then determined by reflection so that σ(ε) = -σ(-ε). Maximum curvature for derived data source The Bend Stiffness variable data source is defined for curvature values between 0 and C max = εmax/Ro where Ro is the radius to the outer fibre. Stress-Strain relationship The relationship between stress and strain can be specified by either Ramberg-Osgood curve or Stress-Strain table. Direct Tensile Strain The Plasticity Wizard calculates bend moment curvature relationship by integrating the stress profile across the pipe cross section. Lines Plasticity Wizard Data The Plasticity Wizard requires the following data: Stress Diameters The inside and outside diameters of the load-bearing cylinder.Displacement. For a Stress-Strain table εmax is simply the largest value of strain specified in the table. Individual page The Individual page reports the following derived values for a selected line type: Diameter profile. whichever is larger. Weight in air The force due to gravity acting on the line type's mass. since this will affect the properties that involve weight. Properties Report The Line Type properties report is available from the popup menu on the data form.w System Modelling: Data and Results. Used in. Clumps may be either net buoyant or heavy as desired. But instead of being free to move it is constrained to move with the node and the forces acting on it are transferred to that node. If the clump is aligned with Line axes then it is centred at the node.w System Modelling: Data and Results. The connection is not modelled fully: the clump is always treated as being at the specified offset vertically above (offset positive) or below (offset negative) the node to which it is attached. Where the clump pierces the water surface. It can be buoyant or heavy and is a small body that experiences forces (weight. from which it inherits all its properties. A clump therefore adds to the mass. Attachment Types can be either Clump Types. Clump Type Name Used to refer to the Clump Type. Attachments with these properties can then be connected to lines. Clumps only have 3 degrees of freedom – X. but it can also include other attachment types that are not currently in use in the model. If it is aligned with global axes then the clump's local directions are the same as the global axis system. If the clump is aligned with Line axes then the clump offset is forced to be zero. Clumps can be aligned with the global axes directions or alternatively they can be aligned with the node to which they are attached.) exactly as for a 3D Buoy. Offset A clump may be offset vertically from the line. 6. If it is aligned with Line axes then its local directions are the same as the node to which it is connected. buoyancy and hydrodynamic forces are applied in proportion to the immersed length of the clump. The attachment types form must include all the attachment types referred to on all of the Lines data forms. Each clump is of a named clump type. Lines All page The All page contains a spreadsheet with two worksheets: The Data sheet echoes the input data for each line type. This allows you to build up a library of standard attachment types that can then be easily used when building Lines. drag etc. Volume Used to calculate buoyancy and added mass for each clump of this type on a line. The Properties sheet presents a table containing. Align with Determines whether the clump is aligned with Global Axes or Line Axes. Each clump is assigned a height and an offset from the node which are used to determine the Z coordinate of the clump for the purposes of evaluating buoyancy and hydrodynamic forces: no moment is applied to the node by the clump.8. The clump types are specified on the Attachment Types form and have the following data. for each line type. buoyancy. for example to represent a line supported below the surface by floats. If the clump is aligned with global axes then it is centred at the Offset position above the node. Flex Joint Types or Stiffener Types. and extends for half its Height above and below this point. the derived values from the Individual page.3 Attachments Attachment Types The Attachment Types form defines the properties of a number of named attachment types. Clumps A clump is a concentrated attachment that is connected to a node on a Line. 340 . as described above. buoyancy and hydrodynamic force of the node to which it is attached. and extends for half its Height either side of this point in the node's axial direction. Height Used for drawing the clump and also to determine how much of the clump is below the water surface. This setting determines the clump's local directions.Y and Z – which are determined by the position of the node to which they are attached. Drag Chain Types. Mass Mass or weight in air. Drag Chains Drag chains are attachments to a line that model straight chains that hang down from the line. Secondly. Length Length of the drag chain. This coefficient is used for all directions of friction. For details see Drag Chain Theory. drag force = PW . Pen Defines the colour. See How Objects Are Drawn. Clump Type Properties Report The Clump Types properties report is available from the popup menu on the data form. which is applied to the line. buoyancy and drag forces to the node to which they are attached. 341 . Added Mass Coefficients Added mass in clump local directions is given by Added mass = PW . ½ . Lines Drag Drag forces are calculated in clump local directions for each clump on a line. line style and thickness of the pen used for drawing this clump type. The drag chain types are specified on the Attachment Types form and have the following data. Water Density . but not any added mass effects. The reported value uses the water density at the sea surface. from which it inherits all its properties.w System Modelling: Data and Results. It reports the following: Weight in air The force due to gravity acting on the clump's mass. Firstly. Cd . (velocity)2 . the chain's drag coefficients can vary with the incidence angle of the relative flow. Drag Area is specified here. They apply weight. then the seabed provides a supporting reaction force and a friction force. The value can be set to '~'. Effective Diameter Effective diameter of the drag chain. Friction Coefficient Coefficient of friction for contact with the seabed. This is the diameter of the cylinder that has the same displaced mass per unit length.Displacement. Ca . both of which are applied to the node. Displacement The weight of water displaced by the clump's volume. Mass Mass per unit length. if the node comes closer to the seabed than the chain length. drag chains interact with the seabed (in a simple manner). this enables modelling the effect that as the relative flow increases the chain hangs at a greater angle to the vertical and so fluid drag generates more lift. Drag Area where Cd is Drag Coefficient as specified here. Volume where Ca is the Added Mass Coefficient as specified here. velocity is the velocity of the fluid relative to the clump in the appropriate direction. Drag chains include two facilities that can be important in modelling towed systems. Name Used to refer to the Drag Chain Type. in which case the drag chain will instead use the axial friction coefficient of the node to which the drag chain is attached. Mass is assumed to be uniformly distributed along the length of the drag chain. Each drag chain is of a named drag chain type. Water Density . Weight in water Equals Weight in air . w System Modelling: Data and Results. You can specify separate values for bending about the x and ydirections. Lines Drawing Defines the colour. Each stiffener has properties determined by a named Stiffener Type. See Drag Chain Theory for further details. Drag Coefficients The fluid drag forces on the chain are specified by giving a table of the normal and axial drag coefficients. Diameter The data as specified on the data form. The Graph button shows the resulting coefficient variation. Coefficients are specified for a range of incidence angles between 0° and 90° and linear interpolation is used to obtain coefficients for intermediate angles. line style and thickness of the pen used for drawing flex joints of this type. OrcaFlex warns if the drag coefficient data do not satisfy this. This turns out to require that the gradient of the normal drag coefficient curve Cdn(α) should be greater than -2. line style and thickness of the pen used for drawing drag chains of this type. Note: To be realistic. Drag Chain Type Properties Report The Drag Chain Types properties report is available from the popup menu on the data form. It reports the following: Length. So α = 0° means flow axially along the drag chain and α = 90° means flow normal to the drag chain. Stiffeners Stiffeners are attachments to a line intended for use modelling bend stiffeners. as a function of the incidence angle α between the relative velocity vector and the drag chain. Symmetry is used to obtain coefficients for angles outside the range 0° to 90°. Similarly to line end connection stiffness the bend stiffness is specified in terms of moment per degree of deflection. the normal drag force should increase monotonically as the incidence angle α increases from 0 to 90. A y-bend stiffness value of '~' is interpreted as 'same as x-bend stiffness'. The Stiffener Types are specified on the Attachment Types form and have the following data: 342 . Each flex joint has properties determined by a named Flex Joint Type. Total Mass The total mass of the drag chain given by Length × Mass per unit Length. The Flex Joint Types are specified on the Attachment Types form and have the following data: Name Used to refer to the Flex Joint Type.Cdn(α) / tan(α) for all α. you set the stiffness for the flex joint to zero. See How Objects Are Drawn. If. Flex Joints Flex joints are attachments to a line that add additional bending stiffness to a particular node (specified by the attachment's z-position). Total weight in air Equals Total Mass × g. Total displacement The weight of the volume of fluid displaced by the drag chain. See How Objects Are Drawn. for example. then you effectively make that node pinjointed. Bend Stiffness Specifies the bend stiffness of the Flex Joint Type. This additional local stiffness acts in series with the stiffness of the underlying line type bend stiffness.Total displacement. The volume is given by Length × πD 2/4 where D is the effective diameter as specified on the data form. Total wet weight Equals Total weight in air . Drawing Defines the colour. bending and torsional response. Usually this will be a profiled homogeneous pipe. 6. If the contact friction means that the protected line effectively carries the axial loads and inertia of the stiffener then this option should be used. Lines Name Used to refer to the Stiffener Type.4 Rayleigh Damping Rayleigh damping is used to model structural damping for Lines and is only available when using the implicit integration scheme. If the line type is profiled then the length is determined by the profile data and so cannot be edited here. Classical Rayleigh damping Classical Rayleigh damping uses a system damping matrix C defined as: C = μM + λK where μ is the mass proportional Rayleigh damping coefficient. e. This correspondence is illustrated in the following table which assumes a stiffener length of 10: Protected line Stiffener Protected line attachment connection protected arc length arc length arc length range 0 0 0-10 5 0 5-15 10 5 5-15 50 10 40-50 For a bend stiffener at End A of a line the connection arc length would set to 0 relative to End A. Line Type Determines the physical properties of the stiffener. Axial load/inertia transfer Specifies how the axial loads and axial inertia are transferred from the stiffener to the protected line. K is the system structural stiffness matrix. For a stiffener which is connected to the protected line by means of a full length friction grip. a Cumberland Grip. Length Defines the length of the stiffener. Relative to Defines the point on the stiffener which corresponds to the protected line attachment position. More technical details of how this data item is used are given in Modelling Bend Stiffeners. Connection Arc Length. If over full length is specified then the axial loads and axial inertia are transferred and shared across the full length of the stiffener. M is the system structural mass matrix. If at connection point is specified then the axial loads and axial inertia for the entire stiffener line are transferred to the protected line at the connection point. With this formulation the damping ratio is the same for axial.8. Similarly for a bend stiffener at End B of a line the connection arc length would set to 0 relative to End B.5(μ/ω + λω) where ξ is the damping ratio (a value of 1 corresponds to critical damping).w System Modelling: Data and Results. 343 . This option is suitable when you wish to neglect the axial effects of friction due to contact between protected line and stiffener. λ is the stiffness proportional Rayleigh damping coefficient. Classical Rayleigh damping results in different damping ratios for different response frequencies according to the following equation: ξ = 0.g. Because the stiffener properties are included in addition to the protected line properties this line type should just specify the properties of the stiffener. then you should use the over the full length option for axial load/inertia transfer. The separated model allows for different damping ratio in axial. Guidance Variation of damping ratio Rayleigh damping is viscous damping that is proportional to a linear combination of mass and stiffness. For Stiffness proportional damping only one response period can be specified. 344 . The stiffness proportional term contributes damping that is linearly proportional to response frequency and the mass proportional term contributes damping that is inversely proportional to response frequency. Rayleigh damping mode OrcaFlex offers four distinct methods for specifying the Rayleigh damping coefficients: Stiffness proportional. Note that K = Ka + Kb + Kt. Separated Rayleigh damping In addition to classical Rayleigh damping OrcaFlex offers a separated Rayleigh damping model where C is defined as: C = μM + λaKa + λbKb + λtKt where λa is the stiffness proportional Rayleigh damping coefficient for axial deformation. λt is the stiffness proportional Rayleigh damping coefficient for torsional deformation. The graph's x-axis can be either period of frequency. Stiffness proportional and Mass and stiffness proportional methods These methods allow you to specify structural damping in terms of % critical damping ratio. Lines ω is the response frequency in rad/s. Rayleigh damping does afford certain mathematical conveniences and is widely used to model internal structural damping. K are the mass and stiffness matrices respectively and μ. λb is the stiffness proportional Rayleigh damping coefficient for bending deformation. these frequency dependencies can be seen in the formula for damping ratio ξ = π(μ/f + λf) where f is the response frequency. Mathematically. λ are constants of proportionality. If Response Period 1 is set to '~' then OrcaFlex will choose response periods automatically based on the wave period. each with the following data. Ka is the system structural stiffness matrix corresponding to axial deformation. The damping matrix C is given by C = μM + λK where M. Coefficients (classical) and Coefficients (separated) methods For these methods you specify the damping coefficients directly. Data Each Line Type has structural damping properties determined by a named Rayleigh Damping Coefficient data set. Coefficients (separated). Coefficients (classical). bending and torsional response. Kb is the system structural stiffness matrix corresponding to bending deformation. OrcaFlex uses the classical Rayleigh damping model and reports the mass and stiffness proportional coefficients μ and λ. Multiple Rayleigh Damping Coefficient data sets can be defined. One of the less attractive features of Rayleigh damping is that the achieved damping ratio varies as response frequency varies.w System Modelling: Data and Results. It can be seen from this that the mass proportional term gives damping ratio inversely proportional to response frequency and the stiffness proportional term gives damping ratio linearly proportional to response frequency. or peak period Tp for a random wave. Damping ratio graph The damping ratio graph plots the damping ratio that will be achieved for a range of response frequencies. In addition you need to specify response periods at which the damping ratio will be achieved. Mass and stiffness proportional. Kt is the system structural stiffness matrix corresponding to torsional deformation. This method is generally recommended and is particularly useful if you are running a batch of cases with varying wave conditions. This technique will apply the specified damping ratio at responses with frequency fmin and fmax. Clearly Rayleigh damping constants must be chosen carefully to avoid the mass proportional term resulting in over-damping of the low frequency response. The mass proportional damping is therefore normally neglected for compliant structures undergoing large rigid body motions. Identify the minimum and maximum frequencies present in the system response. 2. Stiffness proportional damping is very effective at artificially removing high frequency responses from an analysis and this is a danger that must be avoided. λ=0. Note: Since this approach leads to a damping ratio less than the specified damping ratio for frequencies between fmin and fmax it could be argued that the response will be under-damped." In other words the recommendation for such systems is to use stiffness proportional damping (the red curve above).025.023) Figure: Variation Of Damping Ratio With Frequency Artificial over-damping of system response Consider a system which has two primary responses: one at the wave frequency and the other at a much lower frequency. If your system response is concentrated at the wave frequency for all critical design cases then it is safe to apply stiffness proportional damping. fmin and fmax. an analogous argument can also be made about any high frequency response. for example due to vessel drift. This is a good argument. Identify a number of critical load cases. For example the DNV dynamic riser code DNV-OS-F201 (Appendix A. It is common practice to do this by using the stiffness proportional term only. If only stiffness proportional damping is used then any high frequency response will be over-damped. For frequencies between fmin and fmax the damping ratio will be less than the specified damping ratio which ensures that artificial over-damping is avoided. Since high frequency responses are often damaging to a system it is important to model them accurately. Generally this conservative under-damping is far less significant than the non-conservative over-damping that we are trying to avoid. Avoiding over-damping of system response We recommend the following procedure for applying Rayleigh damping: 1. Apply mass and stiffness proportional Rayleigh damping with response periods set to 1/fmin and 1/fmax. Lines The plot below illustrates how the separate mass and stiffness damping terms contribute to the overall damping ratio: Mass and Stiffness Mass term Stiffness term 6% Damping ratio 5% 4% 3% 2% 1% 0% 0 1 2 3 4 5 Response angular frequency (rad/s) (μ=0. 4.w System Modelling: Data and Results. It is quite common for systems to have responses at frequencies higher than the wave frequency. K103) makes the following recommendation: "It should also be observed that the mass proportional damping would give damping due to rigid body motions. 3. 345 . However. Run these cases without Rayleigh damping. Modelling Details Note: The line properties report contains detailed information on how the P-y model data are interpreted and applied in the OrcaFlex model. whereas in the API RP 2A code the value is expressed as a weight value (force per unit volume). the two API RP 2A formulations provide load-deflection curves that vary with depth given constant input data. However. It is. Similarly. The problem is that the damping ratio depends on the amplitude of response. The P-y model data can be specified to vary with depth beneath the seabed.g. Lines Discussion The above procedure will help you avoid non-conservative over-damping of high or low frequency responses in your system. Instead we recommend that you use a hysteretic bend stiffness which gives a more accurate model of the riser. This effect is strongly amplitude dependent and is poorly represented by Rayleigh damping. 6. Deflection. Note that ε c is specified as a percentage strain. When a P-y model is associated with a line. However. For this reason Rayleigh damping can usually be ignored for analysis of subsea lines. the horizontal load-deflection curves for the line are set up as follows: 346 . the API RP 2A Sand option uses the API RP 2A (2000) load-deflection curves for sand. Effective unit soil density (Soft Clay and Sand) The effective density of the soil. Note: The value specified in OrcaFlex is a density value (mass per unit volume). For systems which show significantly different responses when Rayleigh damping is applied you should check that this is not due to the over-damping issues described above. Resistance (Table) The load-deflection curve in tabulated form. equal to the saturated soil density minus the sea water density. k (Sand) The input parameters to the API RP 2A Sand model. You can define one or more named P-y models which can then be associated with individual Line objects. εc (Soft Clay) The input parameters to the API RP 2A Soft Clay model. For subsea lines the structural damping is usually negligible in comparison with the damping due to hydrodynamic drag. Input data for P-y Models Name Used to refer to the P-y Model. Undrained shear strength. of course. C2. C3.w System Modelling: Data and Results. The P-y curve data are treated as constant over this range of depths. important to apply it carefully as described above.8. jumper hoses) the situation is different. In this situation Rayleigh damping can be very useful. For such lines it is very easy for resonant responses to be excited and if no damping is modelled then these responses do not decay. These lines have no hydrodynamic damping and so the structural damping can be significant. The P-y Table option allows you to specify the load-deflection curves directly in tabular form. Model type One of the following options: The API RP 2A Soft Clay option uses the load-deflection curves for piles in soft clay under short-term static loading as specified in API RP 2A (2000). This makes the damping ratio very difficult to set and it will differ for different load cases. For in-air lines (e. One common phenomenon that is sometimes modelled with Rayleigh damping is the damping due to internal friction between layers of a pressurised. J. C1.5 P-y Models Data P-y models are used to specify horizontal soil loads for near-vertical line objects that extend beneath the seabed. Depth below seabed Specifies the range of depths over which each set of P-y curve data applies. Can we adopt a simpler approach? For a great many of the systems that are analysed by OrcaFlex it turns out that structural damping has little or no effect on system performance. it is quite laborious and time-consuming. unbonded flexible riser. added mass and hydrodynamic inertia effects are suppressed. Other lines in the model which do not use P-y models are still subject to normal seabed reaction forces. In particular. The use of P-y models also influences the interfaces to SHEAR7 and VIVA. Buoyancy and pressure calculations are not affected by the presence of a P-y model. and with direction determined by the bottom node's end orientation. and then projecting into the horizontal plane. The deflection is obtained by subtracting the node's instantaneous position. P 0.e. Note: It is expected that the shallowest P-y curve will start from the seabed. see below. dY. You may extend the sea density profile beneath the seabed if you want to vary the fluid density used to calculate these effects. respectively. towards P0. This load is applied in the horizontal plane. The load is then defined to be pDL where D and L are the node's contact diameter and length. Adjacent node's nominal positions are separated by the length of the line segment. From the deflection value y. i. Wake interference modelling (both wake creation and reaction to wakes) is suppressed. Nodes that have P-y springs attached are further modified as follows: Drag. When a P-y model is active a number of modifications are made to the modelling of the line. P0 y P0 P Inclination Inclination Ez End A Ex Ex End B Ez Figure: P-y modelling 347 y P . However. The node at the bottom end of the line is assigned a nominal position defined by its position in the reset state. lift. dZ) then y = √(dX2 + dY2). P 0. The magnitude of this horizontal vector is taken to be the deflection y. the soil resistance p is calculated. The depth of each node's nominal position is then used to determine which set of P-y curve data is used. Time domain VIV loading is suppressed. have Depth From equal to zero. Each P-y model type ultimately leads to a relationship between lateral deflection y and soil resistance p. All other nodes have nominal positions on a straight line passing through the bottom node's nominal position. The deflection and resistance at each node are available as results variables. The P-y load and deflection are calculated radially in the horizontal plane. the program does not enforce this and will not attach P-y springs to any nodes that are above this initial depth yet below the seabed. all normal seabed reaction forces are suppressed for the line.w System Modelling: Data and Results. from its nominal position. If we write P-P0 in component form as (dX. Lines Immediately prior to the static calculation each node on the line is assigned a nominal position. as described below. P. 1 0. The resistance p is then defined to be: p = (Apu/D) tanh(kHy/Apu) where A = max(0.2-1 for X<XR and 6. J is a dimensionless empirical constant and X is the depth below soil surface. p u.6-2 should be evaluated and pu taken to be the smaller value.2-2 is used for that node and all subsequent nodes. the program processes each node with a soft clay P-y model in turn.2-1) pu = 3c + ɣX + JcX/D (6.2-1 produces the smaller value. the resistance associated with that largest specified deflection value is used.2-1 is meant to capture the reduced lateral bearing capacity of the soil close to the surface. The first equation. then 6.2-1 and 6. p u. The code provides two equations for this: (6.6-1 and 6. 3-0. API RP 2A Sand The load-deflection formulation is based on the ultimate bearing capacity of the soil. Once a node has been found for which 6.2-1 gives a greater value of pu than 6.0 1.8H/D).8. The intent of the code is that pu is defined by whichever of 6. the depth to which the reduced resistance zone extends.23 0.8.8.00 ∞ where yc = 2. The code approaches this by defining XR. Both equations 6. API RP 1111. Note: The table above is taken from API RP 2A Supplement 3 and differs from earlier versions of the API code. ɣ is the effective unit weight of soil.8.8. The code provides two equations for this: (6.2-1 and 6.0 0.3 0. 348 .8.8.8.6 Code Checks The Code Checks data form gathers together all input data related to code checks. The approach used by the program is as follows.2-2) pu = 9c where c is the undrained shear strength.5 used the version of the table that was presented in earlier versions of the API code.00 8. 6. and must be specified in increasing order.w System Modelling: Data and Results.2-2.72 3. that smaller value of pu is used.2-2.8.2-2 for X≥XR.8. So long as 6. The following code checks are implemented: API RP 2RD.8. The two prospective values of pu are calculated using 6.6 and later use the version of the table presented above.8. Once pu has been determined. Lines Load-deflection curves API RP 2A Soft Clay The load-deflection formulation is based on the ultimate unit lateral bearing capacity of the soil. For deflections exceeding the largest specified deflection value.8.2-2 gives a smaller value. OrcaFlex 9.8.8.8.50 1. ɣ is the effective unit weight of soil and H is the depth below soil surface.8.5εcD. p is calculated by linear interpolation of the following table: p/pu y/yc 0. linear interpolation is used.9.00 0. D is the pile diameter. This approach using XR breaks down when the soil properties vary with depth. 6.6-2) pu = C3DɣH where D is the pile diameter. The deflection column must include the value zero.0 0. and applying 6.0 1.8.33 0. For other deflection values. Starting at zero depth. P-y Table The input data specifies a table of deflection and resistance values. OrcaFlex 9.6-1) pu = (C1H + C2D)ɣH (6. The loads (tension and bend moment) which are used in the calculations below are influenced by the stress loading factors before being used.2 of API RP 2RD as: σAPI = max [{(σpr-σpθ)2 + (σpθ-σpz)2 + (σpz-σpr)2}/2]½ where σpr = . equation 8. The code check calculations are made available through a number of line results variables. DNV OS F201. denoted σy in API RP 2RD.2. API RP 2RD Stress. There is a single instance of a model wide data item.w System Modelling: Data and Results. Fa This data item is not explicitly defined in the standard. The exception to this rule is the DNV Functional Load page which contains data shared between the DNV OS F101 and F201 code checks. PD 8010. is reported as a percentage and is defined to be: UAPI = σAPI / (CfCaσy) where Ca is 2/3 The strength check for API RP 2RD is therefore equivalent to the inequality U API ≤ 1. section 4.4) using the following equation: tmin = t .2.Pi σpz = Tw/A ± M(ODstress . Some of the code checks require quite a lot of input data and so data for those code checks span multiple pages. (ODstress . i. tcorrosion. is a von-Mises type stress defined in section 5.1. σy The material minimum yield strength (SMYS).tcorrosion where t is the nominal wall thickness.3. see API RP 1111. section 5.3. in a one-to-one relationship with the model's line types. In contrast. which category a particular data item falls into. Generally each page contains data that is applicable to a single code check. SMYS. table 2 and section 5.IDstress)/2 The max in the formula for σAPI accounts for the fact that the ± sign in the formula for σpz makes σpz double-valued. The data falls into two main categories: model wide and per line type. (ODstress . tcorrosion The corrosion thickness. there are separate instances of per line type data.3. The data form contains a number of different pages. API RP 1111 Data Allowable Load Factor.2.1.IDstress) / (ODstress + IDstress) σpθ = (Pi .4. UAPI. To automate modifications to code check data please refer to: Batch Processing: Examples of setting data. Cf See API RP 2RD. Corrosion thickness.IDstress)/2.2.ODstress + Pi. Lines DNV OS F101. API RP 2RD Utilisation. 349 .1. It is self-evident from the layout of the data pages.(Po.t)/2Ixy t is the nominal wall thickness.e. Results For terminology see Pipe Stress Calculation. section 5. Text Data Files: Examples of setting data. API RP 2RD Data Design case factor.Po)ODstress/2tmin . is used to determine the minimum wall thickness (denoted by t min in API RP 2RD. σAPI. section 4. It is used to specify the choice of possible values for the righthand side of the inequality used in the combined load design.4. So changes to such data items affect all objects in the model. 3. see API RP 1111. Results The loads (tension and bend moment) which are used in the calculations below are influenced by the stress loading factors before being used.e. section 4.3. see API RP 1111.3. It is given by if Pi < Po FbsSAFε/(εbg) + (Po . Fbs This data item is not explicitly defined in the standard. section 4.2. E This is the modulus of elasticity used in determining the elastic collapse pressure. Note that if you have specified a value for Young's Modulus on the Structure page of the Line Type data form. section 4.2.1. and 15. and the result is reported as zero. to satisfy the inequality in API RP 1111 the result should be less than one. section 4.2.1. to satisfy the inequality in API RP 1111 the result should be less than one.3. It is given by {[(Pi .Po)/Pb]2 + (Te/Ty)2}1/2 / Fa where Pb = 0. Ovality.2. i. section 4. API RP 1111 rewritten in the form of a unity check.1.3. SAF This is the strain amplification factor for use with combined pressure and bending loads.e. Fc This is the collapse factor for use with combined pressure and bending loads. p b and the yield tension. see API RP 1111. it represents the bending safety factor for use with combined pressure and bending loads.3. U This is the specified minimum ultimate tensile strength of pipe used in determining the burst pressure.2. Section 4. i. i. g.3.IDstress2)/4 otherwise the Line is in compression. section 4. It is given by if Te>0 Te/(0.3. Ty. see API RP 1111. δ This is the ovality for use in determining the collapse reduction factor.1. see API RP 1111.3. Bending Safety Factor. p c. Young's Modulus.2. Section 4. API RP 1111 CLD (Combined Load Design) The result reported is equivalent to equation 8. API RP 1111 rewritten in the form of a unity check. S This is the specified minimum yield strength of the pipe used in determining the burst pressure.3. API RP 1111 LLD (Longitudinal Load Design) The result reported is equivalent to equation 6. 14.Pi)/(FcPcg) otherwise FbsSAFε/(εbg) where ε is the Max Bending Strain and εb = t/(2ODstress) 350 .2.1 SMTS.2.1.w System Modelling: Data and Results.2. Section 4. see API RP 1111.e. Strain Amplification Factor. see API RP 1111.6Ty) where Ty = SA A = π(ODstress2 .e.45(S + U) loge(ODstress/IDstress) API RP 1111 BEP (Bending and External Pressure) The result reported is equivalent to the inequalities 13.2.2. In the standard this is defined as f1 when being used for installation bending and f2 when being used for in-place bending. pb.2. to satisfy the inequalities in API RP 1111 the result should be less than one. Lines Collapse Factor. Te < 0. i. SMYS. API RP 1111 rewritten in the form of a unity check. you must still separately give a value for this data item if you want to request an API RP 1111 Bending and External Pressure result. section 4. 351 . API RP 1111 CLD. loads arising from the physical existence of the system. If the functional load is specified by a simulation file then this model must be consistent with the currently active model. Line Type Factors: Strain Resistance Factor. Table 5-10. γc See DNV OS F101.IDstress)/2 API RP 1111 Max Combined This is the maximum value of the API RP 1111 LLD. γF See DNV OS F101. γSC See DNV OS F101. γE See DNV OS F101. γRF Specifies a smaller alternative functional load factor. section 4. This is done by either selecting Current model or Simulation file. If Current model is selected then the static state of the currently active model will be used as the functional load case.w System Modelling: Data and Results. Typically this will be a static state simulation. Load Factors: Reduced Functional. you must nominate a functional load case. you must specify the functional load case. Table 4-4. section 5. section 4. Table 4-5. the functional loads will still be calculated from the static state. Lines g = 1/(1 + 20δ) Pc = PyPe/(Py2 + Pe2)1/2 where Py = 2S(t/ODstress) Pe = 2E(t/ODstress)3/(1-ν2) and t = (ODstress . If Simulation file is selected then you must specify a simulation file that represents the functional load case. see DNV OS F101. This data item is set on the DNV Functional Load page. Table 4-4. section 5. DNV OS F101 Data Functional Load Specified By To allow the environmental load to be separated from the function load. Load Factors: Condition. This is used to satisfy the requirement that if the functional load effect reduces the combined load effect a smaller functional load factor shall be used. must exist. such as drag from wind and current or a static vessel initial position representing a mean offset due to wave. wind and current. Load Factors: Environmental. Table 5-3. The simulation file is specified either by full path or relative path. Table 5-2.e. section 5. for which a DNV-OS-F101 or DNV-OS-F201 code check result will be requested. Any line. and API RP 1111 BEP code check results. in the DNV OS F101 and DNV OS F201 code checks. DNV Functional Load Functional Load Specified By To facilitate the requirement to separate the functional load from the environmental load. so it should not include any form of environmental loading. section 4. with the same name. The following data items are specified on the DNV OS F101 Factors page and the DNV OS F101 Properties page of the Code Checks data form: Load Factors: Functional. γε See DNV OS F101. γm See DNV OS F101. i. Line Type Factors: Safety Class Factor. section 4. The functional load case should only include contributions from functional loads. Line Type Factors: Material Resistance. in both the currently active model and the functional load case. If you do specify a dynamic simulation file. and have the same segmentation in both models. Table 4-4. αgw See DNV OS F101. αh See DNV OS F101.E(t) = My(t) . Young's Modulus. Line Type Factors: Simplified Strain Limit See DNV OS F101. Results The loads (tension and bend moment) which are used in the calculations below are influenced by the stress loading factors before being used. can be treated as a linear superposition of the environmental load. section 13. Table 5-5. The loads can then be separated: Mx. Line Type Factors: Girth Weld Factor.Direct Tensile Strain. Pi. is given by the maximum of 352 . is given by the maximum of |γFγcTeF + γETeE| and |γRFγcTeF + γETeE| The design moment effect. L(t). E Note that if you have specified a value for Young's Modulus on the Structure page of the Line Type data form. as per Appendix C in DNV OS F201. If it is DNV OS F101 Load Controlled then the "Load" will be the effective tension. the environmental load is separated from the functional load using the functional load case.5 and Table 7. D 1000. F0 See DNV OS F101.εF where ε is the compressive strain. section 5. Table 7. Out of Roundness. αfab See DNV OS F101. The load.My. and the functional load. MSd. Pmin Specifies the minimum internal pressure that can be sustained. given by the Max Bending Strain .F My. D 1100.Mx. The design load effects are then calculated as follows The design tension effect. section 5. C 300. Table 5-6. Lines Line Type Factors: Fabrication Factor. The default value '~' means that P min will be taken as the internal pressure. αpm See DNV OS F101. fu See DNV OS F101. TeSd. which.F TeE(t) = Te(t) .w System Modelling: Data and Results. section 7. fy See DNV OS F101. If it is DNV OS F101 Displacement Controlled then it will be the compressive strain. C 300. at time t.TeF εE(t) = ε(t) . see Line Pressure Effects for details. The Local buckling – combined loading criteria. When you ask for either the load or displacement controlled DNV OS F101 code check results. D 600. The load used will depend on which DNV OS F101 code check result you ask for.IDstress)/2. of the Line (at the specified arc length). and the y-bend moment. The default value '~' means that t2 will be taken as (ODstress . D 606.11. section 5. the x-bend moment. section 13. in the currently active model is assumed to be the combined load. Table 13-5. LE(t). section 5. t2 See DNV OS F101. section 5. If you specify a Pmin other than the default value then this will be used for all arc lengths of the Line that use this Line Type. DNV OS F101. Line Type Factors: Plastic Moment Reduction Factor.E(t) = Mx(t) . LF. you must still separately give a value for this data item if you want to request a DNV OS F101 code check result. is implemented as separate results for the Load Controlled and Displacement Controlled conditions as defined in Section 5. section 5. D 700.Po)/pb] If Pi ≤ Po the load controlled code check result is given by [γmγSC|MSd|/αcαpmMp + (γmγSCTeSd/αcTep)2]2 + [γmγSC(Po . is used in the case where the internal pressure is greater than the external pressure.(Pi .ODstress/t2)/90 αp is the pressure factor given by if (Pi .5] y = -2(-u)0.Pmin)/pc]2 353 . pc.w System Modelling: Data and Results. pb.3β[1 .Po)/αcpb]2 where Mp and Tep are the moment and tensile plastic capacities respectively.5[(2/27)b3 .b/3 where b = -pel c = -(pp2 + pppelf0ODstress/t2) d = Pelpp2 u = (-b2/3 + c)/3 v = 0. and requires the solution of the third degree polynomial (pc-pel)(pc2-pp2) = pcpelppf0ODstress/t2 where pel = 2E(t2/ODstress)3/(1-ν2) and pp = fyαfab2t2/ODstress An analytical solution to this polynomial is given in Section 13.5(ODstress-t2)] where fcb = Min[fy. is used in the case where the external pressure is greater than the internal pressure. DNV OS F101.5cos(Φ/3 + π/3) DNV OS F101 Load Controlled If Pi > Po the load controlled code check result is given by [γmγSC|MSd|/αcαpmMp + (γmγSCTeSd/αcTep)2]2 + [αp(Pi .β otherwise αp = 1 . and is given by pb = 4t2fcb/[30. given by Tep = fyπ(ODstress .β) + βfu/fy where β = (60 . pc = y .15] The characteristic resistance for external pressure. is given by the maximum of γFγcεF + γEεE and γRFγcεF + γEεE The load controlled and displacement controlled conditions share the requirement for several derived values to be calculated: The pressure containment resistance. εSd.t2)2t2 αc is the flow stress parameter given by αc = (1 . fu/1.bc/3 + d] Φ = cos-1[-v/(-u3)0.t2)t2 Mp = fy(ODstress .Po)/pb < 2/3 αp = 1 . Lines |γFγcMF + γEME| and |γRFγcMF + γEME| The design compressive strain effect. w System Modelling: Data and Results, Lines DNV OS F101 Tension Utilisation The result is given by TeSd/Tep where TeSd and Tep are defined above. The load controlled criterion, specified in section 5, D605 and D607, DNV OS F101, apply for Te Sd/Tep < 0.4. This result can be used in parallel with the DNV OS F101 Load Controlled result to check that this tension requirement is met. DNV OS F101 Displacement Controlled The displacement controlled code check result is given by if Pi ≥ Po and εSd ≥ 0 γεεSd/εc(t2, Pmin - Po) if Pi < Po and εSd > 0 then the displacement controlled code check result is given by [γεεSd/εc(t2, 0)]0.8 + γmγSC(Po - Pmin)/pc where εSd is the design compressive strain and εc(t, Pnet) = 0.78(t/ODstress - 0.01)(1 + 5.75(Pnet)/pb)αh-1.5αgw otherwise the pipe is not in compressive strain and the code check result is 0. DNV OS F101 Simplified Strain The result represents the simplified laying criteria for the overbend, section 13, G 300, DNV OS F101. It is given by abs(εzz)/SimplifiedStrainLimit where εzz is the Worst ZZ Strain. The SimplifiedStrainLimit would be set to the value in Table 13-5, DNV OS 101, of Criterion I or II, depending on whether static or dynamic analysis is being conducted. DNV OS F101 Simplified Stress The result represents the simplified laying criteria for the sagbend, section 13, G 300, DNV OS F101. It is given by σvm/(0.87*fy) where σvm is the Max von Mises Stress. DNV OS F201 Data Functional Load Specified By To allow the environmental load to be separated from the function load, you must nominate a functional load case. This data item is set on the DNV Functional Load page. The following data items are specified on the DNV OS F201 Factors page and the DNV OS F201 Properties page of the Code Checks data form: Load Factors: Functional, γF See DNV OS F201, Table 5-2. Load Factors: Environmental, γE See DNV OS F201, Table 5-2. Load Factors: Condition, γc See DNV OS F201, Table 5-11. Moment Condition, γcm This data item is not explicitly defined in the DNV standard. It has been introduced to facilitate the allowance that, if the bending moment can be assumed secondary, the bending moment used in the code checks may be multiplied by a condition factor, see DNV OS F201, section 5, D 700. If you want to include a condition factor on only the bending moment then it should be entered in this data item. If you want to include a condition factor in the product of the resistance factors, i.e. γcγmγSC, which is applied to the bend moment, tension, and pressure terms, then it should be entered in the γc data item. For the expressions defining how the condition factors have been included in the code check equations see the Results section below. 354 w System Modelling: Data and Results, Lines Load Factors: Reduced Functional, γRF This data item is not explicitly defined in the DNV standard. It has been introduced to allow you to specify a smaller alternative functional load factor. This is used to satisfy the requirement that if the functional load effect reduces the combined load effect a smaller functional load factor shall be used. See DNV OS F201, Table 5-2. Load Factors: Reduced Environmental, γRE This data item is not explicitly defined in the DNV standard. It has been introduced to allow you to specify a smaller alternative environmental load factor. This is used to satisfy the requirement that if the environmental load effect reduces the combined load effect a smaller environmental load factor shall be used. See DNV OS F201, Table 5-2. Line Type Factors: Safety Class Factor, γSC See DNV OS F201, Table 5-3. Line Type Factors: Material Resistance, γm See DNV OS F201, Table 5-4. Line Type Factors: Fabrication Factor, αfab See DNV OS F201, Table 5-7. Line Type Factors: WSD Usage, η See DNV OS F201, Table 5-8. Pmin Specifies the minimum internal pressure that can be sustained. The default value '~' means that P min will be taken as the internal pressure, Pi, of the Line (at the specified arc length), see Line Pressure Effects for details. If you specify a Pmin other than the default value then this will be used for all arc lengths of the Line that use this Line Type. t2 See DNV OS F201, section 5, C 203. The default value '~' means that t2 will be taken as (ODstress - IDstress)/2. fy See DNV OS F201, Table 5-5. fu See DNV OS F201, Table 5-5. Young's Modulus, E Note that if you have specified a value for Young's Modulus on the Structure page of the Line Type data form, you must still separately give a value for this data item if you want to request a DNV OS F201 code check result. Out of Roundness, f0 See DNV OS F201, section 5, G 201. Results The loads (tension and bend moment) which are used in the calculations below are influenced by the stress loading factors before being used. The LRFD combined loading criteria and the alternative WSD format, as defined in Section 5, D 500 and D 600 respectively, are implemented as separate results. The LRFD and WSD formats share the requirement for several derived values to be calculated: The burst resistance pressure, pb, is used in the case where the internal pressure is greater than the external pressure, and is given by pb = 4t2min[fy; fu/1.15]/(31/2(ODstress-t2)) The collapse pressure, pc, is used in the case where the external pressure is greater than the internal pressure, and requires the solution of the third degree polynomial (pc-pel)(pc2-pp2) = pcpelppf0ODstress/t2 where pel = 2E(t2/ODstress)3/(1-ν2) and pp = fyαfab2t2/ODstress 355 w System Modelling: Data and Results, Lines The analytical solution used to solve this polynomial is given in Section 13, D 700, DNV OS F101 and is also documented in Code Checks: DNV OS F101. DNV OS F201 LRFD Format When you ask for the DNV OS F201 LRFD result, the environmental load is separated from the functional load using the functional load case. The load, at time t, in the currently active model is assumed to be the combined load, L(t), which, as per Appendix C of DNV OS F201, can be treated as a linear superposition of the environmental load, LE(t), and the functional load, LF. The loads can then be separated: Mx,E(t) = Mx(t) - Mx,F My,E(t) = My(t) - My,F TeE(t) = Te(t) - TeF This means that if you ask for the DNV OS F201 LRFD result when the model is in the static state and the functional load is specified by the Current model there will be no environmental load contribution. The design load effects, required by the DNV OS F201 LRFD code check result, are given by Ted = γFTeF + γETeE Mx,d = γFMx,F + γEMx,E My,d = γFMy,F + γEMy,E |Md| = (Mx,d2 + My,d2)1/2 The above design load effects (moment and tension) are individually evaluated four times, using the different permutations of the environmental and functional load factors, i.e. γ F and γE, γRF and γRE, γRF and γE, and γF and γRE. The combinations of factors that yield the largest magnitude, for the individual load effects, are used, i.e. a different combination of factors might be used for the tension and the moment. The above summations of the contributing load effect categories exclude the terms associated with accidental loads. DNV OS F201 guides that normally, functional and environmental loads are not considered simultaneously with accidental loads in global analyses. However, when conducting an SLS or ALS assessment, as per DNV OS F201, the environmental load effect factor, γE, and the accidental load effect factor, γA, are both equal to 1.0, so there is no requirement to separate loads and the accidental associated loading could be included in the OrcaFlex model alongside the environmental loading. The LRFD code check result is given by if Pi > Po and Pi-Po < pb γcγmγSC(γcm|Md|{1-[(Pi - Po)/pb]2}1/2/Mk + (Ted/Tk)2) + [(Pi - Po)/pb]2 else if Pi > Po and Pi-Po ≥ pb, the above would evaluate to a complex value, the result is given by γcγmγSC(Ted/Tk)2 + [(Pi - Po)/pb]2 Finally, if Pi ≤ Po then the LRFD code check result is given by (γcγmγSC)2[γcm|Md|/Mk + (Ted/Tk)2]2 + [γcγmγSC(Po - Pmin)/pc]2 For each of the three possibilities above, Mk and Tk are the moment and tensile plastic resistances respectively, given by Tk = fyπαc(ODstress - t2)t2 Mk = fyαc(ODstress - t2)2t2 αc, the flow stress parameter, is given by αc = Min[1.2, (1 - β) + βfu/fy] where if ODstress/t2 < 15 β = 0.4 + qh if 15 ≤ ODstress/t2 < 60 β = (0.4 + qh)(60 - ODstress/t2)/45 otherwise β=0 where if Pi > Po qh = (2/31/2)(Pi - Po)/pb otherwise 356 w System Modelling: Data and Results, Lines qh = 0 DNV OS F201 WSD Format The WSD code check result is given by if Pi > Po and Pi-Po < pb (γcm|M|{1-[(Pi - Po)/pb]2}1/2/Mk + (Te/Tk)2 + [(Pi - Po)/pb]2)/η2 else if Pi > Po and Pi-Po ≥ pb (Te/Tk)2 + [(Pi - Po)/pb]2)/η2 otherwise {[γcm|M|/Mk + (Te/Tk)2]2 + (Po - Pmin)/pc)2}/η4 PD 8010 Data Young's Modulus, E This is the modulus of elasticity used in determining the collapse pressure, p c; the characteristic torque, τc; and the exponent in the Load Combinations Check, γ. See PD 8010, sections G.1.2, G.1.5, and G.1.6, respectively. Note that if you have specified a value for Young's Modulus on the Structure page of the Line Type data form, you must still separately give a value for this data item if you want to request a PD 8010 Torsion Check or a PD 8010 Load Combinations Check result. SMYS, σy This is the specified minimum yield strength of the pipe used in determining the allowable stress, σ A; elastic collapse pressure, pc; the yield load, Fy; the plastic moment capacity, Mp; the characteristic torque, τc; and the exponent in the Load Combinations Check, γ. See PD 8010, sections 6.4.2.1, G.1.2, G.1.3, G.1.4, G.1.5, and G.1.6. Fabrication Factor, αfab This data item is not explicitly included in any of the equations in the standard. It is included to facilitate the requirement that for fabrication processes which introduce cold deformations giving different strength in tension and compression, a fabrication factor should be determined. See PD 8010, section 6.4.4.1 General, Note 1. In the absence of explicit guidance in PD 8010, it is assumed that it is applied in a fashion consistent with DNV OS F101, i.e. that it is considered in determining the elastic collapse pressure, pc. Ovalization, F0 This is the ovalization used in determining the elastic collapse pressure, p c, see PD 8010, section G.1.2 Design Factor, Fd This is the design factor, see PD 8010, section 6.4.1 Results The loads (tension, bend moment, torque, and shear force) which are used in the calculations below are influenced by the stress loading factors before being used. The nominal thickness, tnom, used throughout the calculations below, is given by tnom = (ODstress - IDstress)/2 PD 8010 Allowable Stress Check The result reported is equivalent to equation 2, section 6.4.2.1, PD 8010, rewritten in the form of a unity check, i.e. to satisfy PD 8010 the result should be less than one. It is given by σA/(fdσy) where σA = (σh2 + σL2 - σhσL + 3τ2)0.5 where if ODstress/tnom > 20 σh = (Pi - Po)ODstress/(2tnom) otherwise σh = (Pi - Po)(ODstress2 + IDstress2)/(ODstress2 - IDstress2) and τ = |Torque|.ODstress / (2Iz) + 2S /A 357 w System Modelling: Data and Results, Lines where A is the pipe wall cross sectional area, i.e. A = (π/4)(ODstress2 - IDstress2) The longitudinal stress, σL, which varies over the pipe wall cross section, is chosen to ensure that the equivalent stress, σA, evaluates to the largest possible value. This is done by calculating the equivalent stress using the minimum and the maximum longitudinal stress in the pipe wall cross section and choosing the largest of the two possible values for the equivalent stress. The minimum and maximum longitudinal stresses are given by σL = Direct Tensile Stress ± Max Bending Stress PD 8010 Axial Compression Check The result reported is equivalent to the axial compression requirement in section G.1.3, PD 8010, rewritten in the form of a unity check, i.e. to satisfy PD 8010 the result should be less than one. It is given by if Fx > 0 Fx/Fxc where Fx = - Tw and Fxc = Fy = π(ODstress-tnom)tnomσy otherwise the Line is in tension, i.e. Fx < 0, and the result is reported as zero. PD 8010 Bending Check The result reported is equivalent to the bending moment requirement in section G.1.4, PD 8010, rewritten in the form of a unity check, i.e. to satisfy PD 8010 the result should be less than one. It is given by |M|/Mc where Mc = Mp(1 - 0.0024ODstress/tnom) where Mp = (ODstress-tnom)2tnomσy PD 8010 Torsion Check The result reported is equivalent to the torsion requirement in section G.1.5, PD 8010, rewritten in the form of a unity check, i.e. to satisfy PD 8010 the result should be less than one. It is given by τshear/τc where τshear is the maximum shear stress due to torsion given by τshear = |Torque|.ODstress / (2Iz) and if ατ < 1.5 τc = 0.542τyατ if 1.5 ≤ ατ ≤ 9 τc = τy(0.813 + 0.068(ατ - 1.5)0.5) otherwise τ c = τy where τy = σy/30.5 and ατ = (E/τy)(tnom/ODstress)3/2 PD 8010 Load Combinations Check The result reported is equivalent to equation G.14, section G.1.6, PD 8010, rewritten in the form of a unity check, i.e. to satisfy PD 8010 the result should be less than one. It is given by if Pi < Po (|M|/Mc + Fx/Fxc)γ + (Po-Pi)/Pc otherwise (|M|/Mc + Fx/Fxc) where 358 w System Modelling: Data and Results, Lines if Tw < 0 Fx = - Tw otherwise Fx = 0 and γ = 1 + 300tnomσhb/(ODstressσhcr) where σhb = ODstress(Po-Pi)/(2tnom) and if σhE ≤ (2/3)σy σhcr = σhE otherwise σhcr = σy{1-(1/3)[2σy/(3σhE)]2} where σhE = E[tnom/(ODstress-tnom)]2 PD 8010 Bending Strain Check The result reported is equivalent to equation G.19, section G.1.7, PD 8010, rewritten in the form of a unity check, i.e. to satisfy PD 8010 the result should be less than one. It is given by if Pi < Po εb/εbc + (Po-Pi)/Pc otherwise εb/εbc where εb is the Max Bending Strain and εbc = 15(tnom/ODstress)2 Collapse Pressure, Pc The Load Combinations Check and Bending Strain Check share a requirement for the collapse pressure, Pc, to be determined. This requires the solution of a third degree polynomial, see section G.1.2, PD 8010. The solution to this equation is given in DNV OS F101 and is also documented in Code Checks: DNV OS F101. Note that for the DNV OS F101 description to be applicable to PD 8010, t2 would be replaced with tnom. The Fabrication Factor, α fab, is included as described in the DNV OS F101 documentation. 6.8.7 Line Contact Modelling The Line Contact facility enables you to model contact between pairs of lines, and it is capable of modelling all sorts of contact situations. The model works by placing penetrators at the nodes or other points of one of the two lines, which then contact the inside or outside surface of a curved cylinder, whose axis follows a smooth spline fitted along the axis of the other line. For example, the line contact model permits OrcaFlex to model systems where: One line is contained within another, such as pipe-in-pipe systems, pull-in operations. One line is constrained to follow another at certain arc lengths, such as drilling riser choke and kill lines, installation guide wires, piggy-back risers. One line strikes the outer surface of another, as seen in riser interference cases. Line Contact versus Line Clashing OrcaFlex also includes another way of modelling contact between lines, called Line Clashing. This is a different way of modelling contact between lines, and the Line Contact and Line Clashing models have different features. To help you judge which might be most suitable for your application, here are the main differences, advantages and disadvantages: The line clashing model is essentially a segment-segment contact model. It models contact by treating each segment of the clash-checked line sections as being a straight cylinder, with an elastic outside surface, and then calculating any penetration between pairs of those cylinders and applying contact loads proportional to and opposing that penetration. The line contact model is a point-surface contact model, in which localised penetrators are attached at the nodes, or at other points, on one of the two lines (referred to as the penetrating 359 w System Modelling: Data and Results, Lines line), and these contact the inner or outer surface of a curved cylindrical solid whose axis follows a smooth spline fitted through the nodes of the other line (referred to as the splined line). The line contact model is a more sophisticated model that can be used for many different purposes. It can model internal contact, such as pipe-in-pipe or J-tube pull-in, as well as external contact. Friction can be included during dynamics in both the axial and circumferential directions. Line contact can model sliding contact, including cases where the lines move a lot relative to each other while in contact. The line clashing model, on the other hand, only models contact between the outer surfaces of the lines. Line clashing is not really suitable for cases where the contact persists while the contact location slides significantly along either line, since clashing does not include friction and the interaction is between straight segments. This means that if the contact location reaches a node then the clashing lines are likely to get locked together at that node (rather like a pair of multi-segment jointed rods would behave if they wrapped around each other). If the line contact model is used for outside contact then there is a danger that the lines may pass through each other without contact occurring. This occurs if the nodes or penetrators on the penetrating line are more widely spaced than the outside diameter of the splined line. This is because the curved solid cylinder along the splined line could pass between the penetrators on the penetrating line, without making any contact. Because of this issue you would need to use short segments or place extra penetrators on the penetrating line; to ensure that line contact is captured. This problem does not arise with the line clashing model, since the whole of each clashchecked segment, rather than a set of points along its length, is checked for contact with all other clash-checked segments. So with the line clashing model, lines can only pass through one another without contact if the segments move a whole diameter or farther in a single time step. Line contact is included in the static analysis, whereas line clashing is not – it is only active in the dynamic analysis. Line clashing can model contact of one part of a line with another part of the same line. This is not possible in line contact – you would need to model the real continuous line with two separate lines, typically joined with a negligible 6D Buoy, in order to model contact between the two parts. Interaction model Line contact is specified as a relationship between two distinct lines in an OrcaFlex model. One of those lines is the splined line, which has a smooth spline curve fitted between the line nodes. These splines allow OrcaFlex to represent the line as a smooth, deformable cylinder for contact. The other line in the relationship is the penetrating line. Penetrators attached to the nodes of the penetrating line interact with the splined line by contact with a flexible cylindrical elastic solid whose axis follows the spline. Note: The splines used for line contact modelling are distinct from the splines that may be used for a line's step 1 statics method. Contact is modelled by OrcaFlex attaching penetrators to some or all of the nodes of the penetrating line. By default, these are placed coincident with the line nodes, but their distribution along the line and offset from the line nodes may alternatively be set with user-specified data. When contact occurs between one of these penetrators and the contact surface presented by the splined line, force and moment are applied to the penetrator, which transfers those loads to the line node to which it is attached. Equal and opposite load is also applied to the contact surface, and that load is transferred to the nodes at either end of the splined line segment. The contact between penetrating line nodes and splined line segment elastic solids is the same as the contact between OrcaFlex lines and elastic solid shapes. Friction can therefore be applied to the contact during dynamics. Relative motion of the two lines will lead to rolling or sliding contact. The lines cannot be 'locked' together by this model. In order for the three interactions listed earlier to be implemented using the existing shape contact model, some further data about your intentions for the penetration must be provided to the line contact relationship. There are three types of behaviour illustrated below. Note: In the figures, the deviation of the spline (dashed centreline) from the line segments (solid centerline) has been greatly exaggerated. It is expected that during practical use the segmentation will be sufficiently fine that the splines will remain close to the line segments. Penetrating Line is Inside The contained line is represented by the penetrating line. When the penetrating line nodes are within the length of the containing line, their penetrators will contact the inner surface (bore) of the containing line. The inner surface of the containing line is the only contact surface, so the contained line nodes cannot escape other than by running off the end of the containing line. The containing line is represented by the splined line. 360 w System Modelling: Data and Results, Lines Spline z y Splined Line Segment x Contact Surface y x z Penetrating Line Node and Penetrator Line End Axes Figure: Line Contact with penetrating line inside splined line. The contact surface is the inner surface of the splined line. The penetrating line is the inner line. Penetrating Line is Around Some or all of the penetrating line nodes have penetrators which apply a constraint to the splined line. At other points the lines do not interact. The splined line runs within the constraints applied by the penetrating line. The splined line can move relative to the penetrators, and so the smooth splined shape is used to present a contact surface. The splined line is considered as a solid cylinder for this type of contact. This means that the only contact surface is the outer surface of the cylinder whose axis is defined by the segment splines. Spline z y Splined Line Segment x Contact Surface y x Line End Axes Figure: z Penetrating Line Node and Ring Penetrator Line Contact with penetrating line around splined line. The contact surface is now at the outer diameter of the splined line. The splined line is the inner line. 361 w System Modelling: Data and Results, Lines Penetrating Line is Outside The two lines are expected to be outside one another, and the nodes of the penetrating line make contact with the outer surface of the cylinder whose axis is defined by the splined line. In this case it is not usually important which of the two lines is chosen to have penetrators at its nodes, and which presents the contact surface. Spline z y Splined Line Segment x Contact Surface Line End Axes y x z Penetrating Line Nodes Figure: Line Contact with penetrating line outside splined line Offset Penetrators If Penetrator Locations are used then penetrators may be offset from the nodes of the penetrating line. One expected use of this facility is the representation of piggyback riser systems. Lines in this configuration are clamped together with some fixed offset, rather than being inside one another. If the Around interaction method is used to model clamps placed between two lines, the penetrating line can be thought of as placing rings around the splined line. The detail of the modelling is therefore relatively close to reality. The use of offset penetrators with the Around method is drawn below. 