wOrcaFlex Manual Orcina Ltd. Daltongate Ulverston Cumbria LA12 7AJ UK Telephone: Fax: E-mail: Web Site: +44 (0) 1229 584742 +44 (0) 1229 587191
[email protected] www.orcina.com 1 w CONTENTS 1 INTRODUCTION 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Introduction Installing OrcaFlex Running OrcaFlex Demonstration Version Frequently Asked Questions Validation and QA Orcina Terms and Conditions References and Links 9 9 9 11 13 13 14 15 17 20 2 TUTORIAL 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 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 24 24 24 24 25 26 26 27 27 28 28 3 EXAMPLES 3.1 3.2 Introduction A - Riser Systems - simple models 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 A01 Catenary Riser A02 Lazy Wave Riser A03 Steep Wave Riser A04/A05 Lazy S Riser A06 Steep S Riser A07 Pliant Wave Riser A08 Pliant S Riser B01 Jumper to High Tower B02 Riser to Low Tower B03 Multiple Towers B04 Releasable Turret B05 Detailed Pliant Wave B06 Full Field Layout 29 29 32 32 34 34 35 36 37 38 3.3 B - Riser Systems - more complex 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.3.6 38 38 39 40 41 42 42 3.4 C - Steel Catenary Risers 43 2 w 3.4.1 3.4.2 3.4.3 C01 Catenary SCR C02 Lazy SCR C03 Steep SCR D01 Drilling Support D02 SPAR D03 Tension Leg Platform E01/E02 Buoyed Moorings E03 Released Mooring Buoy E04 Branched Mooring F01 CALM Buoy F02 Chinese Lantern F03 Current Meter Mooring F04 Deep Water Mooring G01 Pipelay G02 Lay on Tower G03 Crane Lower G04 Pull Up Line End into Moonpool G05/G06 Midline Pull Up G07 Pipe Lift G08 Snag Pull-in G09 Anchor-last Deployment G10 Lower with Bend Limiter H01 Stowed Line H02 Floating Line H03 Jacket to Semisub I01 Streamer Array I02 Deployment with Sub J01 Batch Script J02 Results J03 Stress Analysis J04 Fatigue analysis K01 Line on Line Impact K02 Line on Line Slide Example RAO Text File 43 43 44 3.5 D - Tensioned Risers, TLPs, SPARs 3.5.1 3.5.2 3.5.3 45 45 46 47 3.6 E - Mooring Systems 3.6.1 3.6.2 3.6.3 47 47 48 48 3.7 F - Buoy Systems 3.7.1 3.7.2 3.7.3 3.7.4 49 49 50 50 51 3.8 G - Installation 3.8.1 3.8.2 3.8.3 3.8.4 3.8.5 3.8.6 3.8.7 3.8.8 3.8.9 52 52 53 53 54 55 56 57 58 59 3.9 H - Offloading Systems 3.9.1 3.9.2 3.9.3 3.10.1 3.10.2 3.11.1 3.11.2 3.11.3 3.11.4 3.12.1 3.12.2 3.13.1 60 60 61 62 3.10 I - Towed Arrays 3.11 J - Pre and Post Processing 63 63 64 65 65 65 66 67 3.12 K - Line on Line Contact 3.13 L - RAO Import 68 68 69 70 70 4 USER INTERFACE 4.1 Introduction 4.1.1 4.1.2 4.1.3 Program Windows The Model Model Browser 3 72 72 72 72 73 w 4.1.4 4.1.5 4.1.6 4.1.7 4.1.8 4.1.9 Libraries Model States Using Model States Toolbar Status Bar Mouse and Keyboard Actions Menus File Menu Edit Menu Model Menu Calculation Menu View Menu Results Menu Tools Menu Window Menu Help Menu 3D Views View Parameters View Control Zooming Views How Objects are Drawn Selecting Objects Creating and Destroying Objects Dragging Objects Connecting Objects Printing, Copying and Exporting Views Replays Replay Parameters Replay Control Superimpose Times Multiple File Replays Data Forms Data Fields Data Form Editing Variable Data Data in Time History Files Results Selecting Variables Summary and Full Results Statistics Linked Statistics Offset Tables Time History and XY Graphs Range Graphs Offset Graphs 74 76 78 78 79 80 4.2 Menus 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.2.8 4.2.9 4.2.10 82 82 83 84 85 86 87 89 89 90 90 4.3 3D Views 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 4.3.7 4.3.8 4.3.9 4.3.10 91 91 92 92 93 93 95 95 95 95 96 4.4 Replays 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 96 96 97 98 98 99 4.5 Data Forms 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 100 100 101 102 104 105 4.6 Results 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.6.6 4.6.7 4.6.8 4.6.9 106 106 107 108 108 108 109 109 110 111 4 w 4.6.10 Presenting OrcaFlex Results Graphs Modifying Graphs Spreadsheets 112 4.7 4.8 4.9 4.10 4.11 4.12 Graphs 4.7.1 4.7.2 4.8.1 113 113 114 Spreadsheets Text Windows Comparing Data Preferences Printing and Exporting 115 115 115 116 116 119 5 BATCH AND POST-PROCESSING 5.1 5.2 Introduction Batch Processing 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 5.2.6 Batch Processing Script Files Script Syntax Script Commands Handling Script Errors Obtaining Variable Names Fatigue Analysis Load Cases Commands Data S-N Curve Data Results Fatigue Points How Damage is Calculated Post-processing Results Results Spreadsheet Instruction Format Pre-defined Commands Tips and Tricks Error Handling Stress Spreadsheet 120 120 120 120 121 122 122 124 124 5.3 Fatigue Analysis 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.3.7 5.3.8 125 125 126 126 127 130 131 131 132 5.4 Post-processing Results 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.4.6 5.4.7 134 134 134 136 137 138 139 139 6 THEORY 6.1 6.2 6.3 6.4 6.5 Coordinate Systems Direction Conventions Object Connections Interpolation Methods Static Analysis 6.5.1 6.5.2 6.5.3 Static Analysis Statics of Lines Statics of Buoys and Vessels 141 141 142 143 144 146 146 146 150 5 w 6.5.4 Multiple Statics for Vessels Dynamic Analysis Calculation Method Ramping 151 6.6 Dynamic Analysis 6.6.1 6.6.2 6.6.3 151 151 152 154 6.7 6.8 6.9 Buoyancy Variation with Depth Current Theory Waves 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 6.9.13 Wave Theory Kinematic Stretching Ochi-Hubble Spectra Non-linear Wave Theories Stokes' 5th Dean's Stream Function Theory Fenton's cnoidal theory Ranges of Applicability Breaking waves Particle velocities and accelerations Currents Seabed Slope Physically implausible solutions 154 155 155 155 156 157 158 158 159 160 160 161 161 161 162 162 6.10 Seabed Theory 6.11 Line Theory 6.11.1 6.11.2 6.11.3 6.11.4 6.11.5 6.11.6 6.11.7 6.11.8 6.11.9 6.11.10 6.11.11 6.11.12 6.11.13 6.11.14 6.11.15 6.11.16 6.11.17 6.11.18 6.12.1 6.12.2 6.12.3 6.12.4 6.12.5 Overview Structural Model Details Calculation Stages Line End Orientation Line Local Orientation Morison's Equation Treatment of Compression Contents Flow Effects Line Pressure Effects Pipe Stress Calculation Pipe Stress Matrix Hydrodynamic Loads Drag Chains Line End Conditions Line Interaction with the Sea Surface Seabed Touchdown and Friction Interaction with Seabed and Shapes Clashing RAOs and Phases RAO Quality Checks Drag Loads Added Mass and Damping Wave Drift Loads 162 163 163 165 166 170 171 171 173 173 175 177 178 179 181 183 183 184 186 187 6.12 Vessel Theory 189 189 190 192 195 196 6.13 3D Buoy Theory 6.14 6D Buoy Theory 198 199 6 w 6.14.1 6.14.2 6.14.3 6D Buoy Theory Lumped Buoy Theory Spar Buoy and Towed Fish Theory 199 200 201 6.15 Shape Theory 6.16 Winch Theory 205 207 7 SYSTEM MODELLING - DATA AND RESULTS 210 7.1 7.2 Introduction General Data 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.2.6 General Data Statics Statics Convergence Dynamics Logging Target Damping Environment Sea Data Current Data Wind Data Wave Data Drawing Data Data for Ochi-Hubble Spectra Data for Time History Waves Wave Preview Setting up a Random Sea Results Shapes Shape Data Blocks Cylinders Planes Drawing Results Vessels Vessel Data Vessel Types Modelling Vessel Slow Drift Vessel Results 3D Buoys Data Results 6D Buoys Wings Common Data 210 212 212 212 214 214 215 216 7.3 Environment 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 7.3.6 7.3.7 7.3.8 7.3.9 7.3.10 7.3.11 216 216 217 220 221 222 226 227 227 229 230 233 7.4 Shapes 7.4.1 7.4.2 7.4.3 7.4.4 7.4.5 7.4.6 7.4.7 234 234 235 236 237 238 238 239 7.5 Vessels 7.5.1 7.5.2 7.5.3 7.5.4 7.5.5 239 239 240 248 261 262 7.6 3D Buoys 7.6.1 7.6.2 7.6.3 264 264 264 265 7.7 6D Buoys 7.7.1 7.7.2 7.7.3 266 266 267 268 7 w 7.7.4 7.7.5 7.7.6 7.7.7 7.7.8 7.7.9 7.7.10 7.7.11 7.7.12 7.7.13 Applied Load Wing Data Wing Type Data Lumped Buoy Properties Lumped Buoy Drawing Data Spar Buoy and Towed Fish Properties Results Buoy Hydrodynamics Hydrodynamic Properties of a Rectangular Box Modelling a Surface-Piercing Buoy Lines Line Data Attachments Line Types Line Results Drag Chain Results Line Type Wizard Modelling Mooring Chains Modelling Lines with Floats Modelling Ropes Modelling Homogeneous Pipes Modelling Hoses and Cables Modelling Line Ends Modelling Compression in Flexibles Links General Data Connections Properties Results Winches Winch Data Wire Properties Control Drive Unit Results 270 270 271 273 274 275 277 279 280 283 7.8 Lines 7.8.1 7.8.2 7.8.3 7.8.4 7.8.5 7.8.6 7.8.7 7.8.8 7.8.9 7.8.10 7.8.11 7.8.12 7.8.13 7.8.14 286 286 288 300 303 308 320 320 322 327 332 336 338 341 344 7.9 Links 7.9.1 7.9.2 7.9.3 7.9.4 7.9.5 7.10.1 7.10.2 7.10.3 7.10.4 7.10.5 7.10.6 346 346 346 347 347 348 7.10 Winches 348 348 350 351 351 352 353 8 VIV TOOLBOX 8.1 VIV Toolbox 354 354 9 TECHNICAL NOTES 9.1 9.2 9.3 9.4 9.5 Modelling Bend Restrictors Modelling Design Waves Modelling Guide Tubes Modelling Mid-water Arches Typical Line Type Properties 356 356 357 359 359 361 8 w 1 1.1 INTRODUCTION INTRODUCTION Welcome to OrcaFlex (version 8.2a), a marine dynamics program developed by Orcina for static and dynamic analysis of flexible pipeline and cable systems in an offshore / marine environment. OrcaFlex is widely used in the offshore industry for analysis of flexible risers from offshore production platforms and tanker loading buoys, cable lay, installation of subsea equipment, oceanographic moorings, pull-in analysis, etc. 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. OrcaFlex makes extensive use of graphics to assist understanding. The program can be operated in batch mode for routine analysis work and there are also special facilities for post-processing your results. 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. A simple 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. Other applications include oceanographic systems, aquaculture and non-marine systems. OrcaFlex is fully 3D and can handle multi-line systems, floating lines, line dynamics after release, etc. Inputs include ship motions, regular and random waves. Results output includes animated replay plus full graphical and numerical presentation. If you are new to OrcaFlex then please see the tutorial and examples. For further details of OrcaFlex and our other software, please contact Orcina or your Orcina agent. Copyright notices • • • Copyright Orcina Ltd. 1987-2002. All rights reserved. OrcaFlex contains Formula One from Visual Components. Copyright 1994-1997. All rights reserved. OrcaFlex uses LAPACK for certain linear algebra calculations. 1.2 INSTALLING ORCAFLEX Hardware Requirements OrcaFlex can be installed and run on any PC compatible computer that has: • • • • Windows 95, 98, ME, NT 4, 2000, XP or later versions, At least 32 Mb of memory, At least 40 Mb of free disk space. A screen resolution of at least 800 x 600 (small fonts), However, OrcaFlex is a very powerful package and to get the best results we would recommend: 9 w • • • • The fastest possible processor. This is the most important factor since OrcaFlex is a computation-intensive program and simulation run times can be long for complex models. At least 128 Mb of memory. This is less important but some aspects of OrcaFlex do perform better when more memory is available. As much disk space as you require to store simulation files. Simulation files vary in size, but can be 10's of megabytes each for complex models. A screen resolution of 1024 x 768 (or higher) and a 16-bit colour palette. Installation To install OrcaFlex: • • If you are using Windows NT, 2000 or XP then first log on with Administrator privileges. If installing from CD, insert the OrcaFlex CD and run the Autorun.exe program on the CD (on many machines this program will run automatically when you insert the CD). Then select 'Install'. If you have received OrcaFlex by e-mail or from the web you should have the OrcaFlex installation program Setup.exe. You will also need licence files (*.lic) for each dongle that you want to use (if you have not received them you might be able to use the licence file(s) from your previous OrcaFlex CD). Place the licence files and the file Setup.exe together in a directory on your machine and then run the Setup.exe program. You will also need to install the OrcaFlex dongle supplied by Orcina when you purchased or leased OrcaFlex. See below for details. • • For further details, including information on network and silent installation, see the ReadMe file on the OrcaFlex CD. If you have any difficulty installing OrcaFlex please contact Orcina or your Orcina agent. Orcina Shell Extension When you install OrcaFlex you are asked whether you also want to install the Orcina Shell Extension. Installing this tells Windows about the OrcaFlex data and simulation file types (.dat and .sim) and associates them with OrcaFlex. You can then start OrcaFlex and open an OrcaFlex file by simply double-clicking the file. The shell extension also provides file properties information in Explorer, such as which version of OrcaFlex wrote the file and the Comments text for the model in the file. For details see the file CD:\OrcShlEx\ReadMe.htm on the OrcaFlex CD. Installing the Dongle OrcaFlex is supplied with a dongle, a small hardware device that must be attached to the machine, or else to the network to which the machine is attached. Note: The dongle is effectively your licence to run one copy (or more, if the dongle is enabled for more copies) of OrcaFlex. It is, in essence, what you have purchased or leased, and it should be treated with appropriate care and security. If you lose your dongle you cannot run OrcaFlex. Warning: Orcina can normally resupply disks or manuals (a charge being made to cover costs) if they are lost or damaged. But we can only supply a new dongle in the case where the dongle has failed and the old dongle is first returned to us. 10 w Dongles labelled 'Hxxx' (where xxx is the dongle number) must be plugged into the machine on which OrcaFlex is run. Dongles labelled 'Nxxx' can be used in the same way as ‘Hxxx’ dongles, but they can also be used over a computer network, allowing several used to share the program. In the latter case the dongle should be installed by your network administrator; instructions can be found in the Dongle directory of the OrcaFlex CD. Types of Dongle Dongle are available for two types of connector - for connection to the parallel port or to a USB port. The two types have exactly the same facilities (the difference is simply whether they are connected to a parallel port or a USB port) but there are pros and cons of the two types: • The new USB port dongles may not suit if you are using older machines or operating systems. This is because some older machines may not have a USB port. Also, Windows NT4 and early versions of Windows 95 (prior to OSR 2.1) do not support USB devices without modification. Windows 98, ME and 2000, XP all support USB devices (as will future versions of Windows). On the other hand USB ports are a more modern and better technology and are taking over from the old parallel port. All recent machines we have seen have USB ports and indeed some portable/laptop computers now have a USB port and no parallel port. USB ports are designed to be capable of having multiple devices attached to one port, so you can plug in the USB dongle and other devices (printers, plotters, etc.) and they won't interfere with each other. The parallel port, on the other hand, wasn't originally designed with multiple devices in mind, so dongle suppliers had to use non-standard interfacing methods to try to make the dongle transparent to other devices. This is not always successful and we have seen a few cases where a printer could not be used on the same parallel port as the dongle. This problem will not arise with USB dongles. • • Parallel Port Dongles By default we send parallel port dongles, which have 25-pin connectors. The computer side of the dongle has a 25-pin male connector which plugs into the standard PC parallel port, which has a female connector. Please take care not to insert the dongle into a serial port, which is sometimes a 25-pin male connector on the back of the computer; no harm should occur, but the program will not be able to run. If the parallel port is also needed for another device such as a printer, then the dongle should be plugged into the computer and the printer then plugged into the back of the dongle. The dongle is transparent and should not interfere with signals passing through it to other devices. If you have any difficulties fitting the dongle, please double check that it is fitted to the right port and that it is the correct way round. Dongle Troubleshooting We supply, with OrcaFlex, a dongle utility and troubleshooting program called OrcaDong.exe. If OrcaFlex cannot find the dongle then you can use this program to check various things and hopefully find the cause of the problem. For details see the file OrcaDong.hlp. The OrcaDong program and its help file can be found in the OrcaFlex installation directory. They are also in the Dongle directory on the OrcaFlex CD, together with other less commonly needed dongle files. If you need further help then please contact Orcina. 