362 At a change in the line types along the splined line. Spline z y Splined Line Segment x Contact Surface y x Offset Penetrators z Line End Axes Penetrating Line Nodes Figure: Inside Line Contact with penetrators offset from line nodes Splined line cylindrical solid diameter The flexible. Lines Spline z y Splined Line Segment x Contact Surface y x Offset Ring Penetrators z Line End Axes Penetrating Line Nodes Figure: Around Line Contact with penetrators offset from line nodes The Inside interaction model can also be used to place offset penetrators between the two lines that will provide clamp behaviour. and the line type bore diameter (including modification due to linings) will be used for inside contact. and an illustration is provided below for completeness. cylindrical elastic solid whose axis follows the spline of the splined line takes its diameter from the line types used on the segments of the splined line. the diameter may change. This presents a discontinuity in the model. The line type contact diameter is used for outside or around contact. 363 .w System Modelling: Data and Results. which may cause simulations to become unstable. OrcaFlex interpolates linearly at a change in diameter. Scaling for the contained line's seabed contact. The Containment Enabled choice determines if such scaling is applied to the contained line. Lines To avoid such a discontinuity. The figure below shows penetrators in two cases where the assumptions made result in the same scaling factor of approximately 0. Containment Scaling When a penetrating line is inside or around a splined line. one of the lines may protrude from the end of the other. Scaling for line contact depends on what proportion of the contact length represented by each penetrator overlaps with the length of the splined line. Scaling may also be applied to the contained line's interaction with the seabed and elastic solids and the contained line's fluid kinematics when this occurs. over 10% of segment length on both sides of the node at the change in line type.w System Modelling: Data and Results. This is illustrated below. When OrcaFlex determines how much length from a line node or penetrator overlaps the length of another line. Larger diameter line type Smaller diameter line type Contact diameter 10% of segment length 10% of segment length Splined line node between line sections Figure: A change in diameter is interpolated across the change in line sections.4 being used. any angle between the two lines is ignored. Node Length Splined Line Node Overlap Length Penetrating Nodes Segment Midpoint Figure: Assumed segment position Scaling assumes that penetrator length is aligned with the splined line axis. solid contact and fluid kinematics depends on how much of the line length represented by each of the contained line's nodes overlaps with the length of the containing line. Scaling is applied to the line contact force. 364 . And the fluid dynamic forces applied to a given inner line node will be calculated based on external fluid velocity and acceleration vectors that are taken to equal the velocity and acceleration of that part of the outer line that contains the inner node at that time. OrcaFlex will instead apply fluid forces from the contents fluid and contents motion in the containing outer line. This option (b) allows contact relationships to be set up to model pullin of a single inner line through multiple free-flooding outer lines. The line results Relative Velocity. use the implicit integration scheme. then the external fluid velocity and acceleration used to calculate the fluid dynamic forces on the inner line node will be the velocity and acceleration of the part of the outer line that contains that inner node at that time. This shielding behaviour is enabled or disabled using the Containment Enabled check-box for a line contact relationship. then the external pressure and density are as for a normal (i. and therefore the environmental velocity and seabed resistance values are scaled down to zero. but only if either (a) the outer line involved is the same in all those relationships. The containment behaviour depends on the Contents Method used by the outer line. fluid inertia loads between contained line nodes and the contents fluid of the containing line are not included. Axial Relative Velocity. If these effects must be included in your analysis. If the explicit integration scheme is used. Normal Relative Velocity. These effects therefore do not affect fully contained nodes at all during the simulation. If the inner node is part-contained. When this occurs. See above for details of how the containment scaling factor λ is calculated. Reynolds Number. or (b) the outer lines involved all have their Contents Method set to be free-flooding. not those of the fluid contents of the containing line. If the outer line Contents Method is Uniform. in the same way that the inner line's contact with elastic solids and the seabed is shielded. or the splined line if the penetrating line is Around) might be contained inside the outer line. Note: A line can be an inner line in more than one contact relationship. Attachments to any contained inner node will therefore – probably wrongly – be subject to fluid loading based on the fluid density. e. drag chains. If the outer line Contents Method is free-flooding. OrcaFlex can automatically shield the contained length of inner line from the environmental fluid forces. If the inner node is not within the outer line at all. For the fluid dynamic loads on the inner line. due to any current and waves.e. Often. plus 1-λ times the motion of the sea. then the external fluid velocity and acceleration used to calculate the fluid dynamic forces will be λ times the motion of the outer line end. as follows: The outer line cannot have its Contents Method set to Slug Flow – it must be either Uniform or Free-Flooding. then some length of the inner line (the penetrating line if it is Inside. stiffeners or 6D Buoys will experience external fluid conditions that ignore any containment of the inner node to which they are attached. then the external fluid velocity and acceleration used will be those of the sea. all of the length of inner line that it represents is inside the outer line at that time). for part or all of the simulation. non-contained) line.e. The relative velocity and seabed resistance results reported are scaled by each node's containment scaling factor in order to arrive at the conditions actually applied during the simulation. with proportion λ of its node length inside the outer line and proportion 1-λ protruding beyond the end of the outer line. Strouhal Frequency. Warnings: The containment modelling does not apply to any attachments to the inner line. So any attached clumps. They therefore report the fluid conditions or seabed interaction that the node would have experienced if it had been fully exposed to the environment. then the entire inner line is treated as being fully contained within the outer line at all times. the node is completely contained. pressure and kinematics of the sea. providing each inner line node leaves one outer line before entering the next outer line. Seabed Normal Resistance and Seabed Normal Resistance/D (when the default linear seabed resistance model is used) do not take into account line containment. and each inner line node is inside at most one of those outer lines at any one time. Lines Scaled Fluid Loads When a line contact relationship specifies that its penetrating line is Inside or Around the splined line. For a shielded length of line. 365 .w System Modelling: Data and Results. In this case the external pressure and buoyancy force experienced by the inner line nodes will be calculated using the internal contents pressure and density of the outer line.g. OrcaFlex will calculate what proportion of each inner line node is contained within the outer line at each instant. If the inner node is fully contained (i. An inner line node that enters into. then all of the inner line will be shielded from the environment. i. by the outer line. and so shielded. the inner line can protrude from the ends of the outer. Note that you should take care if any VIV modelling. Ad. If a line contact relationship specifies a penetrator discretisation count greater than one. wake interference or lift forces due to seabed proximity are specified for an inner line section for which containment might occur. OrcaFlex generates that number of penetrators in place of what would otherwise be a single penetrator. which can only represent contact at a single point. This results in a singularity in the force model which can lead to noisy or unstable simulations. If these outer lines do not have free-flooding contents. pull tubes or riser guides. an outer line end during the simulation will therefore experience a discontinuity when the force from these effects is suddenly disabled (when entering containment) or re-enabled (when emerging from containment). Do. The discretised penetrators are evenly distributed in such a way as to best represent the original single penetrator's contact surface. that has been discretised into multiple penetrators. This is not appropropriate for any inner line nodes that are contained.: Dd = scale*Do and Ad = scale*Ao By default the contact length is the contact area divided by the contact diameter. equal to that of the original single penetrator's diameter. Penetrator Discretisation Penetrator discretisation is intended to be used when the line contact penetrators and the spline have the same. Specifically: Any VIV modelling and lift forces specified in the data will be disabled on an inner line node whenever any amount of the length of line modelled by the node is contained. as part of the Penetrator Locations data. the contact can be robustly defined. using a penetrator discretisation count of 3 and a penetrator discretisation scale of 0. placed around the original contact surface. By discretising the original penetrator into multiple smaller penetrators. i.w System Modelling: Data and Results. diameters. the contact length is not scaled. An example of this is a centralised pipe. and its buoyancy will be calculated using the outer line's contents density. even though it is no longer inside the outer line length. and so is invariant under the above scaling. and area. such as bend stiffeners. and will still react to any wake from upstream lines that generate wake. but will still not be exposed to the environment. Penetrator discretisation is only available for penetrators from Inside or Around relationships. Ao multiplied by the penetrator discretisation scale. and areas. In such a case the true contact force occurs at all points on the circumference of the penetrator simultaneously and so is ill-defined by a single penetrator.e. 366 . or very similar.: L = Ad/Dd = (scale*Ao)/(scale*Do) = Ao/Do When specified. drawn in blue. if that is specified in the data. The new set of discretised penetrators are given contact diameters.e. So it is therefore recommended that you do not specify wake generation or wake reaction for any inner line section that will be contained at any time during the simulation.4. Any Wake interference effects specified in the data are not affected by inner line containment – they will continue to be included even if the inner line node is contained within the outer line. This is a common source of error when modelling relatively short outer lines. from a penetrating line that is in an Inside relationship. where the centralisers are in an interference fit with the outer pipe. Lines If the outer line Contents Method is Uniform. since they will be shielded by the outer line. drawn in black. This is most easily described pictorially: the below figure illustrates an original single penetrator. Dd. The inner line nodes will therefore still generate wake. or emerges from. y x Figure: Around penetrator discretisation using count=3 and scale=1. Lines y x Figure: Inside penetrator discretisation using count=3 and scale=0.w System Modelling: Data and Results. Using Penetrator Discretisation Usually when discretising a penetrator from an Inside relationship one would choose a penetrator discretisation scale less than one.6.6.4. in this example the discretisation is specified using a penetrator discretisation count of 3 and a penetrator discretisation scale of 1. Again the original penetrator is drawn in black and the new set of discretised penetrators are drawn in blue. The discretisation of a penetrator from a penetrating line that is in an Around relationship is illustrated in the below figure. conversely when discretising a penetrator from an Around relationship one would choose a penetrator discretisation scale greater than one. Using a larger number of discretised penetrators will result in a 367 . is proportional to the penetrator contact area which is scaled by the penetrator discretisation scale. One such change that can be significant is the effective stiffness between the penetrating line and the splined line. the reaction force is proportional to the penetrator discretisation scale. Data Line contact data for all lines in the model are specified on a single data form with two pages: Relationships and Penetrator Locations. In this case there would be multiple overlapping penetrators. Containment Enabled This choice instructs OrcaFlex whether fluid loads and elastic solid contact on the inner line in this relationship should take account of its containment within the outer line. You should use a penetrator discretisation count and scale that will ensure a well defined contact surface and you can then use the contact relationship’s line contact normal stiffness to meet the desired level of effective stiffness between the penetrating line and the splined line. When using different count and scale values you can expect to see quite different model behaviour in some cases. the distribution and position of penetrators on the penetrating line can be specified in detail. One reason for this change in effective stiffness is that the reaction force a penetrator feels. as such it defines how many penetrators will come into contact with the spline simultaneously. Outside or Around the splined line. and specify the contact and containment relationship between them. A simple example of when the effective stiffness between the penetrating line and the spline would increase is the case where the penetrator discretisation scale is left as one. which directly influences how stiff the overall contact is between the two lines. and a penetrator discretisation count greater than one is specified. Penetrating Line Is. The splined line will present a curved cylindrical contact surface to the penetrators attached to the penetrating line. An example of when the effective stiffness between the penetrating line and the spline would decrease is the case where a penetrator from an inside relationship is discretised using a very small penetrator discretisation scale and a low penetrator discretisation count. For more detail on how this interaction is modelled. 368 . will then come into contact with this surface if they meet it. The default behaviour is to attach a penetrator at every node on the penetrating line. depending on whether the penetrating line is specified to be Inside. at the node centre. Another reason for the change in effective stiffness is the penetrator discretisation count defines the number of discretised penetrators and their distribution around the contact surface. This is simply because the representation of the physical system has changed. For details of how containment is handled see Line Contact Modelling. at each row of the penetrator locations data set. i. In this case only a few discretised penetrators would contact simultaneously and their contact areas will have been reduced proportional to the penetrator discretisation scale.e. as specified by the Penetrator Locations data. Lines better representation of the true physical contact surface being modelled but this comes at the expense of the computational overhead associated with the extra penetrators.e. If you are confident that there is only going to be a single point of contact. Penetrators on the penetrating line. the same size as the original penetrator. then penetrator discretisation is not required because the contact surface is well-defined by a single penetrator. see the modelling page. by defining a named data set of penetrator locations on the Penetrator Locations page of the data form. and the curved cylinder axis will follow a smooth spline curve that follows and passes through the nodes of the splined line. and experience reaction and friction forces that are calculated using the Normal Stiffness and Shear Stiffness. i. that would all contact the spline simultaneously and so the effective stiffness would increase proportional to the count. Alternatively. and then selecting that name set on the Relationships page. Splined Line These three choices select two lines from those present in the model. Relationships Penetrating Line. The splined line contact surface will be either the external or internal surface of its curved cylinder. when it penetrates the spline. Penetrator Discretisation Count and Scale Count specifies the number of penetrators used to represent the contact at each node or. at any given penetrator location. Penetrator Locations Penetrators are attached to some or all of the nodes of the penetrating line. if Penetrator Locations data has been specified. unscaled.w System Modelling: Data and Results. These results are available using the Results Selection form. Angles. So OrcaFlex groups the results variables into the following categories: Positions. If the axial coefficient is set to '~' then the normal friction coefficient is used for all directions of motion. starting from zero at end A. in which case de-selecting them reduces the displayed list of variables to a more manageable set. Contact. For details of how penetrator discretisation is conducted see Penetrator Discretisation. Shear stiffness is used by the friction calculation. Results from the modal analysis and fatigue analysis are described elsewhere – see the Modal Analysis and Fatigue Analysis sections. in which case no contact forces will be applied. To get the full list of available variables simply select all the categories. Normal and Shear Stiffness Normal Stiffness is the reaction force that the contact generates per unit depth of penetration per unit area of contact. To ease results selection the Show boxes on the results form allow you to choose which of these categories of variables are shown in the Variable list. Penetrator Locations Number of data sets. Contact Area. End Loads. in line axes directions. y and z position relative to the penetrating line. These locations can therefore be used by more than one relationship if desired. Fluid Loads. and the x and y values specify the offset from the penetrating line axis. Lines If the count is greater than one then the Scale is used to calculate the effective contact radius and the effective contact area of the penetrators. The contact length specifies the length considered for scaling. Motions. But normally there are several categories of variable that you do not currently need. Contact Length The contact properties of these penetrators are specified here. Friction Coefficients Normal and axial friction coefficients. Contact Diameter. 6. Name A set of penetrator locations represents a specific distribution of line contact penetrators along the penetrating line. but fluid loads will still be affected by any containment that the relationship gives. Code Checks. 369 . OrcaFlex will attach a penetrator to the line node nearest to the arc length required. Moments. If a value of '~' is specified for the contact length it is calculated as the contact area divided by the contact diameter. Each data set is named. For full details of the friction calculation see Friction Theory. Selecting which Categories of Line Results are Shown For Lines there are a large number of results variables available on the Results form. The z value specifies the arc length along the penetrating line.8. A value of '~' results in the Normal Stiffness being used. Position. Stiffness may be set to zero.w System Modelling: Data and Results. A radial offset of the penetrator from the line node can be specified using the x-y position data. z relative to The penetrator locations are specified by giving their x. Pipe Stress / Strain.8 Line Results This section describes the line results that are available for the static and dynamic analyses. Forces. rather than being associated with a particular relationship. The available result points depend on which variable you request. OrcaFlex reports results for the 'nearest appropriate' result point.Theta) of the point within the cross section. two extra columns become visible in the Position table. stress components) you must also specify the position of the point within the cross section through the specified arc length. Clearance Results Clearance results can be reported either as clearances from this line to all other lines or from this line to a specified other line. These extra columns specify the polar coordinates (R. Note: The actual arc length for which line results are reported may not be exactly the specified arc length. where N is the total number of segments in the line. The Node column can also be used as an alternative way of setting the arc length. Three rows in the table are dedicated to special arc lengths on the line: The first and last rows in the Position table are dedicated to the line's end points A and B. 370 . see the diagram in the Pipe Stress Calculation section. There are multiple rows in the table. You are then offered the Variables that are available for the point specified by the currently-selected row. Arc Length and Node Columns The Arc Length column specifies how far along the line the point is. When you ask for a variable at a specified arc length OrcaFlex gives the value for the 'nearest appropriate' result point. If you specify an arc length that is exactly at the boundary of two sections then OrcaFlex uses the section that starts at that arc length. This is defined to be the first node on the seabed (starting from the Top End). we call these points 'result points'. The adjacent Arc Length cell will then be set to the arc length to that node. mid-segment points and line ends. measured from zero at End A. Results are not available for points between these two radii. Lines Specifying the Position on the Line For line results you need to specify the position on the line at which you want results. For information. The global coordinates of the selected node.w System Modelling: Data and Results.g. The horizontal component of distance between the selected node and the touchdown point. Layback Available at nodes. so you can set up rows specifying a number of different points of interest and then easily switch between them by choosing which row you select. meaning 'unspecified'. Whenever one of these variables is selected in the Variables list. meaning the radii corresponding to the Stress ID or Stress OD respectively. You can set the Node column to the number of a node on the line. When there are no nodes on the seabed then the results variable is reported as N/A (meaning 'not available') and the graph shows no value. Each row in the table specifies one point on the line. Y and Z Available at nodes. The R column can only be set to either Inner or Outer. You choose which of the options is used from the drop-down list labelled "Clearances are reported as clearances from". The node number must be in the range 1 (the node at End A) to N+1 (the node at End B). R and Theta Columns For some variables (e. If the results variable selected is a segment variable (i. is only available at mid-segment points) then the value reported for the touchdown point is the mid-segment valued in the segment that precedes the Touchdown node. Result Points OrcaFlex uses a discretised model and so results are only available at nodes. Positions X. OrcaFlex always labels results with the actual arc length to the result point to which they apply. so you can check to ensure that you are getting results at the result point you want. This is done by setting the entries in a row in the Position table on the results form. In a row that you don't want to use you can set the Node or Arc Length column to '~'. See Result Points below. The phrase 'nearest appropriate' here means that OrcaFlex considers the available result points that are in the same section as the arc length you specified and then chooses the one that is nearest to the arc length you specified. The next to last row in the table is dedicated to the Touchdown point. they are documented in the description of the variable.e. if you set the Arc Length column then the adjacent Node cell is set to the number of the nearest node to that arc length. a. GY-Acceleration. Ezx-Angle and Ezy-Angle (so values outside the range -360° to +360° might be reported). If the log sample interval is small then the results may be inaccurate due to loss of precision due to subtraction. This relative acceleration can be thought of as the acceleration of the point P relative to the free-falling state. The magnitude and components. g Available at nodes. with its measurement directions aligned with the node axes directions. The angle between the relative velocity direction and the line axial direction. Range jump suppression is applied to Azimuth and Gamma (so values outside the range -360° to +360° might be reported). These angles report the local orientation of the line relative to global axes. GY-Velocity. That is. then Layback is not defined. relative to the vertically downwards acceleration due to gravity. The amplitude of the oscillation in the transverse VIV direction divided by the node's VIV diameter. Because of this the accuracy of the results (especially the accelerations) will depend on the log sample interval. g. g. of the node. The arc length from End A to the selected point. of the acceleration vector. if the selected node is after the touchdown point. x-Acceleration rel. If the log sample interval is large then the results will not show higher frequency components of velocity and acceleration. Acceleration. allowing for any motion of the object to which the line is attached. The direction angles of the results point (either an end node or a mid-segment point). 371 . Range jump suppression is applied to Exy-Angle. A value in the range 0° to 90°. Ez-Angle is in the range 0° to 180°. This is normally only useful for the touchdown point. that is if there are no nodes on the seabed. g. Arc Length Available at nodes. Angles Azimuth. This is the acceleration that would be reported by an accelerometer attached to the node (since an accelerometer reading of zero corresponds to free-falling). No-Moment Azimuth. in the transverse VIV direction. GZ-Acceleration Available at nodes. Motions Velocity. The gamma angle is defined as for line ends – see Line End Orientation. The twist per unit length experienced by the segment. Ezx-Angle. using the central difference scheme. Twist Available at mid-segment points. y-Acceleration rel. z-Acceleration rel. These results are only available if the end orientation angles are defined. in node axes directions. Fluid Incidence Angle Available at nodes. No-Moment Declination Available at line ends. since for other points it is constant. relative to global axes. Expansion Factor Available at mid-segments. For the touchdown point it gives the arc length from End A to the first node on the seabed. GX-Velocity. The azimuth and declination angles. Warning: The velocity results are derived by numerically differentiating the logged positions of the node with respect to time. Likewise. The expansion factor of the selected segment. Ezy-Angle Available at mid-segment points and line ends.w System Modelling: Data and Results. Exy-Angle. Declination is in the range 0° to 180°. Acceleration rel. This is the node's offset from the non-VIV node position. Ez-Angle. of the no-moment direction at the end. GX-Acceleration. Estimated Transverse A/D Available only at nodes that use one of the time domain VIV models. The magnitude and components (with respect to global axes) of the velocity and acceleration of the node. GZ-Velocity. See End Direction Results. The acceleration results are derived by a further such numerical differentiation. or zero if there is no touchdown. Transverse VIV Offset Available at nodes. these results report the vector a . g. Lines Layback is not defined (N/A) if there is no touchdown point. Declination and Gamma Available at mid-segment points and line ends. relative to the end axes of the nearest line end.g. In-plane Shear Force. Forces Effective Tension and Wall Tension Available at mid-segment points and line ends. Lines No-Moment Declination is in the range 0° to 180°. Bend Moment component. This result is most useful when the free-flooding or slug flow contents methods are in use. The direction angles of the end force vector. The azimuth and declination of the end force vector. its component in the user specified local direction theta and its components in the in-plane and out-ofplane directions. its components in the local x and y-directions. End Force Ez-Angle. VIV Neg Separation Point. The reported wall tension is the total wall tension. For details of the difference between the effective tension. In-plane Bend Moment. Range jump suppression is applied to No-Moment Azimuth (so values outside the range -360° to +360° might be reported). End Force Ezy-Angle Available at line ends.w System Modelling: Data and Results. Positive values denote tension and negative values denote compression. Contents Density Available at nodes. End Force Exy-Angle. x-Bend Moment. End Force Declination is in the range 0° to 180°. For details. Shear Force component. Te. Transverse Vortex Force. In particular see the note on that page if the line type stress diameters differ from the outer and inner diameters. GX-Vortex Force. Range jump suppression is applied to End Force Azimuth (so values outside the range -360° to +360° might be reported). y-Bend Moment. GY-Vortex Force. End Force Declination Available at line ends. The magnitude of bend moment. relative to global axes. Moments Bend Moment. The in-plane direction is normal to both the line's axis and the out-of-plane direction. y-Shear Force. Out-of-plane Bend Moment Available at mid-segment points and line ends. and the wall tension. Inline Vortex Force. Inline Drag Amplification Factor Available only at nodes that use one of the wake oscillator VIV models. See End Direction Results. 372 . see the documentation of the relevant time domain VIV model. If the line's axis is vertical then these directions are ill-defined and therefore no values can be reported. Tw. Available at mid-segment points and line ends. scaled by the tensile stress loading factor. These results are only available if the end orientation angles are defined. The values reported are the angular positions of the stagnation and separation points. VIV Pos Separation Point Available only at nodes that use one of the vortex tracking VIV models. End Force Ezx-Angle. The magnitude of structural force normal to the line axis. Shear Force. with respect to the frame of reference of the line end. Range jump suppression is applied to the other 3 end force angles (so values outside the range -360° to +360° might be reported). Out-of-plane Shear Force Available at mid-segment points and line ends. The instantaneous value of the Inline Drag Amplification Factor. not available if the Allowable Tension is set to '~'. The structural force along the line axis. Vortex Force Magnitude. End Force Azimuth. and its components in the VIV directions and global axes directions. GZ-Vortex Force Available only at nodes that use one of the time domain VIV models. its components in the local x and ydirections. The magnitude of the lift and drag force per unit length of line. T w. Normalised Tension Defined to be Effective Tension divided by Allowable Tension. End Force Ez-Angle is in the range 0° to 180°. see the Line Pressure Effects section. By default this loading factor equals 1. x-Shear Force. its component in the user specified local direction theta and its components in the in-plane and out-of-plane directions. VIV Stagnation Point. The out-of-plane direction is normal to both the line's axis (at the specified arc length) and the vertical direction. The magnitude of curvature. 373 . Out-of-plane Curvature Available at mid-segment points and line ends.w System Modelling: Data and Results. These line clearance results report shortest distances between the segment or line end and the segments of other lines in the model. Line Centreline Clearance reports the centreline clearance from this line to the clearance lines. Line Clearance Available at mid-segment points and line ends. Note: When using non-linear bend stiffness. The results selection form lets you choose to report clearances either: from this line to all other lines or from this line to a specified other line. Notes: Bend radius is defined to be 1 / curvature. Warning: Curvature results are accurate only if the segment length is sufficiently short. Curvature. Defined to be Curvature divided by Allowable Curvature. If minimum bend radius (MBR) is specified as varying with wall tension then this variation is taken into account when calculating Normalised Curvature. be they all other lines or a single specified other line. allowing for their contact diameters. If the line's axis is vertical then these directions are ill-defined and therefore no values can be reported. Normalised Curvature Available at mid-segment points and line ends. Note: Line Clearance can report negative values. y-Curvature. The accuracy can be estimated by performing a sensitivity study on segment length in the area of interest. x-Curvature. The accuracy can be estimated by performing a sensitivity study on segment length in the area of interest. the reported mid-segment curvature depends on whether the bend stiffness is specified to be hysteretic or not. Torque Available at mid-segment points and line ends only. If clashing is being modelled for both segments then a clash force will result from this penetration. In the text below we refer to the other lines used in the clearance calculations as the clearance lines. For details see the note in the Non-linear Bend Stiffness section. Bend Radius component. The component of structural moment along the line axis. the reported mid-segment curvature depends on whether the bend stiffness is specified to be hysteretic or not. Bend Radius. its components in the local x and ydirections. When pre-bend is modelled these results are reported relative to the pre-bent curvature. its component in the user specified local direction theta. These distances can be either the shortest distance between centrelines (Line Centreline Clearance) or the shortest distance between outer edges (Line Clearance). When clearance is reported for a line end it reports the shortest distance from the centreline of the point at the end node to the centreline of any segment on the clearance lines. Note that the clearance reported therefore does not allow for the radii of the lines involved. Contact Line Clearance Results Line Centreline Clearance. its component in the user specified local direction theta and its components in the in-plane and out-ofplane directions. Line Clearance is similar but it reports the clearance between line outer edges. and available only for lines with torsion included. In-plane Curvature. In-plane Bend Radius. This means that the segments in question are penetrating each other. More precisely. Warning: Bend radius results are accurate only if the segment length is sufficiently short. If the curvature is 0 then a value of 'Infinity' is reported. y-Bend Radius. Lines The out-of-plane direction is normal to both the line's axis (at the specified arc length) and the vertical direction. Out-of-plane Bend Radius Available at mid-segment points and line ends. its components in the local x and ydirections. x-Bend Radius. The in-plane direction is normal to both the line's axis and the out-of-plane direction. The magnitude of bend radius. the clearance reported for a segment is the shortest distance from the centreline of the segment to the centreline of any segment on the clearance lines. as defined above. For details see the note in the Non-linear Bend Stiffness section. as defined above. When using non-linear bend stiffness. the in-plane and out-of plane-components and its components in the in-plane and out-of-plane directions. Curvature component. When pre-bend is modelled curvature results are reported relative to the pre-bent curvature. They are available in both range graph and time history form. Line clearance only checks against other lines. Ny. Line Contact x-Force. This then is the potential energy in the spring/damper. building and updating clearance graphs can be slow. Having "live" clearance graphs open while a simulation is running can significantly slow down the simulation. However you can check clearance against part of a vessel. 374 . The mooring line clearance is probably more useful. not against edges of vessels. You can then examine the time history of line clearance for that point on the line. Line Contact x-Force. If multiple clashes occur simultaneously on the same segment then the value reported is the sum of all individual clash energies between this segment and other segments. Line Contact Results Line Contact Force. Notes: For mid-segment points the segment used is the one containing the selected arc length. Line Contact y-Force and Line Contact z-Force are the components of that total Line Contact Force in the line's node Nx-. Line Contact y-Force. for a given period of the simulation. Let us assume that you are reporting clearances from all other lines. between which clashing may not be a concern. Line Clashing Results Note: As well as the results variables documented below OrcaFlex also provides a Line Clashing Report. Warning: For complex models.w System Modelling: Data and Results. buoys. The clash energy for the spring/damper representing contact between these 2 segments is calculated by integrating the magnitude of clash force with respect to depth of penetration. Line Contact Force is the magnitude of the total force per unit length. The magnitude of the clash force between this segment and other lines. Please note that this variable is only available if clash checking has been included for the lines concerned. Solid Contact Results Solid Contact Force Available at nodes. An example is checking for clashing between a single mooring line and one or more of a number of closely spaced flowlines. It is sometimes worth choosing carefully which line to check for clearance. etc. Line Clash Impulse Available at mid-segment points. for example. Line Clash Energy Available at mid-segment points. Clash energy is calculated by integrating the magnitude of clash force with respect to depth of penetration. due to Line Contact with any of the lines in the model with which it has a specified line contact relationship. You can then use the replay to examine which other line is coming closest. See Line Clashing for details. The integral of Line Clash Force with respect to time. Line Clash Force Available at mid-segment points. Line Clash Force is given for the segment containing the selected arc length and results are available in the form of time histories and range graphs. by attaching a dummy single-segment line to the vessel. The magnitude of the total force per unit length. The line clearance graphs for that dummy line will then show how close other lines come to that area of the vessel. Line Contact z-Force Available at nodes. since it only includes clearance to the flowlines. to see when closest approach occurs. The clearance graphs for the flowlines will include clearance to the other flowlines. Lines The line clearance variables are useful for checking for clashing between lines. due to contact with any of the elastic solids in the model. The range graph. Suppose that this segment is denoted by S1 and segment S2 is another segment which S1 is in contact with. If multiple clashes occur simultaneously on the same segment then the value reported is the magnitude of the vector sum of the clash forces involved. Line clearance results are only available if there are at least 2 lines in the model. spanning across the area of interest.and Nz-axes directions. enables you to see where on the line clashing may be a problem. w System Modelling: Data and Results, Lines Seabed Contact Results Seabed Clearance Available at nodes. The clearance is the shortest distance between the node and any point on the seabed, allowing for the contact diameter. The value reported is for the node that is nearest the specified arc length. A negative value indicates that the node is in contact with the seabed. This result is not available for 3D seabeds because it is difficult to calculate. Instead you should use Vertical Seabed Clearance. Vertical Seabed Clearance Available at nodes. The clearance is the vertical distance between the node and the seabed, allowing for the contact diameter. The value reported is for the node that is nearest the specified arc length. A negative value indicates that the node is in contact with the seabed. Seabed Normal Penetration/D Available at nodes. The component of seabed penetration normal to the seabed, divided by the contact diameter. Seabed Normal Resistance, Seabed Normal Resistance/D Available at nodes. Seabed Normal Resistance is the component of seabed resistance normal to the seabed, where seabed resistance means the seabed reaction force per unit length of line. Seabed Normal Resistance/D is the Seabed Normal Resistance divided by the contact diameter. The forces due to both seabed stiffness and seabed damping are included. Warnings: The damping force depends upon node velocity. This is derived by numerically differentiating the logged positions of the node with respect to time, using the central difference scheme. Because of this the accuracy of the results will depend on the log sample interval. See Motions results for more details. Seabed resistance results from interaction with a linear seabed are reported without taking into account possible containment arising from participation in line contact. For more details, see the Containment Scaling section of the line contact documentation. P-y deflection, P-y resistance Available at nodes. The magnitude of deflection and resistance of the P-y spring attached to this node. Pipe Stress / Strain Stress and strain results are available at mid-segment points and at line ends. For terminology see Pipe Stress Calculation. The stress calculations make the following assumptions: At each point along the line all the loads are taken by a single simple cylinder of the specified Stress OD and Stress ID and made of a homogeneous material. The stresses included are those due to tension, bending, shear and hoop stress. The loads (tension, bend moment, shear and torque) which are used in stress calculations are scaled by the stress loading factors before being used. Internal pressure in the line generates wall tension in the line as it would do in a sealed cylinder. For the purpose of calculating the components of the stress matrix the shear stress is assumed to be uniformly distributed across the cross section. Although this is not strictly the case, the shear stress is normally negligible so this simplifying assumption is reasonable. The hoop stress due to static internal and external pressure at the current Z-level is included, and is calculated using the standard Lamé equation for thick walled cylinders. However the effect of dynamic variations in pressure, for example from the passage of the wave, are not included. Limitations of stress calculations The assumptions described above mean that the stress calculations are only valid for pipes such as steel or titanium risers, not for composite flexible risers, ropes chains, etc. If the pipe has non-linear stiffness then the program cannot, in general, accurately calculate pipe stresses. The program uses the same formulae for stress calculation as it does for linear stiffness. For example the bending stress is calculated as Mr/Ixy. An exception to this is made for a homogeneous pipe with non-linear stress-strain. In this situation stress results can be calculated accurately by using the stress-strain data. 375 w System Modelling: Data and Results, Lines If the line type stress diameters differ from the outer and inner diameters then see the warning in the Line Pressure Effects section. The program does not, and indeed cannot, allow for the complex stress concentrations that can occur at joints or at the top and bottom of a riser. Direct Tensile Strain Available at mid-segment points and line ends. This is the component of axial strain due to wall tension (which includes the effects of internal and external pressure). Max Bending Strain Available at mid-segment points and line ends. This is the axial strain due to bending at the outer fibre on the outside of the bend. Worst ZZ Strain Available at mid-segment points and line ends. This equals whichever of Direct Tensile Strain ± Max Bending Strain has the larger absolute value. ZZ Strain Available at mid-segment points. This equals Direct Tensile Strain + Bending Strain. ZZ Strain varies across the cross section and so its value is reported at a specified (R,θ) position. Internal and External Pressure Available at mid-segment points and line ends. The internal and external static pressures, Pi and Po. See Line Pressure Effects for details. Pressures in OrcaFlex are gauge pressures, not absolute pressures. That is, they are relative to atmospheric pressure and so can be as low as minus 1 atmosphere (-101.325 kPa). Net Internal Pressure Available at mid-segment points and line ends. Defined as Pi - Po. Direct Tensile Stress Available at mid-segment points and line ends. This is the axial stress due to wall tension (which includes the effects of internal and external pressure). It is constant across the cross section and equals T w/A. A positive value indicates tension; a negative value indicates compression. Max Bending Stress Available at mid-segment points and line ends. This is the maximum value that the Bending Stress takes anywhere in the cross section. It is given by Max Bending Stress = (C2.M.ODstress/2) / Ixy where C2 is the bending stress loading factor, and this maximum occurs at the extreme fibre on the outside of the bend. For a homogeneous pipe with non-linear stress-strain Max Bending Stress = σ(εzz) - Direct Tensile Stress = σ(εzz) - Tw/A where σ(·) is the specified stress-strain relationship and εzz is the axial strain at the extreme fibre on the outside of the bend data. Worst ZZ Stress Available at mid-segment points and line ends. This is the value of ZZ Stress that has the greatest magnitude anywhere in the cross section. Worst Hoop Stress Available at mid-segment points and line ends. The Hoop Stress is due to internal and external pressure. It varies across the section and can be positive (tension) or negative (compression), and by the Worst Hoop Stress we mean the hoop stress of greatest magnitude. It is obtained by finding the point in the cross section where the unsigned magnitude of the Hoop Stress is largest; this must be either at the inside or outside fibre of the stress area. The Hoop Stress at this point is called the Worst Hoop Stress. Max xy-Shear Stress Available at mid-segment points and line ends. This value is based upon an assumption that the pipe is thin walled. Max xy-Shear Stress = (C4.τ.ODstress/2) / Iz + 2C3S/A where C3 and C4 are the shear and torsional stress loading factors respectively. 376 w System Modelling: Data and Results, Lines von Mises Stress, Max von Mises Stress Available at mid-segment points and line ends. The von Mises stress, σvm, is a stress measure that is often used as a yield criterion. It is a combination of all the components of the stress matrix and in terms of principal stresses it is given by: σvm = [{(σ1-σ2)2 + (σ2-σ3)2 + (σ3-σ1)2}/2]½ where σ1, σ2 and σ3 are the principal stresses, i.e. the eigenvalues of the 3 by 3 stress matrix. The von Mises Stress varies across the cross section, so its value is reported at a specified (R,θ) position. The Max von Mises Stress is an estimate of the maximum value of the von Mises Stress over the cross section. The way it is calculated depends on whether the line includes torsion or not, as follows. If torsion is not included, then OrcaFlex assumes that the torque is zero. In this case the maximum value of the von Mises stress must occur in the plane of bending. OrcaFlex also assumes that the maximum occurs at either the inner or outer fibre. (This is a commonly-used assumption that is almost always valid, since if the internal pressure stress contribution is dominant then the maximum will be at the inner fibre, whereas if bending stress is dominant then it will occur at the outer fibre.) OrcaFlex therefore calculates the von Mises stress at 4 points (R = ±IDstress/2 and ±ODstress/2, in the plane of bending) and reports the largest value. If torsion is included, then the maximum value of the von Mises stress can, in general, occur anywhere in the pipe wall. So OrcaFlex calculates the von Mises stress at a grid of points across the pipe wall and reports the largest value found. Currently, the grid comprises 36 θ-values (i.e. every 10° around the pipe circumference) at each of 5 R-values across the pipe wall. RR Stress, CC Stress, ZZ Stress, RC Stress, RZ Stress, CZ Stress Available at mid-segment points and line ends. These are the individual stress components at a point in the cross section. The point is specified by its polar coordinates (R,θ) within the cross section. See Pipe Stress Calculation and Pipe Stress Matrix for details. Code Checks Code Check results are available at mid-segment points and at line ends, for the following codes: API RP 2RD. API RP 1111. DNV OS F101. DNV OS F201. PD 8010. Fluid Loads If the line experiences sea state disturbance this will be accounted for in the fluid load results. Sea Surface Z Available at nodes. The global Z coordinate of the sea surface directly above the instantaneous position of the selected node. Depth Available at nodes. The depth of the node beneath the sea surface (= Surface Z - Node Z). Sea Surface Clearance Available at nodes. The vertical clearance from node centre to the instantaneous sea surface. Negative values mean that the node is submerged. Proportion Wet Available at nodes. The proportion of the part of the line that the node represents, that is submerged in the sea. The value is in the range 0 to 1, a value of 0 meaning no submersion and 1 meaning is completely submerged. For details see Line Interaction with the Sea Surface. Sea Velocity, Sea Velocity X, Sea Velocity Y, Sea Velocity Z, Sea Acceleration, Sea Acceleration X, Sea Acceleration Y, Sea Acceleration Z The magnitude and global X, Y and Z components of the water particle velocity (due to current and waves) and acceleration (due to waves) at the node position. If the node is above the water surface then zero is reported. 377 w System Modelling: Data and Results, Lines Relative Velocity, Normal Relative Velocity, Axial Relative Velocity Available at nodes. Relative Velocity is the velocity of the fluid relative to the node, i.e. Vfluid - Vnode. The results reported are the magnitude of the relative velocity and its normal and axial components (relative to the line). For the axial component, a positive value means that the fluid is moving (relative to the line) towards End B. The fluid velocity used is the velocity of the principal fluid affecting the node. The principal fluid is defined as follows: 1. If proportion dry > 0.5 and the Include wind loads on Lines option is enabled in the Environment data then the principal fluid is the air. 2. Otherwise the principal fluid is the sea. Note: For a node that is above the water surface OrcaFlex reports a relative velocity based on the fluid velocity at the surface point vertically below the node. Warnings: The relative velocity results are derived using the node velocity results, so see the accuracy warning given above. The relative velocity results are reported without taking into account possible containment arising from participation in line contact. For more details, see the Containment Scaling section of the line contact documentation. Strouhal Frequency Available at nodes. The Strouhal Frequency is defined to be St.V/D where St=0.2, V is the normal component of relative velocity and D is the normal drag diameter. Warning: Strouhal frequency is reported without taking into account possible containment arising from participation in line contact. For more details, see the Containment Scaling section of the line contact documentation. Reynolds Number Available at nodes. The Reynolds number is a measure of the flow regime. OrcaFlex offers a number of different options for the calculation of Reynolds number, specified on the Environment data form. Warning: Reynolds number is reported without taking into account possible containment arising from participation in line contact. For more details, see the Containment Scaling section of the line contact documentation. x-Drag Coefficient, y-Drag Coefficient, z-Drag Coefficient, Lift Coefficient Available at nodes. These are the drag and lift coefficients used in the calculation. For constant coefficients then these results report the values given in the user's data, except for a node at the junction between two sections with different coefficients, where an effective average value is used. If the line's drag or lift coefficients vary with Reynolds number or Height above Seabed then these results report the computed value that was used. If the line uses a wake oscillator VIV model with inline drag amplification then the amplification factor is included in these results. The inline drag amplification factor is also available as a separate result. Wake Velocity Reduction Factor, Wake Cd, Wake Cl Available at nodes only, for lines which include sections that react to wake effects. Wake Velocity Reduction Factor is the factor applied to the velocity at the node as a result of upstream wake effects. Wake Cd and Wake Cl are the drag and lift coefficients respectively, used to calculate the hydrodynamic forces at the node as a result of any upstream wake effects. Note: Wake Cl is positive when the lift force is applied in the y direction of the upstream wake's frame of reference and negative when the lift force is applied in the -y direction of the upstream wake's frame of reference. End Loads The line end load results are based on the end force and end moment vectors at the line end. Note that these results include the structural inertia load and added inertia load due to acceleration of the end node. There are 3 groups of end load results: Standard results like Effective Tension, Bend Moment, etc. are available at line ends as well as at mid-segment points. For example to obtain the end tension at End A you can ask for the Effective Tension (or Wall Tension) at End A. 378 w System Modelling: Data and Results, Lines Magnitude and other components of the end force and end moment vectors. Bend Restrictor Load, which is a special end load result useful for bend restrictor design. Sign Convention When considering the sign of end load components the question arises as to whether the load reported is that applied by the line to its connection or vice versa. The OrcaFlex convention is that the load reported at any point is that applied by the B side of that point to the A side. So at End A we report the end load applied by the line to its connection (e.g. a vessel), but at End B we report the end load applied to the line by its connection. This is in keeping with the OrcaFlex convention for specifying the no-moment direction. Treatment of Links and Winches attached to the end node Normally, the end force and end moment are the total load acting between the end node and the object to which it is connected. This includes forces from any links or winches attached to the end node. However if the line end is free, or has been released, then it is not connected to any object. In this case the end moment is zero and the end force is taken to be the total force acting between the line end and any links or winches attached to the end node. If there are no attached links or winches, or they have been released, then the end force is zero. Standard Results Effective Tension, Wall Tension, Shear Force, x-Shear Force, y-Shear Force, Bend Moment, x-Bend Moment, y-Bend Moment, Curvature, x-Curvature, y-Curvature These results variables are available at the line end nodes, as well as at mid-segment points. Whether you are given end values or mid-segment values depends on the point at which you ask for the results. If you ask for these results at EndA or EndB, or at an arc length that is closer to a line end than to the nearest mid-segment arc length, then the values at the line end will be given. Otherwise the values for the nearest mid-segment point will be given. For mid-segment values see Line Results: Forces, Line Results: Moments and Line Results: Pipe Stresses. At a line end they report the components of the end loads in the local node directions of the end node, as follows: Effective tension is the component of the end force vector in the end node axial direction (= Nz direction). Wall tension is derived from the effective tension at the line end, using the pressure effects formula. Shear is the component of the end force vector normal to the end node axial direction. x-Shear and y-Shear are the components of the end force vector in the end node Nx and Ny directions. Torque is the component of the end moment vector in the end node axial direction. Bend moment is the component of the end moment vector normal to the end node axial direction. x-Bend Moment and y-Bend Moment are the components in the end node Nx and Ny directions. Stress results are based on the end load components in the end node axes directions. Differences between End Loads and End Segment Loads The end values of these results differ from the corresponding values for the end segment for two reasons. Firstly, they include the loads (weight, buoyancy, drag etc.) on the last half segment adjacent to the end. Secondly, they are components in the local node directions (Nx,Ny,Nz) at the end node, whereas the end segment values are components with respect to the segment directions (Sx,Sy,Sz). The end node is often not aligned with the end segment because end connection stiffness turns it towards the end orientation direction. For example: If the end connection stiffness is zero, or if the line end is free or has been released, then the end node directions are aligned with the end segment directions. The end node values then differ from the end segment values only by the loads on the end half segment. If the end connection stiffness is Infinity (and the end is not free or released) then the end node directions stay aligned with the line end axes Ex, Ey, Ez. The end node values are then usually in different directions to the end segment values. For intermediate values of end connection stiffness, the end node directions will be somewhere between the two. They will tend to be nearer to the end fitting directions if the end connection stiffnesses are stronger than the line bend stiffness and torsional stiffness, but nearer to the end segment directions if it is weaker. End Load Magnitude and Components End Force, End Moment, End GX-Force, End GY-Force and End GZ-Force, End GX-Moment, End GY-Moment, End GZ-Moment, 379 w System Modelling: Data and Results, Lines End Lx-Force, End Ly-Force and End Lz-Force, End Lx-Moment, End Ly-Moment, End Lz-Moment, End Ex-Force, End Ey-Force and End Ez-Force, End Ex-Moment, End Ey-Moment, End Ez-Moment These results report the magnitude of the end force and end moment vectors, and their components in the following directions: The directions of the global axes GX, GY, GZ. The directions of the local axes Lx, Ly, Lz of the object to which the line end is connected. For example if the line end is connected to a vessel, the Lx, Ly, Lz are the directions of the vessel axes. The directions of the line end axes Ex, Ey, Ez. See Line End Orientation. For a line with a stiffener attached results are reported separately for the protected line and its stiffener. However, it is sometimes necessary (e.g. when designing end fittings) to report combined end loads including the load from both the protected line and its stiffener. End load results are available for the protected line which include the stiffener end load, in addition to the protected line end load. These results are all prefixed with "Total", e.g. Total End Force, Total End Moment, Total End GZForce etc. Bend Restrictor Load This is defined as Bend Restrictor Load = End Force*(1 - cos(End Force Ez-Angle)). Another commonly used name for this variable is "pseudo-curvature". It is only available for line ends that are pin-connected (zero bending stiffness at the line end connection) and without a stiffener attached. 6.8.9 Drag Chain Results For details on how to select results variables see Selecting Variables. For Drag Chains the following results variables are available. Azimuth and Declination The azimuth and declination of the drag chain, relative to global axes. Supported Length and Hanging Length The supported length is the length deemed to be supported by the seabed. The hanging length is the length of the rest of the drag chain. The supported length plus the hanging length equals the total length of the drag chain. See Drag Chain Seabed Interaction for details on how these values are calculated. Drag Force The magnitude of the drag force acting on the drag chain. This includes both the axial and normal components of the drag force. Axial Drag Force, Normal Drag Force The components of drag force axial and normal to the drag chain. Horizontal Drag Force, Vertical Drag Force The horizontal and vertical components of the drag force. For the vertical drag force a positive value indicates an upwards force. See Drag Chain Theory for details on how the drag force is calculated. 6.8.10 Flex Joint Results For details on how to select results variables see Selecting Variables. For Flex Joints the following results variables are available. Bend Moment, x-Bend Moment, y-Bend Moment The magnitude of bending moment at the Flex Joint and its components in the local x and y-directions. 6.8.11 Line Setup Wizard Intended principally for mooring analyses, this wizard adjusts line configuration to achieve specified tension, declination or layback. The wizard is available when the current simulation is in Reset state and is opened by clicking the Calculation | Line Setup Wizard menu item. 380 w Figure: System Modelling: Data and Results, Lines The Line Setup Wizard Calculation Mode The Wizard has two modes of operation: Calculate Line Lengths or Calculate Anchor Positions. The Calculate Line Lengths option operates by varying the length of the specified section of each included line until the target value is achieved. Because the section length is altered by the Calculate Line Lengths option we recommend that you specify the segmentation using Target Segment Length rather than Number of Segments. Thus if the wizard lengthens the line then the program will automatically add more segments to meet the Target Segment Length. The Calculate Anchor Positions option operates by varying the position of the Bottom End of each included line until the target value is achieved. The Bottom End position is constrained to be on a line in the Lay Azimuth direction so you must set these data items before using the wizard. Note: These calculations use a numerical method which is not 100% robust. We recommend that you set up your model so that your starting conditions have target values that are quite close to your exact target values before using the wizard. If you do this the wizard is more likely to be able to find a solution. Target Values To use the wizard you must first specify the target tensions or declinations. The wizard presents a list of all Lines in the model. The Include this Line option determines which Lines are included in the calculation which allows you to exclude certain Lines. For example, you may be modelling both moorings and flow lines in the same OrcaFlex file. Typically you would only include the moorings in this calculation. The Target Variable option allows you to switch between the following options: Tension. Horizontal End Force. Declination. Layback, defined to be the horizontal component of distance between the Top End of the line and the touchdown point. 381 w System Modelling: Data and Results, Lines No Target, which means that the line will be included in the static calculation but that its data are not to be modified. This is particularly useful if you are analysing buoyed systems where the upper and lower catenaries are modelled with different Lines. For Tension and Declination targets you must also specify where on the line the value is calculated, using the Line End and Arc Length fields. The Arc Length field specifies the arc length measured from the specified Line End. For Horizontal End Force you must specify the Line End, either End A or End B. Finally you specify Tension, Horizontal End Force, Declination or Layback values, as applicable, in the Target Value field. Line section to be modified Specifies which section on the line is to have its length modified when using the Calculate Line Lengths mode. Convergence Parameters The Wizard performs an iterative calculation and these parameters can be used to help convergence. The calculation is abandoned if convergence has not been achieved after the number of steps specified by Max Iterations. For some difficult cases simply increasing this limit may be enough. The non-dimensional Tolerance parameter determines when the calculation is deemed to have converged. The calculation has converged once the following conditions are satisfied: Calculated Value - Target Value < Tolerance × Typical Force, for tension and end force targets, where Typical Force for each line is the total dry weight of the line. Calculated Value - Target Value < Tolerance, for declination targets. Calculated Value - Target Value < Tolerance × Target Value, for a layback target. The Min Damping and Max Damping parameters can sometimes be used to help difficult problems converge. Try increasing the Min Damping factor, say values in the range 1.5 to 10. You can also try increasing the Max Damping factor, say to values in the range 10 to 100. Automation The Line Setup Wizard can be executed in automated fashion either through the InvokeLineSetupWizard batch script command or from the OrcaFlex programming interface. 6.8.12 Line Type Wizard The Line Type Wizard is a tool that helps you set up a Line Type that represents one of the following commonly used structures: Chain. Rope/Wire. Line with Floats. Homogeneous Pipe. Hose. Umbilical. What the Wizard does is ask you for the basic data of the structure – e.g. the bar diameter for a chain – and then calculate for you as much of the line type data as it reasonably can to represent that structure. The Wizard leaves you to set other data – e.g. friction coefficients – where there is no formula on which to base the data. Warning: The values generated by the Wizard are offered in good faith, but due to variations in properties between products they cannot be guaranteed. Please use suppliers' data where this is available. How The Line Type Wizard Works The Wizard works on the currently selected line type on the line types form, so you should first create, name and select the Line Type that you want to set up. You can then open the Wizard using the Wizard button on the Line Types form. The first time you use the Wizard on a given line type you must be in reset state, since you will be setting data. You then tell the Wizard the category of structure that you want to model (chain, rope etc.) and the data for that structure (e.g. chain bar diameter). This information is called the Wizard data, and from it the Wizard derives line type data to correspond to those Wizard data. If necessary you can then manually adjust the derived line type data. Once you have used the Wizard to set up data for a given line type, then the Wizard remembers the Wizard data you gave it. If you re-open the Wizard when in reset state then you can edit the Wizard data and the Wizard will calculate corresponding new derived line type data. Any manual adjustments will need to be done again. 382 w System Modelling: Data and Results, Lines You can also re-open the Wizard when in other states (e.g. in static state or when a simulation is active) but only in order to view the Wizard data. You cannot edit Wizard data or re-derive line type data except in reset state. Note: Remember that the current line type data might not correspond to the current Wizard data, since you might have manually edited the line type data after they were derived by the Wizard. Using the Line Type Wizard The Wizard has three stages, with Next and Back buttons so that you can move between stages to set up the data you want. Stage 1 displays the name of the selected Line Type and asks you to specify the special category that you want. You can then click Next to proceed to the second stage. Stage 2 presents 3 frames of information. The top left frame asks you for the basic data of the special category you have selected. The bottom left frame displays the resulting derived Line Type data – you should check that the values are reasonable. The right-hand frame displays other properties of the resulting Line Type, which are often useful as a check. In some cases these depend on contents density, in which case you can specify the contents density to be used for the calculation of properties. If there are any errors then a message will be displayed. When everything is correct you can click Next to proceed to the last stage. Stage 3 displays all of the Line Type data. Bold text denotes data that have been derived for you by the Wizard, based on the special line type data you specified. Non-bold text represents data that have not been set by the Wizard – these data will be as you last set them. You can adjust any of the data at this stage, overriding the values derived by the Wizard if you wish. You can also still go back to previous stages of the Wizard if further modifications are required. When everything is correct you can click the Finish button, in which case the new data will be written, overwriting the previous data for that line type. Alternatively, you can Cancel to leave the line type unchanged, but then any newly entered special category data will also be lost. 6.8.13 Chain A chain can be modelled in OrcaFlex by using a Line Type with its various properties set to suitable values. This note derives the values to use for anchor chain of nominal (i.e. bar) diameter D, as shown in the Figure: Chain Geometry. The properties of an equivalent line type are given below. Studless Studlink OD 1.80D 1.89D ID 0 0 Contact diameter 3.35D 3.6D Mass/Length 19.9D2 21.9D2 te/m for D in m Axial stiffness 0.854x108D2 1.01x108D2 kN for D in m Bend stiffness 0 0 Compression is Limited yes yes Normal drag coefficient 2.4 2.6 Normal drag diameter D D Axial drag coefficient 1.15 1.4 Axial drag diameter D/π D/π Normal added mass coefficient 1.0 1.0 Axial added mass coefficient 0.5 0.5 Stress diameters '~' '~' Allowable stress '~' '~' Friction coefficient typically 0.4 - 0.8 depending on the seabed 383 96e4.35D (studless) 3. Lines Geometry D = Nominal Diameter AFACE 3. The values are given in terms of the nominal bar diameter of the chain (D).37e4. Link Type Can be either studlink or studless. but due to variations in properties between products they cannot be guaranteed. 384 .35D (studless) 3.and proofloads.(44 . The geometry given in the figure is based on catalogue data available from the chain manufacturer Scana Ramnas (1990 & 1995). which was obtained from the manufacturer's catalogue: Min Breaking Load = c.6D (studlink) Figure: 6D Chain Geometry Data Chains are widely used in a variety of offshore applications.74e4. Studless and Studlink chains with the same nominal diameters are stated to withstand the same break. Grade 3: 1. for a studlink chain. R4 . assumed to be in metres.11e4. ORQ: 2.40 x 107 kN/m2 (studlink).2.D2. Mechanical Properties Catalogue Data When modelling mooring chain the Line Type Wizard aims to derive data for a line type whose characteristics are equivalent to that of a chain.w System Modelling: Data and Results. In deriving these some of the available catalogue data will prove useful and we outline here the relevant aspects.9D2 te/m (studless) or 21. Bar Diameter The diameter of the metal bar that forms the links. most obviously in mooring.80D) kN where c is a grade-dependent constant. the properties window displays minimum breaking loads that depend on the nominal diameter and chain grade. Please use suppliers' data where this is available.9D2 te/m (studlink). where different. Minimum Breaking Loads For information.44 x 107 kN/m2 (studless) or 6. The Mooring Chain figure shows the geometry of a pair of chain links. They are derived using the following relationship. They are offered in good faith. and are given for both a studless chain and.6D (studlink) AEDGE 3. as is the following expression for mass per metre: Mass per metre (M) = 19. The catalogue also gives the following value for the Young's Modulus of the chain that has been deduced from stressstrain relationships in which the cross sectional area of two bars is taken to be the load bearing area: E = 5. Warning: The values generated by the Wizard are approximate only and are intended as first estimates for preliminary use. given in the catalogue data as Grade 2: 1. The Line Type Wizard helps derive a line type to represent a chain based on the following input data. 0D m (studless) or 14. Hence. Compression is Limited In conjunction with a zero value for bend stiffness. That is Contact Diameter = 3. Taking A to be the combined cross sectional area of two bars. Contact Diameter The contact diameter is set to the chain link envelope diameter. Outer.2D3 m3 (studless) or 11.6D m (studlink).6 (studlink). Axial and Bending Stiffness The Line Type Wizard sets up Axial and Bending Stiffness and Compression is Limited for a chain as follows: Axial Stiffness As detailed in Mechanical Properties of Mooring Chains we have values for the Young's Modulus for both studlink and studless chains from catalogue data. For the axial drag coefficient the recommended coefficients are 1. We can obtain this by noting that. Inner and Contact Diameter The Line Type Wizard sets up diameters for a chain as follows: Outer Diameter The effective outer diameter of the equivalent line is obtained using a similar argument to that deployed in obtaining the overall length of bar per link. there is one chain link every 4D length of chain. But.4 (studless) or 2. 385 . The normal drag diameter is D.01 x 108 D2 kN (studlink).80D m (studless) or 1. Lines Derived Data It will be useful to know the centreline length of bar needed to make a single link.89D m (studlink). we also have Volume = L .8 te/m3). πD2/4. Assuming that the chain is made from steel.3D m (studlink). section 701. by considering the geometry of a link. Equating these expressions leads to: Outer Diameter = [4M/(πρs)]½ = 1.35D m (studless) or 3.2D3 m3 (studlink). that is: A = 2(πD2 / 4) m2 leads to: EA = 0. so the Inner Diameter is set to zero. Compression is Limited is set to 'yes'. for a long chain.15 (studless) or 1.w System Modelling: Data and Results. and using ρs as density of steel (= 7.854 x 108 D2 kN (studless) or 1. Drag The Line Type Wizard sets up the drag coefficients and drag diameters for a chain following the guidance of DNV OS E301. note that the volume per metre can be expressed as both: Volume per metre = M/ρs and also as Volume per metre = πOD2/4 where OD is the equivalent diameter for a line with constant volume along its length. Hence: L = Volume / (πD2/4) = 13. and thus for a single link: Mass per link = M / N = 79. DNV OS E301 recommends a normal drag coefficient of 2. this then leads to: Volume per link = (M / N) / ρs = 10.6D3 te (studless) or 87 6D3 te (studlink). where L is centreline length of bar needed to make a single link (including the stud in the case of the studlink chain). the number of links per metre of chain is N = 1/(4D). Inner Diameter Chains do not have any contents.4 (studlink) with a corresponding axial drag diameter of D/π. Firstly. Bending Stiffness For both studlink and studless chains the bending stiffness is set to zero as the chains are assumed to bend when subjected to very small moments. Most of the calculations of the derived line properties are based on data from a catalogue published by Marlow Ropes Ltd (1995). Please note. ρ . that stress results are not meaningful for a chain.8. This value is taken from Bureau Veritas NR 493. but due to variations in properties between products they cannot be guaranteed. An accurate calculation is very problematic and is unlikely to give a value for the normal added mass coefficient far distant from 1.0. for flow normal to a link. The situation for a chain is more complicated as. This is due to the extra force required to displace the water in the vicinity of the submerged part of the line. 6x19 Wire Rope with Fibre Core. mooring and winching.0. Vol is the displaced volume. the normal and then the axial directions.5. The Line Type Wizard sets up Axial Added Mass Coefficient for a chain to: Caa = 0. The Line Type Wizard can be used to derive Line Type data to represent five different types: Nylon (8-strand Multiplait). however. They are offered in good faith. Vol where ρ is density of water. Hence we assume: Can = 1. parts of the link are shielded from the flow but there is also some entrapped water within each edge-on link. table 2. Classification of Mooring Systems for Permanent Offshore Units. 6. Stress Diameters and Allowable Stress These are set to '~' because the entire structure is load bearing. section 3. Note that this documentation uses the SI units system. and 6x19 Wire Rope with Wire Core. 386 . but the program automatically adjusts the formulae to match the units specified by the user.0. The parts of a line displacing the fluid are said to be attracting added mass. Please use suppliers' data where this is available. Polyethylene (8-strand Multiplait). Polyester (8-strand Multiplait). All quantities are expressed as a function of the rope's nominal diameter D. first. so D is in metres in this documentation. Warning: The values generated by the Wizard are approximate only and are intended as first estimates for preliminary use. For asymmetrical bodies the parts attracting added mass will differ in different directions. An added mass term is used to reflect this and it is found to be proportional to the volume of displaced fluid: Added mass = Ca .w System Modelling: Data and Results.14 Rope/Wire D = Nominal rope diameter D Fibre rope Figure: Wire with Fibre core Wire with Wire core Rope/Wire Geometry Ropes and wires have many applications in the offshore industry including towing. Lines Added Mass The Line Type Wizard sets up the Normal Added Mass Coefficient for a chain as follows: When a line is accelerated in water it requires an impulse in excess of that needed for the same acceleration in air. For a circular cylinder in flow normal to its axis: Can = 1. Hence. we consider the effect due to fluid flow exerting a force in. because there are gaps between the fibres and so not all of the specified nominal diameter contributes to buoyancy. The input data required consists of the following: Rope/Wire Nominal Diameter The overall diameter of the rope or wire. 6x19 Wire with Fibre Core (8-strand Multiplait). Mass Per Metre = 3. not the nominal diameter. The line type then has the appropriate buoyancy. to the displaced volume per metre.6476 D2 te/m (for Nylon ropes).14.85 D (for Nylon ropes). with the fibre taken to have the same density as (fresh) water.91. Wire with fibre core 6. in order to give the correct buoyancy. OD. Mass per unit length The Line Type Wizard sets up Mass for a Rope/Wire as follows: The quantity Mass per unit length is available from catalogue data for ropes. These outer diameters are effective diameters that give the line type a displaced volume per unit length that equals the estimated displaced volume per unit length of the rope/wire. where M is the rope/wire mass per unit length and ρ is the average density of the material.38. since the coefficients correspond to the derived line type outer diameter. OD = 0. Polyester 1.4526 D2 te/m (for Polypropylene ropes). OD = 0. The construction affects both the mass per unit length of the line type and the strength of the line type. Construction Can be one of: Nylon (8-strand Multiplait). M/ρ. is set as follows: OD = 0. The majority of the derived line type data are functions of this diameter. The line type outer diameter. Lines Data The Line Type Wizard can be used to create line types representing a variety of ropes and wires. Axial and Bending Stiffness The Line Type Wizard sets up Axial and Bending Stiffness and Compression is Limited for a Rope/Wire as follows 387 .87. Mass Per Metre = 0.9897 D2 te/m (for Wire ropes with wire core). The above formulae for the line type OD were derived by equating the line type displaced volume per unit length.80 D (for Polypropylene ropes). Mass Per Metre = 3. Polyester (8-strand Multiplait). OD = 0.w System Modelling: Data and Results.82 D (for Wire ropes with fibre core). OD = 0.86 D (for Polyester ropes). Wire with Wire core 7.85. Warning: The line type outer diameter derived by the wizard is less than this nominal diameter. Polypropylene 0. Outer and Inner Diameters The Line Type Wizard sets up outer and inner diameters for a Rope/Wire as follows. A simple statistical analysis of the available data leads to the following expressions: Mass Per Metre = 0. The inner diameter is set to zero for all rope construction types. The following average material densities ρ (in te/m 3) were assumed: Nylon 1. Note that this effective diameter is less than the specified rope diameter. where D is the specified rope diameter. Mass Per Metre = 0. The nominal rope diameter and nominal mass are available for a variety of rope constructions. You need to allow for this when setting the line type drag and added mass coefficients. 6x19 Wire with Wire Core (8-strand Multiplait). Polyethylene (8-strand Multiplait).6109 D2 te/m (for Wire ropes with fibre core).7978 D2 te/m (for Polyester ropes). πOD2/4.80 D (for Wire ropes with wire core). The average material density for the Wire with fibre core was estimated by assuming a ratio of 6:1 between the wire and fibre volume. 67 x 107 D2 kN (for Wire ropes with fibre core). and the rate of application of the load. whether the rope is wet or dry.09 x 106 D2 kN (for Polyester ropes).D2 kN Nylon ropes (wet) 139357. Stress Diameters and Allowable Stress These are set to '~' because the entire structure is load bearing. For systems where bend stiffness is a significant factor you should override this value with the true value obtained from the rope supplier.w System Modelling: Data and Results. however. Note that for wire ropes with a wire core the additional axial stiffness is accounted for in the enhanced Young's modulus. E = 1. Axial Stiffness = 4. Lines Axial Stiffness The expressions for axial stiffness are calculated in different ways for the two groups of fibre ropes and wire ropes.03 x 108 kN/m2 (for Wire ropes with fibre core).455 (πD2/4) m2 (for both wire ropes). Bending Stiffness For all rope construction types the bending stiffness offered by the Wizard is zero. These may be useful for setting the Allowable Tension data item for the line type. Axial Stiffness = 1.18 x 105 D2 kN (for Nylon ropes). for the 6x19 strand group. Incorporating all of the factors indicated above we can produce values of axial stiffness for a range of rope diameters. This leads to: Axial Stiffness = 3. where D is rope/wire nominal diameter in metres: Nylon ropes (dry) 163950.D2 kN 388 .D2 kN Polypropylene ropes 105990. Once again using simple statistical techniques we obtain the following expression for axial stiffness of fibre ropes: Axial Stiffness = 1. The MBL values displayed are calculated using the following functional formulae.04 x 107 D2 kN (for Wire ropes with wire core). Minimum Breaking Loads The properties window in the line type wizard displays approximate minimum breaking load (MBL) values for ropes and wires.D2 kN Wire ropes with wire core 633358. Please note. Load/extension characteristics depend on previous load history.D2 kN Wire ropes with fibre core 584175. Axial stiffness for Wire Ropes is calculated directly. stiffness should be about twice the value shown) a wet rope – pre-soaked in water (this is most significant for Nylon ropes which suffer a loss in performance when wet) we use figures for the average performance when the mean extension is 10% (by taking the tangent of the stress-strain curve at 10%).06 x 106 D2 kN (for Polypropylene ropes). Compression is Limited Compression is Limited is set to 'no'. We assume a value for Young's Modulus. rather than estimated from empirical relationships. and work on an assumed metallic area of: A = 0. To reflect the likely working environment of the rope we use data associated with ropes that have been tested under the following conditions: the rope has been pre-worked – loaded to 50% of breaking load and then rested for 24 hours (this causes the rope to bed down so that its elastic behaviour is more consistent and repeatable) subjected to slowly varying loads (for loads varying at wave frequency. Axial Stiffness = 1. Both of these quantities have been obtained from the HER Group Marine Equipment & Wire Rope Handbook. that stress results are not meaningful for complex structures such as ropes or wires. For Fibre Ropes we use the catalogue data.13 x 108 kN/m2 (for Wire ropes with wire core).D2 kN Polyester ropes 170466. of: E = 1. which consist of minimum (dry) strength against nominal diameter for each of the five rope/wire constructions. Lines These formulae were derived from manufacturer's catalogue data.8. This is done by spreading each float's buoyancy. which we refer to as the Base Line Type. This allows the length and segmentation of the buoyed section to be varied easily without having to add and remove individual floats. The section's line type should be set to the equivalent line type and its length should be N x Sf. The following properties are all deemed to be unaffected by the addition of floats to the base line and so are set to have the same values as those of the base line. along that part of the line.e. To use this smeared properties approach you need to do the following: Create a new line type. except that they tend to underestimate MBL for small diameter non-wire ropes. since each float is effectively being smeared equally both ways from its centre. the spacing between float centres (see diagram below).w System Modelling: Data and Results. etc. Floats Dp Sf Figure: Sf Df Sf Geometry of Line and Floats We first define the notation to represent the underlying line onto which the floats are to be attached. which show the situation when N=3. The line type wizard will automatically set up this equivalent line type for you.e.15 Line with Floats You can model floats or buoyancy modules attached to a line by using buoyant Clumps attached at the relevant points. We describe below how the Line Type Wizard derives the properties of the equivalent line type. uniformly over the length of pipe from S f/2 before the float centre to S f/2 after the float centre. i. Axial and Bending Stiffness Compression is Limited Allowable Tension Minimum Bend Radius 389 . The formulae were derived using least squares fitting. drag. see the diagram below. The result is a uniform circular section line which will experience the same forces per unit length as the original line plus floats. Note that this length is a little more than the length between the start of the first float and the end of the last one. but more specific project data should be used where this is available. where N is the number of floats and Sf is the float pitch. and they were found to give a good fit to the manufacturer's data. We then specify the quantities required to represent the floats. i. Note that this approach is also suitable for modelling a regularly weighted section of line. the formula given for wet nylon ropes is based on the manufacturer's statement that they can lose up to 15% of their (dry) strength when wet. where Sf is the float pitch. spread out evenly. Set the new line type's properties to be equivalent to those of the original pipe+floats. Note: Nylon ropes lose some strength when wet. Warning: The values generated by the Wizard are based on current best practice. Set up a line section to model the length of line supported by the floats. 6. However when a number of floats are supporting a length of line it is often easier to model the buoyancy as if it were smeared. due to the projected annulus area of the end of the float. The line without floats is assumed to be of circular cross section and have the following characteristics: ODp – outer diameter. It must be greater than the outside diameter of the underlying base line type. The Line Type Wizard helps you to quickly derive such a line type by specifying both the existing underlying base line type. Float Pitch The average distance between the centres of successive floats. Float Normal Added Mass Coefficient The added mass coefficient for flow normal to the line. Caap – Added Mass coefficient in Axial flow (commonly taken as zero). Float Diameter The outside diameter of each float. for flow along the axis of the line. Canp – Added mass coefficient in Normal flow (commonly taken as 1. Cdnp – drag coefficient in normal flow. for flow along the axis of the line. are detailed in Modelling Lines with Floats. Float Length The axial length of each float. Float Axial Added Mass Coefficient The added mass coefficient for flow along the axis of the line.w System Modelling: Data and Results. IDp – inner diameter. Dnp – normal drag diameter. Float Axial Form Drag Coefficient The drag coefficient associated with the float.0 for circular section). onto which the floats will be added. Float Material Density The density of the material forming the floats. and the associated underlying expressions. The floats are assumed to be short cylinders fitted co-axially on the line at constant spacing: Lf length 390 . Lines Torsional Stiffness Data Adding floats to a line to produce extra buoyancy is a common requirement. Dap – axial drag diameter. Float Hardware Mass This accounts for the extra mass due to the addition of the floats above that due to the material density and covers such items as the clamping/fixing mechanisms. Properties of Base Line Type For modelling lines with floats the line without floats is referred to as the base line type and the following notation is used. Properties of the Floats For modelling lines with floats the following notation is used for the floats. Cdap – drag coefficient in axial flow. due to the floats' skin friction. excluding additional items such as fixing material. and various properties of the floats: Base Line Type The line type on which the floats are mounted. The Line Type data that are derived. Float Normal Drag Coefficient The drag coefficient associated with the float for flow normal to the line. Float Axial Skin Drag Coefficient The drag coefficient associated with the floats. Mp – mass per unit length. Mass per Unit Length The line type mass per unit length is calculated by allowing for the fact that there is one float for every S f length of the section and hence (1/Sf) floats per unit length.Drag Arean-EXP LINE] / Dnp. This allows float clearance to be reported using the Line Contact Clearance result. 391 . fixing clamps.Drag Arean-FLOATS + Cdnp. and where ρ is the density of seawater and v is the flow velocity. axial flow due to skin friction Canf added mass coefficients in normal flow Caaf added mass coefficient in axial flow With the above information we can calculate the volume occupied by an individual float as: Vf = π/4 (Df2 . Equating the two expressions for drag force leads to: Cdn = [Cdnf.ODp2 + Vf /Sf (line with floats) This leads to: Outer Diameter (OD) = (4V/π)½ Inner Diameter The Inner Diameter is unaffected by the addition of floats and so is set to be the same as that of the base line. axial flow due to form Cdaf2 drag coefficient. Outer.ρf + mfh. Lines Df diameter ρf float density Sf float pitch mfh float hardware mass (e.g.Drag Arean-FLOATS + Cdnp. normal to the flow. Dnp. giving: Mass per unit length = Mp + Mf / Sf Normal Drag Coefficient The Line Type Wizard sets up the Normal Drag Coefficient for a Line with Floats as follows: The drag force per unit length of the equivalent line when flow is normal to the line's axis can be expressed as: Drag Forcen = ½ ρv2 Cdn Dnp in which the reference drag area per unit length. We can also express the drag force per unit length experienced by the equivalent line as the sum of the drag forces experienced by the floats and the drag forces experienced by the part of the line not hidden by the floats: Drag Forcen = Drag Forcen-FLOATS + Drag Forcen-EXP LINE = ½ ρv2 [Cdnf.OD2 (equivalent line) Vol per unit length (V) = π/4. Inner and Contact Diameter The Line Type Wizard sets up diameters for a Line with Floats as follows: Outer Diameter The Outer Diameter (OD) of the equivalent line is calculated by equating two equivalent expressions for the volume per unit length of the line: Vol per unit length = π/4.w System Modelling: Data and Results. normal flow Cdaf1 drag coefficient. Contact Diameter The Contact Diameter is set to equal the float diameter Df.Drag Arean-EXP LINE] in which the reference drag area for the floats in normal flow is given by: Drag Arean-FLOATS = Df Lf/Sf and the reference drag area for the exposed line in normal flow is given by: Drag Arean-EXP LINE = Dnp (Sf-Lf)/Sf. bolts. etc.ODp2) Lf which leads to the mass of the float being calculated as follows: Mf = Vf. is given by the normal drag diameter of the base line.) Cdnf drag coefficient. Axial Drag Coefficient The Line Type Wizard sets up the Axial Drag Coefficient for a Line with Floats as follows. due to the skin. we can also express the drag force per unit length experienced by the equivalent line as the sum of the drag forces experienced by the floats and the drag forces experienced by the part of the line not hidden by the floats. due to the annulus. To derive the drag coefficient when flow is axial to the line we adopt a similar approach to that used above for normal flow. due to the skin.Drag Area1a-FLOATS + Cdaf2. the drag force per unit length.Drag Area2a-FLOATS + Cdap. 392 . we can take the above expression for the added mass coefficient in normal flow and replace the coefficients for normal flow with those for axial flow: Caa = (Caaf AMVolFLOATS + Caap AMVolEXP LINE)/(π/4 OD2). The reference volumes for the equivalent line and for the floats and exposed part of the underlying base line are taken to be the same in axial flow as in normal flow.Drag Area2a-FLOATS + Cdap. The formula above is then applied to the drag coefficients in each row of the table. When considering the equivalent line. for the floats in axial flow is given by: Drag Area2a-FLOATS = πDfLf/Sf and the reference drag area. for the floats in axial flow is given by: Drag Area1a-FLOATS = π/4 (Df2-ODp2)/Sf the reference drag area. Lines If the base line type uses drag which varies with Reynold's number. is due solely to skin friction and can be expressed as: Drag Forcea = ½ ρv2 Cda (πDap) in which the reference drag area per unit length is the circumference of the base line (calculated using the axial drag diameter Dap) and where r is the density of seawater and v is the flow velocity. As in the case for flow normal to the line. with the additional buoyancy smeared along its outer surface. For flow normal to the axis of the line the added mass per unit length is given by: Added Massn = ρ π/4 OD2 Can in which the reference volume is the volume of the equivalent line and where ρ is the density of seawater. Hence. Added Mass Coefficients The Line Type Wizard sets up Normal and Axial Added Mass Coefficients for a Line with Floats as follows: Normal Added Mass Coefficient Added mass coefficients are calculated in a similar way to the drag force coefficients. Equating these two expressions leads to: Cda = [Cdaf1. for the exposed line in axial flow is given by: Drag Areaa-EXP LINE = πDap (Sf-Lf)/Sf.Drag Areaa-EXP LINE] / (πDap). Drag Forcea = Drag Forcea-FLOATS + Drag Forcea-EXP LINE = ½ ρv2 [Cdaf1. However. when flow is axial to the line. We can also express the added mass term of the equivalent line as the sum of the added masses due to the floats and due to the underlying line: Added Massn = ρ (Canf AMVolFLOATS + Canp AMVolEXP LINE) in which the reference volume per unit length for the floats (and the portion of line they cover) is given by: AMVolFLOATS = π/4 Df2 Lf/Sf and the reference volume per unit length for the exposed part of the line is given by: AMVolEXP LINE = π/4 ODp2 (Sf-Lf)/Sf Equating the expressions for added mass leads to: Can = (Canf AMVolFLOATS + Canp AMVolEXP LINE)/(π/4 OD2). Axial Added Mass Coefficient The added mass coefficients follow in a similar way to above.Drag Area1a-FLOATS + Cdaf2.w System Modelling: Data and Results. then a variable data table is created which specifies the drag variation with Reynold's number for the equivalent line.Drag Areaa-EXP LINE] in which the reference drag area. the drag forces experienced by the floats are slightly more complicated in axial flow as there will be a drag force due to the exposed annulus on the end of each float and a drag force due to skin friction. w System Modelling: Data and Results. Mass per Unit Length Mass per unit length = ρ (π/4) (OD2 .ID2). Young's modulus etc. since it is the base line which is load bearing.ID2) where ρ is the material density specified. The derived properties are based on the following input data: ρ material density E Young's Modulus ν Poisson Ratio OD Outer Diameter ID Inner Diameter = OD-2t where t is the wall thickness The properties of the derived equivalent line type are given below. Lines Stress Diameters and Allowable Stress The stress diameter and allowable stress are set to be the values used by the base line. for example a metal riser. Axial Stiffness The line type axial stiffness is given by: Axial Stiffness = EA where E is the Young's Modulus and A is the cross sectional area. hence: Axial Stiffness = E(π/4) (OD2 . NN').16 Homogeneous Pipe O N N’ O’ Figure: Homogeneous Pipe The Line Type Wizard for Homogeneous Pipe creates data for a General Category Line Type with properties appropriate to a pipe constructed from a single homogeneous material.8. This allows you to specify material density. and leads to: Bending Stiffness = E(π/64) (OD4 . Bending Stiffness The line type bending stiffness is given by: Bending Stiffness = EI where I is the second moment of area. directly. Note: If you are modelling a homogeneous pipe then it is normally better to do so using a Homogeneous Pipe Category Line Type. 393 . about an axis in the plane of the cross section through the centroid (e. Outer and Inner Diameters The line type outer and inner diameters are set to the pipe diameters specified by the user. 6.g.ID4). Stress Outer and Inner Diameters The line type stress diameters are set to '~'. Lines Compression is Limited As the bending stiffness is significant this is set to 'no'. The Torsional Stiffness. For homogeneous pipes J = 2I. Torsional Stiffness The line type torsional stiffness is set as follows. The umbilical properties assume construction with steel wire armour and thermoplastic hoses and outside diameter up to 250mm. There are three categories of hose available: High pressure which covers high pressure flexible risers and flowlines of unbonded construction with inside diameters in the range 2 to 15 inches (50 to 380mm).17 Hoses and Umbilicals The Line Type Wizard estimates typical properties for hoses and umbilicals based on project data. 394 .w System Modelling: Data and Results. Material Density This is the density of the material used in the construction of the pipe. based on the following data: Material The Wizard provides 3 standard materials for a homogeneous pipe: Steel. Titanium and High Density Polyethylene. They are offered in good faith. Please use suppliers' data where this is available. Poisson Ratio The amount of lateral strain experienced by a material subjected to tensile strain as a negative proportion of the tensile strain. since they are the same as the pipe diameters. Stress Loading Factors These are set to one. In this case you must set Material Density.8. but due to variations in properties between products they cannot be guaranteed. inside diameter around 6 inches (150 mm). The Line Type data that are derived. is therefore given by: Torsional Stiffness = GJ = E/{2(1+ν)} (π/32) (OD4 . and the associated underlying expressions. Outer Diameter. The quantity G is related to the Young's Modulus (E) and Poisson Ratio (ν) of the material through the following relationship: G = E/{2(1+ν)}. Young's Modulus and Poisson Ratio. The torque experienced by a pipe of length l when twisted through an angle θ is given by: Torque = (Gθ/l)J where J is the second moment of area about the axial axis OO' (often called the polar moment of inertia) and G is the Shear Modulus (sometimes called the modulus of rigidity). Wall Thickness These data specify the geometry of the pipe cross section. the default value. For these standard materials OrcaFlex automatically sets Material Density. Data The Line Type Wizard helps build a line type to represent a homogeneous pipe. There is also an option to enter User Specified as the Material. Young's Modulus The ratio of the tensile stress to the tensile strain. representing the Torque resisting a twist of 1 radian. fold-flat hoses with steel reinforcement. Warning: The values generated by the Wizard are approximate only and are intended as first estimates for preliminary use. Low pressure which covers low pressure floating hoses of bonded rubber construction with inside diameter from 2 to 20 inches (50 to 500 mm). Young's Modulus and Poisson Ratio. are detailed in Modelling Homogeneous Pipes. per unit length.ID4). as a simple homogeneous pipe carries all the loads. 6. Fold-flat which covers low pressure. based on the following data. Umbilical cables have many applications including the carrying of electrical communication wires and hydraulic connectors to submersibles.1844 ID te/m (for Fold-Flat). Lines The properties derived by the Wizard are obtained from empirically estimated relationships with the diameter of the hose/cable. Outer and Inner Diameters The Line Type Wizard sets up Outer and Inner Diameters for hoses and umbilicals as follows: Hoses The inner diameter (ID) is specified by the user and the outer diameter (OD) is a function of the inner diameter: OD = 1. A limited amount of available project data has been collated and used to derive purely empirical relationships between the diameter of types of hose and certain line type data quantities. where b is an integer. 395 . The input data consists of: Hose Inner Diameter Each derived line type property is a function of the hose inner diameter. In the details below the diameter is assumed to be in metres and the SI units system is applied throughout. low pressure or fold-flat. expressed as a percentage. Each derived line type property is a function of this diameter.40 ID m (for High Pressure) [90% 150%]. Data for Umbilicals The Line Type Wizard can help build a line type to represent umbilical. The Line Type data quantities that the wizard derives have been estimated from a limited amount of project data. only those relationships of the form: Y = aXb.w System Modelling: Data and Results. These categories roughly cover the available project data. OD = 1. were considered. Data for Hoses The Line Type Wizard helps you build a line type to represent a hose. There is quite a bit more data for high pressure hoses and umbilicals but it is found to have quite a large spread. Hose Type The Hose Type can be one of high pressure. OD = 1.7253 ID te/m (for High Pressure) [55% 145%]. Umbilicals For the umbilicals the mass per metre has been estimated as a function of outer diameter giving: Mass per metre = 1. They have been estimated from a limited amount of data covering only the range of diameters indicated above. the ratio of the observed value to the fitted value. Mass per metre = 0. For simplicity. The single item of input is: Umbilical Diameter The outer diameter of the umbilical.34 ID m (for Fold-Flat). is calculated and the largest and smallest of these is given. Any available stress or wall tension results should therefore be ignored.3642 ID te/m (for Low Pressure).28 ID m (for Low Pressure). The OrcaFlex stress analysis is not applicable to complex structures such as hoses and umbilicals. The amount of data available for low pressure hoses and fold-flat hoses is very small. Mass per metre = 0. Mass per unit length The Line Type Wizard sets up mass for hoses and umbilicals as follows: Hoses For each type of hose the mass per metre has been estimated as a function of inner diameter giving: Mass per metre = 0.8 OD2 te/m (for Umbilical) [35% 170%]. To demonstrate this spread. Umbilicals The inner diameter (ID) is set to zero and the outer diameter (OD) is specified by the user. 40 x 104 ID kN (for Low Pressure). 6. that is the diameter is constant over the length of the segment.w System Modelling: Data and Results. For the umbilicals the axial stiffness has been estimated as a function of outer diameter giving: Axial Stiffness = 1.m2 (for Umbilical) [55% 240%]. Poisson ratio.m2 (for High Pressure) [45% 300%]. hydrodynamic properties etc. However. In order to determine segment length we recommend that you perform sensitivity studies on segment length. Arc length convention Profile arc length is defined relative to the start of the line section and increases from End A towards End B. Axial Stiffness = 6.56 x 103 ID kN (for Fold-Flat).m2 (for Fold-Flat).18 Modelling Stress Joints A tapered stress joint is a riser joint with a tapered cross section.m2 (for Low Pressure).80 x 106 ID kN (for High Pressure) [40% 160%]. Segmentation OrcaFlex line segments are straight. To model a stress joints you need to take the following steps: 1. Create a Line Type Outer Diameter variable data source which defines the stress joint profile. Create a line type with the homogeneous pipe category and set the inner diameter. 2. Lines Axial and Bending Stiffness The Line Type Wizard sets up Axial and Bending Stiffness and Compression is Limited for hoses and umbilicals as follows: Axial Stiffness For each type of hose the axial stiffness has been estimated as a function of inner diameter giving: Axial Stiffness = 2. To illustrate this consider a stress joint defined by the following profile: 396 . Set the line type outer diameter to refer to the variable data source of the profile. Set the Line Type data item on the structure page of the line data form to refer to the profiled line type created above. 4. For the umbilicals the bending stiffness has been estimated as a function of outer diameter giving: Bending Stiffness = 3 x 103 OD3 kN. Such regions also require short segments for accurate modelling and so the use of straight segments to model the profile does not in practice turn out to be a significant limitation. Bending Stiffness For each type of hose the bending stiffness has been estimated as a function of inner diameter giving: Bending Stiffness = 3 x 104 ID4 kN. Each segment in a profile line section has a diameter defined by evaluating the profile data at the mid-point of the segments. Bending Stiffness = 1 x 103 ID3 kN. Because of this you typically need to use quite short segments to model the taper accurately.44 x 106 OD kN (for Umbilical) [15% 415%]. Bending Stiffness = 6 x 102 ID3 kN. Stress joints are modelled in OrcaFlex using profiled line types. note that a stress joint is usually placed in a region of concentrated stress. material data (Young's modulus. material density). Stress joints are typically fabricated from steel or titanium. Stress joints are used to spread loads over a critical section of the riser. 3. Axial Stiffness = 3.8. Compression is Limited As the bending stiffness is significant this is set to 'no'. This is very simple to do using the Reverse button on the variable data form. Lines Stress joint profile A stress joint specified this way would commonly be used in the first section of a line.w Figure: System Modelling: Data and Results. then the End A to End B convention means that the stress joint would be incorrectly configured. This is easy to check with the profile graph available on the line data form: Figure: Stress joint profile at End B. The result looks like this: Figure: Stress joint profile at End B. In order to fix this we simply need to reverse the profile data. The thicker end of the taper should be adjacent to End B of the line. corrected The line profile graph when using the reversed profile shows that the data are now applied as intended: 397 . your stress joint is located adjacent to End B of the line. however. If. incorrectly modelled The problem is that the taper is now in the wrong direction. The two line approach enables reporting of separate results for the protected line and stiffener. and then curvature is prevented from going above that value. High stiffness for curvature values greater than the lock-out curvature. which we refer to as the protected line. Data Although the stiffener is modelled as a separate line you do not need to create this line manually – OrcaFlex creates it automatically as an attachment. displacement and hydrodynamic properties but often these properties are of lesser importance. The main advantage of this approach is that it becomes easier to check that the data are specified correctly because you can keep the data for the protected line separate from the data for the limiter. The bend stiffness for this equivalent line type must account for both the protected line and the limiter.w System Modelling: Data and Results. Lines Figure: Stress joint profile at End B. Typically the low stiffness value will be close to zero and the high stiffness value will be one or two orders of magnitude greater than the stiffness of the protected line. The region of the protected line which is covered by the stiffener is called the protected region. Modelling Bend Limiters Non-linear bend stiffness can be used to model a bend limiter. It may also help to smooth the transition from low to high stiffness. non-linear elastic or hysteretic bending properties. The procedure for setting up a bend stiffener is as follows: 398 . In particular this makes fatigue analysis of the protected line quite simple since the reported loads and stresses for the protected line do not include the contributions of the stiffener. A bend stiffener is a bend restrictor that provides increased bend stiffness in order to distribute more widely the bending. A bend restrictor is any device that controls. The stiffener can have linear or non-linear elastic material properties. The approach is to specify a relationship between curvature and bend moment that has: Low stiffness for curvature values lower than the lock-out curvature. The stiffener is modelled as a profiled homogeneous pipe. correctly modelled 6. You may choose also to account for mass. A bend limiter is a bend restrictor that has no effect until a certain curvature is reached. Modelling Bend Stiffeners Bend stiffeners are modelled in OrcaFlex using two separate lines to represent the stiffener and the line which it protects. The most common modelling approach for bend limiters uses a single equivalent line type object to represent both the protected line and the limiter. An alternative to the equivalent line approach is to model the limiter as a separate object using the bend stiffener attachment (see below). The main difference from an elastomeric stiffener is that a general category line type with non-linear bend stiffness must be used for the attachment line type.19 Modelling Bend Restrictors We begin by introducing some terminology. Try to avoid using too large a value since doing so can result in numerical instability. The protected line can have linear.8. restricts or limits bending on a line. Suppose that the bending stiffnesses are EI p and EIs for protected line and stiffener respectively (we are assuming linear bend stiffness for simplicity). structural and hydrodynamic properties of the stiffener. The stiffener modelling (see below) requires that each node on the stiffener line is associated with a node on the protected line. Create a Stiffener Type which uses this Line Type. VIV data. Drawing data. namely: Include Torsion. The stiffener length must be an exact multiple of the segment length. Usually this will be a profiled homogeneous pipe. Results data. The segment length is determined by the segment length of the protected line in the protected region. The protected region could comprise multiple sections each using different line types. These constraints have the following implications for the segmentation of the protected line: 1.w System Modelling: Data and Results. consider bend moment at a particular location in the protected line and at the corresponding location in the stiffener line. Drag formulation and wake interference data. Drawing and Results The stiffener line is drawn using the drawing data of the protected line to which it is attached. Create a Line Type which defines the material. Segment length. The Modelling Stress Joints topic illustrates this issue in some more detail. the method for doing this varies for axial components as explained in the next section. Note that it is not essential for the protected region to be a single section. Segmentation The stiffener line that OrcaFlex creates is modelled with uniform segment length – that is every segment in the stiffener has the same length. One simple way to satisfy these requirements is to model the protected region as a single section with length equal to the stiffener length. The total load is also split into separate protected line and stiffener loads for effective tension. The bend moment carried by the protected line and stiffener ensemble is given by BMtotal = C(EIp + EIs) where C is the curvature at this location. so long as you satisfy the two rules above. The protected region must have uniform segment length. The stiffener profile uses the convention that profile arc length increases from End A towards End B of the stiffener. Each stiffener node is effectively clamped to its associated protected node. 399 . If you have a bend stiffener connected at End B of a line then you will need to define the profile so that the arc length 0 refers to the tip of the stiffener. It is straightforward to see that BMtotal = BMp + BMs. For example. it is only drawn after the static or dynamic analysis has started. OrcaFlex reports results separately for protected line and stiffener line and this does need some explanation. torque and stress results. shear force. Although the discussion there centres on stress joints many of the points covered are equally applicable to bend stiffeners. 2. The stiffener line inherits a number of properties from its protected line. Set the line attachment position and the Stiffener Type connection arc length so that the stiffener is attached at the desired location on the protected line.EIp and likewise for the stiffener line OrcaFlex reports BM s = C. Lines 1. Results are available for the stiffener line exactly as they are for any other OrcaFlex line. 3. If you have multiple protected lines which all use identical bend stiffeners then you can create a single Stiffener Type which can be re-used on each protected line. However.EIs. Create a line attachment based on this Stiffener Type. Statics friction data. 4. For the protected line OrcaFlex reports the local protected line bend moment BM p = C. Note that the stiffener is not drawn when the program is in reset state. We strongly recommend that you use the Profile Graph available from the Line Data form to check that the stiffener is connected at the correct location on the line with the profile defined as you intended. 2. Modelling details As mentioned above the stiffener is modelled as a separate OrcaFlex line which is created automatically by OrcaFlex as an attachment. wall tension. If the axial load/inertia transfer is specified to occur at the connection point then components of axial load/inertia are transferred to the protected node at the connection point. etc. This is most conveniently done by exporting the End Force vs End Force Ez Angle results as a table of values for each analysis case.e. How this transfer is performed is governed by the Axial load/inertia transfer data of the Stiffener Type. The stiffener line has a displacement determined by its annulus. just as the bend moment is shared. as well as by the load cases. A simplified set of load cases representing the overall loading envelope can then be selected for use in stiffener design. Fluid loading Because the protected line is shielded from the fluid by the stiffener. zero bending stiffness at the line end connection). The line should be modelled with a pinned end (i. The Orcina program OrcaBend has been developed to assist this process. The axial load will be shared between protected line and stiffener as determined by their relative axial stiffnesses. to define out-to-out load cycles for fatigue analysis). Bend Stiffener design using OrcaFlex The modelling approach described above applies where a bend stiffener has already been designed. Buoyancy forces are applied to both lines. The export to Excel can be done manually or automated through the Results spreadsheet. For further information contact Orcina. lift. corresponding to maximum tension. The protected line sees no drag.8. and one of the objectives of the analysis is to confirm that the stiffener provides the required protection. bend stiffener) are handled automatically by the program. it is often sufficient to consider just three points on this graph. The protected line has displacement calculated from its buoyancy diameter in the standard manner. This modelling option effectively neglects any axial friction due to contact between stiffener and protected line. This.20 Modelling non-linear homogeneous pipes A non-linear stress-strain relationship is most commonly used to model either: non-linear behaviour of elastomeric bend stiffeners. since the actual stiffener shape selected is governed in part by the manufacturing process. availability of tooling. It is usually necessary to combine results from several analysis runs in order to fully define the bend stiffener design loading. The effects of a diameter profile and a non-linear material (e. All components of load and inertia normal to the stiffener are transferred directly from each stiffener node to its associated protected node. in many cases the stiffener design does not yet exist and the analysis is needed in order to define design loads.g. then use the End Force Ezx or End Force Ezy Angle as appropriate. or plastic deformation of steel pipes during installation. enables the stiffener to perform its job of spreading the bend loads over the protected region. OrcaFlex can also model non-linear bend stiffness for General Category Line Types. 6. OrcaFlex suppresses fluid loading on the protected line. If the axial load/inertia transfer is specified to occur over the stiffener's full length then components of axial load/inertia are transferred directly from each stiffener node to its associated protected node. In practice. If this is the case.g. Instead each node on the stiffener is clamped to and moves and rotates with its associated node on the protected line. However there are a number of advantages of using the homogeneous pipe approach if it is applicable: The data are entered directly and there is no need to use the Line Type Wizard for Homogeneous Pipe or the Plasticity Wizard which makes data checking simpler. added mass or fluid inertia loads. combining into a single Excel spreadsheet and using the plotting facilities in Excel to generate a single plot with all results superimposed. maximum angle and maximum bend restrictor load: these can be extracted as linked statistics. Recall that End Force Ez-Angle is an absolute magnitude and therefore always takes a positive value. of course. These can be extracted in the form of an X-Y graph showing End Force against End Force Ez-Angle for the first segment. If a signed value is required (e. then run a preliminary analysis with no bend stiffener included. This corresponds to the assumption that the axial contact friction is sufficient that there is no axial slipping. The stiffener line calculates its loads and inertia and then transfers them to the protected line. Lines The stiffener line does not have any free degrees of freedom. The load information required for bend stiffener design then consists of paired values of force and angle at the pinned end.. Bend Stiffener design using OrcaBend The task of bend stiffener design is usually left to the manufacturer. 