1.3 RUNNING ORCAFLEX A shortcut to run OrcaFlex is set up on the Start menu when you install OrcaFlex (see Start\Programs\Orcina Software\OrcaFlex). 11 w This shortcut passes no parameters to OrcaFlex so it gives the default start-up behaviour; see below. If this is not suitable you can configure the start-up behaviour using command-line parameters, for example by setting up your own shortcuts with particular parameter settings. Default Start-up OrcaFlex has two basic modules: full OrcaFlex and statics-only OrcaFlex. A full OrcaFlex licence is needed for dynamic analysis. There is also an additional VIV Toolbox, which is optional and which requires a VIV licence. 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). By default, it first looks for a licence on a local dongle (i.e. one in local mode and connected to the local machine) and then if none is found then it looks for a licence on a network dongle (i.e. one in network mode and accessed via a licence manager over the network). This default behaviour can be changed by commandline parameters. If OrcaFlex finds a network dongle and there is a choice of which licences to claim from it, then OrcaFlex displays a Choose Modules dialog to ask you which modules you want to claim. This helps you share the licences with other users of that network dongle. 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, if that is all you need, so that the full licence is left free for others to use when you do not need it yourself. The Choose Modules dialog can be suppressed using command-line parameters. Command Line Parameters OrcaFlex can accept various parameters on the command line to modify the way it starts up. The syntax is: OrcaFlex.exe Filename Option1 Option2 ... etc. Filename is optional. If present it should be the name of an OrcaFlex data file (.dat) or simulation file (.sim) and after starting up OrcaFlex will automatically open that file. Option1, Option2 etc. are optional parameters that allow you configure the start-up behaviour. They can be any of the following switches. For the first character of an option switch, the hyphen character '-' can be used as an alternative to the '/' character. 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. The following switches allow you to modify this default behaviour. • • /LocalDongle Only search for licences on a local dongle. No search will be made for network dongles. /NetworkDongle Only search for licences on a network dongle. Any local dongle will be ignored. This can be useful if you have a local dongle but want to use a network dongle that has licences for more modules. Module Choice Switches These switches are only relevant if you the dongle found is a network dongle and there is a choice of licences to claim from that dongle. You can specify some or all of your choices using the following command line switches. 12 w • /DisableDynamics Choose the statics-only basic licence. 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. /Disable<Module> Choose not to claim a licence for the additional module with name <Module>. For example /DisableVIV tells the program to choose not to claim a VIV Toolbox licence, which may be useful if you are sharing a VIV licence on a network dongle. • If you do not specify all the choices then the program displays the Choose Modules dialog to ask for your remaining choices. You can suppress this dialog using the following switch. • /DisableInteractiveStartup Do not display the Choose Modules dialog. The program behaves the same as if the user clicks OK on that dialog without changing any module choices. 1.4 DEMONSTRATION VERSION For an overview of OrcaFlex, see the Introduction topic and the tutorial. The demonstration version of OrcaFlex has some facilities disabled - you cannot calculate statics or run simulation, and you cannot save files, print, export or copy to the clipboard. But otherwise the demonstration version is just like the full version, so it allows you to see how exactly the program works. In particular the demonstration version allows you open any prepared OrcaFlex data or simulation file. And if you open a simulation file then you can then examine the results, see replays of the motion etc. There are numerous example files provided on the demonstration CD. 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. To do this, give them the demonstration version and copies of your OrcaFlex simulation files. The demonstration version can be found on your OrcaFlex CD - see CD:\Demo_CD\ReadMe. 1.5 FREQUENTLY ASKED QUESTIONS What do I do if OrcaFlex cannot find my dongle? See the Dongle directory on your OrcaFlex CD. In that directory you will find a special dongle utility program called OrcaDongle that allows you to check your dongle. See the OrcaDongle help file for details. If you still have difficulty, then please contact Orcina. Can I share my OrcaFlex licence(s) with other users over a network? Yes. Your dongle can be installed on one machine on the network and be put into "network mode" and run under a special licence manager program on that machine. You can then install and use OrcaFlex on that or any other machine on the network. You will then be able to use OrcaFlex on any machine on which it has been installed, but within the limit that no more than N copies can be run simultaneously, where N is the number of licences you have in the dongle. For details see the OrcaDongle help file on your OrcaFlex CD (CD:\Dongle\OrcaDong.hlp). Is there any QA documentation for OrcaFlex? Yes. For more details refer to Validation and QA. 13 w Can OrcaFlex automate repetitive tasks like setting up multiple load cases and producing reports? Yes. OrcaFlex has advanced automation features. Multiple load cases based on a single base case can be specified using batch script files. In addition OrcaFlex is supplied with postprocessing spreadsheets written in Excel. The spreadsheets allow you to automate the transfer of results from OrcaFlex simulations to your report. The great benefit of this automation is when you need to re-run simulation files with changed data. Once the script files and the spreadsheets have been setup this process is reduced to just changing the data in the base file. Does OrcaFlex have facilities for Fatigue Analysis of homogeneous pipes? A Fatigue Analysis for homogeneous pipes module is built into OrcaFlex. Fatigue Analysis. For details see What are the values plotted at the ends of range graphs for Effective Tension, Bend Moment and Curvature? These values are End Tension, End Bend Moment and End Curvature respectively. For more details see Range Graphs. Does "mass" in OrcaFlex means mass in air or mass in water? The mass of an object is the object's inherent resistance to acceleration, so it does not depend on whether an object is in air or water. (The extra hydrodynamic resistance to acceleration when in water is a separate property called added mass.) Mass is numerically the same as weight in air (providing the same units are used). How do I make statics converge for my Lines? If there are a lot of lines in the model then you can make investigation of the problem easier by dragging the line up to the top of the list in the model browser. OrcaFlex will then analyse that line first. The default statics settings are statics method "Catenary" with Full Statics set to "Yes". The catenary statics method sometimes struggles with complicated cases, such as when there are buoyant sections or tethers connection to the Line. If the Line statics is not converging with these default settings try setting statics method to "Quick" and Full Statics to "Yes". If you still have problems please refer to Which Line Statics method to use. How do I include an OrcaFlex replay in my presentations? When the replay is running right click on the 3D View windows and select Export Video. This will save the replay as a video in AVI format which can then be included in your presentation. See also Presenting OrcaFlex Results. Can OrcaFlex model Guide Tubes? Yes. There are two standard methods of modelling a pipe or line sliding through a guide. The first is to use two Links to eliminate motion in the X and Y directions. Alternatively a Solid Cylinder can be used to model the guide. For more details see Modelling Guide Tubes. 1.6 VALIDATION AND QA Orcina software is developed under a formal QA system that includes rigorous testing to confirm correct operation. Testing takes place at a series of levels: desk checks (for example against 14 w hand calculations for specific cases); comparisons with analytical solutions where these exist; comparisons with other, independently developed, software packages; and finally comparisons with data from model tests and measurements on real systems. Desk checks are too many and too detailed to deal with here but are of the greatest importance in ensuring a satisfactory product. Suffice to say that we keep full and detailed records of such tests, and that all new features of Orcina programs are extensively tested in this way before release. In addition each new version of an Orcina program is checked in detail against its immediate predecessor. OrcaFlex has been validated against published analytical and numerical results such as those given by Roark (1965) and Timoshenko (1955). Various towed fish cases have been checked against results given by Pode (1951) with good agreement being achieved. OrcaFlex results for the case of a fish being towed by a vessel following a circular path, have been confirmed by comparison with theoretical results (Chapman, 1984). Comparisons have been made with other flexible riser programs by Orcina and by independent users. Comparisons known to us include the following: Comparison carried out by Orcina/Seaflex BP Dunlop Brasnor NOS/Orcina Wellstream/Orcina Software used for comparison FENRIS Riflex Flexriser Fenris, Flexriser and others Flexcom 3D Flexcom 3D, Flexriser Close agreement has been obtained in all cases. Orcina took part in a major comparison of flexible riser programs initiated by the ISSC (Larsen, 1991). The published results show good agreement between OrcaFlex and the other established programs. A related Orcina program, OrcaRiser, has been derived from OrcaFlex and accurately checked against it. It has then been compared with the published results of the API tensioned riser program inter-comparison (API Bulletin 2J). The API report shows results from a number of tensioned riser programs: OrcaRiser results fall in the middle of the scatter band of results from the other programs. As regards comparisons with model and full scale systems, a major validation exercise was carried out to compare OrcaFlex with model test results obtained from a joint industry project (Hartnup et al, 1987). Good agreement was obtained. A large-scale test has been carried out in Lake Pend Oreille (1998) under a joint industry project managed by PMB. Preliminary results show satisfactory correlation with OrcaFlex. OrcaFlex predictions for a towed fish case have been successfully compared with full scale measurements from sea trials. 1.7 ORCINA Orcina is a creative engineering software and consultancy company staffed by mechanical engineers, naval architects, mathematicians and software engineers with long experience in such demanding environments as the offshore, marine and nuclear industries. As well as developing engineering software, we offer a wide range of analysis and design services with particular strength in dynamics, hydrodynamics, fluid mechanics and mathematical modelling. 15 w Contact Details Orcina Ltd. Daltongate Ulverston Cumbria LA12 7AJ UK Telephone: Fax: E-mail: Web Site: +44 (0) 1229 584742 +44 (0) 1229 587191
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[email protected] 1.8 TERMS AND CONDITIONS 1. Definitions In these conditions the following words shall have the following meanings: a) "The Company" shall mean "Orcina Ltd". b) "The Software" shall mean the computer software supplied under this Agreement. c) "The Proposal" shall mean the written proposal for the supply of computer software. d) "Agents" shall mean the Company's appointed representatives. e) "The Client" shall mean the purchaser and its Affiliates. f) The term "Affiliate", when used with respect to one of the parties hereto, shall mean any of the following: (i) the Parent Company thereof. (ii) any company directly or indirectly controlled by, controlling, or under common control with that party. For the purpose of this definition, "control" shall mean owning 50% or more of the stock, equity or property of such company. 2. General a) The conditions set out below together with the Proposal and any Special Conditions referred to therein shall constitute the terms of the Contract. These conditions may not be varied or added to without the agreement in writing of both parties. b) The Contract shall be subject to the non-exclusive jurisdiction of the English courts and shall be interpreted according to English law. 17 w 3. Validity The Proposal is valid for a period of sixty days from date of issue unless otherwise stated in the Proposal or extended by the Company in writing. 4. Multisite Use Under these conditions the Client shall be free to use the Software at any location and to move any copy or copies of the Software from one location to another at his discretion. 5. Charges and Terms of Payment a) Charges shall be as set out in the Proposal. Maintenance charges are subject to review annually. b) Initial lease charges and charges for Software purchase shall be payable in advance unless otherwise agreed in writing. c) Invoices for software maintenance and for lease extensions will be submitted in advance and are due immediately. 6. Duration and Termination of Lease a) Unless otherwise stated in the Proposal, the minimum period of lease shall be one month and the lease period shall be extended automatically one month at a time thereafter until the Company receives notice of termination. b) The lease may be terminated by either party at 7 days written notice. All invoices outstanding at the date of termination shall be payable immediately. On termination, the Client will return to the Company all computer disks, manuals and hardware security devices supplied for the purposes of the lease and will delete all copies of the Software from his computer systems. 7. Intellectual Property Rights and Terms of Use of Computer Software All intellectual property rights (including copyright) in the Software and documentation will remain in the ownership of the Company and one or more non-exclusive licences will be granted to the Client to use the Software upon the following terms: a) Each licence entitles the Client to use the Software on one machine at any one time. The Client must not use the Software simultaneously on more machines or terminals than he holds licences for. b) If the Client is in breach of these terms, immediately upon request by the Company he shall delete all copies of the Software from all computer systems under his control and return to the Company all copies of documentation and any security devices provided for use with the Software. c) The Company shall indemnify the Client against any claim that the Software infringes the Intellectual Property Rights of any third party provided that the Company is given immediate and complete control of any such claim and the Client does not prejudice Company's defence and that the Client gives the Company all reasonable assistance in relation to any such claim. The Company warrants that it has the right to grant this licence 18 w 8. Warranty and Liability a) The Company warrants that the Software will comply with the specifications as set out in the documentation supplied to the Client and will be free from defects in materials and workmanship under normal use for a period of 90 days from the date of delivery to the Client. If within such period the Software fails to perform correctly, the Company will at its discretion rectify any defects free of charge or refund the original price on return of the Software. In no event shall the Company or its Agents be liable for loss of profits, loss of or damage to data, indirect, special, incidental or consequential damages or losses arising out of the use or inability to use the Software. The total joint liability of the Company and its Agents for direct loss caused by breach of this Agreement or its proven negligence shall be restricted to the price paid for the Software. b) The express terms of this contract are in lieu of all warranties, conditions, terms, undertakings and obligations implied by statute, common law, custom, trade usage or otherwise, all of which are hereby excluded to the fullest extent permitted by law save to the extent that the Company shall be liable for any death or personal injury arising as a result of this agreement and which results from its proven negligence. 