400 .w System Modelling: Data and Results. However. Typically this connection point is at the end of the protected line and the axial loads and inertia are thus transferred to the protected line's end connection. Non-linear bend moment / curvature relationships are created for each segment under this assumption. The reference stress parameter is usually taken to be the yield stress. Reference Stress (σy). Model building OrcaFlex uses the stress-strain relationship to generate a table of bend moment against curvature using the same algorithm as the Plasticity Wizard. 401 . Instead we make the assumption that the effect of dynamic variation of direct tensile strain on the bend moment / curvature relationship is small. The use of distinct bend moment / curvature tables also allows OrcaFlex to account for the variation of direct tensile strain within a line. account for dynamic variation of direct tensile strain when calculating wall tension. The program does. On the other hand if you wish to model hysteretic bending behaviour then you must use the General Category Line Types approach. Note also that this discussion of direct tensile strain only pertains to the generation of bend moment / curvature relationships. To see why this is so consider a steel pipe under tension such that the direct tensile strain equals the yield strain. The direct tensile strain. Stress. The bend moment / curvature relationship depends upon: The stress-strain relationship (as described above).w System Modelling: Data and Results. ε(σ) = -ε(-σ) for σ < 0. It is straightforward to convert between the two forms of the equation but please take care to ensure that the data you input correspond to the parameterisation used by OrcaFlex. The direct tensile strain values from this initial static solution are then used to update the nonlinear bend moment / curvature relationships. In principle the bend moment / curvature relationship could be recalculated at each time step of an OrcaFlex calculation. n (Ramberg-Osgood curve only) These data define the relationship between stress (σ) and strain (ε) in terms of a Ramberg-Osgood curve as follows: ε(σ) = σ/E + K(σ/σy)n for σ ≥ 0. effective tension etc. Lines The effects of direct tensile strain variation are again handled automatically by the program (see below). Each segment in the OrcaFlex model uses a distinct bend moment / curvature table which is clearly necessary if the line type has a diameter profile. The inner and outer diameter (as specified in the Line Type data). The program chooses the value of direct tensile strain by first performing a static calculation under the assumption that direct tensile strain is 0. Stress results are derived using the stress-strain relationship. of course. Note that each segment in the model has a distinct bend moment / curvature relationship based on a distinct value of direct tensile strain. Values for positive strain must be entered and the relationship for negative strain is then determined by reflection so that σ(ε) = -σ(-ε). Material E. On the other hand consider an unstressed steel pipe. However this would incur a significant performance cost. Data Stress-Strain Relationship variable data sources are used to define non-linear elastic material properties for homogeneous pipes. Strain (Stress-Strain table only) This table directly specifies the relationship between stress and strain. where the direct tensile strain is zero. This allows us to use a constant value of direct tensile strain for the purpose of deriving the bend moment / curvature relationship. By "constant" we mean that we do not update the bend moment / curvature relationship during the dynamic simulation. Stress-Strain relationship The relationship between stress and strain can be specified by either Ramberg-Osgood curve or Stress-Strain table. Note that there is an alternative parameterisation of the Ramberg-Osgood equation. The direct tensile strain can have a significant effect on the non-linear bending behaviour if it is large. which is why it is denoted σ y here. K. When the pipe is in this state then any small amount of curvature will yield the pipe outer fibres. In this state the pipe can withstand significant curvature before the outer fibres yield. Finally the static calculation is repeated to obtain a solution which accounts for the effects of direct tensile strain. The table is interpolated linearly and for values of strain outside the table linear extrapolation will be used. This means that the only stress results affected are those that depend on bending: Max Bending Stress. Otherwise. 6. Dec = 45 ) End A End B z Declination Angle y Azimuth Angle x Figure: Directions If the line end is attached to a body which can move (a Vessel or Buoy). Free-to-rotate or Fully-restrained Ends In many practical cases.21 Line Ends Lines in OrcaFlex run from End A to End B. then the no-moment direction is defined relative to the body axes and therefore moves with the body. relative to global axes. the orientation of any segment in the line is defined in terms of Azimuth and Declination angles. e. Nevertheless. and a no-moment direction which is described in terms of azimuth and declination.w System Modelling: Data and Results. so if we hang up a catenary of line. the no-moment directions are as shown below: No moment direction ( Az = 0. Dec = 160 ) No moment direction ( Az = 0. it is defined in global axes. von Mises Stress. When should you use one rather than the other? The following notes offer a brief guide: 402 . Note that it is never necessary (or correct) to 'convert' the line stiffness into an end stiffness: the program includes the line stiffness for you automatically. Lines Stress results The non-linear stress-strain relationship is also used to calculate certain stress results from strain values.g. Max von Mises Stress and ZZ Stress. the line ends are neither completely free nor fully restrained.m/degree. but the axial and torsional stiffnesses are still assumed to be linear. In the first case. More commonly. we recommend that you should usually choose one of these conditions. Nonlinear stress-strain leads to a non-linear elastic bend stiffness. See No-Moment Direction. This too uses the End A to End B convention. and then freeze the ends. whose stiffness is in units of moment per unit angle. the end stiffness is set to Infinity. in the second case. the line end is either free to rotate or fully restrained. the end stiffness is set to zero. Azimuth is measured in the X-Y plane. No-moment Direction Associated with each end is a stiffness. Declination is measured downwards from the Z axis. Travelling from A to B. kN. End Stiffness The stiffness associated with the end can be used to represent an item such as a flexjoint.8. 4. End Force and End Force Ez-Angle The figure below shows the end connection of a flexible line fitted with a bend stiffener. In such cases. The moment at the end can then be determined by a local (static) analysis which can be developed to incorporate as much detail as required. If the local loads (weight. then the reaction moment M is zero. 3. M. but remember that there must be sufficient nodes at the line end to interact with the solid. The bend moment at the end fitting. particularly where buoy rotational inertias are small.g. e. and the bend moment at the end fitting is M = T. h. End Force and End Force Ez-Angle are the same whether the end condition is defined as free-to-rotate. No moment direction M F h T Figure: End connection of a flexible line fitted with a Bend Stiffener Design Loads for End Fittings For design of end fittings. mid-water arches for riser systems). θ. Bend stiffness. In such systems. is a function of the lever arm. The line applies a load (tension) T as shown. and the End Force Ez-Angle. if one is fitted and use shorter segments near the line ends so as to represent the moments with sufficient accuracy. or some intermediate condition. System Modelling: Data and Results. The "No moment direction" is defined in the input data. etc. are small by comparison with T.) on the end part of the line. including bend restrictors. as shown. Where fully restrained ends are used. F. and the end connections should be fully restrained. use one or more solids to represent the supporting surface. The rotational motions of the buoy may then be influenced by moment transfer from the ends of lines attached to it. it is necessary to pay more attention to the modelling of the line close to the end.w 1. the end connections to the buoy should be fully restrained. Lines Many systems modelled using OrcaFlex consist of relatively long flexible lines where bend stiffness plays only a minor role in determining the overall forces on and movements of the system. stern rollers. pipelay stingers. drag. line ends may safely be modelled as free-to-rotate. including end moments. Roll-on/roll-off contact (e. An exception to this rule is systems which include one or more 6D Buoys. It is clear from this that 1. A pinned connection at the average contact point is often sufficient. 2. For a more exact representation.g. fully restrained. may have a significant influence on overall system behaviour in such cases. a large diameter underbuoy hose in shallow water. 2. A further exception is systems where the flexible lines are relatively short and stiff. which depends not only on the end condition but also on the bend stiffness distribution in the line/bend stiffener. 5. In particular make allowance for the additional stiffness of a bend stiffener.h. including the bend stiffener. OrcaFlex reports the End Force. then the reaction force F is equal and opposite to T. 403 . the principal parameters provided by OrcaFlex are End Force and End Force Ez-Angle. When the reaction force F acts in the no-moment direction. a are simultaneous values of End Force and End Force Ez-Angle.22 Modelling Compression in Flexibles When a flexible line experiences compression. and reports the corresponding curvature and bend moment based on the half length of the end segment. except where End Force is very small. End Force Ezy-Angle is the component in the local yz plane. OrcaFlex is fully capable of modelling this behaviour provided the discretisation of the model is sufficient. then stop. Once the stiffener design is known the stiffener can be modelled using a bend stiffener attachment. The limiter length must be not less than a*R where a is End Force Ez-Angle and R is the limiter locking radius. Results When examining results at line ends note that if a stiff pipe goes into compression. OrcaFlex reports Bend Restrictor Load P = F*(1-cos(a)) as an aid to bend limiter design. and End Force Ez-Angle may approach 180°.) which are usually negligible become important. End Force Ezx-Angle is the component in the local xz plane. Under static conditions. The bend stiffener should be designed to prevent infringement of the permitted curvature for any (F. Under dynamic loading conditions. This occurs when the line tension T comes close to zero. the Euler load is π2EI/L2.a) pair. Bend Limiter There are two design requirements: 1.e. including allowance for the motion of line end where the line is attached to a vessel or buoy. Bend Limiters: articulated devices which rotate freely to a specified curvature. curvature and bend moment are reported as zero. Bend Stiffener The design process for a stiffener is more complex than for a bellmouth or a bend limiter.a) pairs corresponding to maximum values of End Force F. OrcaFlex reports components of End Force Angle in the local XZ and YZ planes. Design Data for Bend Restrictors We classify bend restrictors into 3 types: Bellmouths: curved surfaces which support the flexible and maintain acceptable curvature. bend stiffness EI. The direction of the end force is then no longer dominated by the line tension. The limiter must be capable of withstanding the maximum bend moment M given by M = R*F*(1-cos(a)) where F. Where bend stiffness at the line end is zero (pinned end or a zero stiffness line). For a simple stick of length L. and other loads (shear. 2. An X-Y graph of F against a (End Force against End Force-Ez Angle) provides a complete definition of the loading for one analysis case. Bend Stiffeners: elastomeric devices which provide a tapered additional bend stiffness. Curvature is calculated in OrcaFlex by dividing the angle change at any node by the sum of the half-segment lengths on each side of the node: bend moment is curvature multiplied by bend stiffness. it is often sufficient to consider just the three (F. The Euler load is a function of the length of the straight section. line tension becomes negative but End Force remains positive. and the critical design load cases are not always self-evident. At the end. local drag and inertia loads etc. the reported End Force Ez-Angle is misleading and a more appropriate estimate should be made from the system geometry. P is sometimes called "pseudo-curvature". i.w System Modelling: Data and Results. it responds by deflecting transversely: the magnitude of the deflection is controlled by bend stiffness. 404 . with each (F.a) pair defining a load case. Ez-Angle for a point near the end of the bend restrictor is a reasonable alternative where End Force Ez-Angle is not suitable. the behaviour of an initially straight section of line under pure axial loading is described by classic Euler buckling theory. The Euler load is derived from a stability analysis: it tells us the value of axial load at which transverse deflection will occur but nothing about the post-buckling behaviour. This can be done using the Ez-Angle results variable. the transverse deflection is resisted by a combination of inertia and bending.8. This defines the maximum compressive load – the "Euler load" – which a particular length of line can withstand before transverse deflection occurs. For cases where the bellmouth is not radially symmetrical. with pin joints at each end. the bend stiffness and the end conditions. In practice. End Force EzAngle a and Bend Restrictor Load P. 6. Ez-Angle for any segment gives the angle of that segment relative to the No Moment Direction at the adjacent line end. Lines This approach is usually sufficient. In these conditions. Different design information is required for each type: Bellmouth The principal design requirement is that bellmouth angle should be greater than the maximum value of End Force Ez-Angle. OrcaFlex takes the angle change between the end segment of the line and the no-moment direction. and a moment. damping and drag. we can make the Euler load for each stick greater than the applied compressive load. but we now have more sticks with which to model the deflected shape. if the segment Euler load is reached then a Warning is given on the result form and in the statistics table. If infringement occurs only during the build-up period. and assumes pinned joints with no bend stiffness at each end of the segment. These can be used to model thrusters. 3). added mass. Clearly. This means that each segment of this line type is treated as a strut capable of taking whatever compressive loads arise in the course of the simulation. Z) and 3 rotational (Rotation 1. This gives us a convenient way of checking the adequacy of our model: provided the compressive load in each segment always remains less than the Euler load for that segment. 6. However it may be acceptable to disregard occasional minor infringements of short duration on the following grounds: Transverse deflection caused by compression takes some time to occur because of inertia. 2. and forces and moments from many different effects can be modelled. including: Weight and inertial loads.g. Connection loads from objects attached to the buoy (e. Provided the wavelength of the deflection is longer than the length of the individual sticks then the rigid stick model can approximate it: shorter sticks give a better approximation. including friction modelling. Y. OrcaFlex makes this comparison automatically for all segments and reports any infringements in the Statistics tables. Under compression. Where infringements are severe and repeated or of long duration the analysis should be repeated with shorter segments in the affected area. then we have to decide what to do about it. The usual setting is "No". The segment Euler load used in OrcaFlex as a basis for comparison is the lowest of the various alternatives. If it occurs during the main part of the simulation. links or winches). By replacing each long stick by several short ones. perhaps as a result of a starting transient. Buoyancy. then the real line which the stick represents will start to deform at a shorter wavelength. For some special cases. Note: In either case. Whether or not to disregard an infringement is a decision which can only be taken by the analyst in the context of the task in hand. 6D Buoys provided the segments are short enough to model the deflected shape properly. lines. The segment Euler load is also plotted in tension range graphs (as a negative value – compression is negative) so that infringements are clearly visible. This is a conservative assumption. If the wing pierces the surface then the wing loads are scaled by the proportion of the wing area that is below the surface. this stick model is no longer adequate. Each stick will then remain straight. and deflections within the stick length become significant. For a surface-piercing buoy these fluid loads take account of the proportion of the buoy that is below the water surface. this is not the most useful model and OrcaFlex offers an alternative. Lines of this sort cannot take compression at all. Buoys have both mass and moments of inertia. due to the relative flow of the sea past the wing. the line deflects: the sticks remain straight and the joints rotate. then we can safely ignore it. the data includes a Compression is Limited option. Contact loads from the vertices of the buoy contacting the seabed or elastic solids.9 6D BUOYS 6D Buoys are objects having all six degrees of freedom – 3 translational (X. such as chains with small bend stiffness. Slam forces as the buoy passes through the sea surface. Why are these two statements equivalent? Imagine the real line replaced by a series of rigid sticks connected by rotational springs at the joints – this is essentially how OrcaFlex models the line. OrcaFlex then does not allow compressive loading greater than the segment Euler load (which is zero if the bend stiffness is zero). then we can have confidence that the behaviour of the line in compression is adequately modelled. 405 . If the compressive load reaches the Euler load for an individual stick. Limit Compression For each line type.w System Modelling: Data and Results. Another way of saying the same thing is that the compressive load in any segment of the line should never exceed the Euler load for the segment. which experiences lift and drag forces. then we should examine the time histories of tension in the affected areas. Applied loads. If the segment Euler load is infringed during a simulation. so the Compression is Limited option can be set to "Yes". A wing is a rectangular surface attached to the buoy at a specified position and orientation. Wing loads. Spar Buoys The second type. Lumped Buoys The first type. are intended for modelling axi-symmetric buoys whose axis is normally vertical. OrcaFlex calculates what proportion of the wing rectangle area is below the instantaneous water surface. but then scales them by PW before they are applied. These loads depend on userspecified coefficients that depend on the incidence angle of the relative fluid flow. Spar Buoys and Towed Fish. by specifying the number of cylinders and their lengths and diameters. but they differ in how the geometry of the buoy is defined and how the fluid loads and surfacepiercing effects are calculated – see below. The wing lift. allowing for the instantaneous position and orientation of each cylinder in the wave. then instead air lift and drag loads are calculated and applied. This necessarily restricts the accuracy with which interactions with the water surface are modelled. are intended for modelling bodies. then OrcaFlex also calculates the air lift and drag loads (as if the wing was not submerged) and scales them by 1-PW. but using the air density.e. This allows you to provide some information about the buoy geometry. Where a lumped buoy pierces the surface it is treated for buoyancy purposes as a simple vertical stick element with a length equal to the specified height of the buoy. which experiences lift force. For partly immersed cylinders. called Towed Fish. the air. before they are applied. Because they are modelled as a stack of concentric cylinders.9. This model does not provide the rotational stiffness that would be experienced by most surface piercing buoys. or both. whose principal axis is normally horizontal. A conical or spherical shape can be approximated as a series of short cylinders of gradually increasing or diminishing diameter. Towed Fish buoys are identical to Spar Buoys except that the stack of cylinders representing the buoy is laid out along the x-axis of the buoy. Each wing has its own data and results available. these are useful for representing lift surfaces. Lumped Buoys.1 Wings 6D Buoys can have a number of wings attached. such as towed fish. i. The fluid referred to here can be the sea. are specified without reference to a specific geometry. Added mass and drag forces are applied only to those parts of the buoy which are in the water at the time for which the force is calculated. Spar Buoys model surface-piercing effects in a much more sophisticated way than Lumped buoys. OrcaFlex then calculates the water lift and drag loads as if the wing was fully submerged.w System Modelling: Data and Results. and buoyancy therefore changes linearly with vertical position without regard to orientation. attached to the buoy at a specified position and orientation. The use of Morison's equation implies that the buoy diameter is small compared to the wavelength (usually the case for CALM buoys and the like) but means that some load terms are not represented. Three types of 6D Buoy are available: Lumped Buoys. called Spar Buoys. velocity and incidence angle. therefore. Effects such as heave stiffness and righting moments in pitch and roll are determined by calculating the intersection of the water surface with each of the cylinders making up the buoy. See Lumped Buoy Properties for further details. both water and air lift and drag loads are applied. added mass and drag are scaled according to the proportion of the cylinder volume that is submerged. and if you have selected to include wind loads on wings (on the Wind page on the Environment data form). 6. its 'proportion wet' PW. These 3 types share some common data. Hydrodynamic loads on Spar Buoys are calculated using Morison's equation. then the lift and drag loads are calculated using the sea density. In addition. diverters etc. the 'proportion dry'. Towed Fish The third type. if you have selected to include wind loads on wings. When the wing is partially submerged. as follows. rather than along the z-axis. Lines can be attached to an offset position on a buoy – this allows the direct study of line clashing. particularly where surface-piercing effects are important (such as for a CALM buoy). each appropriately scaled. When this happens. due to the relative flow of fluid past the wing. i. Whenever the wing is completely below the instantaneous water surface. 406 .e. Slam forces are also calculated and applied separately for each cylinder. For further details see Spar Buoy and Towed Fish Properties. A wing is a rectangular surface. including the separation introduced by spaced attachment points. Spar Buoys and Towed Fish are less suitable for fullysubmerged objects with more complex geometry. drag force and drag moment. Spar Buoys are modelled as a series of co-axial cylinders mounted end to end along the local z-axis (see Spar Buoy and Towed Fish Properties). using the same formulae and coefficients. Whenever the wing is completely above the water surface. 6D Buoys Lines attached to a 6D Buoy can thus experience both moment effects and translations as the buoy rotates. velocity and incidence angle. centred on W. Wy is normal to the wing surface and points towards the positive side of the wing. We refer to the wing's length in the Wz direction as its span and its width in the Wx direction as its chord. The origin of the buoy axes can any point chosen by the user. with origin W at the wing centre and axes Wx. by adjusting the wing gamma angle. so that (Wx. i. These loads are applied at the wing centre and are specified by giving lift.w System Modelling: Data and Results. Wz is the principal axis of the wing. the side towards which positive lift forces act. Name Used to refer to the 6D Buoy. The lift force is the force at 90° to that direction. It is the axis about which the wing can easily be pitched.Wz) form a right-hand triad. are much more complex than this and are not modelled for wings. drag and moment coefficients as a function of the incidence angle α between the relative velocity vector (flow velocity relative to wing) and the wing plane. Wy and Wz. The wing is therefore a rectangle in the Wxz plane. The drag force on a wing is the force applied in the direction of relative flow. increasing the wing gamma angle moves the leading edge in the direction of positive lift. 6. The moment represents the moment (about the wing centre) that arises due to the fact that the centre of pressure may not be at the wing centre.2 Common Data All types of 6D Buoy use a local buoy axes coordinate system. but the buoy axes directions should be in the directions of the principal axes of structural inertia of the buoy – see Mass Moments of Inertia below. 6D Buoys drag and moment results then report the water loads whenever the wing is more than half submerged and the air loads whenever it is less than half submerged. Wings do not have any mass. normal to the axis Wz. added mass or buoyancy due to wings should be added into the properties specified for the buoy itself. Wx and Wz are in the plane of the wing. We normally choose Wz and Wx so that Wx is towards the leading edge of the wing. Therefore any mass.9. However slam loads on the 6D Buoy itself can be modelled – see Slam Force Theory. for instance planing and slamming. 407 .e. Wx is in the plane of the wing. Note: The true effects of a wing breaking surface. added mass or buoyancy associated with them.Wy. With this arrangement. +ve lift Flow Velocity V (relative to wing) Wy Chord Wz Principal Wing Axis W Leading edge Wx Span -ve lift Figure: Wing Model Each wing has its own set of local wing axes. so that Bxyz are in the same directions as GXYZ. If the buoy is Free or Fixed then its initial position is specified by giving the X. then the Initial Position and Attitude specify where on the line it is connected. and finally Rotation 3 about the new (and final) Bz direction. so the buoy axes should be chosen to be in the principal directions of inertia about the centre of mass (or at least be close to those directions). Normally this data item should be set to All so that the static analysis calculates the true equilibrium position and orientation of the buoy. Fixed or connected to a Vessel. In this case the buoy's Initial Position and Attitude are specified relative to global axes. All resulting forces and moments on the buoy are transmitted to the object. then this initial position is used as an initial estimate of the buoy position and the static analysis will move and rotate the buoy from this position until an equilibrium position is found. 6D Buoy or a Line (provided that line includes torsion). Rotation 3. then it is rigidly connected to that object and so moves and rotates with it. Note: These moments of inertia are the diagonal terms in the structural inertia matrix about the specified centre of mass. Then apply Rotation 1 about Bx (=GX). However it is sometimes useful to fix the buoy position or orientation. Its Initial Position and Attitude are specified relative to global axes. Degrees of Freedom Included in Static Analysis Determines which degrees of freedom are calculated by the static analysis. And its initial orientation is specified by giving 3 angles Rotation 1. and with what orientation. X.w System Modelling: Data and Results. See Degrees of Freedom Included in Static Analysis. but with an offset relative to that node's axes that is given by (x. If the buoy is Free then it is free to move in response to wave loads. All: the buoy position and orientation are calculated by the static analysis. The buoy will be connected to that node. Disturbance Vessel Determines whether the 6D Buoy will experience sea state disturbance generated by a particular vessel. Y and Z coordinates of the buoy origin B. Mass Moments of Inertia The solid moments of inertia of the buoy. If the buoy is Fixed then it cannot move. 6D Buoys Type Three types of buoy are available: Lumped Buoys. Mass Mass or weight in air. This arc length may be measured relative to either End A or End B as specified by the user. If the buoy is connected to a Line. Spar Buoys and Towed Fish. If a Free buoy is not included in the static analysis then this initial position is taken to be the static position of the buoy. y and z buoy axes directions through its centre of mass. Initial Position and Attitude Specifies the initial position of the buoy origin and the buoy initial orientation. The off-diagonal terms are taken to be zero. relative to global axes.Y. Connection A 6D Buoy can either be Free. The following data items are common to all types. In this case the buoy's Initial Position and Attitude are specified relative to the object to which it is connected. for example if the static analysis is unable to find the equilibrium position or orientation. about the local x. 0). as follows. If the buoy is included in the static analysis. First align the buoy with global axes. y. 408 . Rotation 2. 6D Buoy or a Line. relative to the global axes. If the buoy is connected to a Vessel. which are successive rotations that define the orientation of the buoy axes Bxyz. This data item only applies to Free buoys and it can be set to one of: None: the buoy position and orientation are not calculated by the static analysis – they are simply set to the initial position and orientation specified on the buoy data form. but its orientation is simply set to the initial orientation set on the buoy data form. The buoy orientation relative to the node axes is specified by the Initial Attitude angles. attached lines etc. The buoy will be connected to the nearest node to that arc length.Z: the buoy position is calculated by the static analysis. followed by Rotation 2 about the new By direction. as follows: The Initial Position z-coordinate specifies the arc length at which the buoy should be connected to the line. Note that this origin is the point at which the relative velocity is calculated and at which the resulting wing lift and drag forces are applied. mass and moments of inertia are applied at this point. Name Used to refer to the wing. or can vary with simulation time. declination and gamma – relative to the buoy axes.w System Modelling: Data and Results. 6. See Buoyancy Variation for details. See Contact Forces for details. Seabed Friction Coefficient OrcaFlex can model Coulomb friction between the buoy and the seabed and elastic solids. These components can be constant. The friction force applied never exceeds μR where R is the contact reaction force and μ is the friction coefficient.4 Wing Data 6D Buoys can have a number of wings attached. Again these components can be constant. which may not be at the centre of area (even though OrcaFlex draws the wing as being centred at this point). 6D Buoys Damping relative to You can choose whether the buoy velocity used with the damping data that you specify (see lumped buoy data or spar buoy or towed fish data) should be the buoy velocity relative to earth. in the local Wx direction. or can vary and be given by an external function. If the buoy rotates then the loads do rotate with it. which means 'incompressible'. Centre of Mass The centre of mass of the buoy. These are specified by giving the components of Applied Force and Applied Moment relative to buoy axes. then the Bulk Modulus can be set to Infinity. vary with simulation time or be given by an external function.3 Applied Loads You can apply to the buoy external Global Loads that do not rotate if the buoy rotates. The weight force. These are specified by giving the components of Applied Force and Applied Moment relative to global axes. If the buoy rotates then the loads do not rotate with it. Contact Total Contact Area This is used to determine contact forces when the buoy comes in to contact with the seabed and with elastic solids. relative to buoy axes. Centre of Wing The position of the wing origin. These are suitable for modelling thrusters. each having its own data and type. The wing is drawn as a simple rectangle centred on this origin. Chord The width of the wing. Span The length of the wing. or the buoy velocity relative to the fluid. relative to the buoy origin. in the local Wz direction. The angles define the orientation of the local wing axes relative to the buoy axes as follows: 409 . In addition. for example. whereas to model skin friction damping the velocity relative to the fluid should be used.9. Orientation The orientation of the wing is specified by giving 3 angles – azimuth. 6. you can specify external Local Loads that do rotate with the buoy. In both cases the Point of Application of the load is specified by giving its x. the rectangle's dimensions being the specified Chord and Span. To model wave radiation damping the velocity relative to earth should be used. The angles can be fixed. See Friction Theory for further details of the friction model used.z coordinates relative to buoy axes. Bulk Modulus Specifies the compressibility of the buoy. It should therefore normally be at the centre of pressure.9.y. Specifying a value of zero allows you to disable contact for the buoy. vary with simulation time or be given by an external function. If a value of '~' is specified then OrcaFlex calculates a default value for total contact area based on the buoy geometry. If the buoy is not significantly compressible. Note: The friction coefficient for contact with elastic solids is specified on the Solid Friction Coefficients data form. The incidence angles in the table must be given in strictly increasing order and the table must cover the full range of incidence angles.ρ. You can check that the angle of attack in the wing plane stays within the range of your data by examining the Beta angle result variable. where positive values mean that the flow is towards the positive side of the wing (i. α. Linear interpolation is used to obtain coefficients over the continuous range of angles. hitting the positive side). Wing Type Determines the properties of the wing. This process is best done with the Draw Local Axes option set on (see the View menu or the Tools | Preferences menu) since the wing axes are then visible on the 3D view and you can check that the resulting orientation is correct. Wing Type Properties The properties of each wing type are specified by giving a table of lift.e. For each of these rotations. not on the angle of attack in the wing plane. Lift. The lift coefficients can be positive or negative and the lift force is given by: Lift Force = P ½. This declines Wz down into its final direction.9.5 Wing Type Data 6D Buoys can have a number of wings attached. 410 . A 'Graph' button is provided. hitting the negative side) and negative values mean that the flow is towards the negative side of the wing (i. which displays a graph of the 3 coefficients so that you can visually check your data. The incidence angle is always in the range -90° to +90°. Aerodynamic loads are only applied if the Include wind loads on 6D Buoy Wings option is enabled in the Environment data. 6. even though your data may only apply over a limited range of in-plane attack angles. Wz now points along the direction whose azimuth and declination angles are as specified. This leaves Wz aligned with Bz but Wx now points in the direction towards which the declination is to be made. You can define a number of wing types – click the "Wing Types" button to access the wing types data form. it is easiest to first set the azimuth and declination values to give the desired Wz-direction.V2 where P is the proportion wet or proportion dry as appropriate. as a function of incidence angle α.e.e. ρ is the fluid density. each having its own data and type. when looked at along the axis of rotation. Then set gamma to give the correct pitch of the wing. drag and moment coefficients as a function of the incidence angle of the flow relative to the wing. 6D Buoys Start with the wing axes Wxyz aligned with the buoy axes Bxyz and then rotate Wxyz about Bz by the azimuth angle. This is the direction of the axis about which the wing pitch is set. Note: The wing lift. OrcaFlex will therefore use the same lift. positive angles mean clockwise rotation and negative angles mean anti-clockwise rotation. This is a rotation about the principal wing axis. When setting these orientation angles. Name Used to refer to the wing type. Finally rotate by the gamma angle about this final Wz direction.A.w System Modelling: Data and Results. A is the area of wing that is inside the fluid and V is the relative flow velocity at the wing centre. drag and moment are assumed to depend only on the incidence angle. Drag and Moment Coefficients These define the hydrodynamic and aerodynamic loads applied to the wing. Now rotate by the declination angle about the new direction of Wy. This equals 90° minus the angle between Wy and the relative flow vector. that the relative flow vector makes to the wing surface. The lift coefficient Cl(α) defines the lift force applied to the wing. so the first and last angle in the table are set to -90° and +90° and cannot be changed. Incidence Angle The incidence angle is the angle. the side or the back of the wing.Cl(α). i. drag and moment coefficients for flow (with the same incidence angle) onto the front. so it allows you to adjust the pitch of the wing. Chord This moment is applied about the line that is in the wing plane and is at 90° to the relative flow vector. For α = ±90° this line is ill-defined and the moment coefficient must be zero. Then the length of the longest side of this cuboid is found. Specify a value of '~' to display the drawing using the absolute coordinates as specified in the . The moment coefficients can be positive or negative and the moment is given by: Moment = P ½. along the line that is at 90° to the relative flow vector and in the plane of that vector and Wy.Cd(α). The drag force is defined by the drag coefficient Cd(α) using the formula: Drag Force = P ½. Shaded Drawing Origin is provided because the shaded drawing and the wing may have different origins. The Browse button allows you to specify the Shaded Drawing File quickly and also provides quick access to the Orcina sample drawings via the Navigate to Orcina sample drawings button. If you use a relative path then the path will be taken as relative to the folder containing the OrcaFlex file. Note: If you use a value of '~' for Draw Size then OrcaFlex uses the coordinates in the . Negative moment coefficients mean the moment tries to turn the wing the opposite way. Alternatively the object can be represented by an imported 3D model by specifying the Shaded Drawing File.V2.x file extension. If these coordinates use a different length units system from your OrcaFlex model then you should specify the units used in the .txt.w System Modelling: Data and Results. The Use Culling option is normally selected since it can provide a useful performance benefit. All directions are scaled equally to arrange that the longest side in the drawing is drawn to the specified Draw Size. 411 . Similarly Shaded Drawing Orientation allows you to reorient the shaded drawing to match the wing's axis system. This moment represents the fact that the position of the centre of pressure may depend on the incidence angle α. Examples of this can be found in the sample shaded drawings provided by Orcina.Cm(α). This must be a Direct X format file. If it is set to Use Buoy's pen then the 6D Buoy pen will be used. wings are drawn as plates with the specified span and chord. 6D Buoys The lift force is applied at the wing centre.ρ. If it is set to Use this pen then the specified pen is used.A. usually with the .x file have their outward facing directions defined correctly. Pen This controls which pen is used to draw a Wing which uses this Wing Type.A.V2 The drag coefficient cannot be negative.x file). In the unusual situation where the outward facing directions are not defined correctly then the . The moment coefficient Cm(α) defines a moment that is applied to the wing. Positive moment coefficients mean that the moment is trying to turn the wing to bring Wy to point along the relative flow direction.ρ. Draw Size is provided to allow you to scale the drawing. If this happens then typically sections of the model will be missing when drawn by OrcaFlex. Shaded Drawing By default. However. Positive lift coefficients mean lift pushing the wing towards its positive side (the +ve Wy side).x file.x file will not display correctly. for shaded 3D Views.x file directly. For α = ±90° this line is ill-defined and the lift coefficient must be zero.x file by including an auxiliary file called AdditionalInformation. in order to work it requires that the triangles defined in the . This longest side is calculated by first fitting the smallest possible cuboid around the vertices of the shaded drawing (these are defined in the . The Shaded Drawing Origin defines the origin of the shaded drawing with respect to the wing's local axis system. so the drag force is always in the relative flow direction. Disabling the Use Culling option resolves this problem. This cuboid is aligned with the shaded drawing's local axes. Similarly you can specify a Unit Moment that is applied when the relative angular velocity is 1 radian/second. 412 . These are loads that are directly proportional to the velocity. 6D Buoys 6. OrcaFlex then scales these magnitudes according to the actual relative velocity and applies the resulting force or moment. which is used to scale the hydrostatic and hydrodynamic forces and to determine the centre of wetted volume. The forces and moments are calculated as follows (ρ is water density.6 Lumped Buoy Properties Vertices z (heave) yaw y (sway) pitch B (B=buoy origin) Figure: roll x (surge) Lumped Buoy A Lumped Buoy is specified relative to its own local frame of reference Bxyz. Height is the buoy vertical dimension. The Height is used for two main purposes: To calculate the contact area used to calculate forces of contact with shapes and the seabed. Separate Cd values are given for force and moment calculations. Drag Hydrodynamic drag forces and moments may be applied to the buoy. or angular velocity. g is acceleration due to gravity). you specify the magnitude of the Unit Force that is applied when the relative velocity is 1 length unit/second. The drag force properties are specified by giving. for each of the local buoy axes directions. Each degree of freedom is calculated independently. These are loads that are proportional to the square of the relative velocity.9.w System Modelling: Data and Results. For each of the local buoy axes directions. Damping Hydrodynamic damping forces and moments may be applied to the buoy. assumed equally spaced about the centre of volume. except that instead of specifying a drag area you must specify a Moment of Area. or angular velocity. Drag moment properties are specified in a similar way. of the sea past the buoy. Geometry Volume is the total volume of the buoy. which is the point at which they are applied. of the buoy relative to the fluid or relative to the earth (as specified in the buoy data). Height is assumed to be independent of buoy rotation. with its centre at the Centre of Volume. The Centre of Mass is specified relative to Bxyz. To calculate the ProportionWet. Note: Drag Area Moment is the 3rd absolute moment of drag area about the axis. defined relative to the local buoy axes Bxyz. the Drag Area that is subject to drag loading in that direction and the corresponding Drag Coefficient. Slam/Water Exit Force The slam force. It is also used to calculate the interaction of the buoy with shapes and the seabed. Separate slam data are specified for water entry and water exit. by giving a reference Hydrodynamic Inertia together with a rotational added inertia coefficient. and also separately for each local axis direction. The fluid inertia matrix is multiplied by the instantaneous fluid acceleration vector to produce the fluid acceleration loads.L. The translational fluid inertia properties of the buoy are specified. and the slam force results will then not be available. The lower-right 3×3 block of cells has units M. and each can be set either to a constant slam coefficient value or else to be variable with submergence relative to the surface.w System Modelling: Data and Results. The added mass matrix is simply added in to the buoy's virtual mass matrix.7 Lumped Buoy Drawing Data Vertices and Edges This defines a "wire frame" representation of the buoy. where M. filled-in shape based on the vertices and edges. the Lumped Buoy is drawn using a solid. Ca. since the sea motion is treated as irrotational. Note: Rotational Cm values are not specified. when the buoy is not fully submerged they will be scaled by the ProportionWet. as the buoy enters or exits the water. If variable slam data are in use for water entry/exit then the Slam Area is not used for that direction of motion. 6. The units of the added mass and fluid inertia matrices are as follows. otherwise that edge is drawn as a cylinder with the specified diameter.9. Damping and Drag topic. Fluid Inertia specified by full matrices With this option the added mass and fluid inertia properties are specified as full 6×6 symmetric matrices. by default. Secondly. If constant slam coefficients are used for entry/exit then no slam/water exit force will be applied for that direction of motion if the specified Slam Area is zero. These accelerations have two main effects. meaning equal to the fully-submerged displaced mass (= volume x water density). The translational Cm values can be set to '~' to mean 1 + Ca. Edge diameter (used only for shaded drawing) For shaded graphics views. so its angular acceleration is taken to be zero and there is therefore no fluid load due to fluid rotational acceleration. by giving a reference Hydrodynamic Mass together with the two inertia coefficients. Ca and Cm. Full details of the calculation are presented in the Lumped Buoy Added Mass. for each of the local buoy axis directions. See Contact Forces for details. The wire frame representation of the buoy is used to draw the buoy. length and time: The upper-left 3×3 block of cells has units M. As an alternative you can use the vertices and edges to define a frame like structure. they result in forces and moments being applied to the buoy – these are referred to as the fluid acceleration loads. Fluid Inertia specified by diagonal values These properties are specified separately for translational and rotational motions. If the edge diameter is '~' then that edge will be used to build a filled in shape. These matrices should be defined at the Centre of Volume and be for the fully submerged geometry that the buoy represents. The vertices are specified by giving their coordinates with respect to buoy axes Bxyz. For further details see Slam Force Theory. 413 . and the edges are specified by giving the vertex numbers of the vertices they connect. L and T indicate the units of mass. The upper-right and lower-left 3×3 blocks have units M. This is often a convenient hydrodynamic reference mass to use. can be modelled by setting the Slam Force Data and (if constant slam coefficient data are specified) the Slam Area. The fluid inertia properties can be specified either by providing the Diagonal values or Full matrices. The rotational fluid inertia properties of the buoy are specified. Firstly. The translational Hydrodynamic Mass values can be set to '~'. the buoy experiences an increase in inertia – this is known as the added mass. 6D Buoys Fluid Inertia Fluid inertia properties are those that are proportional to the acceleration of the sea and the buoy. for each of the local buoy axis directions.L2. The buoy is specified relative to its own local frame of reference Bxyz. A value of '~' is used for the wire frame on the left and a value of 1m is used for the wire frame on the right. The cylinders are numbered from the top downwards.9. A Spar Buoy is modelled as a series of co-axial cylinders mounted end to end along the local z-axis.8 Spar Buoy and Towed Fish Properties The figure below shows the geometry of a Spar Buoy. 6. The geometry of a Towed Fish is identical except that the buoy axis is aligned with the x-axis of the buoy. 6D Buoys Figure: Wire frames with different edge diameter. So in the tables on the buoy data form the cylinder at the base of the stack (lowest x or z) appears at the bottom of the table. The Centre of Mass is specified relative to Bxyz. If you are modelling a CALM or SPAR buoy then see also Modelling a Surface-Piercing Buoy. 414 .w System Modelling: Data and Results. then summed to obtain the total load on the buoy. Hydrodynamic Loads See the Added Mass and Damping and Drag pages on the buoy data form. and includes the appropriate contributions to static stability. relative to buoy axes. In this case then the contained water contributes to the buoy's inertia. Inner Diameter and Length The diameters of the cylinder and its length measured along the axis.w System Modelling: Data and Results. When the buoy pierces the water surface. If the inner diameter is greater than zero then the cylinder is actually a hollow cylindrical pipe. 6D Buoys Buoy Axis Cylinder 1 OD Cylinder 1 Length z Rotation 3 y Rotation 2 B (B=buoy origin) x Rotation 1 Stack Base Position Figure: Spar Buoy Geometry The shape of a Spar Buoy or Towed Fish is specified by the following data on the Geometry page on the buoy data form. Cylinders: Outer Diameter. Stack Base Centre Position The centre of the base of the stack. The remaining parameters determine the hydrodynamic loads acting on each cylinder. These inertial effects are only included in directions normal to the buoy. OrcaFlex allows for the angle of intersection between the sea surface and the buoy axis when calculating the immersed volume and centre of immersed volume. 415 . These parameters define the buoy geometry from which buoyancy forces and moments are determined. Loads are calculated for each cylinder individually. The internal region of the cylinder contains sea water if the buoy is submerged. together with the specified drag areas and coefficients. Slam/Water Exit Force The slam force. set the data as follows. There are two alternative methods that you can adopt when specifying the drag data. 1 or some appropriate reference area) and then adjust the axial Drag Coefficient until the heave response decay rate in OrcaFlex best matches the model test results.9. for each cylinder. For details of the drag load formulae see Spar Buoy and Towed Fish Theory. from model tests or full scale measurements).9 Spar Buoy and Towed Fish Drag & Slam Munk Moment Coefficient Slender bodies in near-axial flow experience a destabilising moment called the Munk moment. is calculated directly from the cylinder geometry by multiplying the outer diameter by the cylinder length. you could set the axial Drag Coefficient to 1 and adjust the axial Drag Area until the heave response decay rate in the OrcaFlex model best matches the model test results. which is calculated by the program. see Drag Area Moments for details. For Spar Buoys and Towed Fish the slam waterplane area used with constant slam coefficient data is not specified by the user – it is taken to be the instantaneous water plane area. That is. For details of the slam force calculation see Slam Force Theory. but you then need to give a Drag Coefficient that corresponds to that specified reference area. If a Slam Coefficient is zero then no slam force is applied for motion in the corresponding direction. the relative velocity of the sea past the cylinder is split into its normal and axial components and these components are used. The drag forces are calculated on each cylinder using the "cross flow" assumption. since OrcaFlex allows for the proportion wet in the drag force formula. The second method is to set the drag data using theoretical values or given in the literature. and we recommend it for CALM and discus buoys – see Modelling a Surface-Piercing Buoy for details. as the buoy enters or exits the water.g. and each can be set either to a constant slam coefficient value or else to be variable with submergence relative to the surface. Set the Drag Area Moments to the 3rd absolute moments of projected area exposed to drag in the direction concerned. Normal drag area calculated from geometry If this option is checked then the normal drag area. This and the Drag Coefficient are multiplied together in the drag moment formula. It is less accurate but can be used if you cannot get any real buoy results against which to calibrate. You can therefore use any positive Drag Area that suits your need.g. you could set the axial Drag Area to a fixed value (e. Hoerner. Or. except that the reference drag area is replaced by a reference Area Moment. This effect can be modelled by specifying a non-zero Munk moment coefficient. Separate slam data are specified for water entry and water exit. Drag Forces and Moments Drag loads are the hydrodynamic loads that are proportional to the square of fluid velocity relative to the cylinder. Set the Drag Areas to the projected surface area that is exposed to drag in that direction and then set the Drag Force Coefficients based on values given in the literature (see Barltrop & Adams. And then set the Drag Moment Coefficients based on values given in the literature. This is the most accurate method. If this option is not checked then the normal drag area. to calculate the normal and axial components of the drag force. For information when modelling a SPAR or CALM buoy see Modelling a Surface-Piercing Buoy. you can calibrate the model to the real results by fixing one of these two data items and then adjusting the other.w System Modelling: Data and Results. 416 . providing you then specify a Drag Coefficient that corresponds to the specified Area Moment. 6D Buoys 6. for each cylinder. If both water entry and exit slam coefficients are zero then the slam force results will not be available.D2)/4 for the axial direction.L for the normal direction and (π. must be specified by the user. For example. can be modelled by specifying non-zero Slam Data. 1991. The first method is to set the OrcaFlex data to get best possible match with real measured results for the buoy (e. The drag forces are specified by giving separate Drag Area and Drag Coefficient values for flow in the normal direction (local x and y directions) and in the axial direction (local z direction). Note that the drag area specified should be the total projected area exposed to drag when the buoy is fully submerged. The Drag Area is a reference area that is multiplied by the Drag Coefficient in the drag force formula. so again you can use any positive Area Moment that suits your need.1965 and DNV-RP-C205). For a simple cylinder of diameter D and length L the total projected drag area is D. The Drag moments are specified and calculated in a similar way to the drag forces. but if the buoy has attachments that will experience drag then their areas must also be included. To use this method. Because the Drag Area and Drag Coefficient data are simply multiplied together. Added Mass Separate added mass coefficients (Ca) are given for flow normal (x and y directions) and axial (z direction) to the cylinder. Second. though only constant values are allowed. Added Mass and Damping Origin This specifies the coordinates. RAO. RAOs and Matrices for Buoy In this option the linear hydrodynamic effects are specified by giving wave force and moment RAOs. and added mass and damping matrices. See Damping Forces and Moments for details. with respect to buoy axes. See below for details. on the Added Mass and Damping page of the spar buoy and towed fish data form. Damping Forces and Moments Damping forces and moments are the hydrodynamic loads that are proportional to cylinder velocity and angular velocity. To suppress all fluid inertia effects you need to set both C a and Cm to zero. They are not modified to account for any variations in buoy attitude or immersion. For the damping forces you can specify whether the velocity used is the cylinder velocity relative to the earth or relative to the fluid. so this option is only suitable for buoys that undergo small oscillations about their mean position. wave radiation damping will not normally apply (unless it is close to the surface). A value of "~" tells OrcaFlex to use the usual "Froude-Krylov plus added mass" formulation for inertia. you can choose whether the velocity that is used in the damping load calculation is the buoy velocity relative to the earth or relative to the fluid. The damping forces and moments are specified by giving the Unit Damping Force and Unit Damping Moment for the normal and axial directions. In this case they will generally be used only with surface-piercing buoys. in which case damping relative to earth should normally be specified.9. instantaneous displacement for constant coefficients and fully-submerged displacement for variable coefficients. such as a diffraction program. the added mass and damping effects are calculated separately for each cylinder using Morison's Equation. in which case the damping data can be set to zero. axial coefficients must be constant. you can choose to specify the added mass and damping either by giving values for each cylinder. Warning: The RAOs and added mass and damping matrices specified must apply to the mean position of the buoy. The coefficients for the normal direction may be variable with submergence. However such linear damping is usually not significant compared to the quadratic drag. where the waves generated by the buoy motion effectively extract energy from the buoy motion. even if Ca is set to zero. Normally these data would come from a separate program. Translational added mass effects are calculated using the displaced mass as the reference mass for each cylinder (specifically. for damping forces) in that direction is 1 length unit per unit time. Rotational added inertia is specified directly (so no reference inertia is involved). or else by giving RAOs and matrices for the whole buoy. Values for Each Cylinder With this option. when the cylinder velocity (relative to earth or fluid. These data can then instead be used to model linear skin friction damping. in that direction. of the point on the buoy at which the RAOs and added mass and damping matrices are applied. Note: The Froude-Krylov force will always be applied to the buoy if Cm is set to '~'. This means that: 417 . These specify the force and moment that the cylinder will experience. These damping terms are primarily intended to represent radiation damping on 6D Buoys.10 Spar Buoy and Towed Fish Added Mass and Damping There are two choices that affect how these first order effects are modelled: First. Separate values can be given for rotation about the cylinder axis and normal to that axis. respectively. Translational inertia coefficients (Cm) are specified in the same way for normal and axial directions.w System Modelling: Data and Results. 6D Buoys 6. It was developed primarily for CALM buoys with diameter in the range 5m to 15m. Note: This option is only appropriate for circularly-symmetric spar buoys whose axis undergoes only small oscillations about vertical. However for a fully-submerged buoy. It is therefore not available for towed fish. in which case damping relative to fluid should normally be specified. See Spar Buoy and Towed Fish Theory for further details. RAOs must be specified for both of the limiting cases. The upper-left 3×3 block of cells has units M. 2. It does not affect calculations in any way. 6.L)/(rad/T). The upper-left 3×3 block of cells has units F/(L/T). for long and short waves. OrcaFlex automatically generates the vertices and edges. The damping matrix is multiplied by the current velocity relative to the buoy at this point to give the damping load. With this option selected the circular cylinders are drawn as such. 418 . The phases must be lags. Damping matrix.L2. 6D Buoys The RAOs are applied to the wave conditions at this point to give the wave loads. You can specify pens for the outside and inside of the cylinders. Because the buoy is assumed to be axi-symmetric these matrices should both have the following axi-symmetric form: a 0 0 0 b 0 a 0 b 0 0 0 c 0 0 0 b 0 d 0 b 0 0 0 d 0 0 0 0 0 0 0 0 0 0 e OrcaFlex warns at simulation time if the matrices are not of this form. There are eight vertices per cylinder and the square base has a side length equal to the diameter of the actual circular cylinder.L)/(L/T). L and T indicate the units of mass. and for at least one other frequency. The lower-left 3×3 block of cells has units (F.L.11 Spar Buoy and Towed Fish Drawing There are two alternative methods of drawing the Spar Buoy and Towed Fish cylinders: 1. The added mass and damping matrices are 6 x 6 symmetric matrices. The lower-right 3×3 block of cells has units M. length and time: Added mass matrix.9. Notes: The selected drawing method only affects the way the object is drawn. i. The vertices of the square-based cuboids are used for calculation of any contact with the seabed or shapes. which are then applied at this point. Draw circular cylinders. In addition you specify how many lines are drawn. The upper-right 3×3 block has units F/(rad/T). where M. Draw square cylinders. Added Mass and Damping Matrices In reality the added mass and damping matrices are frequency-dependent. The units of the added mass and damping matrices are as follows. as a function of wave angular frequency. which is applied at this point. The upper-right and lower-left 3×3 blocks have units M.w System Modelling: Data and Results. The force and moment amplitudes must be the forces and moments that are applied at the buoy origin when a unit amplitude wave is applied.e. but in OrcaFlex you can only enter the matrices for one frequency. Increasing this number makes the buoy drawing more realistic but increases the time taken to draw the buoy. heave force and pitch moment RAOs. The cells below the leading diagonal are non-editable and always equal the corresponding cell values above the diagonal. If this option is selected then each cylinder is drawn as a square-based cuboid. This applies even if you choose for presentation purposes to draw circular cylinders. You should give the values for the principal frequency of excitation expected. so only the cells on and above the leading diagonal are editable. from the time the wave crest passes the buoy origin until the maximum positive force or moment occurs. The lower-right 3×3 block of cells has units (F. in degrees. The RAOs must be specified using the following Orcina conventions. The added mass matrix is applied at this point. Wave Force and Moment RAOs The RAOs are specified in a table giving the amplitudes and phases of the surge force. 9.w System Modelling: Data and Results. This algorithm does not always generate the shaded drawings that you might expect. e. When drawn in wire frame mode they look the same.g. First any edges with specified diameters (i. Lumped Buoys are drawn using the wire frame data. OrcaFlex uses the following procedure to generate this surface from the wire frame vertices and edges. Finally. for shaded 3D Views. diameters not equal to '~') are drawn as cylinders. crane boom latticework. 419 . Consider the following two wire frame vessels. the smallest convex hull enclosing the set is drawn. The remaining edges are used to partition the vertices into sets of connected vertices. 6D Buoys 6. but in shaded mode they differ. but OrcaFlex needs a solid surface for the shaded graphics representation. for each set of connected vertices. This allows you to use such edges to visualise parts of the structure that are not solid. The wire frame drawing data comprises vertices and edges.12 Shaded Drawing By default. Two vertices are deemed to be connected if there exists a path of edges between the two vertices. These edges are now handled and are excluded from the remainder of the procedure. Spar Buoys and Towed Fish are drawn as solid objects using the specified cylinder geometry.e. in order to work it requires that the triangles defined in the . This must be a Direct X format file. This results in two separate convex hulls and a better representation.x file have their outward facing directions defined correctly. This results in a single convex hull for all vertices being drawn. In the unusual situation where the outward facing directions are not defined correctly then the .w System Modelling: Data and Results. The Browse button allows you to specify the Shaded Drawing File quickly and also provides quick access to the Orcina sample drawings via the Navigate to Orcina sample drawings button. The Use Culling option is normally selected since it can provide a useful performance benefit. In the red vessel. the superstructure and hull do not share vertices and so there are two distinct sets of connected vertices.x file will not display 420 . If you use a relative path then the path will be taken as relative to the folder containing the OrcaFlex file.x file extension. Alternatively the object can be represented by an imported 3D model by specifying the Shaded Drawing File. 6D Buoys Figure: Wire Frame and Shaded Drawing For the green vessel the superstructure and the hull share vertices and so all vertices are connected. usually with the . However. Shaded Drawing Origin is provided because the shaded drawing and the buoy may have different origins.x file).9. Volume The volume of the buoy. Then the length of the longest side of this cuboid is found. a free form multi-line text field which is passed to any external function used by the 6D Buoy object. 6D Buoys correctly. This cuboid is aligned with the shaded drawing's local axes. All directions are scaled equally to arrange that the longest side in the drawing is drawn to the specified Draw Size. If these coordinates use a different length units system from your OrcaFlex model then you should specify the units used in the .w System Modelling: Data and Results. Similarly Shaded Drawing Orientation allows you to reorient the shaded drawing to match the buoy's axis system. Any existing Wing.x file by including an auxiliary file called AdditionalInformation. Because other properties are set to zero its value is not significant. z-mass radius of gyration Equals √(Mass Moment of Inertia / Mass). The reported value uses the water density at the sea surface.x file directly. 6. x-mass radius of gyration.Displacement. Weight in water Equals Weight in air . The Shaded Drawing Origin defines the origin of the shaded drawing with respect to the buoy's local axis system.15 Properties Report The 6D Buoy properties report is available from the popup menu on the data form. For example they can be used to connect Lines together.9. 6. All other Lumped Buoy properties are set to zero. 421 . It reports the following: Weight in air The force due to gravity acting on the buoy's mass. Clicking on the Give Buoy negligible properties button has the following effects: Buoy Type will be set as Lumped Buoy. Centre of mass The centre of mass data item. Disabling the Use Culling option resolves this problem. Sometimes they are used as frame of reference objects where the properties are provided by various other objects (usually single segment Lines) connected to the 6D Buoy. If this happens then typically sections of the model will be missing when drawn by OrcaFlex. Examples of this can be found in the sample shaded drawings provided by Orcina.9. Because this is such a common thing to do we have provided a facility on the 6D Buoy data form to set up appropriate properties. Mass will be set to a negligible value.x file. Draw Size is provided to allow you to scale the drawing. Applied Load and Drawing data are not modified. For such uses the 6D Buoy needs negligible structural and hydrodynamic properties. y-mass radius of gyration. 6. Height will not be modified since it cannot be set to zero.14 External Functions Parameters This data item specifies the External Function Parameters. This longest side is calculated by first fitting the smallest possible cuboid around the vertices of the shaded drawing (these are defined in the . Note: If you use a value of '~' for Draw Size then OrcaFlex uses the coordinates in the .13 Other uses 6D Buoys are frequently used for non-standard purposes.txt. Displacement The weight of water displaced by the buoy's volume. Centre of volume Reported with respect to the buoy frame of reference. Specify a value of '~' to display the drawing using the absolute coordinates as specified in the . GX-Acceleration. the height of the buoy and the forces and moments applied by connected objects. y-Acceleration rel. of the user-specified point P on the buoy. OrcaFlex may not be able to achieve the Tolerance specified if it is too small. Reducing the Tolerance value will give a more accurate static equilibrium position. Angular Velocity. these results report the vector a . g. g. a. These results are reported at a user specified point P on the buoy. Azimuth. GY-Velocity. The point P is specified in buoy local coordinates. Statics moment accuracy These are only reported if the buoy is included in statics. The buoy typical force and moment are based on the weight in air. Range jump suppression is applied to Rotation 1 and Rotation 3 (so values outside the range -360° to +360° might be reported). OrcaFlex accepts a position as a static equilibrium position if the largest out of balance load component is less than the statics accuracy. Y and Z coordinates of the buoy origin are reported. Acceleration rel.9. The static analysis searches for an equilibrium position for the buoy – that is a position for which the resultant force and moment on the buoy is zero. g The magnitude and components. Rotation 2 and Rotation 3 Define the orientation of the buoy relative to global axes. 6D Buoys Total contact area Reports the Total contact area data. GZ-Velocity The magnitude and components of the velocity of the buoy.g. Contact for 6D Buoys is calculated at each of these vertices. z-Angular Velocity The magnitude and components of the angular velocity of the buoy. Velocity and Acceleration Results Velocity. z-Acceleration rel. relative to global axes. Declination The azimuth and declination of the local z axis. Because computers have limited numerical precision the static analysis cannot always find a configuration where the out of balance load is exactly zero. g. Number of vertices The number of vertices in the wire frame drawing. Acceleration. 422 . Contact area per vertex Equals Total contact area / Number of vertices. For details on how to select results variables see Selecting Variables. Position and Orientation Results X. See Initial Position and Attitude for the definition of these angles. since the computer has limited numerical precision. This is the acceleration that would be reported by an accelerometer attached at the point P (since an accelerometer reading of zero corresponds to free-falling). GY-Acceleration. Y and Z The position of a user specified point P on the buoy. Rotation 1. We refer to the resultant force and moment as the out of balance load. in buoy axes directions. relative to buoy axes. g. The point P is specified in buoy local coordinates. y-Angular Velocity. The point P is specified in buoy local coordinates. 6. If a value of '~' is set on the data form then the value reported here is the default value calculated by OrcaFlex.w System Modelling: Data and Results. relative to global axes. but will take more iterations.16 Results For 6D Buoys the available results are as follows. The Statics force accuracy equals Tolerance * buoy typical force and the Statics moment accuracy equals Tolerance * buoy typical moment. with its measurement directions aligned with the buoy local axes directions. Statics force accuracy. x-Acceleration rel. They are 3 successive rotations that take the global axes directions to the buoy axes directions.0) then the global X. GZ-Acceleration The magnitude and components of the acceleration of the buoy. These results are reported at a user specified point P on the buoy. relative to the vertically downwards acceleration due to gravity. relative to global axes. That is. Rotation 2 is in the range -90° to +90°. GX-Velocity. This relative acceleration can be thought of as the acceleration of the point P relative to the free-falling state. If P=(0. x-Angular Velocity. of the acceleration vector.0. They report the total force and moment applied to the buoy by the object to which it is connected. z-Angular Acceleration The magnitude and components of the angular acceleration of the buoy. Sea X Velocity. reported in the local buoy axes directions. Sea Velocity. Negative values indicate submergence. Sea Y Acceleration. The moments given are moments about the buoy origin. Y and Z components of the water particle velocity (due to current and waves) and acceleration (due to waves) at P. calculated as follows: For a Lumped Buoy. Lx-Moment. Sea State Results If the buoy experiences sea state disturbance this will be accounted for in the sea state results. Sea Surface Clearance The vertical clearance from P to the instantaneous sea surface. GX-Force. GZ-Force. Dry Length The length of buoy above the water surface. These results (other than Dry Length) are reported at a user specified point P on the buoy. Note that if the vessel motion is specified by a time history then the time history interpolation method used is important since it affects the calculation of vessel acceleration and hence affects the inertial loads. The connection force and moment include the weight of the buoy and the inertial loads due to the vessel acceleration. Force. Sea Z Velocity. Sea X Acceleration. x-Angular Acceleration. Applied Ly-Force. Sea Y Velocity. y-Angular Acceleration. Applied Lz-Force Applied Lx-Moment. Note that these connection force and moment results include the structural and added inertial load on the buoy due to any acceleration of the object to which it is attached. Applied Lz-Moment The sum of all the local and global applied loads. They include the loads from any objects connected to the buoy. 6D Buoys Angular Acceleration. Applied Moment Applied Lx-Force. Moment Lx-Force. but again exclude structural inertia and added inertia loads on the connected object. Lz-Force. GX-Moment. Connection z-Moment These connection load results are only available for buoys that are connected to other objects. where the dry length of an individual cylinder is calculated as: (cylinder length) × (cylinder volume above surface) / (cylinder total volume). GZ-Moment These results are not available for buoys that are connected to other objects – you can instead use the Connection Force and Connection Moment results. where VirtualInertia is the total structural and added inertia of the buoy and any connected objects. Sea Surface Z The global Z coordinate of the instantaneous sea surface directly above or below P. The point P is specified in buoy local coordinates. Ly-Moment. including structural inertia loads and added inertia loads. Lz-Moment. GY-Force. Sea Z Acceleration The magnitude and global X. this is calculated by assuming that the z-extent of a Lumped Buoy is ½Height either side of its centre of volume. If P is above the water surface then zero is reported. relative to buoy axes. Applied Force. Connection y-Force. These results are the total force and moment applied to the buoy. This means that these results can be used for sea fastening calculations. Ly-Force. Ly and Lz results report the components of the connection force and moment in the local buoy axes directions. excluding structural inertia loads and added inertia loads due to acceleration of the buoy. Applied Ly-Moment. Connection y-Moment. Connection Force and Connection Moment report the magnitudes of the connection loads. Sea Acceleration. The reported loads therefore correspond to the left-hand side of the equation of motion TotalLoad = VirtualInertia x Acceleration. Connection z-Force Connection x-Moment. by using a 6D Buoy to model the object to be fastened and then attaching it to a vessel. Connection Moment Connection x-Force. Force and Moment Results Connection Force. For a Spar Buoy it is the sum of the dry lengths of each of its cylinders. measured along the buoy z axis. GY-Moment. 423 . The Lx.w System Modelling: Data and Results. The results are specific to one support which is specified by its number. The moments given are about the buoy origin. If the point(s) of closest approach on the supported line spline fall more than one support cylinder radius away from either end of the supported line then the result is not available. then the result is reported as zero. Support Lift Out and Support Off End Contact Distance results also allow a supported line to be specified. Supports Moment The magnitude and components (at the buoy's origin and in buoy axes directions) of the sum of moments due to the reaction loads on the buoy's supports. Supports Force The magnitude and components (in buoy axes directions) of the sum of reaction loads on the buoy's supports. The Lx. The Support Contact Clearance. The GX. Support Off End Contact Distance If the specified supported line is in contact with a support cylinder at a point beyond the support cylinder's ends this result reports the distance from the end of the support cylinder to the point of closest approach on the axis of the support cylinder. Solid Contact Ly-Force. from the support position to the point(s) of closest approach on the supported line's spline axis. Ly and Lz results report the components of the force and moment in the local buoy axes directions. or all the points of contact on the support cylinders are within the length of the support cylinders. in which case the result is specific to that supported line. Slam Load Results These results are only available for 6D lumped buoys that have non-zero Slam Area and Slam Coefficient. The result allows you to check for potential escape of the specified support line(s) from the specified support. Support Contact Clearance The minimum distance between the contact surfaces of the support cylinders and the supported line spline. If (all supported lines) is specified as the supported line then the minimum contact clearance across all supported lines is reported. Support Results Support results are available for the buoy if it has one or more supports. Support Reaction Force The magnitude and components (in support axes directions) of the of reaction load on the support. Support Lift Out The maximum distance. If the result is negative it means one or more of the supported lines have penetrated one or more of the support cylinders and the result is equal to the deepest penetration. If (all supported lines) is specified as the supported line then the maximum Lift Out across all supported lines is reported. in local buoy axes directions. Solid Contact Lz-Force The magnitude and components.w System Modelling: Data and Results. If the point(s) of closest approach on the supported line spline fall more than one support cylinder radius away from either end of the supported line then the result is not available. If none of the support cylinders and specified supported line(s) are in contact. in the support z direction. If the support has multiple support cylinders associated with it and more than one of them are in contact with the supported line then the maximum Support Off End Contact Distance across these cylinders is reported. and for spar buoys and towed fish that have a non-zero Slam Coefficient. alternatively (all supported lines) can be specified and then the result is taken across all lines supported by the buoy. Solid Contact Force Solid Contact Lx-Force. If (all supported lines) is specified as the supported line then the maximum Support Off End Contact Distance across all supported lines is reported. 6D Buoys Force and Moment report the magnitudes of the loads. of the force due to contact with elastic solids. Essentially the result is the distance the supported line axis has lifted away from the support position in the support z axis direction. GY and GZ results report the components of the force and moment in the global axes directions. Max Support Lift Out The maximum Support Lift Out across all of the buoy's supports. Max Support Off End Contact Distance The maximum Support Off End Contact Distance across all of the buoy's supports. the support cylinders are drawn with finite length but for the purpose of contact they are assumed to have infinite axial extent and so it is possible that the supported line is being contained within the support by part of the support that is not present in the real physical system being represented. 424 . Positive values mean a force trying to push the wing towards its positive side. Beta Angle The angle of the relative flow direction. Wing Azimuth. Otherwise they are the water loads. Zero beta angle means that this projection is in the Wx direction. Moment The lift force. Slam Force acts in the direction normal to the water surface. Incidence Angle The angle. The lift force is applied at 90° to the relative flow direction. etc. negative values are moments trying to turn the wing the opposite way. The value reported is with respect to the principal fluid affecting the wing. Wing Y. Positive values mean that the flow is towards the positive side of the wing (i. then the lift force. in the range -90° to +90°. hitting the positive side).17 Buoy Hydrodynamics 3D and Lumped 6D Buoys are generalised objects for which no geometry is defined in the data other than a height: This is used for proportioning hydrodynamic properties when the object is partially immersed. GY. Drag. especially where a 6D buoy is used to represent a complex shape such as a midwater arch of the sort used to support a flexible riser system. relative to global axes. and you have included wind loads on wings. We cannot give a simple step-by-step procedure for this task since the geometry of different objects can be widely different. 6.w System Modelling: Data and Results. GZ results give components of the total slam load in the global axes directions. measured in the wing plane. the rotational properties are not used. and for drawing a 3D buoy. it is the angle between wing Wx axis and the projection of the relative flow vector onto the wing plane. As an example. The value reported is with respect to the principal fluid affecting the wing. Slam GX-Force. Slam GZ-Force Slam Force reports the total instantaneous slamming load experienced as the body enters or exits the water. The drag moment is applied about the line that is in the wing plane and at 90° to the relative flow direction. that the relative flow vector makes with the plane of the wing. added masses. Slam GY-Force. Wing Z The position of the wing origin. drag force and moment reported are the air loads. This can be a difficult task. Lift. 6D Buoys Slam Force. drag force and drag moment applied to the wing. the hydrodynamic properties in 6 degrees of freedom are derived for a rectangular box. Range jump suppression is applied to the Beta Angle (so values outside the range -360° to +360° might be reported). drag areas. measured positive towards Wz. If a 3D buoy is used. Note: When the wing is less than half submerged. negative values towards its negative side. 425 .e. relative to the buoy. explicitly as data items. Declination and Gamma The orientation angles of the wing.e.9. The GX. Slam GX-Moment. Since the geometry of the object is undefined. Wing Results If the 6D Buoy has wings attached then for each wing the following results are available. More specifically. hitting the negative side) and negative values mean that the flow is towards the negative side of the wing (i. α. This gives a general indication of the way in which the problem should be approached. The drag force is applied in the relative flow direction and is always positive. Slam GY-Moment. it is necessary to define properties such as inertias. 90° means it is along Wz and -90° means it is along the negative Wz direction. Positive values are moments trying to turn the wing to bring the wing y-axis Wy to point along the relative flow direction. Slam GZ-Moment The components in global axes directions of the moment of the slam force about the body reference origin. Wing X. 75 for blocks with square corners. For present purposes the two are identical. The figure plots drag coefficient.ρ. Note: This is not strictly correct. we assume that the drag force contribution from an elementary area dA is given by dF = ½.9. The dimensions of the block are a in the flow direction b and c normal to the flow direction (c>b).V2. However we do not allow for this here. Drag Properties for Rotational Motions There is no standard data source. 6D Buoys 6. Cx against (a/b) for (c/b) from 1 to infinity (2D flow). Note: ESDU 71016 uses Cd for the force in the flow direction.w System Modelling: Data and Results.Cd. z In Z direction: Az = x . z In Y direction: Ay = x .dA where Cd is assumed to be the same for all points on the surface. y Drag Coefficients for Translational Motions These are obtained from ESDU 71016. As an approximation. Figure 1 which gives data for drag of isolated rectangular blocks with one face normal to the flow.9 to 2.18 Hydrodynamic Properties of a Rectangular Box O is the centre of the box Z Y X z O y Figure: x Box Geometry Drag areas In X direction: Ax = y . ESDU 71016 gives pressure distributions for sample blocks in uniform flow which show that the pressure is greatest at the centre and least at the edges. 426 . Cx for the force normal to the face. Cx is in the range 0. ω. There is a similar contribution from the Az area.w System Modelling: Data and Results. set HI = ΔI. plus the hydrodynamic masses and inertias to be used for computation of wave forces.|V| form of the drag force. it is convenient to calculate the sum of (Cd. Cm = 1 + Ca where AI is the added inertia (i. Because of the V.Cd).e. aw where HM is the Hydrodynamic Mass given in the data. Cm) multiplied by the water particle acceleration. On the usual assumptions intrinsic in the use of Morison's Equation (that the body is small by comparison with the wavelength). These are Hydrodynamic Mass in tonnes (or Inertia in tonne.Cd. Translational Motion DNV-RP-C205.Cd). the wave force is given by (Δ + AM) . simple integration from -Z/2 to +Z/2 gives M = 0. Table 6.z4/32. Then Ca = AM/Δ. OrcaFlex calculates the wave force as Cm .ρ.(AM) so we set Cdm = Cd.Cdm).|ω|. where Δ is body displacement and AM is added mass. Added mass is then defined as Hydrodynamic Mass . Then Ca = AI/ΔI.|ω|. The reference volume is the volume of the body which is the same definition we have adopted.0 and over.z4/32) OrcaFlex calculates the drag moment by M = (½. the moment of inertia of the displaced mass.z = (½. consider an elementary strip as shown: For an angular velocity ω about OX.|ωz|.ρ. set AM equal to this value and set Cd equal to 1.AM) for both. Added Mass OrcaFlex requires the added mass and inertia contributions to the mass matrix.m 2). We can therefore use the calculated Ca without further adjustment. The areas Ay and Az will attract drag forces which will result in moments about OX. the rotational analogue of added mass).ρ.ρ.dz.|ωz|. and data are given for b/a = 1. For the area Ay. set HM = Δ for all degrees of freedom. gives added mass data for a square section prism accelerating along its axis. The result is M = (½. Cm = 1 + Ca. Since Cd is generally different for the 2 areas. ω.(x. aw.Cd.z3. aw. 3 rotations). 3 data items are required. This is the drag moment contribution about OX from the Ay area. For translational motions. Consider the X direction: Area normal to flow = Ax. 6D Buoys Z dz z O Figure: X Integration for rotational drag properties Consider the box rotating about OX. Ca.2.ω.x.ρ. 427 . HM .(ωz). The square section is of side a.(ωz). and coefficients Ca and Cm.x.x.|ω| . prism length is b. the drag force on the strip is dF = ½.dz and the moment of this force about OX is dM = ½. For each degree of freedom (3 translations.dz Total moment is obtained by integration. and wave force is defined as (Hydrodynamic mass . We therefore integrate from 0 to Z/2 and multiply the answer by 2. For rotational motions. AM = x. e. then aspect ratio = z/y and reference volume = CA .19 Modelling a Surface-Piercing Buoy Surface-piercing buoys. y2. Equivalent radius normal to flow. For b/a > 1. in this section. (π/4) . This data item allows you to apply extra forces and moments to the buoy. Note: If y < z. Finally. Spar Buoys have many data items available. the area exposed to wind) of the pipe work etc. 6. Set the number of wings to zero. To help in this task we describe. In this case no further adjustment is required. the OrcaFlex Spar Buoy can be used to model any axi-symmetric body. a = √(Ax). aspect ratio of the plate = y/z.ρ. (a2+b2)) In either case. Rotational Motion DNV-RP-C205 gives no data for hydrodynamic inertia of rotating bodies. before complications such as moorings etc. fullysubmerged flow. Hence Ca can be obtained from DNV-RP-C205 by interpolation.(π/4).6 Ca can be read from the upper figure where the value is referred to the moment of inertia of the displaced mass. Rotation about X ΔI = Δ(Y2 + Z2)/12 Added inertia: Using data for spheroids from Newman 1977 : Length in flow direction = 2a = x. You can use this later to model the wind force on the upper part of the buoy. Hence CA from DNV-RP-C205 by interpolation. SPAR buoys or meteorological discus buoys. For b/a < 1. In this case: Ca = CA . and then Cm = 1 + Ca. We therefore set up an OrcaFlex model containing just a Spar Buoy and with no waves or current. in addition to those from any lines that you attach to it.6 The coefficient CA is read from the lower graph in which the reference volume is the sphere of radius b. Length in flow direction = x. in the upper part of the buoy.9.8 of Newman 1977 gives the added inertia for coefficient for spheroids of varying aspect ratio referred to the moment of inertia of the displaced mass. To do this you will need to know the projected area (i. This allows us to get the basic behaviour of the buoy correct. the approach we adopt for setting up an OrcaFlex model of a surface-piercing buoy. is given by πb2 = yz. without any lines attached. We will set up the actual values later. 428 . Hence: Added mass = CA. Hence Ca from Newman 1977. The only data for 3D solids we know of is for spheroids (Newman 1977).y. Set the buoy's Munk Moment Coefficient to zero. Wings are normally only relevant for towed fish. Create a simple model containing just a Spar Buoy Start by modelling the free-floating behaviour of the buoy. If b/a < 1. If y > z. ρ. Hence b/a = x/√(Ax). but it also makes setting up a Spar Buoy model more complicated. Cm = 1 + Ca. are introduced. we start by setting all the buoy's drag and added mass data to zero. z/π).w System Modelling: Data and Results. Despite its name. Fig 4. b. z . 1.0 this approach fails and we use the data given in DNV-RP-C205 for rectangular flat plates. such as CALM buoys. This enables you to model a wide range of effects. so b = √(y . can be modelled in OrcaFlex using the Spar Buoy version of a 6D Buoy. This data item is only used for slender bodies in near-axial. Set the buoy's Applied Load to zero. 6D Buoys For a square of the same area. The reference volume in this case is that of a cylinder of diameter z. length y. say and then Ca = AMx/Δ and Cm = 1 + Ca.z2 = AMx. b3)/(a . so a = x/2. We assume that the same coefficient applies to the moment of inertia of the displaced mass of the rectangular block. (2 . Set the Stack Base Position.Y axes. Set the Degrees of freedom included in statics to None and then run the simulation and look at the time history of buoy Z. 3. You also need to specify the position of the centre of gravity. with perhaps just small oscillations about that position. This means that something is wrong in the data and this needs tracing and correcting before you proceed. This is the position of the centre of the bottom of the buoy. The buoy manufacturer should supply this information.and y-axes should be parallel to the other two principal directions of structural inertia. If the data has been set up correctly then the buoy should have stayed basically in its initial position and attitude.0).0. 5. Set the Added Mass data The x and y added mass coefficients can be set to 1. Check that the buoy is stable Now check that the buoy is stable . 429 .e. which is the standard value for a cylinder in flow normal to its axis. If the buoy falls over then there is something wrong with the CG position or the volume distribution. then they can be calculated approximately from a knowledge of (i) the masses of the various parts of the buoy and (ii) the general distribution of those masses. Usually it is sufficient to assume that Ix = Iy. You can represent tapered sections by a series of short cylinders with diameters changing progressively from one to the next. 4. Now set up a number of cylinders. and you can calculate this point's expected equilibrium position from the buoy draught. 6D Buoys 2. through the centre of gravity. The Stack Base Position therefore has z-coordinate = -h. though at the cost of reduced computation speed. which should be available from the buoy manufacturer. In this case you will need to model the moorings in order to check stability. in order to model the shape of the buoy. e. where h is the distance axially from the bottom of the buoy to the buoy origin. You can check your geometry data by zooming in on the buoy in a 3D View window. even where the buoy diameter is constant over a long length. Added mass in the z direction should be estimated for the buoy from the published literature (DNV rules. Using more cylinders gives more accurate results. and the buoy x. as follows: Iz = the moment of inertia about the buoy axis. set the Rotation 2 value to say 10° and run the simulation. To do this you need the dimensions of the various parts of the buoy. relative to the local coordinate system. Turn on the local axes so that you can check that the buoy origin is in the correct place. and their lengths and diameters.y axes aligned with the global X.w System Modelling: Data and Results. Barltrop & Adams. Set up the geometry data The Spar Buoy has its own local buoy axes coordinate system. Check that the buoy floats at the correct draught Set the Initial Position and Initial Attitude of the buoy so that the buoy is in its expected equilibrium position. In the Initial Attitude data.g. The buoy manufacturer should supply this information. The Bulk Modulus data item is not relevant to a surface-piercing buoy.0. Ix and Iy = the moments of inertia about axes perpendicular to the buoy axis. We recommend using a number of short cylinders. Set the cylinder lengths and diameters so that you get the correct length and volume for each section. which orients the buoy with its axis vertical and the buoy local x. so it can be left at the default value of Infinity. The mass equals the weight of the buoy in air.i. Set up the mass and inertia data Now set the Mass and Moments of Inertia of the buoy. but the buoy z-axis direction must be chosen to be parallel to the axis of the buoy. Set it to (0. 1991) and distributed between the immersed cylinders (remember that hydrodynamic loads are only applied to the immersed parts of the model). relative to the buoy axes. The Initial Attitude defines the initial orientation of the buoy. If you cannot obtain data for the moments of inertia. You can choose the origin for these buoy axes. If the buoy Z has oscillated significantly then the model's equilibrium position does not match the expected equilibrium position. You can estimate the model's equilibrium position by looking at the mean Z position in the time history. The buoy manufacturer should supply this information. The moments of inertia are those of the buoy (in air) about its centre of gravity. Note: The buoy on its own may not be intended to be stable. stability may only be achieved when the moorings are attached. The initial position is the position of the buoy local origin. that if it is pitched over to one side and released then it rights itself. and this must be corrected. 6. and adjustments made as necessary. providing you have subdivided the buoy into short enough cylinders (since these terms involve a high power of L. The Unit Damping Force data can be set to zero. or is partially submerged. set the Drag Area. of the part of the buoy which that cylinder represents. we may represent the pipework and turntable on the deck of a SPAR buoy as an equivalent cylinder) or where the cylinder is shielded from drag by adjacent structure. Drag Moment Coefficients and Unit Damping Moment data. CALM buoys are usually closer to the Discus configuration. If you later find that the buoy shows persistent small amplitude oscillations then you may wish to set a non-zero value to damp this out. namely skin friction on the cylinder surface and form drag on any protuberances on the buoy. Set the drag and damping data The best approach depends on whether the buoy is a SPAR whose length is great by comparison with its diameter. OrcaFlex automatically calculates the proportion of the cylinder that is submerged and scales all the fluid loads on the cylinder using that 'proportion wet' as a factor.e. Here is the approach we use: For the normal direction. these data should then be checked by comparing the heave and pitch natural periods of the model against values obtained from model tests or full scale measurements. the normal drag area is D. Then set the axial Unit Damping Force to zero and run a simulation that matches the conditions that existed in the real heave time history results. where the heave amplitude has decayed to small values. We therefore strongly recommend that you set the data up by calibration against real test results from model or full scale tests. the cylinder length). or a surface-following Discus shape such as an oceanographic buoy.e. For the normal direction these data items can usually all be left as zero. Spar Buoys Set the Drag Areas for each cylinder to the areas.L since that is the area of a cylinder when viewed normal to its axis. 6D Buoys Ideally. 1991.w System Modelling: Data and Results. Note that you should specify the areas that are exposed to drag when the buoy is fully submerged. Drag Force Coefficient and Unit Damping Force as described for Spar buoys above. Instead it is their radial extension that most affects the buoy's pitch properties. starting from a displaced position. but there is little information in the literature to help in setting up these data. Discus and CALM Buoys These types of buoy require different treatment since they have little axial extension. the standard book values do not include energy absorption by wave-making at the free surface. The easiest information to work with are time history graphs of the buoy heave and pitch in still water.g. often with a damping skirt which is submerged at normal draft. Hoerner. 1) and then adjust the other. i. To deal with this OrcaFlex offers the rotational drag and damping data. Having set up this drag and damping data. However. For example. As a result the axial discretisation of the buoy into cylinders does not capture the important effects. then the drag areas should be set accordingly.d2)/4 to model that shielding. if the cylinder is shielded below by another cylinder of diameter d (less than D) then the axial drag area should be reduced by (π. so if this is important to you then set them to model the two main sources. where a cylinder is representing part of the buoy that is not in reality a simple cylinder (for example. For the axial direction these data items model the yaw drag and damping effects. so you can give one of the two data items a fixed positive value (e. this is a linear term (forces directly proportional to velocity). Set the Drag Area Moments. Set the Drag Force Coefficient based on values given in the literature. then the drag loads will be scaled accordingly for you. surface wave generation. And the axial drag area is (π. that are exposed to fluid drag in the direction concerned. For a simple cylinder. it is well worth now running simulations of heave and pitch oscillations and checking that their rate of decay is reasonable and consistent with any real data you have available. but in OrcaFlex this must be done by adjusting the drag coefficients of one or more cylinders. This will give the heave and pitch natural periods and the rates of decay and you can adjust the buoy's drag and damping data until you get a good match with this measured behaviour. 7. of diameter D and length L. These two data items are simply multiplied together when they are used to calculate the drag force. Then adjust the axial Drag Area and Drag Force Coefficients until the OrcaFlex buoy's Z time history matches the real time history. i. Strictly. So if a cylinder is not submerged. this is especially important for a CALM buoy with a skirt. However. The match will probably be poor in the later parts of the time history. For example the pitch damping is often mostly due to radiation damping.D 2)/4 since that is the area of the cylinder when viewed along its axis. For short simple cylinders fully immersed there are standard values given in the literature (see Barltrop & Adams. with the same initial Z displacement.1965 and DNV-RP-C205). This is because the square law drag term is insignificant at small amplitude and instead the damping force takes over. Therefore we now adjust the axial Unit Damping Force to further improve the match 430 . 10. Although they are much less sophisticated than 6D Buoys. with no lines attached. Disturbance Vessel Determines whether the 3D Buoy will experience sea state disturbance generated by a particular vessel. 6. You may find that this disturbs the match in the large amplitude part. See Buoy Degrees of Freedom Included in Static Analysis. For the axial direction. height/2 z B Buoy Axes always aligned with Global Axes y x height/2 Figure: 3D Buoy 6. and may also be used independently. in a similar way to that used above to match the heave time history. See Buoy Degrees of Freedom Included in Static Analysis.10 3D BUOYS OrcaFlex 3D Buoys are simplified point elements with only 3 degrees of freedom: X. 3D Buoys where the amplitude is small.1 Data Name Used to refer to the 3D Buoy. set the Drag Area Moment. If the buoy is not included in the static analysis then this initial position is taken to be the static position of the buoy. but remain aligned with the global axes. Then set the normal Drag Area Moment. 3D Buoys are easier to use and are convenient for modelling buoys at line junctions etc. They do not rotate. Included in Static Analysis Determines whether the equilibrium position of the buoy is calculated by the static analysis. in which case you might need to readjust the drag data. They therefore do not have rotational properties and moments on the buoy are ignored. Drag Moment Coefficient and Unit Damping Moment as described for Spar buoys above. Drag Moment Coefficient and Unit Damping Moment to best match the real pitch time history. 3D Buoys are able to float part-submerged at the surface. 431 . They should therefore be used only where these limitations are unimportant. Y and Z. If the buoy is included in the static analysis. Initial Position Specifies the initial position for the buoy origin as coordinates relative to the global axes. Mass Mass or weight in air.w System Modelling: Data and Results. then this initial position is used as an initial estimate of the buoy position and the statics calculation will move the buoy from this position iteratively until an equilibrium position is found. It is taken to be symmetrical about the buoy's origin. Seabed Friction Coefficient OrcaFlex applies Coulomb friction between the buoy and the seabed. The Height is the vertical distance over which the fluid-related forces change from zero to full force as the buoy pierces the surface. The friction force applied never exceeds μR where R is the seabed reaction force and μ is the friction coefficient. If the buoy experiences sea state disturbance this will be accounted for in any results that depend on wave elevation and kinematics. Because computers have limited numerical precision the static analysis cannot always find a configuration where the out of balance load is exactly zero.2 Properties Report The 3D Buoy properties report is available from the popup menu on the data form. The reported value uses the water density at the sea surface. the displacement and the forces applied by connected objects. See Friction Theory for further details of the friction model used. which means "incompressible". We refer to the resultant force as the out of balance load. Bulk Modulus Specifies the compressibility of the buoy. It also determines the height used to draw the buoy. Drag Drag forces are applied in each of the global axes directions GX. The inertia coefficient. drag etc. If the buoy is not significantly compressible. For each direction you must specify a Drag Coefficient and Drag Area.3 Results For details on how to select results variables see Selecting Variables. since the computer has limited numerical precision. Reducing the Tolerance value will give a more accurate static equilibrium position. Statics moment accuracy These are only reported if the buoy is included in statics. 6. GY and GZ. Weight in water Equals Weight in air . The Statics force accuracy equals Tolerance * buoy typical force. vary according to the depth of immersion. Displacement The weight of water displaced by the buoy's volume.10. Height Used to model floating buoys correctly. The added mass is set to be Ca multiplied by the mass of water currently displaced. OrcaFlex may not be able to achieve the Tolerance specified if it is too small. If a value of '~' is specified then OrcaFlex uses Volume / Height.w System Modelling: Data and Results. Statics force accuracy. is set automatically to equal 1+Ca. Specifying a value of zero allows you to disable contact for the buoy. OrcaFlex accepts a position as a static equilibrium position if the largest out of balance load component is less than the statics accuracy. Contact Area Used to determine contact forces when the buoy comes in to contact with the seabed and with elastic solids. 3D Buoys Volume Used to calculate buoyancy and added mass. 432 . The static analysis searches for an equilibrium position for the buoy – that is a position for which the resultant force on the buoy is zero. See Buoyancy Variation. but will take more iterations. It reports the following: Weight in air The force due to gravity acting on the buoy's mass.Displacement. where the buoyancy. The buoy typical force is based on the weight in air.10. then the Bulk Modulus can be set to Infinity. Added Mass You must specify the added mass coefficient Ca for each global axis direction. Note: The friction coefficient for contact with elastic solids is specified on the Solid Friction Coefficients data form. 6. Cm. Z Positions of the buoy origin. Sea Velocity. if the point is offset on the object involved then this also gives rise to an applied moment. Negative values indicate submergence. The wire tension either side of the intermediate point is then applied to that point. They connect two (or more) points in the model by a winch wire. Sea Acceleration. Sea Z Velocity. Y. GZ-Velocity. As well as connecting its two end points. Velocity. Because of these assumptions. For this purpose. GX-Acceleration. Sea X Velocity. Y and Z components of the water particle velocity (due to current and waves) and acceleration (due to waves) at the position of the buoy. Sea Y Acceleration. no data needs to be given for the winch inertia or winch drive. fed from a winch inertia (typically representing a winch drum) that is then driven by a winch drive (typically representing the winch hydraulics that drive the drum). Sea Z Acceleration The magnitude and global X. in which case it does so as if passing over a small frictionless pulley at that point. Sea Surface Clearance The vertical clearance from the buoy origin to the instantaneous sea surface. Sea Surface Z The global Z coordinate of the sea surface directly above or below the instantaneous position of the buoy origin. pass via intermediate points. GY-Acceleration. measured along the buoy z axis. GX-Velocity. relative to global axes. Sea X Acceleration. Winches For 3D Buoys the available variables are: X. the z-extent of a 3D Buoy is assumed to be Height/2 either side of its volume centre.w System Modelling: Data and Results. Dry Length Length of buoy above the water surface. If the buoy is above the water surface then zero is reported. GZ-Acceleration The magnitude and components (with respect to global axes) of the velocity and acceleration of the buoy. Sea Y Velocity. GY-Velocity. It is assumed that the winch inertia is negligible and the winch drive is perfect. optionally. 6. Acceleration. so that it always exactly achieves the requested constant tension or constant speed. 433 .11 WINCHES Winches provide a way of modelling constant tension or constant speed winches. the winch wire may. Winch may pull via intermediate objects Drive Force f Winch Drive t t Winch Inertia t Wire Tension t Winch wire Figure: Winch Model Two types of winch are available in OrcaFlex: Simple Winches Simple Winches model perfect constant tension or constant speed performance and are easiest to use. y coordinates given are the global X. so applying forces and moments (if the points are offset) to the objects concerned.1 Data Name Used to refer to the Winch. Connect to Object and Object Relative Position The (mass-less) winch wire connects at least two objects. Type May be either Simple or Detailed. 434 . The winch can be switched between these two modes at predetermined times during the simulation and the constant velocity or target tension can also be varied. If the winch drive data are not available. In particular. The z coordinate specifies the arc length along the Line and this arc length may be measured relative to either End A or End B as specified by the user. Release at Start of Stage The winch wire can be released at the start of a given stage of the simulation. If torsion is not modelled then the x. If torsion is modelled then the x. The connection point is attached to the nearest node.Y position.w System Modelling: Data and Results.y coordinates allow you to offset the connection from the centreline. then set this item to '~'.Y coordinates of the anchor point. If no release is required. the object-relative x. If more than 2 are specified then the winch wire passes from the first connection point to the last via the intermediate points specified. when the type of winch to be used has not yet been decided. Since such winches are usually hydraulic devices whose performance deviates quite seriously from the target tension ideal. For Fixed connections the object-relative coordinates given are the global coordinates of the point. by setting this number to the stage number required. the coordinates of the connection point are given relative to the object local frame of reference. We recommend using Simple winches unless you know the characteristics of the winch drive system and believe that its performance significantly differs from the constant tension or speed ideal. damping and drag forces (force decrements proportional to velocity and velocity2 respectively) and winch stiffness effects such as those caused by hydraulic accumulators. Once released the winch no longer applies any forces to the objects it connects. Simple winches are appropriate: At the early design stage. damping and drag – but therefore require more data and are harder to set up. stiffness. For connecting to other objects. OrcaFlex Winches provides facilities for modelling winch deadband. 6. For connecting to an Anchor.11. Each connection is defined by specifying the object connected and the object-relative position of the connection point. The winch drive can be operated in either of two modes: Length Control Mode For modelling constant speed winches. When intermediate connections are specified. The winch wire is paid out or hauled in at a velocity specified in the data. and the z-coordinate is the distance of the anchor above (positive) or below (negative) the seabed at that X. If the duty is such that the winch drive will give near to perfect constant tension or constant speed performance. For connecting to a Line. See Winches. inertia. Winches Detailed Winches Detailed Winches include modelling of the performance of the winch drive system – its deadband. The winch wire tension on either side then pulls on the intermediate points. one at each end of the winch wire.y coordinates are ignored and the connection point is at the centreline of the Line. Winch Control OrcaFlex winches allow quite complex offshore operations to be modelled. Force Control Mode For modelling tension controlled winches. the winch wire slides freely through these intermediate points as if passing via small friction-less pulleys mounted there. the object-relative z coordinate specifies the arc length to the connection point. Specified Length The winch drive is locked with the unstretched length of winch wire out. the winch system inertia is then not modelled at all.ε where ε = wire strain. 6. L 0. When By Stage is selected the winch is controlled on a stage by stage basis. K . vary with simulation time or be given by an external function.11. Setting the winch inertia to a small value to model a low inertia winch can lead to very short natural periods for the winch system. the winch inertia can be set to zero. (Such accelerations are resisted indirectly. This is a linear. See Winch Theory. the winch control Mode can be set to one of the following values. The winch tension contribution from wire stiffness is given by K. Because there is a limit on the number of stages in an OrcaFlex simulation this can be restrictive. To avoid this. Winches 6. which resists changes in the rate of pay out of haul in of the winch wire if the winch is in Force Control mode. Winch Inertia (Detailed Winches only) The inertia of the winch drive. C. The Winch Inertia has no effect if the winch is in Length Control mode. Notes: The winch inertia does not contribute to the mass of any objects to which the winch is attached and so does not directly resist acceleration of any of the connection points. Note: The mass of the winch wire is not modelled.11. control the rate of change of target tension or specify a constant target tension. These then require very short time steps for the simulation.2 Wire Properties Wire Stiffness The elastic stiffness.11. Wire Damping A dimensional stiffness-proportional material damping factor. r = radius at which the wire is fed. through the changes they cause to the winch wire path length and hence to the winch wire tension. vary with simulation time or be given by an external function. drum and wire it is necessary to suitably increase the masses of the objects to which it is attached.w System Modelling: Data and Results. See Winch Theory for full details of the algorithm used when the winch inertia is zero. of course. rather than to a small value. Likewise for the length controlled mode the payout rate of unstretched winch wire can be fixed. The winch wire tension t then depends on the stretched length L of the winch wire path. When Whole Simulation is selected the winch is either tension controlled or length controlled for the whole simulation. for the winch wire.3 Control Control Type Can be either By Stage or Whole Simulation. To represent the rotational inertia of a winch drum. rather than rotational. 6. K. For each stage of the simulation you choose from the winch control modes. but the short natural periods are then avoided. 435 . The winch tension contribution from wire material damping is given by C . Note: The control mode remains fixed for the duration of each stage. being set to the Value specified.) To include the true translational inertia of the winch drive.4 Control by Stage Winch Control for Statics For the static analysis. dε/dt where dε/dt = wire strain rate. of the winch wire. slowing the simulation. inertia. These modes allow you to control the winch payout rate. set the winch inertia to l / r2 where I = drum rotational inertia. For the tension controlled mode the target tension can be fixed. for example. If Specified Payout Rate is set then you must also specify the payout rate of unstretched winch wire. See Winch Theory. Specified Payout The Value specifies the unstretched length of winch wire to be paid out (positive) or hauled in (negative) at a constant rate during this stage. Specified Tension Rate of Change The Value specifies the rate of change in target tension for this stage. the Value specifies the total change in unstretched length during the stage. which then applies drive force to the winch inertia to try to achieve this target tension. For each stage the winch control Mode can be set to one of the following values.w System Modelling: Data and Results. Note: Changes of nominal tension are applied instantly at the start of each stage. Length at Stage End The Value specifies the length of the winch at the end of this stage. Note: The Specified Tension Change and Specified Tension Rate of Change modes allow you. to model a constant tension winch where the tension is determined by an earlier simulation stage. The above comments for the Specified Tension control method also apply to this method. so the Value is used as the actual winch wire tension. Specified Tension Change The Value specifies the change in target tension for this stage. vary with simulation time or be given by an external function. This typically results in smoother responses than Specified Payout or Specified Payout Rate. and this can therefore apply a shock load which. Winch Control for Dynamics During the simulation the winch is controlled on a stage by stage basis. Specified Tension The Value specifies the target constant tension for this stage. Dynamics Mode The winch is controlled either by Specified Tension or by Specified Payout Rate. vary with simulation time or be given by an external function. 6.11. Specified Payout Rate Change The Value specifies the change in the payout rate during this stage. The above comments for the Specified Tension control method also apply to this method. The unstretched length out L0 is then set to correspond to this tension. That is. the Value specifies the total change in nominal tension during the stage. By specifying a tension change of 0 following a payout stage you can lock the winch at the tension used at the end of the payout operation. the tension t being the Value specified. may affect the stability of the simulation. Specified Payout Rate The Value specifies the rate at which the winch wire is to be paid out (positive) or hauled in (negative) during this stage. If Specified Tension is set then you must also specify the target tension. That is. This value can be fixed. The algorithm for the winch drive force is designed to model the characteristics of real-world winches that are nominally "constant tension". so to keep a constant length set the Value to zero. so to keep at a constant nominal tension set the Value to zero. For Simple winches the winch drive is assumed to always achieve this nominal tension. 6.5 Control by Whole Simulation Statics Mode The winch control data for statics is the same as the data specified in the By Stage control type. This value can be fixed. For Detailed winches this nominal tension is used as the target tension for the winch drive. if large enough.6 Drive Unit Note: The drive unit data applies to Detailed Winches only 436 . Winches Specified Tension The winch drive operates in perfect constant tension mode.11. The winch tension then depends simply on the unstretched length of winch wire out. Damping Terms A and B These terms can be used to model damping in a winch's hydraulic drive system. Azimuth and Declination The azimuth and declination angles of the direction of the winch wire between the final 2 connection points. The winch drive force is taken to vary with haul-in/payout velocity2 at rates C and D. See Winch Theory. Connection GZ-Force The magnitude and components relative to global axes of the connection force at the specified winch connection point. Connection Force. Winches Winch Drive The winch drive controls the winch wire in one of two winch control modes: Length Control mode ("Specified Length". Y and Z The global coordinates of the specified winch connection point. for example. negative value means hauling in. This direction is measured from the last connection point towards the previous connection point. Because such winches often deviate quite seriously from the constant tension ideal.11. The winch drive force is taken to vary with haul-in/payout velocity at rates A and B. Declination is in the range 0° to 180°. Drag Terms C and D These terms can be used to model drag in a winch's hydraulic drive system. This is the total distance between the winch connection points. relative to the global axes. See Winch Theory for full details. a free form multi-line text field which is passed to any external function used by the Winch object. It is the rate at which the zero-velocity winch force (the drive force applied when the winch is neither hauling in nor paying out) varies with the total unstretched length of winch wire paid out. Positive value means paying out. Connection GX-Force.7 External Functions Parameters This data item specifies the External Function Parameters. See Winch Theory. 437 . respectively. Length The unstretched length of winch wire paid out. Deadband A deadband of +/.this value is applied to the winch drive force between hauling in and paying out the winch. and the wire properties (Stiffness and Damping). "Specified Tension Change" or "Specified Tension Rate of Change"). "Specified Payout" or "Specified Payout Rate") or Force Control mode ("Specified Tension".8 Results For details on how to select results variables see Selecting Variables. Range jump suppression is applied to Azimuth (so values outside the range 360° to +360° might be reported). winch hydraulic accumulators. Stretched Length The stretched length of winch wire. Tension The tension in the winch wire. Damping. See Winch Theory. facilities are provided for modelling winch Deadband. Length Control mode is for modelling a constant speed winch. For winches the available variables are: X.11. Drag and Stiffness. We adopt the convention that the force reported is that applied by the winch to the object to which it is connected. Force Control mode is for modelling a (nominally) constant tension winch.w System Modelling: Data and Results. 6. Connection GY-Force. 