9. Maintenance, Upgrades and Technical Support a) It is the Company's policy continually to develop its software products in response to market requirements. When new versions are released, program upgrades will be supplied free of charge to those customers having a current maintenance contract. b) For all software packages covered by a current maintenance contract or lease agreement the Company provides full technical support by telephone, fax or e-mail without further charge. Limited support may be available for earlier versions of the Software at the Company's discretion but this cannot be guaranteed. c) An annual MUS fee will be chargeable based on the total number of copies of the Software for which the Client holds licences at the renewal date. The fees for second and subsequent copies will be discounted relative to the single copy fee at the same rates as shown in Clause 2 above. d) MUS will be provided for all copies of the Software in the Client's possession, or for none at all at the Client's discretion. If the Client chooses not to continue MUS, then the Company reserves the right to charge an additional fee should the Client wish to reinstate MUS at a later date. 10. Administration The Client will nominate a single point of contact for administrative and invoicing purposes. 11. Transfer of Ownership The Client shall be free to transfer ownership of any copy or copies of the software between Affiliates of the Client, but ownership shall not be transferred to another party without the written agreement of the Company. Where transfer of ownership to another party is agreed, the Company may charge a fee. Specifically, and for the avoidance of doubt, on termination of a joint venture or disposal of a shareholding in a company jointly owned with others, any copy or copies of the Software supplied under this Agreement shall revert to the Client or one of its Affiliates unless the Company has given its agreement in writing to the transfer of ownership to another party. 19 w 12. Confidentiality The Client undertakes to treat as confidential and keep secret all information contained in the Software and documentation. The Client shall not without the prior written consent of the Company divulge any part of such information to any person except its employees, agents and consultants. The Client shall notify the Company should it become aware of any breach of such confidence by any person to whom the Client divulges all or any part of such information. 13. Arbitration Any dispute or difference arising out of the contract shall be referred to the arbitration of a person to be mutually agreed upon or failing agreement to some person nominated by the President of the Institution of Mechanical Engineers. 1.9 REFERENCES AND LINKS API Recommended Practice 2A-WSD (RP 2A-WSD). American Petroleum References API, 1993. Institute. API. Comparison of Analyses of Marine Drilling Risers. API Bulletin. 2J. Barltrop N D P, and Adams A J, 1991. Dynamics of fixed marine structures. Butterworth Heinemann for MTD. 3rd Edition. Batchelor G K, 1967. An introduction to fluid dynamics. Cambridge University Press. Carter D J T, 1982. Prediction of Waveheight and Period for a Constant Wind Velocity Using the JONSWAP Results, Ocean Engineering, 9, no. 1, 17-33. Casarella M J and Parsons M, 1970. Cable Systems Under Hydrodynamic Loading. Marine Technology Society Journal 4, No. 4, 27-44. Chapman D A, 1984. Towed Cable Behaviour During Ship Turning Manoeuvres. Ocean Engineering. 11, No. 4. CMPT, 1998. Floating structures: A guide for design and analysis. Edited by Barltrop N D P. Centre for Marine and Petroleum Technology publication 101/98, Oilfield Publications Limited. Dean R G, 1965. Stream function representation of non-linear ocean waves. J. Geophys. Res. 70, 4561-4572. DNV, 1991. Environmental Conditions and Environmental Loads Classification Notes 30.5. March. ESDU, 1971. Fluid forces, pressures and moments on rectangular blocks. ESDU 71016 ESDU International, London. Falco M, Fossati F and Resta F, 1999. On the vortex induced vibration of submarine cables: Design optimization of wrapped cables for controlling vibrations. 3rd International Symposium on Cable Dynamics, Trondheim, Norway. Faltinsen O M, 1990. Sea loads on ships and offshore structures. Cambridge University Press. Fenton J D, 1979. A high-order cnoidal wave theory. J. Fluid Mech. 94, 129-161. Fenton J D, 1985. A fifth-order Stokes theory for steady waves. J. Waterway, Port, Coastal & Ocean Eng. ASCE. 111, 216-234. 20 w Fenton J D, 1990. Non-linear wave theories. Chapter in "The Sea - Volume 9: Ocean Engineering Science", edited by B. Le MeHaute and D. M. Hanes. Wiley: New York. 3-25. Fenton J D, 1995. Personal communication - preprint of chapter in forthcoming book on cnoidal wave theory. Gregory R W and Paidoussis M P, 1996. Unstable oscillation of tubular cantilevers conveying fluid: Part 1:Theory. Proc. R. Soc. 293 Series A, 512-527 Hartnup G C, Airey R G and Fraser J M, 1987. Model Basin Testing of Flexible Marine Risers. OMAE Houston. Hoerner S F 1965. Fluid Dynamic Drag, Published by the author at Hoerner Fluid Dynamics, NJ 08723, USA. Isherwood R M, 1987. Applied Ocean Research, Vol 9, No. 1 (January), pp 47-50. Iwan W D, 1981. The vortex-induced oscillation of non-uniform structural systems. Journal of Sound and Vibration, 79, pp 291-301. Iwan W D and Blevins R D, 1974. A Model for Vortex Induced Oscillation of Structures. Journal of Applied Mechanics, September 1974, pp 581-586. Larsen C M, 1991. Flexible Riser Analysis - Comparison of Results from Computer Programs. Marine Structures, Elsevier Applied Science. Maddox S J, 1998. Fatigue strength of welded structures. Woodhead Publishing Ltd, ISBN 1 85573 013 8. Morison J R, O’Brien M D, Johnson J W, and Schaaf S A, 1950. The force exerted by surface waves on piles. Petrol Trans AIME. 189. Mueller H F, 1968. Hydrodynamic forces and moments of streamlined bodies of revolution at large incidence. Schiffstechnik. 15, 99-104. Newman J N. 1974. Second-order, slowly-varying forces on vessels in irregular waves. Proc Int Symp Dynamics of Marine Vehicles and Structures in Waves, Ed. Bishop RED and Price WG, Mech Eng Publications Ltd, London. Newman J N, 1977. Marine Hydrodynamics, MIT Press NDP, 1995. Regulations relating to loadbearing structures in the petroleum activities. Norwegian Petroleum Directorate. Ochi M K and Hubble E N, 1976. Six-parameter wave spectra; Proc 15th Coastal Engineering Conference, 301-328. Oil Companies International Marine Forum, 1994. Prediction of Wind and Current Loads on VLCCs, 2nd edition, Witherby & Co., London. Paidoussis M P, 1970. Dynamics of tubular cantilevers conveying fluid. Engineering Science, 12, No 2, 85-103. J. Mechanical Paidoussis M P and Deksnis E B, 1970. Articulated models of cantilevers conveying fluid : The study of a paradox'. J. Mechanical Engineering Science, 12, No 4, 288-300. Paidoussis M P and Lathier B E, 1976. Dynamics of Timoshenko beams conveying fluid. J. Mechanical Engineering Science, 18, No 4, 210-220. Pode L, 1951. Tables for Computing the Equilibrium Configuration of a Flexible Cable in a Uniform Stream. DTMB Report. 687 Principles of Naval Architecture. Revised edition, edited by J P Comstock, 1967. Society of Naval Architects and Marine Engineers, New York. 21 w Puech A, 1984. The Use of Anchors in Offshore Petroleum Operations. Editions Technique Rawson and Tupper, 1984. Basic Ship Theory 3rd ed, 2: Ship Dynamics and Design, 482. Longman Scientific & Technical (Harlow). Rienecker M M and Fenton J D, 1981. A Fourier approximation method for steady water waves. J. Fluid Mech. 104, 119-137. Roark R J, 1965. Formulas for Stress and Strain. 4th edition McGraw-Hill. Sarpkaya T, Shoaff R L, 1979. Inviscid Model of Two-Dimensional Vortex Shedding by a Circular Cylinder. Article No. 79-0281R, AIAA Journal, 17, no. 11, 1193-1200. Sarpkaya T, Shoaff R L, 1979. A discrete-vortex analysis of flow about stationary and transversely oscillating circular cylinders. Report no. NPS-69SL79011, Naval Postgraduate School, Monterey, California. Rychlik I, 1987. A new definition of the rainflow cycle counting method. Int. J. Fatigue, 9, No 2, 119-121. Skjelbreia L and Hendrickson J, 1961. Fifth order gravity wave theory. Proc. 7th Conf. Coastal Eng. 184-196. Sobey R J, Goodwin P, Thieke R J and Westberg R J, 1987. Wave theories. J. Waterway, Port, Coastal & Ocean Eng. ASCE 113, 565-587. Sparks C, 1980. Le comportement mecanique des risers influence des principaux parametres. Revue de l'Institut Francais du Petrol, 35, no. 5, 811. Sparks C, 1983. Comportement mecanique des tuyaux influence de la traction, de la pression et du poids lineique : Application aux risers. Revue de l'Institut Francais du Petrol, 38, no. 4, 481. Taylor R and Valent P, 1984. Design Guide for Drag Embedment Anchors, Engineering Laboratory (USA), TN No N-1688. Thwaites, 1960. Incompressible Aerodynamics, Oxford, 399-401. Timoshenko S,1955. Vibration Problems in Engineering, van Nostrand. Triantafyllou M S, Yue D K P and Tein D Y S, 1994. Damping of moored floating structures. OTC 7489, Houston, 215-224. Tucker et al, 1984. Applied Ocean Research, 6, No 2. Tucker M J, 1991. Waves in Ocean Engineering. Ellis Horwood Ltd. (Chichester). Wichers J E W, 1979. Slowly oscillating mooring forces in single point mooring systems. BOSS79 (Second International Conference on Behaviour of Offshore Structures). Wichers J E W, 1988. A Simulation Model for a Single Point Moored Tanker. Delft University Thesis. Young A D, 1989. Boundary Layers. BSP Professional Books, 87-91. Naval Civil Links Atlantia Offshore Limited 1177 West Loop South, Suite 1200 Houston, TX 77027, USA Attention: Dr. S. Leverette Email:
[email protected] Tel: 713 850 8885 Fax: 713 850 1178 22 w David Tein Consulting Engineers, Ltd. 11777 Katy Freeway, Suite 434 South Houston, TX 77079 Phone: (281) 531-0888 Fax: (281) 531-5888 Email:
[email protected] 23 w 2 2.1 TUTORIAL GETTING STARTED This short tutorial gives you a very quick run through the model building and results presentation features of OrcaFlex. On completion of the tutorial we suggest that you also look through the pre-run examples - see Example Files. On starting up OrcaFlex, you are presented with a 3D view showing just a blue line representing the sea surface and a brown line representing the seabed. At the top of the screen are menus, a tool bar and a status bar arranged in the manner common to most Windows software. As usual in Windows software, nearly all actions can be done in several ways: here, to avoid confusion, we will usually only refer to one way of doing the action we want, generally using the mouse. 2.2 BUILDING A SIMPLE SYSTEM To start with, we will build a simple system consisting of one line and one vessel only. on the toolbar. The cursor changes from Using the mouse, click on the new vessel button 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. Place the cursor anywhere on the screen and click the mouse button. A "ship" shape appears on screen, positioned at the sea surface, and the cursor reverts to the pointer shape. To select the vessel, 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. Now press and hold down the mouse button and move the mouse around. The vessel follows the mouse horizontally, but remains at the sea surface. (To alter vessel vertical position, or other details, select the vessel with the mouse, then double click to open the Vessel data window.) 2.3 ADDING A LINE Now add a line. Using the mouse, click on the new line button . The crosshair cursor reappears - move the mouse to a point just to the right of the vessel and click. The line appears as a catenary loop at the mouse position. Move the mouse to a point close to the left hand end of the line, press and hold down the mouse button and move the mouse around. The end of the line moves around following the mouse, and the line is redrawn at each position. Release the mouse button, move to the right hand end, click and drag. This time the right hand end of the line is dragged around. In this way, you can put the ends of the lines roughly where you want them. (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.) Move the line ends until the left hand end of the line is close to the bow of the ship, the right hand end lies above the water and the line hangs down into the water. At this point, the line has a default set of properties and both ends are at fixed positions relative to the Global origin. For the moment we will leave the line properties (length, mass, etc.) at their default values, but we will connect the left hand end to the ship. Do this as follows: 1. Click on the line near the left hand end, to select that end of the line; make sure you have selected the line, not the vessel or the sea. The message box at the left hand end of the status bar tells you what is currently selected. If you have selected the wrong thing, try again. (Note that you don't have to click at the end of the line in order to select it - anywhere 24 w in the left hand half of the line will select the left hand end. As a rule, it is better to choose a point well away from any other object when selecting something with the mouse.) 2. Release the mouse and move it to the vessel, hold down the CTRL key and click. The message box will confirm the connection and, to indicate the connection, the triangle at the end of the line will now be the same colour as the vessel. Now select the vessel again and drag it around with the mouse. The left hand end of the line now moves with the vessel. Leave the vessel positioned roughly as before with the line in a slack catenary. 2.4 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 view direction (the direction you are looking) is shown in the Window Title bar in azimuth/elevation form (azimuth=270; elevation=0). You can move your view point up, down, right or left, and you can zoom in or out, using the view control near the top left corner of the window. Click on each of the top 3 buttons buttons in turn: then click again with the SHIFT key held down. The SHIFT key reverses the action of the button. If you want to move the view centre without rotating, use the scroll bars at the bottom and right edges of the window. By judicious use of the buttons and scroll bars you should be able to find any view you like. Alternatively, you can alter the view with the mouse. Hold down the ALT key and left mouse button and drag. A rectangle on screen shows the area which will be zoomed to fill the window when the mouse button is released. SHIFT+ALT+left mouse button zooms out - the existing view shrinks to fit in the rectangle. Warning: OrcaFlex will allow you to look up at the model from underneath, effectively from under the seabed! Because the view is isometric and all lines are visible, it is not always apparent that this has occurred. When this has happened, the elevation angle is shown as negative in the title bar. CTRL+P There are three "hot keys" which are particularly useful for controlling the view. For example gives a plan view from above; CTRL+E gives an elevation; CTRL+Q rotates the view through 90° about the vertical axis. (CTRL+P and CTRL+E leave the view azimuth unchanged.) Now click the button on the 3D View to bring up the Edit View Parameters form. 