6. Velocity The rate of pay out of winch wire. Stiffness This can be used to model. respectively. Links have no mass or hydrodynamic loading and simply apply an equal and opposite force to the two points. They pull the two points together.y coordinates are ignored and the connection point is at the centreline of the Line. The z coordinate specifies the arc length along the Line and this arc length may be measured relative to either End A or End B as specified by the user. the object-relative x.12 LINKS Links are simple spring or spring/damper connections linking two points in the model. the coordinates of the connection point are given relative to the object local frame of reference. with a force that depends on their relative positions and velocities.1 Data Name Used to refer to the Link. or a buoy to an anchor. Links 6. for example a node on a line to a vessel. and the z-coordinate is the distance of the anchor above (positive) or below (negative) the seabed at that X.y coordinates allow you to offset the connection from the centreline. Spring/Dampers Combined spring and independent damper units. For connecting to other objects. If torsion is modelled then the x.w System Modelling: Data and Results. Two types of Link are available: Tethers Simple elastic ties that can take tension but not compression. The unstretched length and stiffness of the tether are specified. Type may be either: Tether: a simple elastic tie having linear stiffness and no damping. the object-relative z coordinate specifies the arc length to the connection point. If torsion is not modelled then the x.Y coordinates of the anchor point. Connect to Object and Object Relative Position Specifies the objects to be linked. For connecting to an Anchor. for example buoy ties can sometimes be modelled using links.Y position. The spring can take both compression and tension and can have either a linear or a piecewise-linear length-force relationship. They are useful for modelling items such as wires where the mass and hydrodynamic effects are small and can be neglected. 438 . or hold them apart. Spring/Damper: a combined spring and independent damper. Tether: Spring-Damper: Figure: Types of Link 6. The connection point is attached to the nearest node. For Fixed connections the object-relative coordinates given are the global coordinates of the point. For connecting to a Line.y coordinates given are the global X. The tether remains slack and does not apply a force if the distance between the ends is less than the unstretched length.12. The damper velocity-force relationship can also be either linear or piecewise-linear. each of which can be either linear or piecewiselinear. 6. but instead goes into compression. Links Release at Start of Stage The link can be released at the start of a given stage of the simulation. Linear Both the spring and damper in a Spring/Damper can have either simple linear force characteristics or else a userspecified piecewise-linear force table. Azimuth and Declination The azimuth and declination angles. End B X. End B Y and End B Z The global coordinates of the link. For links the following variables are available: Tension The total tension in the link. For a passive damper the tensions specified should therefore normally have the same sign as the velocities. those specified in the table the program will use linear interpolation.w System Modelling: Data and Results. L0 is the specified Unstretched Length. Length The current stretched length of the link. or outside.2 Results For details on how to select results variables see Selecting Variables. by setting this number to the stage number required. or extrapolation. dL/dt is the rate of change of L. 439 .dL/dt where c is the specified Damping.12. For a linear spring in a Spring/Damper the tension (positive) or compression (negative) is given by: T = k(L-L0) The linear spring does not go slack if L is less than L0. The table must be arranged in increasing order of length (velocity) and a negative tension indicates compression. Stiffness For a tether the tension T depends on its strain and stiffness as follows: T = k(L-L0)/L0 for L>L0 T = 0 for L≤L0 where k is the specified Stiffness. End A Y. since otherwise the damper will apply negative damping. L is the stretched length between the two ends. relative to global axes. Warning: Please note that this is not the same formula as for tethers. Velocity The rate of increase of the stretched length. End A Z. Non-linear force tables For a non-linear spring (or damper) the force characteristic is specified as a table of tension against length (or velocity). If no release is required. Damping A linear damper in a Spring/Damper exerts an extra tension of c. Unstretched Length Is the unstretched length of the Tether or Spring. of the End A to End B direction of the link. then set this item to '~'. Once released a link no longer applies any forces to the objects it connects. For lengths (velocities) between. End A X. to calculate the tension. Drawing shapes have no physical effect on the model and are just intended for drawing purposes. Trapped water are used to model moonpools or other areas where fluid motion is suppressed. Shapes 6. the inside of spars or behind breakwaters. cylinders and curved plates. 440 . The value given for Stiffness is therefore not normally important. the Stiffness should not be set too high since this can introduce very short natural periods which in turn require very short simulation time steps. Elastic solids are intended only for modelling the overall limitation on movement that a physical barrier presents. Trapped water Trapped water can be used to model hydrodynamic shielding – i. although the actual stiffness of real barriers is usually very high. blocks. Elastic solids An elastic solid represents a physical barrier to the motion of lines and buoys.e. It is made of a material of a specified stiffness and resists penetration by applying a reaction force normal to the nearest surface of the elastic solid and proportional to the depth of penetration of the object into the elastic solid. Note that friction for contact with elastic solids is only included during dynamics. areas such as moonpools. On the other hand. Elastic solids are used to model physical obstacles. the force acting on it is the sum of the individual forces from each elastic solid. so elastic solids that are smaller than the segment length can "slip" between adjacent nodes. Cylinder and Curved plate shapes Shapes are simple 3 dimensional geometric objects that can be configured in a variety of ways: 1. Friction coefficients are specified on the Solid Friction Coefficients data form.w System Modelling: Data and Results. Lines only interact with elastic solids by their nodes coming into contact. 3. Where an object interacts with more than one elastic solid simultaneously. You may choose between a number of different basic geometric shapes and several shapes can then be placed together to defined more complex shapes. The stiffness is the force per unit area of contact per unit depth of penetration. they are not intended to model an object's interaction with the barrier in detail. The segment length in a line should be therefore be small compared with the dimensions of any elastic solid with which the line may make contact. 2. which determines the rate at which the force applied to an object increases with the area of contact and depth of penetration into the elastic solid. Each elastic solid has an associated stiffness. Contact with elastic solids can model friction. providing it is high enough to keep penetration small.13 SHAPES Figure: Examples of Block. The basic shapes available are planes. For example the calculation of the contact area and penetration depth are very simplistic and do not allow for the detailed geometric shape of the object. where wave and current effects are suppressed. Connection Can be Fixed. giving a solid that is drawn but which has no effect on the other objects in the system. for example. Damping is always zero when using the implicit integration scheme. Drawing shapes Drawing shapes have no physical effect on the model. Such feedback is undesirable so the buoy ignores any trapped water shapes that are connected to it. 3D Buoys or 6D Buoys). Position Each shape has position data. Type Either Elastic Solid or Trapped Water. Cylinder. For Anchored connections the object-relative x. and the z-coordinate is the distance of the anchor above (positive) or below (negative) the seabed at that X. Damping The percentage of critical damping for the elastic solid. This point is taken as the origin of the shape's local x. Note: Objects ignore any trapped water shapes which are connected to that particular object. To aid visualisation. which in turn would affect the fluid forces on the buoy and hence its motion). Pens and Number of Lines Each surface of the solid is drawn as a wire frame using one the specified pens. So if the trapped water shape is fixed then no fluid motion occurs in the shape – this could be used to model a breakwater. For Fixed connections this is the global position of the point. Stiffness may be set to zero. A value of 0 disables friction. 441 . Data for Elastic Solids Normal Stiffness This is the reaction force that the solid applies per unit depth of penetration per unit area of contact. Shapes Inside a trapped water shape the fluid motion is calculated as if the fluid was moving with the shape. the coordinates of the connection point are given relative to the object local frame of reference. the Outside pen is used if the surface is being viewed from the outside of the solid. Shape Can be one of Block. For blocks it is named Origin.z axes. See Shape Theory for technical details. A value of '~' results in the Normal Stiffness being used.1 Data Name Used to refer to the shape.Y position. They can be used to draw objects of interest and do not interact with other objects.Y coordinates of the anchor point. but takes a little longer to draw. Curved Plate or Plane. For connections to other objects.13. and the Inside pen is used if it is being viewed from the inside. Anchored or connected to another object (Vessels. But if the shape is connected to a moving vessel. for cylinders and curved plates it is named End Position and for planes it is named Point on Plane. 6.y coordinates given are the global X.y.w System Modelling: Data and Results. If this wasn't done then if you connected a trapped water shape to a buoy and part of the buoy was in the trapped water shape then a feedback would occur (the buoy motion determines the motion of the shape. The Number of Lines determines how many lines are used in the wire frames – a larger value gives a more realistic picture. then the trapped water is assumed to move with the vessel – this could be used to model a moonpool. Shear Stiffness The Shear Stiffness is used by the friction calculation. 13. so that Bxyz are in the same directions as Lxyz. y=0 to Size(y). With respect to its local axes.3 Cylinders r = Inner Radius R = Outer Radius R End 2 Position r End 1 Position A cylinder shape is a thick walled hollow pipe defined by giving: Inner and Outer Diameter. For example. defined by giving: Size This defines the block's dimensions in its local x. z=0 to Size(z). that define its orientation relative to the object to which the block is attached. y and z directions. Then apply Rotation 1 about Bx (=Lx). Rotation 1. First align the block with the local axes of the object to which it is attached. Azimuth and Declination of the axis.w System Modelling: Data and Results. Orientation This is defined by giving three rotation angles. the block occupies the volume x=0 to Size(x). Length. then the 3 rotations define the orientation of the block axes Bxyz as follows.13. if the block is attached to an object with local axes Lxyz. 2 and 3. and finally Rotation 2 about the new (and final) Bz direction. 6.2 Blocks z z-size y Block Position B x y-size x-size A Block shape is a rectangular cuboid. or else relative to global axes if it is not attached to another object. followed by Rotation 2 about the new By direction. 442 . Shapes 6. 4 Curved Plates Figure: Some example curved plate shapes Curved plate shapes are particularly suited to modelling bellmouths although they are not restricted to this application. Cubic Bessel interpolation is used to generate a smooth profile. 443 . The middle picture above is not hollow whereas the other two are. Note: You may need to specify an artificially large value for thickness in order to avoid objects passing through the shape's wall during the static calculation. Curved plates can be either filled in or hollow. For objects that rotate. that define its orientation relative to the object to which the shape is attached. whilst a very large number gives a pseudo-opaque cylinder at the expense of drawing speed. It differs in that the radius of the shape can vary smoothly between the ends. If the cylinder is an elastic solid then reaction forces are applied: Radially inwards if an object comes into contact with the inner curved surface.w System Modelling: Data and Results. The Azimuth and Declination values define the direction of the principal axis. If the shape is hollow then the profile defines the radius to the inner surface. Two gives a very simple wire frame profile of the cylinder. 6. such as vessels and 6D Buoys. The curved plate shape is similar to the cylinder. The number of facets used is the Number of Lines specified.13. the axis direction therefore rotates with the object. If the shape is not hollow then the profile defines the radius to the outer surface. Radially outwards if an object comes into contact with the outer curved surface. or else relative to global axes if it is not attached to another object. Shape is hollow If ticked then the shape is hollow and has both inner and outer surfaces. Shapes The azimuth and declination define the direction of the axis relative to the local axes of the object to which the end is connected.e. If the Inner Diameter is zero then a solid disc is formed. This thickness specifies the thickness normal to the shape's axis or centreline. Cylinders are drawn using circles to represent the end faces and a number of rectangular facets to represent around the curved surfaces. A value of 360° gives a complete revolution as shown in the first 2 pictures above. Profile A table specifying the variation of diameter with distance along the shape's axis or centreline. Azimuth. Included Angle of Revolution The curved plate is a solid of revolution. Thickness If the shape is hollow then this data item specifies the wall thickness. The radius is the radial distance (i. For Fixed or Anchored ends it is defined relative to global axes. The Gamma value specifies rotation of the shape about its own axis and so is only relevant when the Included Angle of Revolution is not equal to 360°. Other values can be used to model partial or cut-away curved plates – for example the right-most picture above has an included angle of 90°. Normally outwards if an object comes into contact with one of the end faces. Declination and Gamma. Orientation This is defined by giving three rotation angles. in direction normal to the shape axis) from the axis to the surface. the plane slopes upwards in the positive y direction at 30° to the object's local xy plane. 444 .5 Planes Direction of Maximum Slope Slope Point on Plane A plane shape is an infinite plane surface – one side of the plane is outside and the other is inside. Where it is necessary to keep the display simple you should set Number of Lines to 2 for blocks and cylinders. and then Cylinders. You are encouraged to experiment. and on the positive z side (i. as follows. relative to the object to which it is connected. see How Objects Are Drawn. relative to the global XY plane (i. but simplicity is best.6 Drawing Wire frame drawing Representation of shapes in the wire frame drawing mode can be confusing. If the number of lines is set large for blocks or cylinders they appear as solid objects. the Slope Angle is specified by giving the angle of elevation of the line of maximum slope. for shaded 3D Views. 6. This is specified in terms of the length of the scale bar on the 3D view. Shapes 6. with the specified Number of Lines. For pen details.w System Modelling: Data and Results. relative to the horizontal).13.13. For a fixed or anchored shape. Hint: Although the program provides depth clues to the eye by drawing rear faces in a different colour. For example with a Slope Angle of 30° and a Slope Direction of 90°. but only a part of the infinite plane local to the view centre is shown on the 3D view. by defining background shapes before foreground ones. For planes you can control how they are drawn with the Grid Density data item. The Slope Direction is specified as the direction of the line of maximum upwards slope. above for a Fixed or Anchored plane) otherwise. Please note also that the Number of Lines only affects the drawing. but otherwise the solids in the model are drawn in the sequence that they were created. the eye can sometimes be fooled by the picture – try rotating the view back and forth a few times. horizontal) in the case of a Fixed or Anchored plane. For a shape connected to another object. Shaded Drawing By default.e. For example a plane having a Slope Angle of 30° and a Slope Direction of 90° slopes upwards in the positive Y direction at 30° to the horizontal. The position of the plane is defined by specifying a Point on Plane through which it passes. Planes extend to infinity in all directions. using a spacing determined by the view size. The 'inside' of a plane is on the negative z side (i. A density of d means that there are d lines per scale bar length. and not the calculations (which are correctly performed with curved geometry). A plane with zero slope angle is therefore parallel to the xy plane of the object to which it is connected. below for a Fixed or Anchored plane) if the Slope Angle is in the range -90° to +90°. although they may take a long time to draw. Planes and Blocks are drawn first. You may exercise control over the display by selecting the number of lines drawn for each object. Planes are drawn as a rectangular grid.e.e. The angle of the plane is specified by giving its (maximum) Slope Angle and Slope Direction. or parallel to the global XY plane (i. A Slope Angle of 90° is therefore a vertical plane. OrcaFlex does not provide hidden-line removal so shape objects are displayed by simple wire-frame drawings. You can sometimes take advantage of this. and the sequence in which they are drawn. to obtain a pseudo-hidden line effect. relative to global axes. so higher density values give a finer grid (but takes longer to draw). the Slope Angle and Slope Direction are relative to the object's local xy plane.e. shapes are drawn as solid objects using the specified geometry. This must be a Direct X format file. GY-Acceleration. The Shaded Drawing Origin defines the origin of the shaded drawing with respect to the shape's local axis system. A value of 100% specifies transparency and leads to a completely seethrough surface. Contact Ly-Force and Contact Lz-Force The magnitude and components of the total force applied by an elastic solid to other objects in the model. GX-Velocity. GX-Acceleration. GZ-Velocity. There are two modes of operation: Connections or Other data.w System Modelling: Data and Results. Shaded Drawing Origin is provided because the shaded drawing and the shape may have different origins. However. Y. Then the length of the longest side of this cuboid is found. Contact Force. GY-Velocity. Note: If you use a value of '~' for Draw Size then OrcaFlex uses the coordinates in the . If this happens then typically sections of the model will be missing when drawn by OrcaFlex. Contact GX-Force.x file will not display correctly. Contact GZ-Force.7 Results For details on how to select results variables see Selecting Variables. Ly. 445 .x file have their outward facing directions defined correctly.x file. All directions are scaled equally to arrange that the longest side in the drawing is drawn to the specified Draw Size. This cuboid is aligned with the shaded drawing's local axes. X. Shaded Drawing Plane Translucency (only available for planes) Controls how translucent the plane appears in the Shaded Graphics mode. usually with the . in order to work it requires that the triangles defined in the . Z The global coordinates of the shape origin. A value of 0% gives a solid surface and all objects behind the surface will not be visible. 6. You can choose to filter which object types appear in the list – each object type (Lines. Note: This data item is not used if an imported 3D model is used to draw the shape. In the unusual situation where the outward facing directions are not defined correctly then the .14 ALL OBJECTS DATA FORM The All Objects Data Form allows you to view or edit data for all the objects in the model on a single form. The components are reported relative to either global axes (GX.x file directly. This is particularly useful for simultaneous viewing or editing of properties of multiple objects. Specify a value of '~' to display the drawing using the absolute coordinates as specified in the . Contact GY-Force.txt. Links or Winches) can be included or excluded from the list. GZ) or local axes (Lx. Connections The Connections mode allows you to edit connection specific data for all Lines. This longest side is calculated by first fitting the smallest possible cuboid around the vertices of the shaded drawing (these are defined in the . These variables are only available for elastic solids. Disabling the Use Culling option resolves this problem.x file by including an auxiliary file called AdditionalInformation. GY. GZ-Acceleration The magnitude and components (with respect to global axes) of the velocity and acceleration of the shape origin. Acceleration. The Use Culling option is normally selected since it can provide a useful performance benefit. Links and Winches in the model. The form can be opened using the model browser.x file extension. Contact Lx-Force.x file). Examples of this can be found in the sample shaded drawings provided by Orcina. If these coordinates use a different length units system from your OrcaFlex model then you should specify the units used in the . Velocity.13. If you use a relative path then the path will be taken as relative to the folder containing the OrcaFlex file. Draw Size is provided to allow you to scale the drawing. All Objects Data Form Alternatively the object can be represented by an imported 3D model by specifying the Shaded Drawing File. Similarly Shaded Drawing Orientation allows you to reorient the shaded drawing to match the shape's axis system. 6. The Browse button allows you to specify the Shaded Drawing File quickly and also provides quick access to the Orcina sample drawings via the Navigate to Orcina sample drawings button. Lz). This is only available if a connection point is anchored. To do this easily. All Objects Data Form w Positions and Connections pages The Positions and Connections pages allow you to view or edit all the connection data. And for the reference axes directions you can choose between: The global axes directions. Release stage for line ends. For the reference origin you can choose between: The global origin. The θ coordinates should again be set to 0°. and with each line spanning 200m horizontally. Similarly. Z). The easiest reference frame for this is with the reference origin being End A and the reference axes being the spar axes. The reference frame has its origin at your chosen Reference Origin and has its axes are parallel to those of your chosen Reference Axes. so if you change one then the other is automatically updated to match. OrcaFlex keeps the two sets of coordinates synchronised. But this time. the reference line end (either End A or End B) for the z coordinate. relative to the same reference frame. This facility is useful for cases. On the other hand. it is easier (especially if the seabed is sloping) to go to the Connections page and set Connect To Object to be Anchored and then go to the Positions page and set the Object Relative Position z coordinate to zero. all at radius 5m from the spar axis and all 3m below the spar origin. first sort into Connection order so that all the End A connections are grouped together. Connection orientation and stiffnesses for line ends. You can now use copy/paste or fill down to set all the other A ends to the same reference origin. for example mooring arrays. θ. The polar coordinates (R. and the polar coordinates are updated to match. 180° and 270°. For Links and Winches connected to a line. Z) are those of the connection position relative to the selected polar coordinates frame of reference (see below). Suppose you want to place the A ends of the lines so that they are evenly spaced circumferentially around the spar. The origin of the frame of reference of any connected object. for the first line. with the anchors again evenly spaced circumferentially. If you change any other data then the Cartesian Object Relative Position coordinates are taken to be the master data and so left unchanged. axes and R and Z coordinates. Example of Using Polar Coordinates The choices of reference frame for the polar coordinates may seem complex at first sight. The position of the other end of the object – available for Lines and Links only.System Modelling: Data and Results. This is the same data as on the individual data forms and includes the following data items: The positions (as Cartesian coordinates) relative to the frame of reference of the object to which the connection is attached. relative to a choice of frames of reference. 180° and 270° and the R coordinates set to 200m. where a series of connections need to be laid out around a circle. 90°. Then. 90°. but they allow various useful coordinate transformations to be done easily and accurately. You have a quite a lot of flexibility to choose what reference frame you want for the polar coordinates. Here is an example. set the reference frame origin and axes to be the spar origin and spar axes and set its polar coordinates to be R=5. The point on the seabed that is directly below the global origin. the Object Relative Position data are the Cartesian coordinates of the connection relative to the frame of reference of the object to which it is connected. each of which has End A connected to the spar and End B anchored. The Cartesian coordinates of the connection. Rsin(θ). suppose you want the End B connections to be anchored to the seabed. Height above seabed for anchored line ends. The axes directions of the frame of reference of any connected object. and Z=-3. Consider mooring a spar with an array of 4 lines. Finally you can set the θ coordinates for the A ends to 0°. Polar Coordinates page The Polar Coordinates page provides a way of viewing or setting the positions of the connections using polar coordinates. 446 . to set the vertical positions of the B ends. are (Rcos(θ). w System Modelling: Data and Results. The copy/paste or fill down keyboard shortcuts are particularly useful here. All Objects Data Form Other data The Other data mode presents tables of data for Vessels. Winches and Shapes. Another useful technique is to build a table of data in Excel with identical layout of columns and rows. Links. The notable exception is the Line sections page in which each row contains data for a single section of a Line. Lines. This allows you to make use of Excel's formulae and data handling facilities to prepare data. This tabulation allows data for multiple objects to be set in an efficient and coordinated way. 6D Buoys. and then to paste it into OrcaFlex in a single operation. 3D Buoys. 447 . The tables are laid out with each row containing related data for a single object. . plus the degrees of freedom of any vessels and buoys in the model whose values are calculated by the static analysis. if requested. and that line is subject to a non-zero current (relative to any starting velocity specified for the static analysis). Here the offset vectors are the translational offset vectors (in length units) and the rotational offset vectors (in degrees). in addition to the translational positions of each node that is free to move. So for a modal analysis of a line that does not include torsion. see the Modal Analysis theory section. then the included degrees of freedom also consider the rotational orientation of each node of the line that is free to rotate. The largest vector translation or rotation of any free node or object included in the modal analysis therefore has unit amplitude. For a modal analysis of a line that does include torsion then the mode shape will be normalised such that either the largest translation of any free-to-move node is 1 length unit. not the shapes of the natural modes or the mode loads.e. Data and Results MODAL ANALYSIS 7. all mid-nodes and any end nodes that are Free. Mode Shape For a given mode. If you include the mode shapes then the analysis takes longer. To open this form. or else the largest rotation of any free-to-rotate node is 1 degree. For large systems it is much quicker to calculate only a small number of modes – see Modal Analysis Theory for more details. since it will report modes of oscillation about that static mean position. as described above. or translational and rotational position if 6 DOF (for a vessel) or All (for a buoy).w 7 Modal Analysis. and a discussion of its limitations. translational position only if 3 DOF (for a vessel) or X. the degrees of freedom included in the mode shape are those specified to be included in the static analysis for that object – i. 449 . transverse or axial motion.Z (for a buoy).e. These offset vectors are formed from the degrees of freedom that are included in the modal analysis. When you have made your selections click the Calculate button. then the included degrees of freedom are the translational position of each node of the line that is free to move. If the modal analysis is for a single line and that line does not include torsion. Performing modal analysis To perform a modal analysis you need to specify the following: What you want to analyse: the whole system or a single line. or of a single line. then the included degrees of freedom are the free degrees of freedom of all the lines in the model. The modal analysis will then calculate the undamped natural periods and. If you exclude the mode shapes then the analysis only calculates the natural periods. If the modal analysis is for a single line and that line does include torsion.Y. Which modes you want to calculate. This classification can be useful when deciding which modes are appropriate to be included in a VIV analysis. i. and the classification is reported as folllows: Offset distribution displays a measure of how inline. transverse.1 DATA AND RESULTS The modal analysis form enables you to calculate and view the undamped natural modes of the whole system. Mode Shape Normalisation Each mode is normalised to have the magnitude of its largest offset vector equal to 1. For full details of the calculation. the mode shape consists of the displacements about the mean position when that mode is excited. and the size of any rotational offsets in the mode shape. You can ask for All modes or a specified range of modes. the mode shapes. Note that modal analysis is only available when the static position of the model has been calculated. of each of the free degrees of freedom that have been included in the modal analysis. For details see Mode Offset Distribution. where a unit of translational motion is one of the length units of the model and unit rotational motion is rotation by one degree. see the Modal Analysis command on the Results menu. Mode Type If the mode shapes have been calculated with a single line modal analysis. If the modal analysis is for the whole system. the mode shape is normalised such that the largest translational offset of any free node in the line is 1 length unit. None. This includes all mid-nodes and end nodes that are either Free or else connected to another object with non-infinite rotational connection stiffness. Whether you want to calculate the mode shapes or just the natural periods. axial and (if torsion is included for that line) how rotational the mode is. So for a vessel or 6D Buoy. This classification is based upon how much of the mode shape translational offsets are inline. then a broad classification of the mode type is calculated and included in the modes table. or if the line is entirely above the water. The mode loads are therefore the changes obtained in line loads if the normalised mode shape was applied as an offset about the mean position. with all non-linear effects ignored and with fluid damping effects ignored (since it is an undamped modal analysis). Both the mode shape and the mode loads represent dynamic oscillations about the mean static state condition.. bend moment and torque. The drawing exaggeration value allows you to vary the amplitude of the drawn mode shape. The animate mode shape and draw node axes options allow further control of the mode shape drawing. and the curves for the first line occupy the left-hand side of the graph. The mode loads are only available if you calculate the mode shapes. Modes Table The Modes Table displays a spreadsheet giving details of the calculated modes in numerical form. axial. for modes with either very long or very short periods. fixed. So if there is no current defined. Note that when that drop-down list has the focus (click it to give it the focus) then you can use the arrow keys to quickly increment or decrement the mode shape number that is displayed. You may need to zoom out in order to see the system. Y and Z components. The components can be plotted with respect to either global or local axes. The mode loads therefore correspond to the mode shape given in the Modes Table. You can use the mode drop-down list to control which mode is shown on the view. The mode loads are reported at both the line ends. Then the first line's mode shapes are plotted over arc length range 0 m to 50 m. Modes View If mode shapes have been calculated then the Modes View page displays a 3D view of the system showing one selected mode shape superimposed on the static position of the system. this option can make visualisation of the mode shape quite difficult. Note: The Offset Distribution and Mode Type information is only available for single line analyses where there is relative flow normal to the line. and you may need to adjust the view angle to suit the mode that you are viewing. For single line analyses. that would arise if the objects included in the analysis oscillated in a given single mode. If the mode shapes have not been calculated then the table only gives the periods and frequencies of the modes. If you select the mode period option then the animation has a cycle period equal to the mode period. and similarly for inline. Separate curves are plotted for X. and you can control the view angle. The current direction is also shown on the view. Data and Results Mode type classifies each mode according to the offset distribution. Loads Table The Mode Loads are the amplitudes of the dynamic variations in shear force. The modes are numbered in order of increasing frequency. then the curves for each of the lines follow one another across the graph. as components in the line axes directions at the mid-segment point. mostly axial. if the model or single line were to oscillate in that mode shape at that mode frequency. reported with respect to your choice of global axes directions or local axes directions. followed by the mode shape curves for the other lines (in the same order as in the model browser when view by types is used). Mixed means that none of the components are more than 50% of the total. provided that there is relative flow normal to the line. 450 . For example consider a system that has three lines. with each line's arc length range added on to the end of the total length of the previous lines. the offset distribution and mode type for the selected mode is also shown. as components in the line end node axes directions. and finally the third line's mode shapes plotted over arc length range 100 m to 150 m.w Modal Analysis. mostly inline. If the mode shape is being animated then there is a further choice to make. in all the lines included in the modal analysis. then this information will not be available. the animation period. rotational and mostly rotational. as on any 3D view. Mostly transverse means that it is between 50% and 90%. zoom etc. and at each mid-segment point. Modes Graph The Modes Graph page displays the mode shapes as range graphs against arc length along the lines. and their magnitudes are affected by the normalisation of the mode shape. tension. If a whole system modal analysis has been performed and there are multiple lines included. In this situation the arc length axis on the graph covers values from zero up to the sum of the lengths of all the lines in the system. Otherwise it also gives the mode shapes. For example an out of plane mode for a catenary is best viewed by looking along the plane of the catenary. animates the mode with a 5s cycle period. Transverse means that the transverse component is more than 90% of the total. per unit mode amplitude. However. The alternative option. followed by the second line's mode shapes plotted from 50 m to 100 m. each 50 m long. The mode type and offset distribution. where a and ω are unknowns to be found by solving the equation. The undamped equation of motion is: Mx''(t) = -Kx(t) where x(t) is the offset (at time t) from mean position. M is the mass and K is the stiffness of the spring.a. The mode period and frequency. one line after another. Each row of the table refers to a single mode and contains the following information: The mode number. These modes are given in increasing order of frequency and are numbered starting from 1. First consider a single degree of freedom system consisting of a mass attached to a linear spring. VIV The VIV page provides a table of information that is useful for VIV analysis.sin(ωt) = -K.w Modal Analysis.sin(ωt) so when we substitute into the equation of motion we obtain: -M. You can use the Filter modes boxes to choose which types of modes are included in the table. So the load variations obtained from an OrcaFlex simulation in which the line positions are specified to follow the mode shape will not in general match the mode loads exactly. The table reports modes in order of increasing mode number. but here is a brief outline. The initial default selection is to export the transverse and mostly transverse modes. of the form x(t) = a. x''(t) is the acceleration. 7. you might wish to view only the transverse modes if you are studying transverse VIV. This is currently only available for single line modal analyses. Since this analysis neglects any damping the results are referred to as the undamped modes. then the curves for each of the lines follow one another across the graph. The highest numbered modes are unlikely to be realistic since they are oscillations whose wavelengths are of the same order as the segment length. Loads Graph The Loads Graph page displays the mode loads as range graphs against arc length along the lines. For any given level of discretisation the accuracy is better for the lower modes and progressively worsens as you go to higher and higher modes. and it is only available if the mode shapes are calculated and the line is at least partially under the water and subject to a non-zero current (relative to any starting velocity specified for the static analysis). However. but most systems are non-linear and the OrcaFlex simulation includes non-linear effects. The lines are ordered in the order in which they appear in the model browser when view by types is used. If a whole system modal analysis has been performed and there are multiple lines included. bend moment and torque. The solution of the equation is known to be simple harmonic. The analysis calculates the natural modes of the discretised model.a. Differentiating x(t) gives: x''(t) = -ω2.a.sin(ωt) (1) which can be rearranged to give: 451 . Separate graphs are given for shear force. not those of the real continuous system.and y-direction components of the load. the discretised modes are close to the continuous ones and for a mode number the accuracy improves as more and more elements are used to model the system. The tension and torque graphs present only one curve. giving the tension or torque in the line axial direction. i.sin(ωt). Outline Theory Modal analysis is a standard technique that is well-documented in the literature. The shear force and bend moment graphs include separate curves for the line x. in the same manner as the Modes Graph. Note: The modal analysis assumes that the system is linear. since the OrcaFlex simulation results will usually include significant non-linear contributions. For example. the mode loads for each line in the model are all presented together in a single table.ω2. Theory When a whole system modal analysis has been performed.2 THEORY A modal analysis calculates the undamped natural modes of a system.e. tension. Export to modes file specifies whether or not the mode will be included in the file exported by the Export SHEAR7 Mds File and Export VIVA Modes Files buttons. For details see SHEAR7 Mds file. Eigen-solvers Two eigen-solvers are used to perform modal analysis. This has the effect of restraining movement of the nodes on the seabed in the plane of the seabed. those dependent on x') are neglected. But different degrees of freedom oscillate with different amplitudes. These fluid load terms are neglected in the modal analysis. N. In this situation OrcaFlex uses an average of the possible stiffness values. is 10. Consequently if you ask for modes 5 to 10 then the solver has to find modes 1 to 4 first and so the number of modes extracted. in general. ill-defined because it can be many-values depending on whether the perturbation increases or decreases curvature. The Lanczos algorithm works by finding the largest (or smallest) eigenvalue first. If n ≤ N/3 and n ≤ 1000 then an iterative Lanczos algorithm will be used.w Modal Analysis. Consider a discretised line in OrcaFlex with N degrees of freedom. and M and K become N×N matrices. such a system is linear and modal analysis may be adequately accurate. but computers work with discretised models with finite numbers of degrees of freedom. Otherwise a direct method based on tridiagonal matrix diagonalisation is used. This modification to the seabed friction model results in a symmetric. where ωi is a scalar and ai is a vector with N elements. because they arise from displacements even though the magnitude of the loads themselves are dependent on velocities. n. The local tangent stiffness is. 452 . The external function interface provides no mechanism for specifying the local tangent bend stiffness. Theory ω = (K/M)½. elastic bend stiffness the local tangent stiffness is used. Seabed friction The theory outlined above requires that the mass and stiffness matrices are symmetric which is not always the case in an OrcaFlex model. In this situation the above equations still apply. corresponding to the single degree of freedom. which is desirable for a modal analysis of a system with seabed contact. then the next largest (or smallest) and so on. For non-linear. Clearly this presents a problem. say. So. Hence OrcaFlex uses the nominal bend stiffness as provided by the external function. For large problems the iterative Lanczos algorithm is much faster and requires much less memory and so should be used if at all possible. for example. This stiffness term corresponds to the stiffness of a linear spring acting in the plane of the seabed. It is an oscillation of the line in which all the degrees of freedom oscillate at the same angular frequency ωi. and with a stiffness of K sA. given by the components of ai. Equation (1) is an eigen-problem with N solutions.e. A. fluid loads do contribute stiffness terms because perturbations of position and orientation can result in changes of direction of the fluid load vector. Ks and the node's contact area. x and x'' become vectors with N elements. and hence an infinite number of undamped natural modes. This is the angular frequency of the oscillation and so the natural period T is given by: T = 2π(M/K)½ For this simple harmonic oscillator there is just a single undamped natural mode. Non-linear bend stiffness Modal analysis inherently assumes linearity of the system under consideration. For small oscillations about the static configuration. For hysteretic bend stiffness the situation is more complex. The choice of which to use is made based on the number of modes extracted. that is when the deflection from its friction target position exceeds Dcrit. However. but they now have to be interpreted as matrix/vector equations where ω and T remain scalars. One final subtlety concerns the precise definition of n in the above inequalities. the effects of drag loading are neglected in the modal analysis. The most important example of this is the friction model. and the number of degrees of freedom. For a continuous riser there are an infinite number of degrees of freedom. Yet another case to consider is externally calculated bend stiffness. the ith solution being ωi and ai. The non-conservatism of the standard OrcaFlex friction model arises when a node is slipping. a. conservative system and hence enables modal analysis to be performed successfully. This ith solution is called the ith natural mode. Friction is a non-conservative effect and non-conservatism equates to non-symmetric terms in the stiffness matrix. Stiffness terms due to fluid loading As mentioned above. These are stiffness terms. the modal analysis is an undamped analysis which means that damping terms (i. This amplitude variation is called the mode shape. When performing modal analysis OrcaFlex assumes that nodes on the seabed are restrained by a linear stiffness effect determined by the seabed's shear stiffness. as opposed to damping terms. n. connecting the node and its target position. w Modal Analysis. Then OrcaFlex calculates the inline. If the line includes torsion. r. Therefore. and to set the initial default selection of whether the mode should be exported to the SHEAR7 Mds file if that facility is used. but we also sum the three components because all we require is a single measure of how much rotational content is present in the mode offset vector. then a further component Mr is required to represent the overall rotational content of the mode shape. However. Tt and Ta be T's components in the local inline. See Mode Type. Ma and Mr components of the mode shape as percentages of their sum M = M i + Mt + Ma + Mr. is the dominant contribution to lateral stiffness and so the limitations described above are often not significant. Rt and Ra are formed from the rotational part of the mode offset vector. Theory Clearly the modal analysis will be less accurate for hysteretic and externally calculated bend stiffness than it is for the other bend stiffness options. Mt. transverse. axial and rotational motion. OrcaFlex classifies modes according to how the mode shape is distributed between inline. let T i. Mode Offset Distribution For VIV analysis purposes. and reports these percentages as offset distribution values. So: Mode shape rotational component = Mr = (∑ L(rRi)2)½ + (∑ L(rRt)2)½ + (∑ L(rRa)2)½ If the line does not include torsion then M r=0. the program neglects added mass when the data are frequency dependent. If the added mass varies significantly with period. as opposed to bend stiffness. The scaling by L is included so that the values are independent of the level of discretisation. the added mass of a vessel is usually a significant factor in the analysis. transverse and axial components of the overall translation in the mode shape as follows: Mode shape inline component = Mi = (∑ LTi2)½ Mode shape transverse component = Mt = (∑ LTt2)½ Mode shape axial component = Ma = (∑ LTa2)½ where the summations are over all nodes in the line. However. then you may need to perform multiple modal analyses with different added mass matrices. axial and rotational the mode is. over the range of mode periods under consideration. 453 . let T be the translational part of the mode offset vector at a given node. These values are only used to report some measure of how inline. OrcaFlex then expresses Mi. This allows an appropriate comparison between the magnitude of translation and the magnitude of rotation. For a given mode. if the vessel added mass and damping data are specified as frequency dependent there is no easy way for the modal analysis to account for this dependence on frequency. it is often the case that tension. The root sum of squares formulation used above is the multi-dimensional equivalent of the standard 3D formula |V| = (Vi2 + Vt2 + Va2)½. In order to perform a more accurate modal analysis you can use the constant option for added mass specification. Vessel added mass When performing a whole system modal analysis with vessel degrees of freedom included. to give them dimensions of length. for modal analysis. and these are then multiplied by the node's radius of gyration about the line axis. transverse. In this situation you provide a single added mass matrix which is included in the system-wide mass matrix. transverse and axial directions and let L be the length of line represented by that node. Because you can only specify a single added mass matrix you must first assess what modes are of interest and choose appropriate added mass values. Again we sum over all the line nodes. Components Ri. . Usually this means that the simulation files should be stored on a local disk of the machine performing the fatigue calculation. or externally calculated stress (suitable for bespoke applications). 3. data and results. For the other methods the exposure level is specified as the total time exposed to waves within the wave class. Open the fatigue analysis tool and set up the fatigue analysis data. For regular analysis the simulation should use a regular wave representative of the wave class and for rainflow analysis the simulation should use an irregular wave representative of the wave class. For SHEAR7 fatigue analysis the load cases are specified by a set of SHEAR7 . Mooring line fatigue calculates damage from effective tension ranges using T-N curves. Introduction FATIGUE ANALYSIS 8. The fatigue calculation performance is often limited by disk access – consequently it is important that the disk access speed is as fast as possible. with its own menus. Check the data for errors.w 8 Fatigue Analysis. The calculation makes use of all available processor cores to process load cases concurrently. 455 . 2. damage is summed in a variety of ways: Deterministic regular wave fatigue analysis. Use the normal OrcaFlex facilities to set up and run simulations that model the various load cases that the line will experience.1 INTRODUCTION The OrcaFlex fatigue analysis is a post-processor which calculates fatigue damage using a variety of methods. Calculate and collate the damage.plt output files. For both regular and rainflow analysis you typically represent each wave class with a distinct OrcaFlex simulation file. for a SHEAR7 analysis. Notes: The calculation stage of a fatigue analysis can take a long time . Damage is then collated and summed for specified load cases and then presented. stress factors (for umbilicals and flexibles). This fatigue analysis data are held separately from the other OrcaFlex data and can be saved in a separate file with the file extension . Likewise. 4. The reason this is possible is that the spectral response analysis provides information about how the system responds to a range of wave frequencies. For spectral analysis multiple wave classes with similar Hs values may be represented by a single response calculation simulation. Damage can be calculated in a variety of ways: The S-N curve approaches recover stress using homogeneous pipe stress (for metal risers). typically this is done with a wave scatter table. The fatigue analysis tool is accessed by selecting the Fatigue Analysis command from the OrcaFlex Results menu. Each load case is assigned an exposure level. either as plots or in tabular fashion. create a set of SHEAR7 .plt output files to represent your VIV load cases. Stochastic irregular wave fatigue analysis using spectral methods. This option allows you to collate fatigue damage from a number of SHEAR7 load cases. It is essentially a self-contained sub-program within OrcaFlex. For regular load cases this is the total number of occurrences of waves within the wave class. The SHEAR7 option is rather different because damage is calculated external to OrcaFlex by SHEAR7. These are most easily generated using the SHEAR7 interface. To help with this there is an Estimate Calculation Time facility and fatigue analyses can be run in batch mode. together with the standard OrcaFlex automation facilities – the . Deterministic irregular wave fatigue analysis using the rainflow cycle counting method.ftg. Damage is then calculated based on the specified S-N curve. especially a rainflow analysis with a lot of load cases.plt files are automatically exported if you run the direct SHEAR7 interface in batch mode. Alternatively. The steps involved in performing a fatigue analysis are: 1. Typically you will have a range of simulations which cover the range of Hs values in your wave scatter table. The approach is to divide the range of sea states that the system will experience into a number of wave classes. Load Cases Before the fatigue analysis can be performed you must first prepare a set of OrcaFlex simulation files that model the same system but under the various load conditions that the system will experience in its lifetime. but allows you to specify the file name to save to.yml extension is used for the text file format. we cannot achieve the same level of compatibility as that for binary data files.yml). The time and storage requirements can be somewhat alleviated by careful selection of load cases. Commands Choice of fatigue analysis method As described above OrcaFlex can perform three different types of fatigue analysis: regular. when OrcaFlex attempts to open a binary . If results have not been calculated then the file will contain input data only. Note that results can only be saved to the binary format file (. If the file does contain results then these will be available without having to perform the time-consuming calculation again. Save Saves the data to the currently selected file name (shown in title bar of the window). as well as giving much more reliable and accurate answers. These are YAML files and are intended to be used for automation purposes. Recommendations The advent of multi-core processors and the wave scatter conversion facility mean that regular wave fatigue analysis is often just as fast as spectral fatigue analysis. Just as is the case for OrcaFlex data files. These files can be either binary format (. The other factor which can be adjusted is the duration of the irregular wave load case simulations. If you do perform a spectral fatigue analysis in OrcaFlex then it is very important that you check that the spectral response RAOs are smooth. This allows you to view results at a later date without having to perform the calculation again. In our experience it is often possible to achieve accurate damage predictions with simulations of 20 minutes duration.2 COMMANDS File Menu New Clears previously entered Fatigue Analysis data and resets data to default values. Whilst we strive to achieve as much compatibility as possible for text data files across program versions. the binary file has strong version compatibility features. Because of this we no longer recommend the use of spectral fatigue analysis in OrcaFlex. The spectral fatigue analysis method was originally included to provide a very quick alternative to the other methods. This is largely due to weaknesses and limitations in the response calculation approach used to generate response RAOs. This then reduces the choice of methods to regular and rainflow. Open Opens a Fatigue Analysis file. Because of the calculation time and disk storage advantages it is clearly desirable to use regular wave fatigue. more detailed check.w Fatigue Analysis. The spectral fatigue method in OrcaFlex is much more difficult to use effectively than the other methods. rainflow or spectral. Certainly during system design these advantages are significant because they allow for greater coverage and exploration of the design space. 8.ftg extension is used for binary format files.ftg file written by a later version of the program it is able to report informative compatibility warnings. If the regular wave fatigue analysis predicts a system life significantly in excess of the design life then this final detailed check could be omitted. The . If results have been calculated then these are also saved to the file.ftg) or text files (. Another effective strategy is to use regular fatigue analysis for the bulk of the time and switch to rainflow analysis for a final. Save As This is the same as Save. Rainflow fatigue is the most accurate of the methods. The response calculation method often results in very noisy RAOs which in turn result in gross over-predictions of damage. The wave scatter conversion facility provides an efficient and productive way to generate a regular wave scatter table from a random sea scatter table. The .ftg). For example. but also the most time consuming and demanding of disk storage. It is our experience that use of the spectral fatigue method usually results in poor and inaccurate results. Provided that the regular wave bin discretisation is performed well. Regular wave fatigue analysis is much faster and requires much less disk storage than rainflow fatigue. the results from a regular wave fatigue analysis will generally agree well with an equivalent rainflow analysis. The program is not able to be as helpful and informative when working with text data files across program versions. 456 . This option is appropriate for metal risers. Most Recent Files List A list of the most recently used files. For each of these load cases a single-occurrence damage value is calculated based on the last wave cycle in the simulation. Analysis Menu Estimate Calculation Time Gives an estimate of how long it will take to do the fatigue analysis and present the results. homogeneous. This option allows you to collate fatigue damage from a number of SHEAR7 load cases. If you want to work with just the input data then this command loads just the input data which is a much quicker process. The size of the list can be adjusted from the Preferences form.3 DATA Title Used to label all output of the fatigue analysis. Finally these total load case damage values are then summed for each load case to give the overall total damage. This approach is commonly used for umbilicals but could also be used for unbonded flexibles. For example it checks that all the specified load case simulation files exist and that the named line and the specified arc length intervals exist in each load case. linear material. is very similar to the stress factor option. Analysis Type Three types of fatigue analysis are available: Regular analysis must be based on a series of regular wave simulations that represent the various load cases that will occur.g. It uses a cycle counting technique to break down each random wave case into a series of half-cycles. The damage calculation is based on ZZ Stress. Rainflow analysis is normally based on a series of random wave simulations. For details see the book by Maddox and the paper by Rychlik. The final option. The SHEAR7 option is rather different because damage is calculated external to OrcaFlex by SHEAR7. This damage value is then scaled up by the specified number of cycles expected to occur during the structure's life. 8. e. and then sums the damage from each halfcycle according to the Palmgren-Miner law. externally calculated stress. since the check can often detect data errors that would otherwise only be found part way through what may be quite a long fatigue analysis. Selecting an item on the list causes the file to be loaded. so we recommend that the Check command is used before the Fatigue Analysis is run. Damage calculation A variety of methods are available for calculating damage: Homogeneous pipe stress which assumes a pipe made of a straight. A progress window is displayed and you can cancel the analysis if desired. Calculate The Calculate command starts the Fatigue Analysis. Check The Check command performs a preliminary check of the fatigue analysis data. or if there are many log samples in the load case simulations. Data Open Data If the file contains results and there are a large number of load cases then the file can take a long time to load. The mooring fatigue option calculates damage from effective tension ranges using T-N curves.w Fatigue Analysis. Please refer to the External Function Examples for more details. This is useful for long analyses. or finally if there are a lot of segments in the arc length intervals specified. An approach based on stress factors. uniform. and this gives the total load case damage value. rainflow analyses involving a lot of cases or long simulations. The fatigue analysis can take a long time if there are many load cases. The Check command is generally much quicker that the fatigue analysis itself. The difference is that stress is calculated by means of an externally specified results variable. It is particularly important to use the Check command when a new fatigue analysis has been first set up or when significant changes have been made to the data. Here the stress is assumed to comprise a tensile contribution (proportional to either wall tension or effective tension) and a bending contribution (proportional to curvature). This 457 . When the calculation is complete the results are displayed in a spreadsheet window. Line Name The name. Dirlik's formula is applicable even if the variation of the response is not a narrow banded process. the fatigue analysis can use inches (giving stresses in ksi) even if the simulation files use feet as the length unit. for both the fatigue analysis data and for its results. Units The units to be used for the fatigue analysis. which is then scaled to the specified total exposure time. Simulation Period The period of the pre-run simulation file that defines the load case. then enter the new data. However the named lines in the various load cases must. You can either specify the full path or a relative path. of course. 