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. Edit the view parameters if you wish by positioning the cursor in the appropriate box and editing as required. If you should accidentally lose the model completely from view (perhaps by zooming in too close, 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. Press the Reset button on the Edit View Parameters form. This also resets back to the default view. Zoom out repeatedly until the model reappears. Close the 3D View and add a new one (use the Window|Add 3D View menu item). The new window will have the default view centre and view size. 25 w 2.5 Note: STATIC ANALYSIS If you are running the demonstration version of OrcaFlex then this facility is not available. . The message To run a static analysis of the system, click on the Static Analysis button box reports which line is being analysed and how many iterations have occurred. 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", and the Static Analysis button changes to light grey to indicate that this command is no longer available. The appearance of the line will have changed a little. When editing the model, OrcaFlex uses a quick approximation to a catenary shape for general guidance only, and this shape is replaced with the true catenary shape when static analysis has been carried out. (See Static Analysis for more details). We can now examine the results of the static analysis by clicking on the Results button This opens a Results Selection window. You are offered the following choices: • • Results in numerical and graphical form, with various further choices which determine what the table or graph will contain. Results for all objects or one selected object. . Ignore the graph options for the moment, select Summary Results and All Objects, then click Table. The Results window then shows a summary of the static analysis results. Use the scroll bar at the right hand side to view all the information in the summary table. To view more static analysis results repeat this process: click on the Results button and select as before. 2.6 DYNAMIC ANALYSIS We are now ready to run the simulation. If you are running the demonstration version of OrcaFlex then you cannot do this, but instead you can load up the results of a pre-run simulation - see Examples. . As the simulation progresses, the status bar reports Click the Run Simulation button current simulation time and expected (real) time to finish the analysis, and the 3D view shows the motions of the system as the wave passes through. After the simulation has been run (or loaded), the Object icons are replaced by four Replay Control buttons . Click the Start Replay button . An animated replay of the simulation is shown in the 3D view window. Use the view control keys and mouse as before to change the view. The replay consists of a series of "frames" at equal intervals of time. Just as you can "zoom" in and out in space for a closer view, so OrcaFlex lets you "zoom" in and out in time. Click on the , edit Interval to 0.2s and click OK. The animated replay is now Replay Parameters button slower (because more frames are being shown) but the motion is much smoother than before. Now click again on Replay Parameters, set Replay Period to Whole Simulation and click on the Continuous box to deselect. The replay period shown is the whole of the simulation period. You will now see the simulation start from still water, the wave building and with it the motions of 26 w the system. Simulation time is shown in the Status bar, top left. Negative time means the wave is still building up from still water to full amplitude. At the end of the simulation the replay pauses, then begins again. to pause the replay. Clicking repeatedly on this Now click on the Replay Step button button steps through the replay one frame at a time - a very useful facility for examining a particular part of the motion in detail. Click with the SHIFT key held down to step backwards. To exit from "single frame" mode click on the Stop Replay button . You can then restart the animation by clicking on 'Start Replay' as before. To slow down or speed up the replay, click on 'Replay Parameters' and adjust the speed. 2.7 MULTIPLE VIEWS You can add another view of the system if you wish by clicking on the View button . Click again to add a third view, etc. Each view can be manipulated independently to give, say, simultaneous plan and elevation views. To make all views replay together, click on Replay Control and check the All Views box. To remove an unwanted view simply close its view window. To rearrange the screen and make best use of the space, click Window and choose Tile Horizontal, Tile Vertical (F4) or Cascade (SHIFT+F4). Alternatively, you can minimise windows so that they appear as small icons on the background, or you can re-size them or move them around manually with the mouse. 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. 2.8 LOOKING AT RESULTS . This opens a Results Selection window. Now click on the Results button • • You are offered the following choices: results as Tables or Graphs, with various further choices which determine what the table or graph will contain. results for all objects or one selected object. Select Time History for any line, then select Effective Tension at End A and click the Graph button. The graph appears in a new window. You can call up time histories of a wide range of parameters for most objects. For lines, you can also call up Range Graphs of effective tension, curvature, bend moment: and many other variables: these show maximum, mean and minimum values of the variable plotted against position along the line. Detailed numerical results are available by selecting Summary Results, Full Results and Statistics. Time history and range graph results are also available in numerical form - select the variable you want and press the Values button. The results can be exported as Excel compatible spreadsheets for further processing as required. Further numerical results are available in text form by selecting Summary Results, Full Results and Statistics. Windows displaying system views or graphs can be automatically arranged (Tiled or Cascaded) on screen as they appear by selecting Window|Auto Arrange (this is the default setting on start up). Windows displaying text are not automatically arranged on opening, but are included in any subsequent rearrangement of the screen. 27 w Results Post-Processing Extra post-processing facilities are available through Excel spreadsheets. 2.9 GETTING OUTPUT You can get printed copies of data, results tables, system views and results graphs by means of the File|Print menu. Output can also be transferred into a word processor or other application, either using copy+paste via the clipboard or else export/import via a file. Note: Printing facilities are not available in the demonstration version of OrcaFlex. 2.10 INPUT DATA Take a look through the input data forms. Start by resetting the program: click on the Reset button and answer 'Yes' to the warning prompt. This returns OrcaFlex to the reset state, in which you can edit the data freely. (While a simulation is active you can only edit certain noncritical items, such as the colours used for drawing.) Now click on the Model Browser button Model Browser. . This displays the data structure in tree form in the Select an item and double click with the mouse to bring up the data form. Many of the data items are self explanatory. For details of a data item, select the item with the mouse and press the F1 key. Alternatively use the question mark Help icon in the top right corner of the form. Have a look around all the object data forms available to get an idea of the capabilities of OrcaFlex. End of Tutorial We hope you have found this tutorial useful. To familiarise yourself with OrcaFlex, try building and running models of a number of different systems. The manual also includes a range of examples and technical notes which expand on particular points of interest or difficulty. Finally, please remember that we at Orcina are on call to handle your questions if you are stuck. 28 w 3 3.1 EXAMPLES INTRODUCTION OrcaFlex comes with a tutorial and a comprehensive collection of example files. The full set of example files are on the OrcaFlex CD (see CD:\Demo_CD\OrcaFlex\Examples), and when OrcaFlex is installed some or all of the examples (depending on your installation options) are copied into the OrcaFlex installation directory. There are a lot of examples, so they are listed twice below. The first list is organised by type of application and the second list by OrcaFlex feature. Most examples include both data files (*.dat) and pre-run simulation files (*.sim). Open the simulation file and then reset to the default view for that example (see the right-click popup menu on the 3D view or use the CTRL+T shortcut). Note that the examples have been chosen to illustrate the capability of OrcaFlex and are not necessarily examples of good engineering practice. In fact, one of the great advantages of OrcaFlex is that you can try out a wide range of ideas very quickly, and filter the good ones from the not so good. Examples Listed by Type of Application Riser Systems - Simple Models A01 Catenary Riser A02 Lazy Wave Riser A03 Steep Wave Riser A04 Lazy S Riser - detailed A05 Lazy S Riser - simple A06 Steep S Riser A07 Pliant Wave Riser A08 Pliant S Riser Riser Systems - more complex B01 Jumper to High Tower B02 Riser to Low Tower B03 Multiple Towers B04 Releasable Turret B05 Detailed Pliant Wave B06 Full Field Layout Steel Catenary Risers C01 Catenary SCR C02 Lazy SCR C03 Steep SCR Tensioned Risers, TLPs, SPARs D01 Drilling Support D02 SPAR D03 TLP 29 w Mooring Systems E01 Buoyed Mooring (No Waves) E02 Buoyed Mooring (Waves) E03 Released Mooring Buoy E04 Branched Mooring Buoy Systems F01 CALM Buoy F02 Chinese Lantern F03 Current Meter Mooring F04 Deep Water Mooring Installation G01 Pipelay G02 Lay on tower G03 Crane Lower G04 End Pull-up G05 Midline Pull-up G06 Midline Local G07 Pipe Lift G08 Snag Pull-in G09 Anchor-last Deployment G10 Lower with Bend Limiter Offloading Systems H01 Stowed Line H02 Floating Line H03 Jacket to Semisub Towed Arrays I01 Streamer Array I02 Deployment with Sub Pre and Post processing J01 Batch Script J02 Results J03 Stress Analysis J04 Fatigue Analysis Line-on-line Contact K01 Line on Line impact K02 Line on Line slide Examples Listed by OrcaFlex Feature Topic General Units C01 Examples 30 w Simulation stages Environment Sloped seabeds Profiled seabed Vessel Drawing vessel type vs vessel Vessel sides using solids Using a vessel to model a stationary object Vessel forward speed vs current Vessel forward motion Line types Line Types Wizard: Smearing Line Types Wizard: Chains Line Types Wizard: Wires Limit compression Stress diameters Variable/non-linear properties Line ends Line end orientation Lay azimuth Use of different pens Encastré ends Line end stiffness values Slip joints Lines Clumps Alternative first stage static methods Prescribed shape Branched lines Vertical cantilevers Replacing lines with winches Replacing lines with buoys Buoys Generating buoy/seabed friction Wings Winches Identifying winch initial length Links Links for contact force Links:- non-linear stiffness G01 D01 G04/G05/G07 G03 I01 F02/G04/H01 F02/G08 G04/G05/G06 A08/E04/H01/I01 B01 G04/G05 I02 A01 A01 A07 B01 C03 D01 A02/C02/C03 A04/A05 F03 A04/A05/E04 C02 A01/G10 D01 H01 H03 I01 B04/I02 A01/C03 B05 B04 31 w Modelling guides Restraining with links Solids Solids for visualisation Statics Multiple buoy convergence Winch or spring to assist statics convergence Results Coarse segmentation problems Rectified curvature Clashing Solid/line interaction control in statics Line/line clashing Line/line vs line/solid contact Tethers Tethers as links Tethers as lines Midwater arch Riser connected to midwater arches - options Others Marking structures for clearance checks Trapped water Use of global and local models D01 D02/G04 G04/G05 A04/A05 A07/A08 B05 A06 G08/H03 G08 / H03 A01/C01 A02 E01/E02/I01 H02 A03/B02/F03/G01/G03/G08/I02 D02 B04/G09 3.2 A - RISER SYSTEMS - SIMPLE MODELS 3.2.1 A01 Catenary Riser See the A directory in the OrcaFlex Examples. Introduction This is the simplest riser configuration. Two lines descend from a vessel to the seabed. Although close to vertical when they leave the vessel, they are parallel with the seabed at touchdown. The example also shows OrcaFlex ability to model a sloped seabed, non-linear axial stiffness and variation of drag coefficient with Reynolds Number. Building the model To slope the seabed, the angle of slope from horizontal needs to be defined, as does its heading. In this example the slope is 5º up from horizontal and has a heading of 180º, i.e. along the -X axis. In the view +X is to the right, therefore the slope rises to the left. The settings are shown on the 'Seabed' tab on the Environment Data form. 32 w The catenary is very simple to build. Add a line. Attach End A to the vessel and anchor End B, giving it a Z coordinate of zero so it is exactly on the seabed. The default catenary convergence option is best. To assist the convergence routine, specify the end orientations and the lay direction. In this example the line ends have an azimuth of 0º, i.e. the line runs from End A to End B along the +X axis. At End A declination is 153º, i.e. the line leaves the vessel 27º from vertically downwards. At End B declination is 95º, i.e. parallel to the seabed (in the more usual case of a horizontal seabed, declination would be 90º). Note that in each case the orientation is given with respect to the local axes of the attached structure. For End A this is the vessel, for End B the sloped seabed. Friction would have had an effect on the line position when it was being installed on the seabed. The lay azimuth, the heading of the line as it was laid on the seabed, allows this friction effect to be included when determining the static position. For this catenary we assumed End B was laid first, then moving to End A. Therefore the lay azimuth is 180º. For the second line, copy and paste in the model browser, then offset the ends along Y. From the Model Browser, select Variable Data and look at the 'Drag Coefficients’ section. A table called ‘Re vs Cd’ is presented relating Reynolds Number to Drag Coefficient. Select Profile to see it as a curve. Note that the relationship here is specific to one OD and surface roughness. It cannot be applied for all lines. Now look at axial stiffness. It has been set so there is a different slope when in compression than tension. One of the lines will use constant axial stiffness, the other will use variable. From the Model Browser, select Line Types and look at the Hydrodynamics section. The Normal x Drag Coefficient selected is ‘Re vs Cd’. At each time step OrcaFlex will calculate the Reynolds Number at the node and apply the appropriate Cd value. This will also be applied for the y direction as ‘~’ has been selected. See axial stiffness for details. A catenary needs refined segmentation at the touchdown point. If noise occurs in the tension time histories it may be due to too coarse segmentation about the touchdown point. Note that the natural period of the line may also reduce as a result, requiring smaller step sizes. A catenary is also prone to compression at the seabed in deep water. If a wave is being generated in the line ahead of touchdown it may be due to coarse segmentation, see above. However if the compression remains the same after refinement, it is probably real. From the Model Browser, select '10" Cat' and double click to open its 'Line Data' form. Select the 'Structure' tab and look at the segmentation for the line. The lengths are as short as 0.5m at the touchdown point. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Look at the range graph of the line x-Drag Coefficient in the latest wave. Note how it varies between 0.4 and 1.2. Look at the range graph of effective tension for both lines. Zoom in from 100m (about touchdown point) to the end. Note the difference in compressive load distribution between results for constant and variable tension. These are not great in this example but could be significant in a deep water system. Look at the range graph of curvature for both lines. Zoom in from 100m to 140m, about touchdown. Note that the constant axial stiffness results in slightly higher curvature at the touchdown. The second, far smaller peak occurs in the length on the seabed and is due to the 33 w umbilical curving out of plane to relieve compression. (CTRL+P). Look at the animation in plan view 3.2.2 A02 Lazy Wave Riser See the A directory in the OrcaFlex Examples. Introduction A lazy wave formation is similar to a catenary but has support provided at about midwater by distributed buoyancy modules. 'Lazy' means that the riser centreline is parallel with the seabed on contact while 'Wave' describes the line shape as a result of the buoyancy modules. Building the model The line is built in the same manner as for a catenary, see Catenary Riser. However, at least two line types are applied. The first has the properties of the bare line. The second has the combined properties of the line and the buoyancy modules. Each module can be modelled individually in OrcaFlex. However it is more efficient and convenient to smear the properties of the modules over the buoyed length of the riser, as shown in this example. This can be achieved quickly using the Line Type Wizard facility, if the riser and module properties are known. The Line Type Wizard is only fully accessible when the program is in the Reset state. Press the 'Reset' button or F12. Open the Line Types data form, select '10" + Floats' and then press the Wizard button. You are now in the Wizard routine. Step through it to see how the '10"+Floats' properties were built. This facility allows you to easily experiment with module properties and pitch (spacing) to get the configuration you wish. Now open the 10" Wave data form and select the Structure tab. This example has 110m of bare riser descending from the vessel, followed by 50m of riser with modules then 60m of bare riser again before finishing at the seabed. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Look at the curvature range graph through the latest wave. Note the sudden change in curvature at 110m and 160m where the buoyed length begins and ends. The other sudden drop is at about 190m, the touchdown point. Look at the curvature time history at an arc of 110m. This is the resultant curvature and is rectified, i.e. always positive, so the curve trough has been reflected to become a peak. Now look at the curvature about the line local Y-axis, within the XZ plane. This is called y-curvature. This has not been rectified so shows that the line reverses in curvature through the wave cycle. Now look at the y-curvature range graph through the latest wave and compare it to the one for the resultant curvature. 3.2.3 A03 Steep Wave Riser See the A directory in the OrcaFlex Examples. Introduction A steep wave formation has support provided at about midwater by distributed buoyancy modules and has a vertical connection at the seabed. 'Steep' means that the riser centreline is 34 w vertical at the lowest end while 'Wave' describes the line shape as a result of the buoyancy modules. This model also shows the OrcaFlex facility to input multiple wave trains. Building the model The line is built in a similar manner as for a Lazy wave, see Lazy Wave Riser. However the lower end is vertical rather than horizontal when it reaches the seabed. The end declination is therefore 180º, indicating the line is heading vertically down, rather than 90º indicating horizontal. In this example End B is anchored 5m above the seabed on top of a terminal. The terminal is represented by a solid block. As it is only there for visual purposes, it has no contact stiffness. From the Model Browser, select ‘Environment’ and go to the Waves form. There are two wave trains specified. The first is a random wave train called 'Local', representing local wind-driven seas. The second is a long regular wave train called 'Swell', representing a swell from a distant storm. When you select one of the wave train names, the data for that wave train appears. To see the sea surface when the waves are superimposed, go to 'Waves: Preview' and select 'View Profile'. There is a wave peak just after time zero, so the simulation start time has been set to 5 seconds. This helps the build-up transients dissipate before the first wave peak excitation occurs. Note the headings for the two wave trains differ by 10º. You can see this is a plan view (CTRL+P), since the axis symbol in the top right shows both wave headings. Results Go to the default view (CTRL+T) and look at the animation through stage 1. Look at the for effective tension time history graph at End A for the whole simulation, and at the y-curvature range graph for stage 1. The y-curvature is the curvature about the line local Yaxis, i.e. within the XZ plane. Note how it shows the sag and hog of the line as well as the curvature just above the seabed termination. As this is an in-plane case, curvature about the local X-axis is negligible. 3.2.4 A04/A05 Lazy S Riser See the A directory in the OrcaFlex Examples. Introduction A lazy S formation is similar to a catenary but has support provided at about midwater by an arch structure. 'Lazy' means that the riser centreline is parallel with the seabed on contact while 'S' describes the line shape as a result of the arch. Building the model The riser is modelled as two lines. The upper line descends from the vessel to the arch while the lower line descends from the arch to the seabed. The arch is modelled using an OrcaFlex 6D lumped buoy model. It is important to get the physical and hydrodynamic properties of the arch as accurate as possible as they have a significant effect on the system behaviour. See Modelling Mid-Water Arches. The lines are usually protected from over bending at the arch by a trough structure. Two examples of modelling this are shown. 35 w The detailed model has the trough as two cylindrical solids attached to the arch. The solids must have stiffness specified, so they can push the lines out, and the segmentation of the line lengths in contact must be fine enough to allow them to curve around the solids. This takes longer to set up but gives the best representation of riser/trough interaction as it allows the risers to roll on and off the arch. The upper lines have End A at the vessel, descending at 10º from vertical. End B is at the arch top and is horizontal i.e. 90º. Note that end orientations are with respect to the local axes of the objects to which they are attached. The lower lines have End A at the arch top and End B on the seabed. Both ends are horizontal with respect to the arch and seabed axes. Note that if weather loads are to be applied out of the riser plane, it is advisable to make the connections at the arch Encastré, i.e. apply infinite bend stiffness. This will prevent the lines at these ends rotating freely out of the plane, which would not occur in the real world due to the end fittings. The simple model shows the lines are pinned at either side of the arch. The mass and volume of line and its contents between the pinned connections is then included in the arch model. Note that the line length either side of the arch has been reduced by 6.5m, the length of line from the pin to the arch top. The other main difference between the two models is the tether arrangement. Most arches have the tethers connected via bridles, i.e. two short chains (bridles) either side of the arch connected to the tether top via a tie plate to form a 'Y' shape. In the simple model the tethers are attached directly to the arch with the bridles shown as part of the arch drawing only. In the detailed model the bridles are included as lines attached to the arch while the tethers are attached to the bridles via 3D buoys. A 3D buoy can be used as chains have no bend stiffness, so rotational moments do not need to be transferred. The Line Type Wizard routine quickly builds chain properties for you. Select '2" Chain' on the Line Types data form then press the Wizard button. You are now in the Line Type Wizard routine. Step through it to see how the '2" Chain' properties were built. Wire properties can also be generated with Wizard by selecting the Rope category. Note that, unlike the risers, the chain properties have the 'Limit Compression' option turned on. This is as chains go slack rather than resisting compression. The maximum compression possible is therefore zero. The simpler model is easier to set up and gives quicker runs. However it will not give the detailed riser/arch interaction due to the line lifting off and dropping onto the arch. It will also not show the loads on the bridles such as snatch loads. Results Go to the default view, CTRL+T, and look at the animation through the latest wave for both cases. Zoom in on the arch and observe its motion. Look at the motion of the arch in the global X direction, surge in this case, through the whole simulation. Note how quickly it settles into a cyclic motion. 3.2.5 A06 Steep S Riser See the A directory in the OrcaFlex Examples. Introduction A steep S formation is supported at about midwater by an arch structure and has a vertical connection at the seabed. 'Steep' means that the riser centreline is vertical at the lowest end while 'S' describes the line shape as a result of the arch. 36 w Building the model The line is built in a similar manner as for a Lazy S, see Lazy S Riser. However the lower end is vertical rather than horizontal when it reaches the arch anchor base. The end declination is therefore 180º, indicating the line is heading vertically down, rather than 90º indicating horizontal. In this example the lower line End B is anchored 5m above the seabed on top of the arch gravity base, represented by a solid block. As it is only there for visual purposes, the block has no contact stiffness. Note also that the lower line convergence routine is now a spline. A solid acts by pushing a node towards its nearest surface. If 'Catenary' or 'Quick' options were selected, the line would begin nearly vertically but slightly towards the vessel due to the current heading in this example. The solid would therefore push it out towards the nearer vessel side of the arch. Try it and see. The line must therefore be forced to remain on the right hand side of the arch and this is achieved by a spline. It does not need to be very precise, as the static analysis will refine the line position. It just needs to be enough to hold the line to the right of the arch at the start of the static analysis. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Zoom in on the arch and observe its motion. 3.2.6 A07 Pliant Wave Riser See the A directory in the OrcaFlex Examples. Introduction A pliant wave formation is a lazy wave with the addition of a tether restraining the touchdown point. Building the model The line is built in the same manner as for a lazy wave, see Lazy Wave Riser. In this example three line types are applied. The first has the properties of the bare line. The second has the combined properties of the line and the buoyancy modules. While the third has the pitch (spacing) of the modules halved. The second set of buoyed properties was generated by copying the first set and using Line Type Wizard to halve the pitch. OrcaFlex then generates the new properties for you. Also look at the pen setting in line types data form. Each property has a different colour and pen thickness so they can be identified easily in the view. Note that '10" Prod 1' needs to have 'Use Line Types Pen' in the Drawing tab selected for these settings to show. The system is made pliant by the addition of a tether. This example has the tether modelled as an OrcaFlex link '10"Prod#1'. This is the simplest way of modelling the tether and is sufficient for most cases. Note that the link has no mass or hydrodynamic properties. The 9.9m long link is anchored at 1.8m above the seabed, allowing for the height of an anchor. It is then attached to the line at an arc length of 176m from End A. The link can only be attached to a node. Therefore segments must be sized so that a node is present at the required position. In this example the second '10"Product' section ends at this arc length. 37 w Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Look at the y-curvature range graph in the latest wave. The y-curvature is the curvature about the line local Y-axis, i.e. within the XZ plane. Note how it shows the sag and hog of the line as well as the curvature at the tether and touchdown. 3.2.7 A08 Pliant S Riser See the A directory in the OrcaFlex Examples. Introduction A pliant S formation is a lazy S with the addition of a tether restraining the touchdown point. Building the model The line is built in the same manner as for a lazy S, see Lazy S Riser. This system has several risers attached to a communal arch. Instead of modelling the trough structure, the lines are pinned at either side of the arch. The mass and volume of the lengths on the arch are then incorporated into the arch model. This is the simplest way of modelling the risers on the arch. It is easy to set up and gives quicker runs. However a better representation is given by the more detailed model, which allows the lines to lie on solids representing the troughs. See the Lazy S Riser examples for a comparison. The arch in this example is held in place by a tether and bridle arrangement. As lines cannot be directly linked to each other, the tethers and bridles are joined via simple 3D buoys, 'Bridle E' and 'Bridle W'. These are given negligible properties, as they are simply a means of joining the lines and do not contribute to the behaviour of the system. See Links. The system is made pliant by the addition of tethers to the lines. This example has the tethers modelled as OrcaFlex links. This is the simplest way of modelling the tether and is sufficient for most cases. Note that the link has no mass or hydrodynamic properties. As they connect to nodes on the lines, the line segments must be arranged so a node is present at the required arc length. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Observe how close the lines get to the semi-submersible structure. Look at the tension time history of any of the lines through the whole simulation. Note how quickly the transient noise is damped out. Plot time histories of the arch motion through the whole simulation. The trends show that the arch has not yet settled into a fully cyclic motion. A longer run is required. 3.3 B - RISER SYSTEMS - MORE COMPLEX 3.3.1 B01 Jumper to High Tower See the B directory in the OrcaFlex Examples. 38 w Introduction This example has jumpers connected from a vessel to the top of a high tower, i.e. the tower top is close to the surface. The lines then descend to the seabed as rigid structures within the tower. An installation of this type can be found in the Girassol field. As this is a deep water system, the tower top will flex under the weather and jumper loads. It has therefore been modelled as a very stiff line with one end fixed, i.e. a vertical cantilever. As the motion may be dependent on loads from the jumpers as well as the waves and current, all attached jumpers need to be modelled. If the tower motions are known, it can be modelled as a vessel with the motions specified. This would mean that individual jumpers could be analysed, if required, as they would have no effect on the modelled motion of the tower. Building the model The eight jumpers extend from the vessel side to the top of the deep water tower. They are heading vertically downwards relative to the vessel when they leave it and are restrained in this position by applying infinite bend stiffness at the end. They are then heading 30º from vertically upwards relative to the tower top when they arrive there. Again bending stiffness at the line end restrains it in this position. Note that a fully restrained end, often called an Encastré, is only required if it is expected to affect the behaviour of the line or the attached structure. In this case the lines are short so more sensitive to end effects. Also the line connection loads may affect the tower top behaviour. Try running the model with pin joints, by setting the connection stiffness to zero, to see how the behaviour changes. The tower is basically a very long, thin, vertical cantilever with a mass on the free end representing the attachment structures. As the ratio of tower diameter to length is very small, 1e^-3, it can be considered a very stiff riser that will move under environmental and system loads. It has therefore been modelled as a line, anchored at the seabed and attached to a 6D spar buoy at the top. Infinite bend stiffness has been applied at both ends. The spar buoy is the simplest of the 6D buoys available. It is therefore convenient for modelling the mass of structures at the top of the arch and for connecting lines. Remember that lines cannot be directly connected to each other so an intermediate buoy is required. As the tower rotations need to be considered, a 6D buoy is used. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. The tower appears to hardly move. A time history graph of 'X' motion (surge) and 'rotation 2' (pitch) for 'top buoy' show some motion is occurring. 