8. 8. 458 . then the results from that simulation file will automatically be converted to the units specified for the fatigue analysis. Finally these total load case damage values are then summed for each load case to give the overall total damage. The PSD is obtained from a response calculation simulation. and then change back to the original units again. This is useful. This calculates RAOs for the load variables of interest and these are then combined with the load case wave spectrum to give PSDs for load. The units are specified in the same way as elsewhere in OrcaFlex. all represent the same physical line and use the same discretisation in the areas being analysed. that the line will experience.4 LOAD CASES DATA FOR REGULAR ANALYSIS Simulation File Name The name of the simulation file which represents the load case. Similarly. If they do not match. of course. For this reason we recommend using Dirlik's formula. The method requires a power spectral density function (PSD) for a particular load variable (stress or tension).w Fatigue Analysis. for example. all represent the same physical line and use the same discretisation in the areas being analysed. However the named lines in the various load cases must. Finally these total load case damage values are then summed for each load case to give the overall total damage. Cycle Range Distribution (spectral analysis only) The spectral fatigue calculation assumes that cycle ranges follow a statistical distribution which is specified by this data item. The distribution can be either Dirlik's formula or the Rayleigh distribution. in this load case simulation file. then all existing fatigue analysis data are automatically changed to match the new units. This is useful if you want to enter data in some other set of units. Load Cases Data for Regular Analysis gives the damage value for that load case. Note: Normally the line name will be the same in all of the load cases (though this is not necessary). since it allows the fatigue analysis to be done using m and MN as the length and force units (giving stresses in MN/m2 = MPa). even if the simulation load cases use m and kN (which corresponds to stresses in kN/m2 = kPa). If you change units. of the line to be analysed. Note that the units specified for the fatigue analysis need not match the units that were used in the various load case simulation files. The damage is scaled to the specified total exposure time for the load case. in this load case simulation file. Note: Normally the line name will be the same in all of the load cases (though this is not necessary). The Rayleigh distribution is appropriate if the variation of the response is a narrow banded random Gaussian process. of this particular set of load conditions. since you can simply change to the units of the new data. in US units. Number of Cycles The number of wave cycles. Exposure Time The total time the system is exposed to this load case. Spectral analysis calculates damage in the frequency domain using statistical methods. of the line to be analysed.5 LOAD CASES DATA FOR RAINFLOW ANALYSIS Simulation File Name The name of the simulation file which represents the load case. Line Name The name. These PSDs are then used to calculate damage using either Dirlik's formula or the Rayleigh distribution. You can either specify the full path or a relative path. For details see Data for Torsethaugen Spectrum. The spectral fatigue calculation then proceeds by combining these response RAOs with a wave spectrum to produce power spectral density (PSD) functions. if Automatic is selected then you specify Hs and Tz and the other JONSWAP parameters are calculated automatically and reported. However the named lines in the various load cases must. This determines a number of wave classes. Line Name The name. 459 . Spectral Form. This wave scatter table gives 16 wave classes and so the fatigue analysis data in OrcaFlex would be set up with 16 corresponding load cases with appropriate Hs and Tz values. If you select Specified you must specify all 6 parameters and OrcaFlex then derives and displays the corresponding overall Hs and Tz values. based on the overall significant wave height Hs that you have specified. of course. all represent the same physical line and use the same discretisation in the areas being analysed. You can also specify fm or Tp but since Tz. You can either specify the full path or a relative path. This specifies the general form of the wave spectrum. Partially Specified or Fully Specified. this determines exactly how the spectral parameters for each load case are specified.w Fatigue Analysis. For details see Data for Ochi-Hubble Spectrum.6 LOAD CASES DATA FOR SPECTRAL ANALYSIS Simulation File Name The name of the simulation file which represents the load case. If you select Automatic the program calculates the parameters of the most probable spectrum. suppose that you were working with the following (truncated) wave scatter table: 4-5 3-4 Hs 6 2-3 9 3 18 6 22 132 117 1-2 3 57 201 249 0-1 15 48 69 45 4-5 5-6 6-7 7-8 Tz The values in the table represent joint probabilities in parts per thousand. Note: Normally the line name will be the same in all of the load cases (though this is not necessary). You can also specify fm but since Tp and fm are tied together then setting either one changes the other to match. e. Tp and fm are tied together then setting any one of them changes the other two to match. Load Cases Data for Spectral Analysis 8. Setting up load cases for Spectral Analysis When performing a spectral fatigue analysis you will typically have a wave scatter table describing the relative probability of storm occurrence. The load cases data should be setup to match load cases with wave classes. The parameters for the chosen spectral form are specified as follows: If JONSWAP is selected then Spectral Parameters can be either Automatic. Ochi-Hubble or Torsethaugen. Exposure Time The total time the system is exposed to this load case. For example. or Specified. For details see Data for JONSWAP and ISSC Spectra. Spectral Parameters For spectral analysis the simulation file specifies a response calculation simulation file from which response RAOs are derived. Again. For details see Data for JONSWAP and ISSC Spectra. in this load case simulation file. of the line to be analysed. so that a value of 201 represents a probability of 0. Spectral Form can be one of JONSWAP. If ISSC is selected then you must specify H s and Tz for each load case.g. ISSC.Tz pairs. If Torsethaugen is selected then you must specify Hs and Tp for each load case. storms defined by H s. If Ochi-Hubble is selected then Spectral Parameters can be either Automatic. This determines exactly how the spectral parameters for each load case are specified.201. For example. Again. 460 . wave direction and so on which are appropriate for the load case being analysed. For example the Hs1.w Fatigue Analysis. current profile and direction. Load Cases Data for Spectral Analysis Simulation files for spectral fatigue analysis load cases The simulation files used to represent a load case for spectral fatigue analysis should model all aspects of the system and environment other than the wave spectrum. 3-4 and 4-5. the Hs. There are 4 wave classes corresponding to the 0-1 Hs range. The other Hs ranges are dealt with similarly and so the load cases table would look as below: Figure: Example load cases table If the non-linearities in the system are not so significant then you may be able to obtain accurate results with fewer simulation files. the accuracy of such a simplification should be tested with sensitivity studies. So you must specify vessel offset.e. This effectively calculates system responses (i. Certain systems are dominated by linear physical effects and the RAOs may not in fact be dependent on wave height. Essentially the RAOs can be considered as being dependent on wave height. Choice of Hs for response calculation simulation files The Spectral Response Analysis method which is used to calculate system responses (RAOs) includes non-linear effects such as hydrodynamic drag. In the example above we might choose to run a response calculation simulation for each row of the wave scatter table (assuming that the system had significant non-linearities). In order for these non-linear effects to be well modelled the choice of Hs for the response calculation simulation files is important. How significant this dependence is will vary from case to case. 1-2. RAOs) for a range of wave frequencies.e. To determine how significant this effect is we would recommend sensitivity studies. The load case corresponding to each of these wave classes would then be represented by the same simulation file.Tz pairs) to produce fatigue damage estimates for the load case. Hs2 and Hs3 simulations could be combined into a single Hs2 simulation etc. The spectral fatigue analysis then combines these RAOs with the load case wave spectra (i. This would give 5 simulation files for Hs ranges 0-1. The wave type for the load case simulation file must be response calculation. 2-3. This may be desirable to reduce the amount of time taken to run the simulations. 8. Kt and Kc are the tension and curvature stress factors.Cycos θ) where S is stress. allowing you to pass parameters to the external function. For externally calculated stress. any occurrences of the text %theta% is replaced with the actual value of theta. In effect this formula defines stress to be the sum of contributions due to direct tensile strain and bending strain. this data item has an extra use: it is passed to the external function that calculates stress in the ExternalResultText of the ObjectExtra structure. Component Name This is used to identify the component in the results. The actual ExternalResultText strings passed to the external function would be of the form theta=0. The most important use is to pass the θ value to the external function. So suppose that the component name was specified to be theta=%theta%.7 LOAD CASES DATA FOR SHEAR7 Load Case File Name The name of the SHEAR7 . Cy). respectively. Components can be used to represent different layers or components in the cross section of an umbilical or a flexible. Stress Result (externally calculated stress only) The name of the externally calculated result variable that provides the stress values. Cx and Cy are the components of curvature in the line's local x and y directions. Load Cases Data for SHEAR7 Response calculation simulation duration The other decision to make is over the length of the response calculation simulations. in degrees. The damage for the load case is calculated by multiplying the exposure time by the damage rate read from the load case . You define a number of components for which damage is to be calculated.0 etc. stress is given by S = K tT ± Kc|C|. before the external function is called to derive a stress result. So. stress is given by S = KtT. T is either wall tension or effective tension.plt output file which represents the load case. The convention is that. the terms which refer to θ) is to account for the fact that bending strain varies with θ. for a point at 90° to the plane of bending. Tension and Curvature Stress Factors (stress factors only) The stresses used to calculate damage are calculated according to the formula: S = KtT + Kc(Cxsin θ . Tension Variable (stress factors only) Specifies wall tension or effective tension is used to calculate stress. theta=45.8 COMPONENTS DATA The Components Data page is only available when damage is calculated using stress factors or using externally calculated stress. Please refer to the External Function Examples for more details. 8. 461 . for a point in the plane of bending. Similarly. Suppliers of such products are usually able to provide the necessary stress factors. 8. Exposure Time The total time the system is exposed to this load case. and θ is the circumferential location of the fatigue point. You need to simulate for long enough to get accurate results.w Fatigue Analysis.plt file. as specified by the tension variable data. The stress factors will typically be calculated from experimental data or from detailed analytic models of the umbilical or riser cross section.e. where C is the curvature vector (Cx.9 ANALYSIS DATA The Analysis Data page contains the following data items. which specify the parts of the line to be analysed. The circumferential variation (i.0. respectively. S-N Curve Specifies which S-N curve is used for damage calculations for this component. As for the issue of H s discussed above we would recommend using sensitivity studies to determine how long is required. You can either specify the full path or a relative path. as determined by the region boundary data item. and hence not available. This data item is implemented solely to provide some convenience to results reporting. N(S). If calculation time is significant then you can save calculation time by analysing those parts of the line. you will need to specify separate arc length intervals for those parts. Warning: The included arc lengths must be the same in each load case. S-N Curve (homogeneous pipe stresses only) Specifies which S-N curve is used for damage calculations in this arc length interval. for mooring and SHEAR7 fatigue. otherwise a bi-linear curve is used. For example. For simple cases you can use just one arc length interval covering the whole line. When the curve is specified by parameters the user specifies parameters. If a value is specified for the line length then the x/L values are re-dimensionalised using that specified value. at which fatigue analysis will be performed. The arc length intervals can be overlapping. so the line to be analysed should have the same number and distribution of segments in each of the load case simulations. but takes a little longer. A value of '~' results in arc lengths being reported as nondimensional x/L values. which is the stress range below which no damage occurs. If needed you can define a number of different S-N curves and use them at different arc lengths along a line. 462 .w Fatigue Analysis. Radial Position (homogeneous pipe stresses only) Specifies whether the fatigue analysis is performed at the inner or outer fibre of the pipe.10 S-N AND T-N CURVES S-N Curves An S-N curve defines the number of cycles to failure. or parts. Notes: To use different stress correction factors for different parts of the line. T-N Curve (mooring fatigue only) Specifies which T-N curve is used for damage calculations in this arc length interval. FL. However it is often clear which part. SCF and Thickness Correction Factor (homogeneous pipe stresses only) When stress ranges are used with the S-N curve to calculate damage. this would be desirable if you wished to calculate damage for both inner and outer fibres of a homogeneous pipe.m log10(S) The curve can be either linear or bi-linear. If the total damage at any fatigue point exceeds the Critical Damage then that damage figure will be highlighted in the results. Arc Length Intervals You define the parts of the line that are to be analysed by specifying a number of Arc Length Intervals in the form of From and To arc length values. If this is set to Infinity then the curve will be linear. Number of Thetas The number of points (N) around the pipe circumference. With each S-N curve you must also specify an associated stress endurance limit. when a material is repeatedly cycled through a given stress range S. the stress ranges are scaled by the Stress Concentration Factor (SCF) and the Thickness Correction Factor before calculating damage. If no stress correction is required then these factors should both be set to 1. OrcaFlex uses the S-N curve to calculate the damage in a fatigue analysis. OrcaFlex will analyse cross sections at each line end and mid-segment whose arc length z is in the range From ≤ z ≤ To. and the curve is then given by either of the following equivalent formulae: N = a S-m log10(N) = log10(a) . log10(a) and m. Line Length (SHEAR7 fatigue only) Specifies the length of the line being consider by the SHEAR7 analysis. This value is not required. There will be N fatigue points uniformly distributed at 360°/N intervals around the pipe circumference. of the line are liable to fatigue problems. the native form for SHEAR7. The S-N curve itself can be specified either by parameters or by a table. 8. A larger number of thetas gives a more comprehensive analysis. S-N and T-N Curves Critical Damage Is a warning level. By most damaging we mean the load cases with the largest values of maxz.θ. The damage graphs all plot D(z) = max θ D(z. Mean stress effects can be accounted for using Goodman. These define the number of cycles to failure. Graphical output The graphical output produces plots of fatigue damage or fatigue life against arc length – range graphs of fatigue.12 RESULTS Fatigue results are presented in a separate window. m. 8. First change the fatigue analysis units and set the units system to be User. For individual load cases T is the exposure time for the load case. You can handle this problem as follows. Normally you should not need to modify the parameters from their default values. We recommend that you contact Orcina for further details should you encounter problems with spectral fatigue convergence.θ). restore the units to those that you want for the fatigue analysis. Hence log10(a2) is reported. Integration Parameters A bi-linear curve. but cannot be modified. Worst cases: the total exposure damage value from the five most damaging load cases. For total life T is the total exposure time of all the load cases. the latter option being more appropriate for vertical risers.11 INTEGRATION PARAMETERS Integration parameters are only available when the spectral fatigue analysis option is selected. so you can then enter the S-N parameters in terms of MPa. However. 463 . if the spectral fatigue calculation has problems with convergence then it may prove productive to try different values for these parameters. m1. For details of how the S-N curve is used to calculate the damage see How Damage is Calculated. Finally. The curve is then given by the following formula: N = k(T/RBS)-m When the curve is specified by a table the user gives a table of corresponding values of T and N. m2 for the high cycle region (N > region boundary). S-N curve parameters are typically quoted with respect to stresses in MPa.θ). m2 and the region boundary. The parameters will automatically be converted to allow for the change in units. is specified by parameters log10(a1). The life graphs plot the corresponding life values T/D(z) where T is the exposure time. Individual load case damage/life: the total exposure damage/life from the specified load case. The T-N curve can be specified either by parameters or by a table. Because the curve must be continuous. that is the maximum damage value at a given arc length z.m1 log10(S) for N ≤ region boundary log10(N) = log10(a2) . the length units to be m and the force units to be MN. When the curve is specified by parameters the user specifies three parameters. T-N Curves For mooring fatigue damage is calculated with T-N curves. The bi-linear S-N curve is thus specified by the following equations: log10(N) = log10(a1) . the value of log10(a2) is determined by log10(a1).θ). This could be overall total damage or the total exposure damage value for an individual load case. S-N Curve Units The S-N curve parameters entered must be consistent with the fatigue analysis units. m1 for the low-cycle region (N ≤ region boundary) and log10(a2). The graphs can be customised in a number of ways: The arc length axis can be either horizontal or vertical. Results are available in either graphical or tabular form. k and the reference breaking strength (RBS). N(T). For other values of S we use log linear interpolation or extrapolation to find the value of N.w Fatigue Analysis.m2 log10(S) for N > region boundary When the curve is specified by a table the user gives a table of corresponding values of S and N. but you might be doing the fatigue analysis using some other stress units. This corresponds to stresses in MPa. the maximum damage value over all z. For other values of T we use log linear interpolation or extrapolation to find the value of N. 8. For details of how the T-N curve is used to calculate the damage see How Damage is Calculated. Soderberg or Gerber models. when a material is repeatedly cycled through a given effective tension range T.θ D(z. Graphs are available for: Total damage/life: the overall total damage/life. We denote a damage value at arc length z and circumferential position as D(z. Automation The arc length axis can be inverted. Each such table contains a row of results for each fatigue point in that arc length cross section. Finally. Again this is particularly useful for vertical risers with arc length values that increase from the top end to the bottom end. Tabular output The tabular output is presented in a spreadsheet that has one Damage Tables sheet. For SHEAR7 fatigue. If you want to print the results then for best results you should first export them and then use Excel to do the printing. Printing and Exporting To save the results you will need to export the spreadsheet as an Excel sheet. For example: 464 . Individual arc length intervals can be plotted. according to the value of this data item. together with general information such as the environmental data that applied to that load case. facility for automating the production of text fatigue files. Customising results output The tabular results output can be customised using the options on the Results page of the main fatigue form. This can significantly reduce the time and memory required to generate the results tables. which lists any fatigue points at which the overall total damage has exceeded the specified critical damage value. There is one table of stress results for each arc length covered by the specified arc length intervals. tension results rather than stress results are reported. When it is inverted increasing values run from right to left (if it is horizontal) and top to bottom (if it is vertical).w Fatigue Analysis. plus one Load Case sheet for each load case. damage per day or damage per year. Load Case sheets The Load Case sheets contain the derived stress results for each fatigue point that has been analysed. overall total damage values that exceed the specified critical damage value are highlighted in red.13 AUTOMATION The fatigue analysis capabilities can be automated in a number of different ways. Fatigue damage/life can optionally be plotted on a logarithmic scale. This can significantly reduce the time and memory required to generate the results tables. In all of these tables. A table summarising the overall damage over total exposure for all arc lengths is presented. only damage values are reported. the Damage Table sheet provides damage tables for each arc length cross section analysed. the maximum stress range and the resulting load case damage values. These results are the stress ranges (for each of the stress components). There is also a sheet echoing the S-N curve data. These report. Details of where on the line the worst total damage occurred are also reported. Damage Table sheet The Damage Table sheet starts with an Excessive Damage table. YAML text files The YAML format fatigue files can be used for automation in exactly the same manner as OrcaFlex data files. A typical text fatigue file would load a base file. In particular the OrcaFlex Spreadsheet provides a simple. the total exposure damage value from each load case and the overall total damage. for each fatigue point in the cross section. Output load case tables If this option is deselected then the load case sheets are omitted from the fatigue results. In addition to the detailed tables a damage summary table is presented which tabulates the load case damage at each fatigue point. 8. and then make a small number of modifications. yet effective. since the damage calculation has been performed by SHEAR7. Output detailed load case tables If this option is deselected then the detailed tables on the load case sheets are omitted from the fatigue results. Load case damage units Load case damage values are reported as damage per hour. For mooring fatigue. ftg RadialPosition[1] = Inner Run inner.14 FATIGUE POINTS Damage is calculated at a number of line end and mid-segment cross sections along the line.15 HOW DAMAGE IS CALCULATED For each load case and fatigue point OrcaFlex calculates damage values as follows: 465 . θ) where R is the radial distance from the centre-line and θ is measured from the line's local x-axis towards its y-axis. Damage calculated by homogeneous pipe stresses Each cross section is described by polar coordinates (R.ftg The OrcaFlex spreadsheet facility for automating script file generation can be used to generate batch script files for fatigue. Fatigue Points # Type: Fatigue BaseFile: base. The available commands are: Select. OrcaFlex calculates the damage at either the inner or outer fibre of the pipe and so R is either ODstress/2 or IDstress/2. OrcaFlex programming interface The C/C++. the batch processing code assumes that the YAML file specifies an OrcaFlex model rather than a fatigue analysis.5° intervals 0°. Delphi. Python and MATLAB programming interfaces to OrcaFlex all support automation of fatigue analysis. as described above. Each included arc length defines a cross section through the pipe. 8. For example. Damage calculated by stress factors For stress factor fatigue the radial position is implicit in the stress factors and so is not explicitly used in the calculation.ftg Load base.w Fatigue Analysis. 22. Run and NewFatigue. as specified by defining Arc Length Intervals in the Analysis Data. Mooring fatigue damage For mooring fatigue there is no need to consider radial and circumferential variation and so there is one fatigue point for each arc length considered.5 SNcurveCount = 2 SNcurveName[2] = ProjectSteel Select SNcurve ProjectSteel SNDataEnduranceLimit = 0.ftg RadialPosition[1] = Outer Run outer. then they will be equally spaced at 360°/16 = 22.0 SCF[0] = 1. Load.0 Save fatigue.0 ToArclength[1] = 30. NewFatigue DamageCalculation = "Homogeneous pipe stress" AnalysisType = Rainflow ArclengthIntervalsCount = 1 FromArclength[1] = 0.ftg Load base. For θ we calculate damage at equally spaced intervals determined by the specified Number of Thetas. As with all other functionality. 45° etc. Assignment using the Name = Value syntax is also supported. The following contrived example illustrates all these commands.ftg RadialPosition[1]: Inner Note: The comment line in the above example is needed if you are going to batch process YAML text files. Batch script The batch script facility includes a number of commands for fatigue analysis automation. Without the comment line.5°. the Python and MATLAB interfaces are the easiest to use. Damage is calculated at circumferential locations determined by the specified Number of Thetas. 8. if you specify 16 theta values. Save. is calculated. to be used in the zero mean stress S-N curve. This value is the damage value at that fatigue point due to one occurrence of that load case. Three models of mean stress effects are provided: Goodman. Note that the factor of one half is present because the rainflow algorithm counts half-cycles rather than full-cycles. The damage value corresponding to the response time history is calculated – see below for details. How Damage is Calculated The time history of response. Finally. allowing for mean stress effects. For homogeneous pipes the ZZ stress variable is used. For spectral fatigue. then the equivalent stress range S e is used. Mean stress effects Mean stress effects are handled by modifying each stress range according to a formula dependent on the mean stress level. For mooring fatigue the response variable is effective tension. For regular analysis. The calculation requires a power spectral density function (PSD) for stress. Rainflow analysis The stress time history is analysed using the rainflow cycle counting method. The above step gives the total exposure damage value from that load case at this fatigue point. N(S). The load case damage values are scaled to allow for the exposure associated with that load case.w Fatigue Analysis.Sm/SMTS) for 0 < Sm < SMTS Se = Sr for -SMTS < Sm ≤ 0 where Sr is the true stress range. Regular analysis The minimum and maximum values of stress over the last simulated wave cycle define a stress range S.Sm/SMYS) for 0 < Sm < SMYS Se = Sr for -SMYS < Sm ≤ 0 where SMYS is the yield strength as specified in the S-N data. The associated single-occurrence load case damage value is then given by D(κS) where κ is the product of the stress concentration factor and the thickness correction factor. the equivalent stress. The Goodman model is: Se = Sr / (1 . The PSD is obtained from a response calculation simulation. The Soderberg model is: Se = Sr / (1 . below which no damage occurs. in that load case. The associated single-occurrence load case damage value is then given by ½∑D(κSi) where the summation is over all the half-cycles. This calculates RAOs for stress which is then combined with the load case wave spectrum to give the PSD for stress. For rainflow analysis. Sm is the mean value of the local turning points in the stress time history. and also defines a endurance limit. These PSD are then used to calculate damage using either Dirlik's formula or the Rayleigh 466 . Spectral analysis For spectral analysis damage is calculated in the frequency domain using statistical methods. S m is defined to be the mean of the min and max stress values associated with the stress range S r. these total exposure load case damage values are summed over all load cases to obtain the overall total damage value at that fatigue point. Sm is the mean stress and SMTS is the ultimate tensile strength as specified in the SN data. Sm. Each method is defined by a formula for Se. For stress factor fatigue then the stress is calculated based on the stress factors. FL. Again. OrcaFlex uses these to calculate a damage value given by: D(S) = 1/N(S) if S > FL D(S) = 0 if S ≤ FL This damage value can be thought of as the proportion of the fatigue life that is used up by 1 cycle of stress range S. say Si where i runs from 1 to the number of stress ranges. S m is the mean of the time history used to determine the stress RAOs. Damage Calculation using S-N curves The S-N curve defines the number of cycles to failure. Soderberg and Gerber. If mean stress effects are included then the equivalent stress range Se is used. for stress range S. if mean stress effects are included. This gives a number of stress ranges for half-cycles.[Sm/SMTS]2) for -SMTS < Sm < SMTS The definition of mean stress. The Gerber model is: Se = Sr / (1 . at that fatigue point. depends on the analysis method being used. 467 . OrcaFlex merely provides a means to collate. This value is multipled by the load case exposure time to produce the damage associated with that load case. Damage Calculation for SHEAR7 fatigue SHEAR7 fatigue is rather different from the other fatigue methods because damage is calculated external to OrcaFlex by SHEAR7. thickness correction factor and mean stress effects are all accounted for in the spectral damage calculation. For detailed references on how spectral fatigue analysis calculates damage from stress PSDs please refer to: Barltrop and Adams (1991) which has an excellent section on spectral fatigue analysis. Likewise there are no analogs of stress concentration factor and thickness correction factor. As for S-N curves. Damage Calculation using T-N curves T-N curves are handled in a similar way. The SHEAR7 damage calculation is based on the damage rate output in the SHEAR7 .w Fatigue Analysis. N(T). OrcaFlex defines damage as: D(T) = 1/N(T) The summation of damage is then performed in an identical manner to that performed for S-N curves. Dirlik (1985) is the original reference for Dirlik's stress range distribution formula. A T-N curve defines the number of cycles to failure. How Damage is Calculated distribution. The stress concentration factor. sum and plot the damage from a number of different SHEAR7 load cases in a convenient manner. There is no analog of endurance limit for T-N curves. for effective tension range T.plt file. . OrcaFlex provides facilities for exporting SHEAR7 data and modes files based on an OrcaFlex model. There are separate choices for the static and dynamic analyses. First OrcaFlex sets the line's drag coefficients to those specified on the OrcaFlex line type form. In order to do this OrcaFlex must be told where to locate the executable file.pdf). They are all time domain models. Typically the lift file will be the standard one supplied with SHEAR7. VIVA can be run manually with these files as input. and so are not limited to steady state conditions.1 FREQUENCY DOMAIN MODELS 9. and other results calculated by SHEAR7.1 SHEAR7 SHEAR7 is a frequency domain VIV prediction program developed by Prof. Frequency Domain Models VIV ANALYSIS OrcaFlex offers a variety of modelling options for the analysis of vortex induced vibration (VIV) of lines. OrcaFlex can create VIVA data and modes files based on an OrcaFlex model. SHEAR7 lift file location The SHEAR7 interface operates by executing the SHEAR7 executable file. The link to SHEAR7 is based around OrcaFlex's ability to export SHEAR7 data files (. They are both independent non-Orcina programs written and distributed by other companies. or called directly from OrcaFlex. Please contact AMOG for details. Note: SHEAR7 must be licensed separately to OrcaFlex. You must also specify extra data. Again. Of all these models. A separate user guide for the time domain VIV models is available (Time Domain VIV Models. 2. OrcaFlex then calls SHEAR7 to analyse VIV for that position and the line drag coefficients are updated. The VIV modelling features have been developed in cooperation with academics in the UK and USA.w 9 VIV Analysis. 469 . so to use them you need to purchase and install them on your machine. SHEAR7 will then be executed when you perform the OrcaFlex static analysis. These data are specified on the SHEAR7 data form and is only available when SHEAR7 is selected for the statics VIV option on the VIV page of the line data form. The other models are built in to OrcaFlex so no further software is needed. The frequency domain models are only applicable to the static analysis and the time domain models are only applicable to the dynamic analysis. Using VIV Models You choose which VIV model to use (if any) on the VIV page on the line data form. Two vortex tracking models. usually called common. VIVA. OrcaFlex SHEAR7 Interface To use SHEAR7 for VIV analysis of a line.cl. on the line data form and on the SHEAR7 data form. 3. are available in OrcaFlex – see Results Output below.cl in the same directory as the executable file. 9. If the lift file location is left blank OrcaFlex attempts to use a file called common. K Vandiver at MIT and distributed by AMOG. specific to SHEAR7. These SHEAR7 drag coefficients. and the drag coefficients predicted by SHEAR7 will be used instead of the user-specified drag coefficients from the line type form. including both frequency domain and time domain approaches.dat) and SHEAR7 modes files (. Available VIV Models OrcaFlex provides facilities for using the following different VIV models: SHEAR7. They are both frequency domain models. or executed directly from OrcaFlex. SHEAR7 executable file location. SHEAR7 can then be run manually using these files as input. SHEAR7 coupling method The SHEAR7 interface performs a coupled statics calculation since the SHEAR7 analysis depends on the position of the line and vice versa. SHEAR7 and VIVA are the two main programs in current use in the industry. so they only analyse steady state conditions. Two wake oscillator models: the Milan model and the Iwan and Blevins model. In addition SHEAR7 requires a file to specify lift coefficients. These file locations can be specified as either full paths or as paths relative to the directory containing the OrcaFlex file. OrcaFlex then calculates the static position of the line using those drag coefficients. The coupled static analysis is done as follows: 1.1. set the line's Statics VIV data item to SHEAR7.mds). However. or from Distributed OrcaFlex. The partially coupled approaches are more akin to running SHEAR7 manually. The specified lift file is copied to the temporary directory and renamed as common. 3. A SHEAR7 .mds file must be generated separately which is normally done either from the modal analysis form or using batch script.mds. 470 . Steps 3 and 4 are then repeated until the static position has converged.mds file is created in the temporary directory and called common. 6. especially for more complex models. 2.dat file is generated in the temporary directory. A temporary directory is created to contain the SHEAR7 input and output files. The partial. user modes file coupling option.mds file at each coupling iteration can be time consuming.mds file. A value of '~' for the first mode is interpreted as the lowest numbered transverse mode.cl. The SHEAR7 executable is run and the SHEAR7 output files are read by OrcaFlex.mds file The location of the . the ultimate static solution will differ because it does include the effect of drag enhancement. The . OrcaFlex then recalculates the static position of the line for those new drag coefficients. Frequency Domain Models 4. When running SHEAR7 manually the only way to account for drag enhancement is to manually modify drag coefficients in the OrcaFlex model which is extremely impractical.mds file. The SHEAR7 .mds file on the first coupling iteration which is then used in all subsequent coupling iterations. SHEAR7 . A value of '~' for the last mode is interpreted as the highest numbered transverse mode. These data items are interpreted in exactly the same way as the FirstMode and LastMode parameters to the SHEAR7MdsFile batch script command.mds file to be passed to SHEAR7. These data are not required if you select the partial. user modes file coupling option. The output files are automatically exported if you run the static analysis in batch mode. Results output When OrcaFlex calls SHEAR7 it captures output files and includes them in the Full Results tables for the Line. This value is only required if you select the partial. The SHEAR7 interface offers a variety of coupling options which differ in how they handle the SHEAR7 . By transverse we mean that the modal analysis classifies the mode as either Transverse or Mostly Transverse. that is every time SHEAR7 is called.mds file is created is determined by the chosen coupling option as described above. 5. 4. The iteration is deemed to have converged when none of the nodes has changed position (compared with the previous iteration) by more than Convergence Tolerance * NodeLength. The files are exported with file names based on the model file name and the line name. where NodeLength is the length of line represented by that node. user modes file coupling option uses an .plt file is parsed by OrcaFlex to find the drag enhancements factors Cf. 5.mds file at each coupling iteration. These output files can also be exported from the SHEAR7 data form and by using the SHEAR7OutputFile batch script command. How this . The . The location can be specified as either a full path or as a path relative to the directory containing the OrcaFlex file. The enhanced drag coefficients can be obtained from a static state range graph of x-Drag Coefficient (or indeed yDrag Coefficient which is identical). The partial. The method usually requires only 2 or 3 coupling iterations to converge.w VIV Analysis. and so the partially coupled approach can be significantly faster. automatic modes file coupling option creates an . The full coupling option generates a new . The fully coupled approach does have the disadvantage that generating an .mds file specified on the data form for all coupling iterations. First and last modes These data items specify which modes are to be included in the . Technical details The SHEAR7 interface operates by calling the SHEAR7 executable directly as follows: 1. Bending Stress Curvature Load Factor (SHEAR7 version 4. Reduced Velocity Bandwidths For SHEAR7 version 4.dmg . Output summary Locations These data specify the locations at which a summary of the response is given in the SHEAR7 . SHEAR7 data The majority of the information in a SHEAR7 data file can be derived from the data for an OrcaFlex Line. Include SHEAR7 data in text data file By default the SHEAR7 data are not included in text data files saved by OrcaFlex.plt file do not correspond to the node locations in the OrcaFlex model.3/4. Out file selection (SHEAR7 version 4.6 and later) Specifies which out files (. Exporting from Batch Script The SHEAR7 data file can be exported from an OrcaFlex batch script using the SHEAR7DataFile command. Output options (SHEAR7 version 4. We cannot guarantee that other versions of SHEAR7 will be compatible with the SHEAR7 interface. run SHEAR7.5 you specify just a single value for reduced velocity bandwidth. This is done from the SHEAR7 data form which can be opened from the Model Browser. .5 and later. there are a number of other values which SHEAR7 needs and these are documented below. However. . Structural Damping Ratio Corresponds to the SHEAR7 data item of the same name.out. This value specifies which version of the data file is produced by OrcaFlex. This can occur if the discretisation of a user-supplied . If this value is set to '~' Shear7 will use its own internally calculated values. Mostly these values are given the same name as used by SHEAR7.4 you specify the single-mode and multi-mode reduced velocity bandwidth. A more convenient way to work is to use the SHEAR7 interface which can automatically save the required SHEAR7 input files. A value of '~' can be used for the Arc Length Range Start to mean 'End A'.6 and later you specify a value for reduced velocity bandwidth for each section. extract drag amplification factors and perform a coupled static analysis.out1. We have developed and tested the SHEAR7 interface with the SHEAR7 versions listed on the SHEAR7 data form. . 471 . SHEAR7 data file To export a SHEAR7 data files you must first provide extra data that SHEAR7 requires but which is not needed by OrcaFlex. Likewise.7 and later) Corresponds to the SHEAR7 data item of the same name.7 or later) The options control whether or not SHEAR7 is instructed to output . For SHEAR7 version 4. SHEAR7 File Version Different versions of SHEAR7 use slightly different data file formats. Line Specifies the OrcaFlex Line to be described in the SHEAR7 data file.w VIV Analysis.fat and . You can check this option to override that default and ensure that SHEAR7 data are included in text data files. OrcaFlex uses linear interpolation of the C f values if the locations read from the . For SHEAR7 version 4.anm. If you are using the SHEAR7 interface then the SHEAR7 data are always included in text data files irrespective of this setting.out2) are generated. a value of '~' for Arc Length Range End means 'End B'. Frequency Domain Models This process depends very heavily on the current implementation details of SHEAR7. When you have input all the necessary data on the SHEAR7 data form you create the SHEAR7 data file by clicking on the Export SHEAR7 Data File button.out file. Note that your model must include at least one Line for the SHEAR7 data form to be available. . For full details on how they are used please refer to the SHEAR7 documentation.str files require version 4. The model must be in Statics Complete state when you export the SHEAR7 data file but please note that data on the SHEAR7 data form is editable while in this state.mds file differs from that of the OrcaFlex model.str files. You also specify the probability of occurrence (a number between 0 and 1) of the flow profile and the flow profile ID. For earlier SHEAR7 versions you specify a single global value. S-N Curves Specifies the S-N curves to be used by SHEAR7 for its fatigue calculations.7 and later) Specifies the type of VIV response to analyse.cl file. Lift Coefficient Factor corresponds to the SHEAR7 data item called Lift Coefficient Reduction Factor.3/4. 472 . This allows for hydrodynamic damping. low and high reduced velocity are specified. but excludes any excitation due to current. VIV Diameter The VIV diameter specifies the diameter used by the VIV model. either transverse or inline. Strouhal Type can be Rough Cylinder or User Specified. Young's Modulus Young's modulus for the strength member. For a node at the intersection of two sections the VIV diameter of the following section is used.5 and later) Corresponds to the SHEAR7 data item of the same name. Lift Coefficient Table. If User Specified is chosen then you must also specify a Strouhal Number. Reduced Velocity Damping Coefficients Damping Coefficients for still water. Separate values can be specified for each section. which is taken to mean 'same as the section normal drag diameter'.6 you specify this value per section.6 you can define multiple S-N curves each with an endurance limit and then select which one to use on a section by section basis. The VIV Diameter can be set to '~'. The value specified is used for all nodes in that section. Lift Coefficient Factor Lift Coefficient Table specifies which table is used from the common.5 and later) Corresponds to the SHEAR7 data item of the same name. Rough Cylinder corresponds to the SHEAR7 Strouhal code 200. In SHEAR7 version 4.cl file. An endurance limit can be specified – this is called the "cutoff stress range" in the SHEAR7 documentation. Power Ratio exponent (SHEAR7 version 4. Number of Lift Coefficient Tables (SHEAR7 version 4. You can specify that the current profile contains one entry for each node in the line. Primary zone amplitude limit (SHEAR7 version 4.4 and earlier this data item was named cutoff level. The current speed is exported as zero for any part of the line which uses a P-y model.w VIV Analysis. Frequency Domain Models Power Ratio Cutoff Level Corresponds to the SHEAR7 data item of the same name. Current Profile The discretisation option allows you to control how the current profile is output. For SHEAR7 version 4. Stress Concentration Factors Specify a global stress concentration factor for the line and optionally a number of local stress concentration factors. However this can give rise to numerical problems in SHEAR7. For SHEAR7 version 4. For earlier SHEAR7 versions you specify a single S-N Curve and endurance limit which apply to the entire line. SHEAR7 uses this for computing stress and damage rate. Strouhal Number The Strouhal type and number defines the relationship of flow velocity and cylinder diameter to the local vortex shedding frequency. Response (SHEAR7 version 4.7 and later) Corresponds to the SHEAR7 data item of the same name. Strouhal Type. Fatigue Calculation Method (SHEAR7 version 4. using the still water coefficient. especially for finely segmented models.4 only) This is the number of tables you want SHEAR7 to read from the common. and so it is preferable to discretise the current more coarsely using the regular spacing option. You must include calculation of the mode shapes and include all modes that might to be needed by SHEAR7.g. axial. Essentially.w VIV Analysis. inline (i. anywhere on your line where you need SHEAR7 structural zone data to change you must ensure that there is an OrcaFlex section boundary. The mass per unit length is also used by SHEAR7 to calculate modal frequencies and again this aspect of the SHEAR7 calculation would be bypassed when using a modes file produced by OrcaFlex. See Values Exported for details. The simplest way to do this is to use the built-in facility to export SHEAR7 data files. Use the Export SHEAR7 Mds File button. This has some implications for how you create your OrcaFlex model. the mass per unit length is used by SHEAR7 to compute damping ratio. The other modelling choice in OrcaFlex that leads to properties varying along the length of a section is when profiled line types (e. See Mode Selection Table below for details. in the VIV direction). Select the VIV page. Area moment of inertia. Although it may be tempting to use many structural zones to represent the variation of properties the SHEAR7 manual strongly recommends not doing so. A freeflooding line has greater mass below the water surface because it is full of water. in its place OrcaFlex outputs zero.Mds file is generated for those modes that are currently ticked for export.e. Accordingly OrcaFlex outputs a single structural zone for a profiled line type section which has the effect of smearing properties and we believe that this is the correct approach to take in the vast majority of cases. You are asked where to save the file. Since most of these properties are constant within an OrcaFlex section you will naturally introduce section boundaries at the locations where they change. Frequency Domain Models SHEAR7 structural zones When OrcaFlex generates the SHEAR7 data file it assumes a one-to-one mapping between OrcaFlex sections and SHEAR7 structural zones. lift coefficient and Strouhal number. SHEAR7 structural zone data comprises the following: Hydrodynamic and strength diameters. However. This helps you decide which modes to export to SHEAR7. the VIV page reports the extent to which the mode is transverse (i. The final column of the table shows which modes are currently selected to be exported to the . Typically these parameters would not be used since OrcaFlex produces a modes file which is more accurate than the internal SHEAR7 modal calculations. Added mass coefficient. For almost all situations in OrcaFlex the mass per unit length is constant along a section. but you can then change the selection as required. 473 . Quite often this issue is of little significance but if you wish you can also change your OrcaFlex model to arrange that there is a section boundary at the water surface.Mds file. Calculate the static position of the model. SHEAR7 Mds file The SHEAR7 Mds file export facility is provided on the Modal Analysis form. A SHEAR7 . Do the modal analysis for the line you want to analyse. Warning: OrcaFlex does not calculate the mode slope. Similar issues arise when the slug flow contents method is specified.e. stress joints) are used. Hydrodynamic damping coefficients. Exporting from Batch Script The SHEAR7 Mds file can be exported from an OrcaFlex batch script using the SHEAR7MdsFile command. or some mixture. On the Results menu select the Modal Analysis. Lift coefficient. Whenever you calculate the modes OrcaFlex ticks just the Transverse and Mostly Transverse modes. To use it: You will need to create a SHEAR7 data file. in the normal drag direction). You may need to introduce OrcaFlex section boundaries which coincide with the locations where these properties change. Because SHEAR7 has a single mass parameter for a structural zone this means that the mass is effectively smeared across the zone. For each mode. See Values Exported for details. One exception to this is a free-flooding line with sections that cross the water surface. However. Strouhal number and hydrodynamic damping coefficients are SHEAR7 specific data which are specified in OrcaFlex on the Section Data page of the SHEAR7 data form. there are a few exceptions. mass per unit length and tension variation. Area moment of inertia and tension variation are used by SHEAR7 to calculate modal frequencies. This rate of change (a vector) equals the change in curvature vector at the node caused by applying the mode offsets V to all the nodes and then dividing by m. for the mean position (this is a vector in the direction normal to the plane of curvature). VL = lateral component vector of V. Then follows a section giving the angular frequencies of the selected modes. 474 . When you calculate (or recalculate) the modes OrcaFlex ticks just the Transverse and Mostly Transverse modes. transverse and axial component vectors. since in this zone SHEAR7 assumes that the mode offset is in the direction of VIV excitation. Mode Type classifies each mode according to the offset distribution. These are calculated as follows. The mode slope is only used in SHEAR7 to correct the predicted RMS acceleration for a vertical riser. The OrcaFlex modal analysis is fully 3D. but you can then change the selection as required.|dC/dm| The reasoning behind these formulae is as follows: SHEAR7 assumes that the exported mode offset is in the transverse direction. giving the Mode Offset. Let: V = the mode shape vector calculated by OrcaFlex at a given node. The table includes the following columns: Offset Distribution displays a measure of how inline. OrcaFlex should therefore ideally export the transverse component of mode offset for the power-in zone and the lateral offset for the power-out zone. Mixed means that none of the components are more than 50% of the total. m = maximum value of |VL| for any node. Then the scalar Mode Offset and Mode Curvature values exported by OrcaFlex to the Mds file are Mode Offset = Sign(Vt). See Discussion and Examples. OrcaFlex therefore provides the mode selection table to help you decide which modes should be exported to SHEAR7. Mode Slope and Mode Curvature. in radians per second. The RMS acceleration is listed in the SHEAR7 . For details see Offset Distribution.e. This assumption applies to the power-in zone. so you will sometimes have to export the modes that are nearest to being transverse.Mds file are purely in that transverse direction.Mds file contains the number of selected modes and the number of nodes in the line. However OrcaFlex does not know the power-in and power-out zones.w VIV Analysis. Values Exported The first line in the .|VL| / m Mode Curvature = Sign(inline component of dC/dm). See the SHEAR7 documentation for details. respectively. This correctly removes the axial component. given by VL = Vi + Vt (vector sum). so in principle you should therefore only export modes that are purely transverse. transverse and axial the mode is. in the special case where one is trying to model the gravitational contamination from tilt that a transversely mounted accelerometer would measure. Warning: OrcaFlex does not calculate the mode slope. C = curvature vector at the node. inline and axial directions.plt plotting files. Mostly Transverse means that it is between 50% and 90%. Frequency Domain Models Mode Selection Table VIV excitation occurs in the transverse direction. However SHEAR7's power-out calculation will still be valid providing the mode offset is lateral (i. in its place OrcaFlex outputs zero. Mostly Inline. Transverse means that the transverse component is more than 90% of the total. so it therefore outputs the lateral offset (suitably signed and normalised) throughout. no axial component). Axial and Mostly Axial. Export to SHEAR7 Mds File determines which modes will be exported to SHEAR7. since they are calculated inside SHEAR7. dC/dm = linear rate of change of C per unit maximum lateral mode offset. Finally there follows a section for each selected mode. In SHEAR7 mode shapes are 1D since it assumes that all the modes in the . In practice the natural modes do not always neatly divide into the transverse. Exported Mode Offset and Mode Curvature The OrcaFlex modal analysis gives vector values. but SHEAR7 requires scalar values. Vi Vt and Va = V's inline. since fluid drag and damping occur in any lateral direction. and if there is no inline component then no error is introduced. and similarly for Inline. The lowest in-plane mode is typically the in-plane fundamental 'swinging' mode. i. Oblique Current If the current is at 10°. the exported values are signed and normalised as specified by SHEAR7. so for a general line configuration a mode can be a mixture of axial (i. U-shape Catenary.e. This defines a vertical plane for the static position. say. It therefore varies along the line and so the transverse modes are some. Out-of-plane Current For this case the transverse direction is in-plane and normal to the line axis. with the wavelength decreasing as the frequency increases. Here in-plane and out-of-plane refers to the vertical plane of the catenary in which the line is hanging. due to the typically high axial stiffness of a line. None of the modes will be purely in this direction. 475 . in which the nodes oscillate in the axial direction. In the parts of the line that are nearly vertical this mode is transverse. the Mode Offset value has maximum magnitude 1 and the Mode Curvature is the change in curvature caused by applying the mode with that magnitude. rather than just its transverse component. i. so again it is clear cut as to which modes to export to SHEAR7. SHEAR7 will assume that each exported mode is purely transverse. causing alternating tension and compression in the line. bending) motion. These are predominantly in the transverse direction and so are suitable for export to SHEAR7. in-plane bending modes and out-of-plane bending modes. Warning: In such cases it is important that only one of the pair is exported to SHEAR7 – the one that is nearest to being in the transverse direction. but the out-of-plane modes are nearest to this direction.w VIV Analysis. However for many configurations the modes broadly fall into one of three categories – tensile modes. however. In-plane Current For this case the transverse direction is the out-of-plane direction. In practice. and OrcaFlex selects these for you. since SHEAR7 will assume that the lateral offset is in fact transverse.e. Frequency Domain Models For a mode that has some inline components there will be an error introduced in the power-in calculation. and the transverse direction is normal to this plane. In this case the bending modes appear as a series of twins. Most of the remaining in-plane modes are bending modes in which the nodes oscillate laterally. to the plane of the catenary. so it is appropriate to export the whole of the dynamic curvature (dC). Such stresses occur due to both transverse and inline oscillations. Finally. so the approximation is less of a problem. of the in-plane modes. so it should be conservative. Discussion and Examples The OrcaFlex modal analysis is fully 3D. the current will make the riser bow out slightly in the current direction. However there are also some tensile in-plane modes present. tensile) and lateral (i. These typically have virtually 100% of their power in the transverse direction. That is. so an approximation is involved.e. This error is equivalent to rotating the VIV excitation to be in the lateral mode offset direction. so the transverse modes are the out-of-plane modes. This mode is therefore often displayed as Mostly Transverse. These tend to be in amongst the higher frequency modes. Vertical Riser For an exactly straight vertical riser there is no unique such vertical plane. OrcaFlex removes the axial components of the modes when exporting to SHEAR7 (see Values Exported) so it is reasonable to export this mode. but not all. The natural modes typically divide neatly into modes that are virtually 100% transverse (the out-of-plane lateral modes). but in orthogonal directions. so they are the best ones to choose. pairs of modes with identical (or near identical) amplitude and frequency. U-shape Catenary. whereas the remaining modes have very little power in the transverse direction.e. then the transverse direction is at 80° to the plane. The approximation is worst for the low modes. the transverse modes. but near the bottom of the U the motion is near axial. For the higher modes the out-of-plane modes and the in-plane lateral modes tend to have quite similar frequencies and shapes. inline (the in-plane lateral modes) or axial (the tensile modes). This approximation gets worse as the angle of the current to the plane increases up to 45°. It is therefore clear cut as to which modes to export to SHEAR7. The mode curvature values are used in SHEAR7 to calculate the dynamic bending stresses that are induced when the mode is excited. U-shape Catenary. M Triantafyllou at MIT and distributed by JD Marine (formerly DTCEL). OrcaFlex then calls VIVA to analyse VIV for that position and the line drag coefficients are updated to those calculated by VIVA for the specified Target Mode. As part of the project. 476 . These VIVA drag coefficients. Note: VIVA must be licensed separately to OrcaFlex. Unfortunately. VIVA will then be executed when you perform the OrcaFlex static analysis. Orcina was a participating member of a Joint Industry Project. and on the VIVA data form. set the line's Statics VIV data item to VIVA. automatic modes file coupling option creates a modes files on the first coupling iteration which is then used in all subsequent coupling iterations. OrcaFlex then calls VIVA which carries out a frequency domain calculation of VIV response based on an energy balance. where NodeLength is the length of line represented by that node. However. Results include amplitudes of vibration. All development and testing of the OrcaFlex side of the interface has been performed with a beta release of VIVA. started in 2000 and run by DTCEL and Prof.w VIV Analysis. First OrcaFlex sets the line's drag coefficients to those specified on the OrcaFlex line type form. Please contact JD Marine to obtain a version of VIVA compatible with this version of OrcaFlex. VIVA coupling method The VIVA interface offers a variety of coupling options which differ in how they handle the modes files. When running VIVA manually the only way to account for drag enhancement is to manually modify drag coefficients in the OrcaFlex model which is extremely impractical. Triantafyllou of MIT. 5. You must also specify extra data. 3. OrcaFlex then calculates the static position of the line using those drag coefficients. The full coupling option generates new modes files at each coupling iteration. The software link allows a riser model to be built in OrcaFlex taking advantage of the existing interactive user interface. and so the partially coupled approach can be significantly faster. the ultimate static solution will differ because it does include the effect of drag enhancement. A combined multi-mode response is also reported. The partially coupled approaches are more akin to running VIVA manually. at the time of writing. The coupled static analysis is done as follows: 1. Please contact JD Marine for details. the version of VIVA that OrcaFlex requires has not been released. and the drag coefficients predicted by VIVA (for the specified Target Mode) will be used instead of the user-specified drag coefficients from the line type form. The drag coefficients can be used by OrcaFlex to carry out a coupled steady-state VIV analysis. OrcaFlex VIVA Interface The OrcaFlex interface to VIVA requires that VIVA is installed on your machine. 4. are available in OrcaFlex – see VIVA Results. The iteration is deemed to have converged when none of the nodes has changed position (compared with the previous iteration) by more than Convergence Tolerance * NodeLength. OrcaFlex then recalculates the static position of the line for those new drag coefficients. The fully coupled approach does have the disadvantage that generating modes files at each coupling iteration can be time consuming. mean effective drag coefficients and fatigue life. especially for more complex models. and other results calculated by VIVA. The partial. The method usually requires only 2 or 3 coupling iterations to converge. that is every time VIVA is called.1. To use VIVA for VIV analysis of a line. The partial. A coupled statics calculation is performed since VIVA's analysis depends on the position of the line and vice versa.2 VIVA VIVA is a frequency domain VIV prediction program developed by Prof. 2. Frequency Domain Models 9. specific to VIVA. a software link has been written between OrcaFlex and VIVA. Calculation procedure When Statics VIV is set to VIVA. OrcaFlex calculates the static position of the line using the drag coefficients calculated by VIVA. Results are reported in spreadsheet form for each single excited mode of vibration. user modes file coupling option uses modes files specified on the data form for all coupling iterations. These data are specified on the line data form. Steps 3 and 4 are then repeated until the static position has converged. in. If you are using the coupled VIVA interface. Results output When OrcaFlex calls VIVA it captures output files. that is if Statics VIV is set to VIVA. That is: No_Files. or from Distributed OrcaFlex. These hydrodynamic database files must all be in the same directory as the VIVA executable. VIVA input files are generated in the temporary directory. This file location can be specified as either a full path to the viva. The specified VIVA executable file is copied to the temporary directory. First you make a copy of the VIVA executable in a new directory.exe. The last three input files define the mode frequencies. This value is only required if you select the partial. The files are exported with file names based on the model file name and the line name. The VIVA executable is run and the VIVA output files are read by OrcaFlex. 2.in. user modes file coupling option. The output files are automatically exported if you run the static analysis in batch mode. viva. Free. then the VIVA data are always included in text data files irrespective of this setting. These input files are dyn-n. conditions. MATLAB etc.in. How these modes files are created is determined by the chosen coupling option as described above. VIVA Modes Files Directory The location of the modes files to be passed to VIVA. These data are not required if you select the partial. of the information in these output files is included in the Full Results tables for the Line. freq.in. OrcaFlex uses linear interpolation of the C f values if the locations read from the output files do not correspond to the node locations in the OrcaFlex model. although doing so is a little convoluted. They are described below and appear on either the VIV page of the line data form or the VIVA data form.in and curv_us. Next you place your non-standard hydrodynamic database files alongside this copy of the executable file. It is possible to specify a non-standard set of hydrodynamic database files. 5. VIVA Executable Location The VIVA interface operates by executing the VIVA executable file. Frequency Domain Models First and last modes These data items specify which modes are to be included in the modes files and are interpreted in exactly the same way as the analogous SHEAR7 data items. The output files are parsed by OrcaFlex to find the drag enhancements factors C f. 6. A temporary directory is created to contain the VIVA input and output files.in.in. modes_us.dat.in and all the files specified in No_Files. The majority of the data are found on the VIVA data form and exceptions to that are indicated in the documentation below. You can check this option to override that default and ensure that VIVA data are included in text data files. Technical details The VIVA interface operates by calling the VIVA executable directly as follows: 1. The modes files must be generated separately which is normally done from the modal analysis form. shapes and curvatures. but not all.w VIV Analysis. 477 . These output files can also be exported from the VIVA data form or via one of the OrcaFlex automation interfaces using Python. these hydrodynamic database files will be used. or as a path relative to the directory containing the OrcaFlex file. 3. Because OrcaFlex copies hydrodynamic database files from the same directory as contains the executable file. Model-wide Properties Include VIVA data in text data file By default the VIVA data are not included in text data files saved by OrcaFlex. This can occur if the discretisation of the line is non-uniform. VIVA Data The VIVA data are the data that VIVA needs and which OrcaFlex cannot deduce automatically from the ordinary OrcaFlex data. or if the user specifies a Number of Points (NP) different from the number of nodes in the OrcaFlex model. 4. 7. Forced. The location can be specified as either a full path or as a path relative to the directory containing the OrcaFlex file. In order to do this OrcaFlex must be told where to locate the executable file. The hydrodynamic database files are copied to the temporary directory.in. risfat.exe file. Some. The enhanced drag coefficients can be obtained from a static state range graph of x-Drag Coefficient (or indeed yDrag Coefficient which is identical). user modes file coupling option. Frequency Domain Models Whole Line Properties Convergence Tolerance (line data form) Specifies the tolerance used in the coupled statics iteration. Section-Specific Properties For each section of the line. Either Modal or Constant. You can choose either to use the relative velocity. When this occurs. Use Relative Fluid Velocity VIVA needs to know the flow velocity at each point along the line. Number of Points (NP) VIVA requires an equally spaced discretisation of the line. Interpolation will be used if the OrcaFlex line is not uniformly segmented. Fatigue The S-N data. or if the number of nodes in the line differs from NP. Section Type The VIVA section type can be one of the following options: Smooth: No further VIVA section data are needed. where it is referred to as ZETA. Or it can be set to '~'. Strake (General): You must also specify the height to diameter ratio for the strakes. Target Mode (line data form) VIVA predicts which modes of oscillation might be excited and it gives separate VIV results for each possible excited mode. or else use only the fluid velocity. You must specify which set of VIVA Cd results to use. Damping Type The VIVA damping type data. VIVA detects that the discretisation may be inadequate. For details see the VIVA documentation. Transverse Damping Ratio The structural damping ratio that VIVA should use. you must specify the VIVA section type and its properties. including the velocity of the line. based on the type of response you expect. The value specified is used for all nodes in that section. We recommend that the relative velocity should be used. It is a single value that applies to the whole line. The data supplied to VIVA will contain NP equally spaced points covering the line. response that is a mixture of the possible modes. The OrcaFlex line type and length of the sections are displayed for information.e. by setting the Target Mode data item. 478 . Since VIVA is only called from the OrcaFlex static analysis. Staggered buoyancy/bare: No further VIVA section data are needed. h/D=0. where it is referred to as G_M. Strake (P/D=17. The Target Mode can be set to a mode number. OrcaFlex may need to use interpolation to produce the VIVA input data. For a node at the intersection of two sections the VIV diameter of the following section is used. If you set the Target Mode to a mode number that VIVA does not predict will be excited then OrcaFlex will report a warning and use the line type Cd values. For details see the VIVA documentation. ignoring any velocity of the line.2): No further VIVA section data are needed. For some input files. meaning use the single mode results for that mode number. OrcaFlex will report a warning which can usually be resolved by increasing the value of NP.w VIV Analysis. The S-N curve is specified in the standard OrcaFlex way using the following formulation: N = a S-m The data supplied on the data form are the values of log10(a) and m. VIV Diameter The VIV diameter specifies the diameter used by the VIV model. Fairing: You must also specify the chord length and thickness of the fairing. but they are not editable (to edit them see the Structure page on the OrcaFlex line data form). Separate values can be specified for each section. this data item only has any effect if the model starting velocity is nonzero. since it is the total relative velocity that generates vortices. meaning use the multi-mode results. which is taken to mean 'same as the section normal drag diameter'. In addition it gives VIV results for multi-mode response. The VIV Diameter can be set to '~'. and stress concentration factor used by VIVA's fatigue calculations. i. Drag Coefficient The predicted drag coefficient. These are results predicted by VIVA if single-mode VIV response occurs in that mode. two being wake oscillator models and two being vortex tracking models. For details see the VIVA documentation. and the equally spaced discretisation used by VIVA must be sufficient to capture the modes that are important to the VIVA analysis. VIVA Modes Files The VIVA input files that are exported from OrcaFlex specify that transverse mode frequencies. There is a separate worksheet for each excited mode. The second table is the multi-mode equivalent of the single mode results table.2 TIME DOMAIN MODELS There are four time domain models. Vetco 30 deg. shapes and curvatures are supplied in files freq.in. That is there are NP equally spaced results points. as calculated by VIVA. Max Amplitude The largest offset of any node in this mode. These files are created by an OrcaFlex modal analysis. They include: Max Amplitude The amplitude of predicted VIV motion at that point. For details of these VIVA data see the VIVA documentation. Single Mode Results The worksheet for a given single excited mode gives a table of Single Mode results as a function of arc length along the line. The drag coefficients currently in use are those corresponding to the specified Target Mode. Life The predicted fatigue life. it gives the same information. i. Time Domain Models Vetco 0 deg. The procedure for selecting transverse modes is identical to that used for SHEAR7. The table is given in the discretisation used by VIVA. Max Stress The dynamic bend moment and stress amplitudes due to VIV. Note that they do not include the bend moment and stress due to the mean position of the line.in.in and curv_us. VIVA Results The VIVA results are presented in OrcaFlex as extra worksheets in the Full Results tables. It has the following columns: Mode Number The mode number Natural Mode Frequency With and Without VIV These columns give the natural frequencies of the mode. The VIVA results are described briefly below. Whereas in those With VIV the VIVA default added mass coefficients have been modified to allow for VIV. The first table summarises the bending modes that VIVA predicts as being excited. In order for the calculation to be accurate both the OrcaFlex model discretisation. 9. but this time for the case where multi-mode VIV response occurs. Vetco 60 deg. Other sources of fatigue need to be accounted for separately. The worksheets give the results from the latest VIVA call. Max Bend Moment.w VIV Analysis. Multi-Mode Results The Multi-Mode worksheet gives two tables. plus an extra worksheet for the multi-mode response. allowing for VIV. Vetco 120 deg or Vetco 150 deg: No further VIVA section data are needed. Note that this value only accounts for the fatigue due to VIV. Those Without VIV are calculated using VIVA's own default added mass coefficients (not those specified in the OrcaFlex line type data). the mode shapes and curvatures files may be interpolated from the original OrcaFlex modes which reflect the OrcaFlex model discretisation. modes_us. Because VIVA requires an equally spaced discretisation of the line.e. Note: Amplitudes in VIVA results are single amplitudes. 479 . Vetco 90 deg. measured from the mean position to the peak. This discretisation of the data supplied to VIVA is determined by the number of points (NP) specified on the VIVA data form. Vortex Tracking (2) Model The outer time step sets the time step used by the vortex tracking model. the 'non-VIV node position' is used as the mean position for the Milan oscillator. The data described below are common to all the time domain models. during the build-up stage of the simulation.w VIV Analysis. the fraction to use depending on which model is being used. For the Milan wake oscillator only. The node velocity vector is filtered and the resulting 'non-VIV' velocity is subtracted from the fluid velocity to obtain a 'non-VIV' relative velocity vector. The Strouhal Period (Ts) is defined as D/(S*V) where D is line diameter. For example. so the outer time step does not usually have much effect on the simulation speed. we recommend that the outer time step is set to approximately 1/100th or 1/200th of the Strouhal period. without letting the VIV motion feed back into the velocity input into the wake oscillator model. Then. 480 . Based on our experience so far. The calculations done in this variable time step are typically much more time-consuming than the other calculations in the simulation. but if it is too small then a lot of vortices must be tracked and this significantly slows the model. Assuming a Strouhal number of 0. Note: This ramping is only applied for the components of vortex force which are calculated by the VIV model. this filtering is needed with the wake oscillator models in order to allow non-VIV motion of the node to contribute to VIV. The node position vector is also filtered and the resulting 'non-VIV node position' is used when calculating the Transverse VIV Offset. so that the line has a chance to quickly react to changes in fluid force. but the inline component of force is calculated using the standard Morison drag formulation. So. it is important that the outer time step (on the General Data form) is set to a value that is small compared with the Strouhal Period. The outer time step needs to be set to a fraction of this Strouhal period. as follows. with this filter cut-off period. the ramping is done for the transverse component of force. for the wake oscillators. Outer Time Step For all the time domain models. Data for the Whole Line Filter Period OrcaFlex uses a digital filter. We therefore recommend that the outer time step is set to a very small value. Note: The automated recommended time step feature in OrcaFlex implements the above recommendation for the Wake oscillator models but does not implement the recommendations for the Vortex Tracking models. Then: For the wake oscillator models. Vortex Tracking (1) Model The outer time step determines how often the fluid forces on the line are updated. and also determines how often the fluid forces on the line are updated. For all the time domain models. It should be small enough to discretise the VIV. the inline and transverse directions are based on the 'non-VIV' relative velocity vector. so it does not take into account changes in Strouhal period during the simulation. then the Strouhal period is given by 5D/V where D is the line diameter and V is the relative flow velocity. Time Domain Models With all the time domain models. The model performs its calculations using a variable time step. S is Strouhal number and V is the normal component of relative flow velocity.2. For example. Wake oscillator models The wake oscillator calculations are done every outer time step and experience so far suggests that the integration of the wake oscillator loses accuracy if this time step is greater than about 1/200th of the Strouhal period. the normal component of this 'non-VIV' relative velocity vector is used as the velocity input to the wake oscillator model. Here is more detail. the vortex force applied in the static analysis is the standard Morison drag force. to separate the mean motion of the node from the VIV motion. Note that this check is against the Strouhal period for the flow velocity that applies in the static analysis. preferably a lot less than the variable time step. the wake oscillator models only provide transverse vortex force. the ramping function is used to smoothly change to the vortex force given by the VIV model. At the start of the simulation OrcaFlex checks and warns if the outer time step exceeds this limit at any node on lines that use a wake oscillator. The value specified is used for all nodes in that section. the filter period can be set to a large value that is at least 10 times the period of any expected VIV.g.2 1 0. the filter period should be set to be significantly above. Its response is shown in the following graphs. The VIV Diameter can be set to '~'. again preferably by a factor of 10 or more. not by line motion. Separate values can be specified for each section. which isn't desirable since it allows VIV motion to feed back into the wake oscillator models and into the definitions of the inline and transverse directions. For cases where line motion contributes to VIV it might be harder to achieve the above recommended factors of 10. Filter RAO Amplitude 1. At the other extreme. since otherwise that starting position might not be a sensible mean position for the Milan wake oscillator model to use. in which case it will be necessary to compromise by setting the filter period to a value about half way between the two periods. So if a filter period of Infinity is used then the only line velocity that contributes to the inline and transverse directions is any non-zero starting velocity. However it should also be significantly below. You can use this switch to disable VIV modelling where you think VIV excitation is not significant.4 0. For example: You might disable VIV modelling if the normal component of flow velocity is not significant. In practice. fairings) and you believe they will be effective. For a node at the intersection of two sections the VIV diameter of the following section is used. then the node mean position used by the wake oscillator will remain at the node's starting position found by the static analysis. Data for Each Section The following data can be set for each section of the line. which filters out all oscillatory motion of the line. a filter period of Infinity gives a no-pass filter. So a filter period of zero gives an all-pass filter.6 0. the period of any line motion (e. or the incidence angle is near to being tangential You might disable VIV modelling if there are VIV suppression devices (e. A node at the junction between two sections uses the value for the higher numbered section. and with the wake oscillator models the only velocity input to the model will be any non-zero starting velocity. The reason a significant factor is recommended here is that the filter does not achieve a very sharp cut-off. due to towing or vessel motion) that you want to contribute to VIV. In that case it is important that the line uses Full statics. VIV Enabled You can control which sections of the line the VIV model is applied to.w VIV Analysis. if you set the filter period to Infinity or a very high value. leaving only any non-zero starting velocity. which is taken to mean 'same as the section normal drag diameter'. All the time domain models analyse what goes on at a single specified point on the line. the period of any expected VIV. For simple cases where VIV is excited only by fluid flow. 481 .2 0 0 1 2 3 4 80 60 40 20 0 0 5 Period / FilterPeriod Warning: 160 140 120 100 1 2 3 4 5 Period / FilterPeriod Note also that with the Milan wake oscillator. strakes. which illustrate how it attenuates and lags frequencies that are near to the filter period.g. so OrcaFlex creates one instance of the model for each node in each of the enabled sections. preferably by a factor of 10 or more. Time Domain Models Filter RAO Phase Lag (deg) The filter tries to filter out motion whose period is below the filter period. VIV Diameter The VIV diameter specifies the diameter used by the VIV model.8 0. 9. or comes into contact with the seabed. unless additional assumptions are made. Set them both to 1 to use the vortex force predicted by the VIV model.g. If VIV suppression devices (e. 482 . fairings. Sea Surface and Sea Bed The time domain VIV models (wake oscillator and vortex tracking) make no allowance for surface-piercing or seabed contact effects. then the time domain wake model is reset. We found that there are errors in some of the published models and that many of the wake oscillator models contain disguised references to frequency domain concepts. or breaks contact with the seabed. since the Milan model requires the transverse component of standard drag force to be added to give the total transverse force. The Inline direction is normal to the Axial and Transverse directions. The inline force factor is not available for wake oscillator models. The Transverse direction is normal to the axial direction and normal to the 'non-VIV' relative velocity vector. For the wake oscillator models this means that the wake degree of freedom is reset to zero. These are two of many different wake oscillator models that have been proposed by many different authors. not to the transverse component of the standard drag force. We selected these two models after reviewing the literature and testing a number of different models. If the node is partially submerged (i. instead you should use the Inline Drag Amplification Factor data. This is not available for the vortex tracking models since they include the effect of inline drag amplification.e. the length of line represented by the node is surface-piercing) then the time domain wake model continues to run but the forces it applies to the node are scaled by the node's Proportion Wet. It is the direction of the normal component of the drag force (assuming Cdx=Cdy).2. See Barltrop and Adams page 372. Note: With the Milan wake oscillator model the transverse force generated by the model is not the whole of the transverse force. The data can be specified as a variable data item which varies with Transverse A/D. Time Domain Models The vortex tracking model requires a lot of computing. The inline component of drag is multiplied by this value.1 Wake Oscillator Models OrcaFlex includes two wake oscillator models: the Milan model and the Iwan and Blevins model. The device is also likely to affect the inline drag force. strakes. OrcaFlex therefore handles these effects as follows: If a node comes completely out of the water. VIV Directions For the time domain VIV models. OrcaFlex calculates the following directions: The Axial direction is the local tangential direction. then the model starts again from that reset state. for the vortex tracking model all existing vortices are removed. given by the node's local z-direction. that is the amplitude of transverse oscillation divided by the VIV diameter.w VIV Analysis. shrouds) are fitted to a section of the line then you could allow for their VIV-reduction effect by setting the transverse force factor to a value less than 1. The transverse displacement input into the Milan wake oscillator model is the transverse component of the node position relative to its 'non-VIV' node position. The transverse vortex force factor is only applied to the force generated by the model. It is therefore normal to the line axis and in the plane defined by that axis and the relative flow direction. Vortex Force Factors These factors allow you to scale the inline and transverse components of the vortex force. without adjustment. If the node later comes back into the water. The inline and transverse components of the vortex force are available as results. so you might also want to allow for this by adjusting the inline force factor. so you could improve the speed of simulation by disabling VIV modelling where you believe VIV will not be significant. This makes them difficult to implement in a true time domain analysis. These directions are used for three purposes: The velocity input to the wake oscillator models is the inline component of the 'non-VIV' relative velocity. Inline Drag Amplification Factor Only available for the wake oscillator models. This couples the wake equation of motion to the cylinder equation of motion. In return. Wake Equation of Motion The wake equation of motion is typically a nearly linear. Lift Direction The wake oscillator models are single degree of freedom models. e. Time Domain Models What is a Wake Oscillator Model? A typical wake oscillator model is a heuristic model that uses a single degree of freedom. self generating and self limiting. second order. Node Steady Motion Included The wake oscillator models require the flow velocity as input. This allows non-VIV motion. Almost universally. To use a wake oscillator model set the Dynamics VIV to that model. Each such oscillator then obeys the equations of the chosen model. i. so together the two form a coupled non-linear system. Inline drag amplification The effect of inline drag amplification can be modelled by means of a table relating amplification factor to transverse A/D. You can choose to either use the Default set of values for these parameters or else choose to use your own Specified values. The model gives the lift force magnitude as a function of Q. Data Common to Wake Oscillator Models Model Parameters Both the Milan and the Iwan and Blevins models have various parameters that determine their properties. but is chosen to be one whose qualitative characteristics are known to be similar to VIV. 483 .g. It is not usually derived from physical laws. When this happens the wake oscillator model is effectively being rotated and there is an implicit assumption that this rotation does not significantly affect the wake. to represent the wake behind a rigid cylinder. i. and this force is applied to the cylinder and so affects the motion of the cylinder. so unsteady flow is outside their intended area of application. If the Specified option is chosen then you have complete control over the model parameters. the wake equation of motion involves terms that depend on the motion of the cylinder. Except for the Initial Value (see below).e. to contribute to VIV. The filtering is necessary to prevent the VIV motion itself feeding back into the input to the wake oscillator. providing its period is significantly longer than the filter period. The oscillation of the wake generates a lift force. they only model the transverse direction. wake oscillator models only give the lift force and say nothing about the effect of VIV on the drag force. Current and Wave Motion Are Both Included The input velocity to the wake oscillator models include the fluid velocity due to both current and any waves specified. This sort of modelling ethos is commonly known as an inverse method. Note that this direction can change during the simulation. of the chosen model. Rather. There is no linkage between the wake oscillators except through the structure. either because the line orientation changes or because of wave motion changing the fluid velocity direction. For example there are differential equations that are known to have solutions that are oscillatory. to each node in the line. i. the Default values are the parameters given in the original published papers. However please note that the models were developed and calibrated for steady state conditions.e. In OrcaFlex this input flow velocity is taken to be the fluid velocity minus the filtered node velocity. a force that is normal to the cylinder axis and normal to the flow direction. ordinary differential equation. The main aim behind the wake oscillator paradigm is to model the oscillating lift force. The models can therefore in principle be used to model the effect of waves on VIV. in a towed case. The wake equation of motion involves parameters whose values are calibrated to match empirical results.e. Q say. in the Milan and Iwan and Blevins papers.w VIV Analysis. This is where one attempts to reproduce empirical data without recourse to the fundamental physics of the system. Using a Wake Oscillator Model Wake oscillator models are time domain models and so can only be used in the dynamic analysis. It is therefore effectively being assumed that the interaction between VIV at different levels occurs predominantly through the structure. It models the oscillation of the wake by Q being a function of time that obeys a differential equation that we will call the wake equation of motion. When the simulation is run OrcaFlex creates and attaches a wake oscillator. not through the fluid. one simply writes down a system of equations that have the right sort of characteristics and then adjusts parameters in the equations to tune them to best match the empirical data. The parameters are set so that the limit cycles have the right radius and that the system state tracks around them with the right frequency. Results The Vortex Force is available as a line force results variable. It is important that the filter period is suitably set. one is relying on luck to provide the right answer. relative to the position about which VIV is occurring. if one wants to model the VIV of telephone wires in air. the authors of wake oscillators make no attempt to model the start-up of VIV. Otherwise.w VIV Analysis. The line motion therefore depends significantly on the drag coefficient specified for the transverse direction. The transverse force factor is only applied to the force generated by the Milan model. Milan Model Implementation in OrcaFlex In implementing the Milan model in OrcaFlex we came across the following issues.0. 484 . see the wake oscillator models topic for information that applies to all such models. Note that the Strouhal number interacts with the other model parameters.e. The wake oscillation can take a long time to build up if it is started from zero. so other values of these coefficients take the model outside its domain of calibration. so one cannot expect the model to be applicable for currents that vary over the same time scale as that due to VIV. plus the standard Morison drag force in the inline. Adjusting the Strouhal number is therefore not recommended unless you are calibrating the model parameters against known results. Fossati and Resta. For example. and the other default published values are intended to be used with the default Strouhal number 0. transverse and axial directions. i. Initial Value is the magnitude of the initial value given to the wake degree of freedom used by the models. To find the non-stationary dynamical behaviour of the system far away from such critical regions in the phase space is extremely difficult without simply integrating the equations of motion. The sign of the initial value is chosen randomly for each node in the line. How well do wake oscillators model VIV? Any wake oscillator model is very heavily tied to the data set used to calibrate it. In general. Time Domain Models Warning: The Specified option has been provided principally to allow users the option of calibrating the model against other experimental results. Lift Force In the Milan model the standard Morison drag force in the transverse direction must be added to the force generated by the wake oscillator. where the VIV excitation is due to motion of the line rather (or as well as) fluid flow. This enables OrcaFlex to handle cases such as towed lines. Transverse VIV Offset is also available as a line position results variable. Notes: The Milan model was calibrated by assuming a transverse drag coefficient of 1. The experimental data are usually obtained from a system with a constant fluid in-flow speed. The modelling method used exploits the fact that the solution phase space of the system contains limit cycles that correspond to stationary VIV. OrcaFlex therefore calculates the drag forces as usual and then adds in the force generated by the Milan wake oscillator. Note that this is the sum of the force generated by the wake oscillator model. For this mean position OrcaFlex uses the filtered position of the node. If the current variation is sufficiently slow then the model should be valid. It is a wake oscillator model. which is in the transverse direction but doesn't include the drag force in that direction. This avoids the situation where the nodes on a line all start by moving in the same direction.2. This is due to the nature of the devised mathematical model. The following two model parameters are common to both wake oscillator models. Node Mean Position The Milan model needs the node's offset in the lift direction. not to the transverse component of the standard drag force. so giving it a small non-zero initial value helps to start up the wake oscillation at the start of the simulation. then one should use a data set obtained from a wire vibrating in a wind tunnel. the Reynolds number) of the experimental set-up used to generate the data are sufficiently similar to that of the situation that one wants to model. Strouhal Number. If you are not doing this then we strongly recommend that you use the Default parameters. Milan Wake Oscillator Model The Milan model is an implementation of the model developed by a group in Italy and documented in the paper by Falco. This reports the total lift and drag force.2 and a transverse added mass coefficient of 1. One must ensure that the relevant fluid dynamical and structural dimensionless parameters (for example. relative to its mean position. and it is known to have VIV-type characteristics such as frequency lock-in. 485 . This work showed that the vortex tracking models tend to substantially overpredict VIV amplitudes. plus the standard Morison drag force in the inline. and the hidden wake degree of freedom is such that its rate of change is a measure of the fluid momentum in the transverse direction. The reason for this is that the vorticity is often confined to narrow sheet-like regions and the important fluid forces on a body in the flow are intimately related to the vorticity. but they are much less computationally demanding than 'full' Computational Fluid Dynamics (CFD). This is a type of equation that has been used in other wake oscillator models. Transverse VIV Offset is also available as a line position results variable. The resulting model makes the wake degree of freedom obey a Van der Pol equation. so the drag coefficient specified for the transverse direction is not used. but this can be controlled by limiting the Maximum Number of Vortices Logged. One can focus on the sheet-like regions and this is far more efficient from a computational point of view. In addition note that the force generated by the Iwan and Blevins model (unlike the Milan wake oscillator model) includes the standard Morison drag force in the transverse direction.2 Vortex Tracking Models Overview Two vortex tracking models are available in OrcaFlex. Both are based on the underlying physical equations of boundary layer theory and the Navier-Stokes equation. Vorticity is a measure of a fluid's rotation and it is often advantageous to analyse fluid dynamics in terms of vorticity. The vortex tracking models are based on the relative velocity of the flow past the line. If other results such as these interest you then please contact Orcina for further details. However we believe they are useful for qualitative investigations. The vortex tracking models model the full fluid flow field. The authors calibrated the model against experimental results for fixed and forced cylinders. They can therefore be used both for cases where the excitation is due to current or waves. but the model is less satisfactory when the flow velocity varies a lot along the riser. Iwan and Blevins Wake Oscillator Model This wake oscillator model is as published by Iwan and Blevins.2. 9.w VIV Analysis. which we refer to by number: Vortex Tracking (1) and Vortex Tracking (2). Note that this is the sum of the force generated by the wake oscillator model. but they can also give other results. because it is fixed) then the wake oscillation does not develop and so the Vortex Force decays to zero. Vortex methods are prevalent throughout computational fluid dynamics. In OrcaFlex the vortex tracking models are used to give the force acting on the line. When this model is used OrcaFlex therefore suppresses the transverse component of the usual drag force. Time Domain Models Our experience of the Milan Model If a line end node doesn't move at all (e. The vortex tracking models are much more computationally demanding than the wake oscillator models. The results so far suggest that the Milan model is reasonable for cases where the flow velocity is uniform along the riser. such as the fluid velocity and pressure at any point. In their paper the model is developed from theoretical considerations of momentum. transverse and axial directions. Results The Vortex Force is available as a line force results variable. especially of inline VIV in low to moderate shear conditions. and then compared the model's predictions against experimental results for spring-mounted cylinders. This reports the total lift and drag force. and we hope they will offer a practical analysis technique which gives much of the realism of full CFD without the associated extremely long run times. We have also run the Milan model for flexible riser cases and compared it against experimental results. For example we have experimentally used them to calculate the pressure variations on the line surface due to VIV. and also where the excitation is due to the line moving. Work to date shows considerable promise. which is in the transverse direction but doesn't include the drag force in that direction.g. for example towed cases. In fact they are a type of computational fluid dynamic model. This can make the simulation file very large. Note: We have done validation work comparing the VIV models with real measured results – see the VIV Validation section on the OrcaFlex Validation page of the Orcina website. The Milan model is therefore not suitable for predicting the vortex force on fixed line end nodes. As a result they introduce physical realism that is absent from the wake oscillator models. since the other VIV models can not model this situation. The models involve calculating and tracking many vortices for each node of the line. The vorticity shed from the two sides of the disc is distinguished by being drawn in separate colours. Vortex Tracking Plane The basic vortex tracking model is a 2D fluid model associated with a particular node on the line. to model the vorticity being generated there. Time Domain Models Features Common to both Vortex Tracking Models This section describes the basic vortex tracking model on which both models are based. Each node therefore models its own fluid interaction. The vortex tracking itself handles the rest of the fluid. The drawing below shows a typical vortex plane. it is a cross section through the line. i.w VIV Analysis. which we call the vortex tracking plane. normal to the line axis. we attach a separate vortex tracking plane to each node on the line where VIV modelling is enabled. where viscosity is much less important. The new vortex is placed at the separation point but at a distance λ. The created vortices are tracked downstream by solving the inviscid Navier Stokes equations (which are approximately valid outside the boundary layer). how the vorticity flows after leaving the boundary layer. the boundary layer theory gives the positions of the two separation points. and at these points vorticity is shed from the disc. These are called the separation points. In the drawing above (and in the OrcaFlex 3D view) the stagnation point is shown as a small triangle and the separation points as small blobs. part way around the disc circumference. As the fluid flows around the disc it initially remains in contact with the disc. as seen in the drawing. where viscosity plays a dominant role. but it typically then reaches a point on each side where the flow separates. Some of the fluid flows around one side of the disc and some around the other. The line itself is represented by the grey disc and the fluid flow is coming from the left.e. but since then this method has been superseded by simpler and more accurate methods. where viscosity plays a crucial role. and a new vortex is created at each of these two points. to denote the difference in the direction of rotation – clockwise for vorticity shed from the upper side and anti-clockwise from the lower side. and the point where the flow splits is called the stagnation point. Sarpkaya and Shoaff originally used the Polhausen boundary layer method. In the model 2 λ is the Creation Clearance specified by the user. i. flow Figure: Vortex Tracking Plane The model has two main elements: A boundary layer theory is used to analyse the fluid very near to the disc surface. Boundary Layer When the flow meets the disc it has to flow around the disc circumference and a boundary layer is formed.R from the disc surface. In model 1. 486 .e. At each time step. λ is calculated to be the value that results in the tangential velocity contribution of the new vortex just cancelling out the existing tangential velocity at the separation point. OrcaFlex uses Thwaites' method (see Young 1989) for both models. To apply this 2D model to the 3D situation present in OrcaFlex. This models the wake development. or if the Creation Clearance is set to '~'. It models the 2D 'slice' through the fluid normal to the line axis. The boundary layer theory gives the position of each separation point and the strength of vorticity shed there in one time step. by generating and shedding vortices and then tracking them in its associated vortex tracking plane. In this 2D slice the node is a disc. Boundary layer theory is used to model this region. A new vortex of this strength is then created at the separation point. At each time step the model searches for vortices from detached sheets that have moved in between the two attached sheet. See Sheet Detachment and Coalescing below. These are called the attached sheets. OrcaFlex does this by transferring its vorticity to the nearest coalesced sheet of the opposite sign. Time Domain Models Vortex Tracking After being shed from the boundary layer.2 . 487 . has to limit the number of vortices being modelled. Such a vortex is 'entrained' into the attached sheet of opposite sign to its vorticity. and so vorticity is only being moved a small distance. In reality. of course. Assuming a Strouhal number of 0. an attached sheet can become detached and a new attached sheet then starts forming on that side. Sheet Detachment and Coalescing At any given time there are typically two vortex sheets being fed from the disc – one from each side. In model 1 this is done as follows: The two attached sheets and the one most recently detached sheet are modelled in detail. become detached and flow downstream ad infinitum. Strouhal Number The vortex tracking models do not have any Strouhal number built in. A vortex sheet therefore appears as a linked sequence of circles flowing away from the line. In the above drawing these vortex sheets are shown as red and green lines. At each time step each sheet is rediscretised in a way that keeps the vortices at equally spaced arc lengths along the sheet. The vortex sheet is therefore represented by a sequence of vortex points. one on each side. the vorticity then flows downstream. etc. Doing the removal in this way has the advantage that the total vorticity present is preserved. each one of which represents the vorticity of a short length of vortex sheet. In other words whenever a sheet becomes detached the previous detached sheet is usually replaced by a single vortex point whose strength is the total vorticity in the sheet and whose position is the centroid of the vorticity in that sheet. Vortex Tracking (1) Model The Vortex Tracking (1) model is our implementation and development of the vortex tracking model originally developed by Sarpkaya and Shoaff. i. Typically this happens first on one side of the disc. this value is 1/50th of the (instantaneous) Strouhal period. In reality the vortex sheets form.w VIV Analysis. The colour denotes the sign of the vorticity. then on the other. Sarpkaya and Shoaff originally used singular vortex points. Vortices shed from the same side of the disc are grouped to represent the vortex sheets coming off that side. and this alternating behaviour is typically synchronised with the oscillatory nature of the lift force. so in the vortex tracking model the vorticity is represented by discrete vortex points. with the colour indicating the sign of vorticity. As the flow progresses. the vorticity is shed continuously and it is shed along the neighbouring parts of the line at the same time.2. so as it flows away it forms sheets of vorticity.. but their effect becomes much less as they move further away from the disc.e. rather than being destroyed. since the drawing shows the intersection of the sheets with the vortex plane. See Wake Line and Entrainment below. its effect is assumed to have decayed to the point where it is no longer significant and so it can be removed from the model. Older detached sheets (providing they are not still close to the disc) are simplified by 'coalescing' them to single vortex points. It shares many common features with the Vortex Tracking (2) model – see Features Common to both Vortex Tracking Models. as linked sequences of discrete vortex points. When a coalesced sheet gets beyond a certain distance from the disc. Instead the Strouhal period emerges directly from the physics of the vortex dynamics and boundary layer. R / V where R is the radius of the line and V is the fluid velocity relative to the node. OrcaFlex. In the 3D view the individual vortex points are drawn as circles with their centres joined to represent the vortex sheet line. For computation purposes the model has to discretise the vorticity being shed. It differs in the following ways: It uses a variable time step given by: Δt = 0. but in both vortex tracking models OrcaFlex uses smeared vortex points. The model tries to detect a suitable point in the cycle at which to break the attached sheet away from the disc and start a new attached sheet. The sheet is then referred to as a coalesced sheet. This can lead to very contorted situations and to modelling problems if vortex points come very close to each other. 488 . the wake is modelled using: Detailed modelling of two attached vortex sheets and (usually) one detached vortex sheet. called the wake line. now coalesced. the nearest neighbouring vortex.(D/2R)2 if D>2R where R is the disc radius and λ is the coalescing threshold specified by the user. It uses a coalescing algorithm to control the number of vortices. Such a pair of mutually nearest neighbours are coalesced if their separation is less than Sc.R. The model calculates the tangent line between the two attached sheets. It has undergone testing but has had limited use so far. at each time step. to coalesce pairs of vortices that have come very close to each other. Vortex points in the detached sheet that trail into the wake region can then be absorbed into the attached sheet of the opposite sign. It differs in the following ways: It uses a constant time step. equal to the simulation outer time step.w VIV Analysis. If two vortices are each other's nearest neighbours then they are called 'mutually nearest neighbours'. the two attached sheets and the disc itself is called the wake region. These are shown in the drawing as circles. This is done as follows: At each time step the model finds. is the dashed line in the drawing above. and such a pair are considered for possible coalescing into one. This line. The threshold used depends on whether the two vortices are of the same or opposite signs. Single vortex point modelling of the earlier detached sheets. (Model 1 uses a variable time step. which is also how they appear in the OrcaFlex 3D view.) It does not use sheet detachment to separate the vortices coming from one side of the disc into separate sheets. Coalescing To keep down the number of vortices being tracked. for each vortex. Vortex Tracking (2) Model The Vortex Tracking (2) model is a simplified variant of the Vortex Tracking (1) model. flow Wake Line and Entrainment In practice the tail end of the detached sheet trails into the spiral part of the preceding attached sheet. It does not use entrainment. one red) and the most recent detached sheet (red) can be seen as vortex lines in the drawing below. plus single vortex modelling of a number of coalesced sheets. Sc is given by: Sc = λ. model 2 tries. where Sc is a coalescing separation that depends on the distance D from the two vortices to the disc surface.R if D≤2R Sc = λ. Time Domain Models To summarise. Model 2 shares many features of model 1 – see Features Common to both Vortex Tracking Models. The two attached (one green. Model 1 handles this as follows. nor rediscretisation to keep the vortices at equally spaced arc lengths along the sheet. The region between this wake line. Warning: Model 2 has been developed more recently than model 1. We refer to this process as entrainment. meaning 'log and draw no vortices'. but their position and strength is no longer available to the 3D view. the coalescing separation for vortices that are within 2 disc radii of the disc surface. i.e. 489 . Alternatively the Specified option can be selected which gives you complete control over the model parameters. At each time step the model creates two new vortices. They have not been destroyed and will still be in the calculation. meaning 'log and draw all vortices'. An intermediate value. OrcaFlex warns if the value is more than 0. Its purpose is only to allow you to control the size of the log file (and hence the simulation file) and to control the speed of drawing the 3D view. The smear factor is non-dimensional. This sets the factor λ to the value that results in the tangential velocity contribution of the new vortex at the separation point just cancelling out the previous tangential velocity at that point.R from the disc surface.2. However the drawback of doing this is that you will not see any vortices on the 3D view. You can set the maximum number of vortices to one of: 0 is the default value. There are typically up to several hundred vortices generated per node. whereas larger values spread the vorticity in the vortex over a region surrounding the point. The aim of this is to restrict coalescing near to the disc but encourage it once the vortices have convected significantly away from the disc. and we have found that the model is more stable if the vortices are smeared to reflect this. The log file and simulation file are then as small as possible and the replay as fast as possible. '~'. the vorticity was concentrated at a single point. Data and Results Data The following data needs setting for the vortex tracking models. If you are not doing this then we strongly recommend that you use the Default parameters. since that would be unrealistic.1 and in our experience this gives reasonable performance. The Creation Clearance can also be set to '~'. in disc radius units. This value controls how close to the disc surface these newly-created vortices are placed. Warning: The Specified option has been provided principally to allow users the option of calibrating the model against other experimental results. Note that this setting only affects the display of vortices and does not affect the calculation itself in any way. since the vorticity density at the point itself is actually infinity. Maximum Number of Vortices Logged (per side of the line) This controls the maximum number of vortices that will be displayed and logged. Very small values make each vortex more concentrated into a single point. Vortex Smear Factor This setting controls the degree to which vortices are smeared. Time Domain Models These formulae for Sc mean that the user's data sets. Model Parameters If the Default option is chosen then appropriate default values for the model parameters are used. The default value is 0. and for vortices further away the coalescing separation increases according to the square of the distance from the disc surface. Note that if you do this then as new vortices are generated at the separation points you will see the oldest vortices (typically now downstream) disappear from view. Creation Clearance This is a non-dimensional value that is only used by model 2. for each side of the line. This is what arises in the formal mathematical solution of the inviscid Navier Stokes equations (i. and each vortex needs to log its position and strength so that it can be drawn on the 3D view. In reality viscosity in the fluid spreads the vorticity to some extent. those ignoring fluid viscosity) but it means that each vortex is a singularity. So if all vortices are logged then the log file and simulation file can therefore be quite large. 30 say. in which case the new vortices are placed using the same algorithm as in model 1. Also the replay might be slower because many vortices must be drawn for each frame of the replay.w VIV Analysis. The original Sarpkaya and Shoaff model used point vortices. The smear factor should not be set too high. where λ is the specified creation clearance and R is the disc radius (= half the line outer diameter). See also the data that is common to all the time domain VIV models. They are placed at the separation angle determined by the boundary layer model and at a distance λ. one at each of the two separation points. If the two vortices are coalesced then they are replaced by one vortex whose strength is the sum of their signed strengths and which is placed at their centroid of absolute vorticity. allows you to see the youngest 30 vortices per side of the line.e. so fewer vortices need to be tracked and the simulation is faster.w VIV Analysis. The effect of this is that while the vortex is less than DecayThreshold1 radii downstream then the vortex loses DecayConstant of its strength (e. Vortex Decay Threshold 2 These data items set the rate of vortex strength decay in both vortex tracking models. so the model will have to keep track of more vortices and the simulation will therefore be slower. Coalesce Opposite These are non-dimensional thresholds that are only used for coalescing in model 2. 9. which is in the inline and transverse directions and already includes the drag force in those directions. Conversely. but the axial drag coefficient is used. There are separate threshold values depending on whether the two vortices have equal or opposite signs of vorticity. The decay model is described below. Clearly DecayConstant must be in the range 0 to 1. Vortices are created at the separation points. measured in the relative flow direction from the centre of the line to the vortex. So if one of the two vortices is clockwise and the other is anti-clockwise then the opposite sign threshold will be used. see Coalescing. Drag Coefficients The vortex tracking model includes the drag effects in both the transverse and inline directions. The stagnation and separation points are available as line angle results variables. The same decay model is used in model 2. whereas if they are both clockwise or both anti-clockwise then the same sign threshold will be used.01 means 1% decay) per variable time step.g. but includes the component in the axial direction.3 VIV Drawing With the time domain VIV models you can control how various aspects of VIV are drawn on the 3D view. Note that DecayThreshold1 and DecayThreshold2 can be set to Infinity. Time Domain Models Coalesce Same. increasing the thresholds makes the model coalesce more readily. If the mass ratio (= mass of line / mass of water displaced) is low then the fluid forces are more significant. And when the vortex is more than DecayThreshold2 radii downstream then there is no decay. and in these cases lower coalescing thresholds may be needed so that the fluid behaviour is more accurately modelled. for example to calibrate the model. We therefore recommend that the default values be used unless you wish to experiment with other values. They control how close to each other two vortices have to be before they are allowed to be coalesced into one combined vortex. in the relative flow direction. In model 1.04 for both thresholds gives a reasonable balance between performance and accuracy. If either of them is Infinity then λ = 1DecayConstant always. Note that this is the sum of the force generated by the vortex tracking model. For details. but not in the axial direction. plus the standard Morison drag force in the axial direction. but less accurate. Transverse VIV Offset is also available as a line position results variable. It is as in Sarpkaya and Shoaff's report (page 79) and the default values for these data are as given in that report. When the vortex tracking model is used. This reports the total lift and drag force. at each variable time step the vortex strength is scaled by a factor λ that depends on D as follows: If D ≤ DecayThreshold1*R then λ = (1-DecayConstant) If D ≥ DecayThreshold2*R then λ = 1 If DecayThreshold1*R < D < DecayThreshold2*R then λ varies linearly with D. except that the factor λ is adjusted to allow for the fact that model 2 uses the outer time step instead of the variable time step used in model 1. Reducing the thresholds makes the model coalesce vortices less often. 490 . The adjustment results in the same rate of decay per unit time. OrcaFlex therefore suppresses the components of the usual Morison drag force in the transverse and inline directions. The drag coefficients for the normal directions are therefore not used. While the vortex is between DecayThreshold1 and DecayThreshold2 radii downstream its rate of decay falls linearly (as a function of D) to zero. by setting data on the VIV Drawing page on the line data form. and DecayThreshold1 must be less than DecayThreshold2. so the vortices always lose DecayConstant of their strength per variable time step. The strength of each vortex then decays at a rate that depends on how far the vortex is away from the centre of the disc. Vortex Decay Threshold 1. Results The Vortex Force is available as line force results variables. from (1-DecayConstant) to 1. Vortex Decay Constant. with an initial vortex strength determined by the tangential velocity at the separation point. Our experience so far is that the default values of 0.2. Let R be the disc radius (= half the line outer diameter) and D be the distance. DecayConstant=0. For all the time domain VIV models. The positive and negative vortices are drawn as circles whose areas are proportional to the vortex strengths. Time Domain Models Arc Length Intervals You can control which nodes have VIV detail drawn. 491 . For convenience '~' in the From column means End A of the line. For example. and the wake line are drawn. and '~' in the To column means End B. then the following extra details are drawn. is represented by a line 1 disc radius long (i. Whereas to view the detail for the whole line specify 1 arc length interval and set both its From and To values equal to '~'.w VIV Analysis. The line length is scaled so that a vortex force equal to the standard Morison drag force with Cd=1 in a relative velocity of 1m/s. the vortex force is drawn as a line radiating from the disc centre in the direction of the vortex force. The node is drawn as a disc (even if you have not specified nodes drawn as discs) and the stagnation and separation points are drawn on the edge of the disc. What is Drawn The following VIV details are drawn for all nodes whose arc lengths fall in any one of the specified arc length intervals. The VIV details are drawn for all nodes whose arc lengths fall in any one of the specified intervals. For all these items you can control the pen used for drawing. to view the detail for one node only. this allows you to suppress (by setting the pen style to null) or downplay (by choosing a suitable colour) individual aspects of the detail. With the vortex tracking models. For the vortex tracking models only. by specifying one or more Arc Length Intervals. just reaching the edge of the disc). An arc length interval specifies a contiguous length of line From one specified arc length To another. The constant of proportionality can be controlled by setting Area per Unit Strength. The centre-lines of the positive and negative vortex sheets. and only if the maximum number of vortices logged is set greater than zero. specify 1 arc length interval and set both its From and To values equal to the arc length of that node.e. Note: The vortices and sheet centre-lines drawn are limited by the specified maximum number of vortices logged. for example.