3.3.2 B02 Riser to Low Tower See the B directory in the OrcaFlex Examples. Introduction This example has risers connected from a vessel to the deep water tower, i.e. the tower top is close to the seabed. The risers are protected from over bending at the tower by a trough 39 w structure, as with a lazy S configuration, see Lazy S Riser. An installation of this type can be found in the Troll C field. Building the model The risers are modelled in two halves. The upper catenary extends from the vessel down to the tower top. The lower catenary extends from the tower top to the seabed. The trough structure is modelled as a cylindrical solid, allowing the riser to lift off and drop back on. See Lazy S Riser for a more detailed description of this arrangement. Note that making the ends fixed at the arch, Encastré ends, means that the lines do not rotate freely when environmental loads are applied out of the riser plane. Instead they are held in the riser plane, as would be the case with the real clamps on the tower. A vertical cylinder represents the tower. This has no stiffness as it is for visualisation only. However, if clashing is to be considered, stiffness can be applied. See Line Clashing. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Apart from the vessel roll, not much appears to be happening. Now zoom in to the umbilical near the seabed. The sag can be seen to rise and fall with the motion of the vessel above. Look at a range graph of tension in 'Umb Up 1' through the latest wave cycle. Note that although there is a significant tension variation near the surface, End A, it is nearly negligible near the tower top, End B. The same plot for 'Umb Down 1' shows no tension variation along the arc length from the tower top to the seabed. This indicates environmental loads are insignificant at this depth, as would be expected. 3.3.3 B03 Multiple Towers See the B directory in the OrcaFlex Examples. Introduction This system shows a field of risers and jumpers distributed from a single vessel via three tower structures. An installation of this type can be found in the Girassol field. Building the model The examples Jumper to High Tower and Riser to Low Tower show how each component part is constructed. The main difference is that the high and low towers are now one structure with the jumpers at the top and the risers at the sides, near the base. To manage this, the tower is split into two lines joined by a 6D lump buoy with nominal properties. A 3D buoy cannot be used in this example, as rotations of the ends are important. The OrcaFlex model only shows line centrelines. In this case cylindrical solids have been added to the lower parts of the tower to represent the outer diameters. This means that interference between the risers and the lower part of the tower can be observed in the animation. If the effect of clashing needs to be modelled then this would be set up between the riser and the line representing the lower tower, see Jacket to Semisub for an example. 40 w Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Look in elevation as well. 3.3.4 B04 Releasable Turret See the B directory in the OrcaFlex Examples. Introduction This model represents an FPSO system with a releasable turret. The simulation shows the turret falling away and the FPSO moving off station. An installation of this type can be found in the Terra Nova field. Building the model The mooring lines and pliant wave risers are connected to a 6D spar buoy that has the physical and hydrodynamic properties of the real buoy. Note that these values need to be as accurate as possible to effectively model this system when the buoy is released from the vessel. A solid cylinder has also been attached to give a better visual representation of the buoy shape. The cylinder has been assigned a non-zero stiffness so that interaction with the attached lines is modelled if clashing occurs. The buoy is attached to the vessel by three vertical and four horizontal links. These links are linear spring/dampers that have been set up to fully restrain the buoy. You can split your analysis into as many stages as you like. For a simple case only, Stage 0, build-up, and 1, simulation, are required. However if a number of events are occurring, as in this example, then the analysis will need to be split into more stages. During the build-up stage wave amplitudes are gradually increased up to the required value. This prevents the generation of transient loads due to the sudden application of environmental conditions. Full simulation begins at the start of Stage 1. Therefore OrcaFlex refers to this point as 0sec. See Figure: Time and Simulation Stages. In this example the stages can be summarised as shown below. Stage 0 Stage 1 Stage 2 Build up of Waves Full Waves applied -8.25sec to 0sec 0 sec to 5sec Links released at start and 5sec to 35sec vessel moves forward If you look at the data for 'VertLatch1' you will see that it will release at the start of stage 2, as will the other tethers. The buoy will then be free to drop deeper into the water. After release of the buoy, the vessel will move forward, i.e. to the left of the view as it has a heading of 180º. Look at the data page for 'FPSO'. Prescribed motion shows that it moves forward with a velocity of 2m/s during Stage 2. Results Go to the default view (CTRL+T) and look at the replay through the whole simulation. Note the buoy dropping away at 8.25sec and the vessel starting to move forward. Look at the proximity of the buoy to the underside of the vessel. 41 w 3.3.5 B05 Detailed Pliant Wave See the B directory in the OrcaFlex Examples. Introduction This pliant wave model has more detail in the tether and touchdown is on the edge of a ridge, the vessel being in deeper water. The ridge top and side profiles are included in the model. An installation of this type can be found in the Buffalo field. Building the model The general pliant wave model is described in the example Pliant Wave Riser. The main difference is in the modelling of the tie-down tether. In the simple version it was represented by a simple spring link. In this version the riser and tether are modelled as three lines, the upper length from FPSO to the clamp, the lower from the clamp to the anchor and the chain tether. They are joined together at the clamp, which is a 6D spar buoy. This has the properties of the clamp itself and allows transfer of bending moments from the riser at one end to the one at the other. This more detailed model takes longer to set up and run but includes the physical and hydrodynamic properties of the clamp and chain. The model also shows the OrcaFlex Seabed Profile facility. The seabed, ridge wall and top need to be modelled to ensure no clashing occurs. Simple profiles could be modelled with solids but, as friction is not included in solid/line interaction, its applicability would be limited. Instead the seabed profile can be defined by a series of points and a smooth cubic spline fit. Beyond the defined points the seabed is assumed horizontal. Look at the Seabed tab on the Environment data form for the profile applied here. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Note how the riser remains clear of the ridge and seabed throughout the wave cycle. Plot the range graph of seabed clearance through the latest wave for the 'Umb Up'. Note that it takes account of the seabed profile, as shown by the trough at an arc of about 200m where the seabed rises locally and at an arc of about 400m where the ridge edge juts out. 3.3.6 B06 Full Field Layout See the B directory in the OrcaFlex Examples. Introduction The model contains 2 ships, 22 lines and various other items, and is modelled in a random sea. In practice, it would be unusual to model the whole of a system at once, but this example serves to demonstrate that OrcaFlex can readily handle very complicated systems. OrcaFlex imposes no limits on the number of lines, ships, buoys etc. which can be modelled. Building the model This is made up of a number of configurations. Descriptions of how to build them are in the examples listed below: Pliant Wave Riser 42 w Lazy S Riser Buoyed Mooring (Waves) If the configurations have been built in separate OrcaFlex models, they can be placed into one model using the OrcaFlex Library routine. This allows you to open one file then access a second to copy the data across. Results Go to the default view, CTRL+T, and look at the animation through Stage 1. 3.4 C - STEEL CATENARY RISERS 3.4.1 C01 Catenary SCR See the C directory in the OrcaFlex Examples. Introduction This example has a SPAR buoy with three steel pipes (SCRs) descending from it in a catenary formation. Building the model Note that this example has been set up with user defined units. OrcaFlex allows you to use SI, US or user defined (customised) unit combinations. If the units are changed, OrcaFlex automatically converts all the input data for you. See units for further details. The SPAR is modelled as a vessel with its motions defined by RAOs. SPAR buoys that are tall and thin can be modelled as buoys, though there are limitations to the model, see example SPAR.sim. The pipes are catenaries. The example Catenary Risers gives more information on how to generate this configuration. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Look at the curvature range plot of 'SCR 0º' through the latest wave. This shows the maximum, minimum and mean values experienced along the arc length from the SPAR to the anchor. If there is sufficient segmentation in the model in areas of high curvature, the curve will be smooth at the top, i.e. more than one point near the apex as here. Beware if a spike is seen with only one point at the apex. This can indicate that the segment length is too long to follow the curve and the line model has kinked. Remember you may need to zoom in on the apex to see its shape if segment lengths are very small. 3.4.2 C02 Lazy SCR See the C directory in the OrcaFlex Examples. 43 w Introduction Just as for flexible risers, steel risers can be supported in a lazy wave formation. The line is given support at about midwater by a series of buoyancy modules along its length. 'Lazy' means that the riser centreline is parallel with the seabed on contact while 'Wave' describes the line shape as a result of the buoyancy modules. Building the model Each module can be modelled individually in OrcaFlex. However it is more efficient and convenient to smear the properties of the modules over the buoyed length of the riser, as shown in this example. This can be achieved quickly using the Line Types Wizard facility, if the riser and module properties are known. To analysis the system with an alternative module size or pitch (spacing), modify the properties with the Wizard and re-analyse. Pipe effective diameters are given in the Geometry tab on the Line Types data form. Outside diameter is used for buoyancy and hydrodynamic drag calculations, internal diameter for contents mass. Separate stress diameters can be defined on the Stress tab on the Line Types form. We have done this for the 'Buoyed' line type since the outer diameter of this line has been increased to represent the buoyancy modules. Note that the stress values have no effect on the simulation. They are used in post-processing to obtain the stress results. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Note that the SCR moves very little. Look at the maximum von Mises stress range plot for the SCR through the latest wave. This shows the maximum, minimum and mean values experienced along the arc length from the vessel to the anchor. The increase in stress along the buoyed length can clearly be seen. 3.4.3 C03 Steep SCR See the C directory in the OrcaFlex Examples. Introduction As with flexible risers, a steel riser steep wave formation has support provided at about midwater by distributed buoyancy modules and has a vertical connection at the seabed. 'Steep' means that the riser centreline is vertical at the lowest end while 'Wave' describes the line shape as a result of the buoyancy modules. Building the model To slope the seabed, the angle of slope from horizontal needs to be defined, as does its heading. In this example the slope is 3.03º up from horizontal and has a heading of 0º, i.e. along the +X axis. In the view +X is to the right, therefore the slope rises in this direction. The settings are shown in the Seabed tab on the Environmental Data form. The riser ends have been restrained. The lower end has an infinite bend stiffness applied which means that it is prevented from bending. The upper connection is a flex joint. It has a bend stiffness applied greater than zero but less than infinity. This allows some flexing of the end connection structure. 44 w Each buoyancy module can be modelled individually in OrcaFlex. However it is more efficient and convenient to smear the properties of the modules over the buoyed length of the riser, as shown in this example. This can be achieved quickly using the Line Type Wizard facility, if the riser and module properties are known. To analyse the system with an alternative module size or pitch (spacing), modify the properties with the Wizard and re-analyse. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Note that the configuration moves far less than a flexible riser would, as is to be expected. Look at the direct tensile stress range plot for the SCR through the latest wave. This shows the maximum, minimum and mean values experienced along the arc length from the vessel to the anchor. Note how the pipe goes into compressive stress about midwater. Look at the time history of wall tension at an arc length of 500m. Note that the compressive load is small and is not applied suddenly. 3.5 D - TENSIONED RISERS, TLPS, SPARS 3.5.1 D01 Drilling Support See the D directory in the OrcaFlex Examples. Introduction A tensioned drilling riser descends from a platform to the seabed. Building the model The platform drawing is defined in the Drawing tab on the Vessel Types data form except for the tensioner support structure. This is defined in the Drawing tab on the 'Platform' data form. This allows a general representation to be stored with the vessel type and then customised for each vessel using the type. Go to the 'Platform' and change the line type colour. What happens in the view? The slip joint at the top end is modelled as a single segment with very low axial stiffness but high bend stiffness, similar to that of the riser itself (arguably it should be stiffer). The 4 tensioners, in the usual cruciform arrangement, are modelled using four Links of spring/dampers type. In this case their stiffnesses are non-linear but their damping is linear with velocity (a non-linear option is available). The moonpool edges are modelled as dummy lines 'MP FWD', 'MP PORT', 'MP AFT' and 'MP STBD' attached to the platform. They have negligible properties and need only be one segment long as they are markers. Making their lengths slightly shorter than the distance between their end connections makes convergence quicker. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Zoom in on the riser top end. Look at the tension time histories of the four links and the effective tension in the riser. They all vary evenly. Is this what you would expect? Look at the line clearance range graph for the riser through one wave cycle. This reports how close the riser centreline got to any of the dummy lines marking the moonpool edge. Double 45 w click on the graph to reset the axes. Set X as 0 to 50 in 10 steps, Y as 0 to 50 in 5 steps. Zoom in further by dragging a box around the curve minimum. The riser centreline approaches to 2.725m of the moonpool edge. As the riser has a diameter of 0.65m, this means the minimum clearance is 2.4m. 3.5.2 D02 SPAR See the D directory in the OrcaFlex Examples. Introduction A riser descends from the SPAR to the seabed via a guide down the middle of the spar. A constant tension device is at the top of the riser. Building the model The spar is modelled as a vessel with its response to wave loads given as RAOs. It has two solids attached. One is a representation of the SPAR top. As it is for visual purposes only, it has no contact stiffness. The second solid represents the trapped water in the central moonpool of the SPAR. The trapped water facility is used here to model hydrodynamic shielding of the SPAR body so that wave and current effects are suppressed in the moonpool. See Shapes for further information. Fixed guides are fitted in the moonpool. These restrain the riser in the buoy X and Y directions but allows free motion in the Z direction (we neglect friction between the riser and the guides). Three pairs of links spaced vertically, i.e. along the riser centreline, model the guides. These links are hidden in the view window using the OrcaFlex 'hide' option. Open the model browser and click on Guide 1X with the mouse right hand button. You will see an option to 'show' the link. If this is selected, the link will appear in the view window. Hiding is carried out the same way. The links are specified as Spring/Dampers, not Tethers, so that the spring can take compression. Note that the ends of the links are attached to and move with the SPAR. Note also that each link is made very long so that vertical movement of the node to which it is attached makes very little difference to the force in the link, and the link remains near-normal to the riser. Look at 'Guide 1X'. The stiffness profile has resistance to compression when the link length is 0m to 304.5m and resistance to tension when the length is 305.1m to 609.6m. From 304.5m to 305.1m, a gap of 600mm, the link has no action as the riser is within the guide - i.e. the guide has a "rattle space" of 600mm. It is not generally necessary to give the link the true contact stiffness between a riser and a steel guide tube. The important criterion is that the riser should not penetrate the guide so much as to invalidate the model; in practice this usually means that a few millimetres penetration is quite acceptable. If you have some idea what contact force you are expecting, this will enable you to set an acceptable stiffness. If not, then a preliminary trial run will give you some idea of what you need. In general, it is not a good idea to set the stiffness too high as this may lead to noise in the results and possibly to integration instability and the need to re-run with a shorter timestep. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. The motion appears gentle. 46 w Look at the time history of winch length. This is varying to keep the tension constant. It shows that a greater tension is required to keep the line taut as with the present value it is extending. 3.5.3 D03 Tension Leg Platform See the D directory in the OrcaFlex Examples. Introduction A small TLP is modelled with its moorings and an attached umbilical. Building the model The recommended method of modelling a large TLP is as a vessel with RAO data or prescribed motions. However for this small control buoy we have used the OrcaFlex Spar buoy option. Hydrodynamic loads on the buoy are modelled using Morison's equation. See 6D Buoy Theory. In this case there are four mooring tethers plus an umbilical. The umbilical is constrained by a system of cross-ties to prevent clashing with the tethers and a subsea structure. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. The motion appears gentle. Look at the time histories of TLP motion. 3.6 E - MOORING SYSTEMS 3.6.1 E01/E02 Buoyed Moorings See the E directory in the OrcaFlex Examples. Introduction In fields where there is limited space, mooring lines often pass over other structures. To prevent contact, they are sometimes held up by attaching buoys at intervals along their lengths. This example shows a single mooring line that has had two buoys attached. Each is modelled as a 6D spar buoy attached by a link. Building the model This model has a single line representing the mooring while the two buoys are attached with links. This is the simplest means of connecting buoys to lines. The links are springs with no mass or hydrodynamic properties. Each buoy is modelled as a 6D spar buoy. properties of the real buoys. These have the physical and hydrodynamic With a system containing multiple buoys, the degrees of freedom of the whole model are greatly increased. Convergence to a static equilibrium position can therefore be difficult to find. One solution is to reduce the degrees of freedom of each buoy. OrcaFlex allows you the option for each buoy to restrain all rotations in the static analysis. However, in some systems, the convergence is still difficult to achieve, as here. Therefore a solution is to carry out a dynamic analysis with no waves applied, the 'No Waves' case here. 47 w This allows the system to settle dynamically. The static position can then be updated using the Use Calculated Positions button. Static analysis can then be run using these settled positions to get a final definitive position. The static stage can still take some time, this system taking 433 iterations. If the static results are not required then the settled positions from the 'No waves' model can be used as the starting point for dynamic analysis. Dynamic wave loading will quickly damp out any transients due to the static position not being fully converged. This is the option used in the 'Waves' model. Results Load the waves case and go to the default view, CTRL+T. Look at the animation through the whole simulation. This will show the response to the passing random wave train. Zoom in on the upper buoy and see how it responds to the passing waves. 3.6.2 E03 Released Mooring Buoy See the E directory in the OrcaFlex Examples. Introduction This example shows how to model the effect on a mooring line of one of its attached buoys breaking free. Building the model The model is the same as seen in the example Buoyed Mooring.sim. The difference is that the simulation has been split into stages, as listed below. Stage 0 Stage 1 Stage 2 Build-up of Waves Full Waves applied Buoy Released at start -5sec to 0sec 0sec to 10sec 10sec to 35sec During the build-up stage wave amplitudes are gradually increased up to the required value. This prevents the generation of transient loads due to the sudden application of environmental conditions. Full simulation begins at the start of Stage 1. Therefore OrcaFlex refers to this point as 0sec. See Time Origins in Dynamic Analysis. If you look at the data for link 'BotPendant' you will see that it will release at the start of Stage 2. The buoy is then free to rise to the surface. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Note the lower buoy breaking free at 10 seconds. Look at the Z time history of the mooring at an arc of 550m, the attachment point of the lower buoy. See how it drops deeper in the water after the 10 seconds. Also observe the Z motion of the lower buoy and how its momentum throws it out of the water. This is also shown in the animation. 3.6.3 E04 Branched Mooring See the E directory in the OrcaFlex Examples. 48 w Introduction This is a 3-leg "branched" mooring. The three mooring legs and the rising leg are joined together by a coupling modelled as a buoy. The rising leg is then attached to a vessel. Building the model As the chains have no bend stiffness, it is sufficient to connect them to each other with 3D buoys (translation only). 6D buoys would have been required if there were bend moments to transfer. Note that the chain and wire properties have the 'Limit Compression' option turned on. This is as they go slack rather than resisting compression. The maximum compression possible is therefore zero. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. 3.7 F - BUOY SYSTEMS 3.7.1 F01 CALM Buoy See the F directory in the OrcaFlex Examples. Introduction A CALM buoy is held in place by six equally spaced mooring lines. It is attached to the vessel by a hawser and a transfer hose. Building the model The CALM buoy is modelled as a 6D spar buoy in which the object is represented as a stack of co-axial cylinders. See Spar Buoys. In this case we have used a total of 5 cylinders of which the top one (Cylinder 1) represents the turntable and pipework on the deck of the buoy, and Cylinder 5 represents the projecting skirt. It is important to ensure that the physical and hydrodynamic properties of the buoy are as close as possible to the real CALM buoy properties. See Modelling a Surface Piercing Buoy for further discussion of data preparation for CALM buoys and the like. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. The replay shows that the CALM buoy follows the wave surface quite closely, as expected. Look also at the tension results for one of the moorings - say the 6th Mooring, which is the upwave leg. The range graph of effective tension for the latest wave shows that tension in the line goes to zero over part of its length at some point during the wave cycle. It is interesting to find out where in the wave cycle the tension goes to zero (by looking at tension time histories for various points along the line) then try to understand why. Is it, for example, caused by the buoy pitch motion, or by direct wave loading on the mooring chain, or a combination of these and other effects? And how might we modify the system to prevent the moorings going slack? 49 w 3.7.2 F02 Chinese Lantern See the F directory in the OrcaFlex Examples. Introduction This system consists of risers descending from the underside of a buoy to its base on the seabed in a chinese lantern configuration. As they are fixed at the buoy and its base, there must be sufficient length to prevent the risers going taut due to buoy motions. This excess length is accommodated by encouraging the risers to bulge outwards beneath the buoy, hence the name. Building the model The risers are forced to bend outwards by angling their end orientations and fitting buoyancy modules. Press CTRL+Y to turn the local axes view on. Note the heading of the Z-axis at each end. This shows the line heading on leaving End A, at the buoy, and arriving at End B, at the base. Open the Line data form for Riser 1; the Attachments tab shows where buoyancy is attached. The selected method for the riser static analysis is 'spline'. This configuration has a number of static solutions for the line position, not all of which are stable. Using the spline option, we can force the risers into the correct static shape. Try changing to 'Quick' and see what positions the risers form. Note that both 'Quick' and 'Spline' are the first stage static solutions only - in both cases, the Full statics solution then takes over and calculates the true equilibrium shape. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. In elevation view, the default, it appears that the risers contact the mooring lines. However if you switch to plan view, CTRL+P, then it can be seen that the risers remain between the moorings. Look at the surge, X, heave, Z, and pitch, rotation 2, of the CALM buoy. This has not settled after eight wave cycles. The wave period is 3sec while the buoy has a natural frequency of about 2.7sec so the wave excitation is near resonance. Look at the tension time history of 'Riser 1' through the whole simulation. It shows that the riser goes into compression of up to 20kN. 3.7.3 F03 Current Meter Mooring See the F directory in the OrcaFlex Examples. Introduction To obtain information on current velocity at a location, the meters need to be spaced out at different water depths and should ideally have negligible motion due to wave loads. This is achieved by attaching them on a tether beneath a buoy. The buoy needs to be positioned close enough to the surface so that all required metering depths are available, while deep enough that wave loads have little effect. This example shows several current meters evenly spaced along a tether that is held in place by a buoy. 50 w Building the model The buoy is modelled as a 6D spar buoy with properties as for the real buoy. It is held in place by a line with the properties of a wire rope. The Line Type Wizard was used to generate these values. Select 'Wire' in the Line Types data form and press the Wizard button to see how this was done. The current meters are modelled as clumps attached to the tether. A clump is a concentrated attachment that is connected to a node on a Line. It is a small body that experiences forces (weight, buoyancy, drag etc.) exactly as for a 3D buoy. 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. See Attachments: Clumps. A rectangular solid with no stiffness represents the system anchor. Results Load the data file and run statics. See how the buoy equilibrium position is located. Go to the default view, CTRL+T, and see how the buoy equilibrium position is located. Load the simulation file and look at the animation through the latest wave. Not much appears to be happening. This is confirmed by looking at the time history of the buoy motion and the tension range graph for the tether. What happens if the buoy is raised closer to the sea surface? 3.7.4 F04 Deep Water Mooring See the F directory in the OrcaFlex Examples. Introduction The example shows a buoy positioned at the sea surface in deep water. It is held in place by a long mooring line anchored at the seabed. A regular wave train has been applied. Building the model There are two buoys in this model. The first buoy is surface piercing and, in this case, its motion at the surface is of interest. Therefore it has been modelled as a 6D spar buoy. See Modelling a Surfacing-Piercing Buoy. The second buoy is at midwater, connecting two lines as well as applying buoyancy. As the attached lines have insignificant bend stiffness and the applied wave loads are not great, it can be modelled as a 3D lumped buoy. The mooring is made up of a number of different lines and intermediate structures such as shackles. Rather than building up a complex model requiring many lines and buoys, the upper and lower lines have sections with different line types and the structures have been modelled as attached clumps. This is sufficient for most mooring cases. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. The surface buoy is moving with the wave as expected. However its pitch does not vary much due to the righting load from the mooring. Have a look at the time histories of the buoy motion. Note that the buoy is still moving forward with each wave cycle. Zoom out and look at the whole system. On this scale any motion appears negligible. 51 w 3.8 G - INSTALLATION 3.8.1 G01 Pipelay See the G directory in the OrcaFlex Examples. Introduction Pipe lay over the stern in 60m water depth from a 100m long ship. The support rollers are spaced out along a rigid stinger projecting from the stern, and the lay operation is being modelled in head seas and current. This example also shows one method of modelling a prescribed shape in the length already laid. Building the model The stinger is shown as a series of rectangular solids attached to the ship. These are shown here to help visualisation only - they have no effect on the analysis. Similarly, the rollers are shown as small diameter circular cylinders. However the supporting force on the pipe, which the rollers provide, is actually modelled by links. These provide a more reliable way of achieving the required pipe shape. In the present model, the links are hidden. To see them, open the Model Browser (press F2), select each Link in turn, right click the mouse and select 'Show'. Note that line segmentation is arranged so there is a node present at the precise point where a roller support is required. A link is then attached to each of these nodes. The links are specified as Tethers. They extend normal to the pipe and are made very long so that axial movement of the attached node makes very little difference to the force in the link, and the link remains near-normal to the pipe. Note that they are attached to the vessel so move with it. If the pipe lifts off a roller, the link goes slack so no force is applied. If the pipe contacts the roller, the link is taut, applying a restraining force so the pipe does not fall through. This model has a length beyond the touchdown point forming an ‘S’ shape on the seabed (look at the model in plan view, using CTRL+P). There are two methods of achieving this. One is to use the prescribed shape facility in OrcaFlex; this is discussed in more detail in the G04 example. However the geometry can be tricky when one end lifted up as the projected shape on the seabed needs to be specified. This example uses an alternative method, which is to hold the line in its required shape using very short links during statics. They are then released when dynamics starts. See the links 'Prescribed 1' to 'Prescribed 10', which are holding it in place during statics. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Zoom in on the roller positions and see how the line lifts off and on the last two rollers, Rollers 2 and 3. Look at the time history of tension for each tether. This confirms that the line lifts off Rollers 2 and 3, i.e. they go slack. Look at the effective tension range graph for the pipe during the Latest Wave. It shows maximum, mean and minimum tension plotted against arclength along the pipe from the stern of the ship. All points along the line arclength experience compression at some point through the wave cycle. 52 w Look at the tension time history at an arclength of 280m, just ahead of the touchdown point. As the compression is applied gradually, it indicates that it is a real condition. To confirm it is real and not due to the coarseness of the model, halve the segment lengths in this region and see if the compression reduces. This is discussed in more detail in the Catenary Riser.sim example. 3.8.2 G02 Lay on Tower See the G directory in the OrcaFlex Examples. Introduction This is an example of installing a riser over a subsea tower in 300m water. The riser is being paid out from the moonpool of the installation vessel, and is supported from an auxiliary winch at the stern of the ship. There is a clamp about 10m above the attachment point of the winch, which has to be placed in the centre of the support tower. Building the model A series of static "snapshot" analyses may be sufficient. It is a case which presents considerable difficulties in static analysis, but which can be handled quite readily in OrcaFlex. In the case shown, we have used two winches to represent the main riser handling winch in the moonpool and the auxiliary winch at the stern. The critical phase of the installation is modelled in calm water. The main winch pays out 3m of line and the auxiliary winch then hauls in 3m of line, payout of -3m, to settle the clamp into place. The winches are active in different stages to enable the required order. The stages are as listed below. Stage 0 Stage 1 Main Winch pay-out Main Winch pull-in -8sec to 0sec 0sec to 16sec Stage 0, the wave build-up stage, can be used here as no waves are applied. Remember to look at the full simulation though when replaying the animation. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Note how the flowline lowers onto the tower before the clamp is pulled into position. Also look at the flowline time history of heave, Z, and surge, X, at node 35 (clamp) for the full simulation. 3.8.3 G03 Crane Lower See the G directory in the OrcaFlex Examples. Introduction This is an example of modelling the lowering of a template structure from the sea surface to the seabed using two cranes. In practice it would be more usual to look at a series of "snapshots" rather than the complete lowering operation. Building the model The template being lowered and the two spreader bars have been modelled as 6D buoys because rotations are important. The Towed Fish option is convenient for the spreaders, simply because a Towed Fish is a horizontal stick. 53 w The template has been modelled as a spar buoy so that sudden changes in profile can be taken account of as it enters the water, the spar buoy being built up of a series of stacked cylinders. Note that the buoy drawing has been turned off and instead solids attached to the buoy represent the template shape. There is no friction interaction of solids or buoys with the seabed. Therefore dummy lines have been attached to the bottom of the template. These have negligible properties but will generate a friction force when they are pushed onto the seabed by the buoy. The shackles at the top of the bridles are 3D buoys because their rotation need not be considered. The bridle structures are modelled as Links, but Lines could be used equally well. Note that the links to the spreaders have been attached slightly off axis - if they are put all on the axis, then the bar would have no unique orientation and the static analysis would probably fail to converge. Note that slamming loads and the changes in water particle motion due to the presence of the hulls are not included in the model. The winches have the following payout rates: Stage 0 Stage 1 Stage 2 Stage 3 Settle time Both winches payout 20m Both winches payout 65m 1st winch pays out 20m, other 22m -8sec to 0sec 0sec to 20sec 20sec to 60sec 60sec to 100sec The 2nd winch pays out more than the 1st so that one edge of the template will contact the seabed before the other. Note that in Stage 1 and Stage 3 the payout rate is slow. In these stages discrete events occur. In Stage 1 the template becomes fully submerged. In Stage 3 it contacts the seabed. If the payout is too fast, the analysis step size is insufficient to cope with the changes due to these events and the analysis becomes unstable. An alternative solution would be to reduce the step size but this would slow all the simulation instead of just the relevant stages. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Zoom in on the template at the seabed. Run the animation for Stage 3 only to see one side of the template hitting the seabed before the other. 3.8.4 G04 Pull Up Line End into Moonpool Example of a line end being lifted up from the seabed into a moonpool. See the G directory in the OrcaFlex Examples. Introduction A line is lying on the seabed. One end is then pulled up into the moonpool of the vessel. Building the model The line is positioned on the seabed using a prescribed shape. Look in plan view to see how it appears. End B will be pulled up to the vessel so is free and has its pullhead attached as a clump weight at End B, i.e. the arc length of 200m. 54 w A cylindrical solid represents the trapped water in the vessel moonpool. The trapped water facility is used here to model hydrodynamic shielding of the vessel so that wave and current effects are suppressed in the moonpool. A winch on the vessel is attached to End B of the line. It is used to pull in the line while the vessel moves to keep the moonpool approximately above the line end. The analysis is carried out with the following stages: Stage 0 Stage 1 Stage 2 Stage 3 Wave build up Vessel accelerates to 1.6m/s. Winch pull-in 60m Vessel moves at 1.6m/s. Winch pull-in 50m System settles -3.5sec to 0sec 0sec to 14sec 14sec to 28sec 28sec to 35sec If you look at the data for 'Winch1' you will see that an initial length of 120m has been defined. This is the distance from the winch to the attachment point. The easiest way to determine the distance is to run statics with the winch mode set at a specified tension of zero. Statics results for the winch will then report the distance to the attachment point. The winch mode can then be updated to Specified length and that distance input. A settle time has been allowed at the end of the analysis, as there is usually a lag in some areas of a system's response to a load. Stopping too soon can result in some behaviour being missed. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Note how the vessel moonpool remains above the line end during the process. Look at the time history of riser tension at the pullhead, End B. The operation has been modelled in a much shorter time than would really be taken, and the results show some spurious dynamic effects in consequence. Notably, the top tension drops briefly to zero at t = 28s when the winch pull-in abruptly ceases. We could reduce these false effects by carrying out the pull more slowly. 3.8.5 G05/G06 Midline Pull Up See the G directory in the OrcaFlex Examples. Introduction A long line is laid on the seabed. The middle is then pulled up a short distance to allow maintenance or to position the line in a plough. Building the Global model The line is positioned on the seabed using a prescribed shape. This is the easiest way of defining a straight line on the seabed. The line has both ends free but they need to be sufficiently far away from the middle that they experience negligible loading during the lift. The analysis is carried out with the following stages: Stage 0 Stage 1 Stage 2 System settles Winch pulls in 4m System settles -0.5sec to 0sec 0sec to 10sec 10sec to 15sec 55 w In Stage 1 a winch raises the middle of the line 4m, i.e. payout is -4m. The initial length of winch wire has been set to 100m. This is the distance from the winch to the attachment point on the line. The easiest way to determine the distance is to run statics with the winch mode set at a specified tension of zero. Statics results for the winch will then report the distance to the attachment point. The winch mode can then be updated to 'Specified length' and that distance input. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. The winch tension time history shows a drop in tension when it stops pulling in at 10 seconds. This is a dynamic effect causing the line to overshoot. In practice, the lift would be slower and the overshoot smaller. Look at the curvature range plot through Stage 2, the settle period. This reports maximum, mean and minimum curvature through the stage. Zoom in on the section near 550m arc length. The graph is very angular, indicating that there is insufficient segmentation to define the curvature accurately. This model gives a good indication of lift force and tension in the line but a poor representation of maximum curvature. Local model This is a local model of the high curvature region only. Since the system is symmetrical we have modelled a short section to one side of the lift point only and treated the cable as built in horizontally at the lift point. The winch has been used to apply a tension of 23kN at an angle of about 8° below horizontal. Tension and angle are estimated from the global system model. In practice a static analysis of this local model would be sufficient. This is very fast and can be repeated with increasing number of segments until the curvature at the built-in end converges to a value that no longer varies with segment length. 3.8.6 G07 Pipe Lift See the G directory in the OrcaFlex Examples. Introduction A steel pipe is laid on the seabed. The front section is then pulled up by a series of winches until it is alongside a vessel. It is shown as a dynamic lift including wave effects, but a static analysis of the final configuration would often be sufficient. Building the model The line is positioned on the seabed using a prescribed shape. This is the easiest way of defining a straight line on the seabed. End A is free and is to be pulled up alongside the vessel. Three winches are equally spaced on the vessel side and attached at End A and arc lengths along the pipe. They are used to pull up the line. The analysis is carried out with the following stages: Stage 0 Stage 1 Stage 2 Wave build up Winches pull-in 97m System settles -2sec to 0sec 0sec to 32sec 32sec to 40sec If you look at the data for 'Winch A' you will see that an initial length of 112m has been defined. This is the distance from the winch to the attachment point. The easiest way to determine the distance is to run statics with the winch mode set at a specified tension of zero. Statics results 56 w for the winch will then report the distance to the attachment point. The winch mode can then be updated to 'Specified length' and that distance input. A settle time has been allowed at the end of the analysis, as there is usually a lag in some areas of a system's response to a load. Stopping too soon can result in some behaviour being missed. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Look at the tension time history through the simulation for all three winches. Note that only 'Winch C', furthest from the pipe free end, is in tension for the whole simulation. Why is this? Look at the tension and curvature range plots of the pipe for the whole simulation. These plot the maximum, mean and minimum values along the arc length from the free end to the anchor. The tension range plot confirms that the greatest load is taken by 'Winch C', attached at an arc length of 60m. The curvature range plot also shows the greatest peak at the attachment of 'Winch C'. 3.8.7 G08 Snag Pull-in See the G directory in the OrcaFlex Examples. Introduction A line is pulled in to a wellhead funnel by a winch. Snag catchers ahead of the funnel control the pipe entry. Building the model The snag catchers are modelled as two lines of the required diameter. They and the pipe are given contact stiffness values and the clashing option found on the Structure tab of the data form is turned on. Two cylindrical Shapes, Snag1Shape and Snag2Shape, are used to show where the snag catcher is located. In principle, these cylinders could have been used to control the line movements, but the segmentation of the pipe would have to have been very fine as solids only make contact with lines at line nodes. This would have resulted in very small step sizes and so a very long run. Line/line contact occurs between line segments so that coarser segmentation can be used. This model uses line/line contact, so the cylinder shapes are given zero stiffness. For line/line contact to be modelled, the lines concerned require a contact stiffness in their properties, 10MN/m in this example. Accurate contact stiffness values are rarely known for pipes: in this case, all we require is that the snag catcher effectively constrains the pipe, so an arbitrary value can be applied. See Line Clashing for interpretation of the clash forces. To turn the clashing routine on, say 'yes' to Clash check in 'Pipe A', 'Snag 1' and 'Snag 2' pages. Note that the Clash check will result in slower runs so should only be applied where required. For 'Pipe A' it has only been selected for the first 30m of the pipe, i.e. the length expected to contact the snag catchers. The analysis is carried out with the following stages: 57 w Stage Time -1sec to 0sec 0sec to 46sec 46sec to 66sec 66sec to 71sec Winch 'to Snag' 0 1 2 3 Hold -87.84m Release Payout 'to Hub' Relax Relax -15m Hold Settle To Snag Catcher Into Funnel Settle Pipe End A Note that 'Relax' means the winch length varies to keep the tension at 0kN. The winch 'to snag' has three points. It is attached to End A of the pipe, on the seabed between the snag catchers then 2m vertically above the snag catchers. In Stage 1 it pulls the pipe to the point between the snag catchers, it then releases it. Note that having three points for the winch and only pulling into the second ensures the winch length is never zero. The minimum length will be 2m. The distance required to pull in is given in the winch static results. Remember to deduct 2m for the minimum distance. The winch 'to hub' also has three points, again to prevent the length reducing to zero. It is attached to End A of the pipe, the far end of the funnel on the seabed and 2m vertically above it. In Stage 2 the 'to hub' winch pulls the pipe from the snag catchers to the funnel far end. The distance from snag catcher to funnel end, i.e. the distance the winch must pull-in, should be known. The pull-in is carried out with two winches, as there is no interaction between winch wires and other structures. Therefore if one winch were used, it would pull the line straight to the funnel end, ignoring the snag catchers. A settle time has been allowed at the end of the analysis, as there is usually a lag in some areas of a system's response to a load. Stopping too soon can result in some behaviour being missed. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Watch the line being pulled to between the snag catchers then into the funnel. Zoom in on the snag catchers and funnels. Watch the line curve around one of the snag catchers. Look at the time histories of tension in both winches through the whole simulation. Both graphs show tension overshoots and oscillations. These are a consequence of speeding the operation to save time - the actual pull-in operation would probably take an hour or more compared to about 1 minute here. Slowing the rate of winch pull-in will reduce the overshoots and oscillation amplitudes. 3.8.8 G09 Anchor-last Deployment See the G directory in the OrcaFlex Examples. Introduction This model shows the deployment of a typical deep water oceanographic mooring. These moorings are often streamed out behind a moving vessel, with the top end buoy as the first object in the water, furthest from the vessel. When the whole length of the mooring has been 58 w deployed, the anchor is tied off at the vessel fantail, and the vessel proceeds to the correct mooring position. Without stopping the vessel, the anchor is cut free, and the whole mooring free-falls until the anchor hits the seabed. The simulation is used to determine the final position of the anchor relative to the vessel's position when the anchor ties are cut. It is also used to determine the tensions in the line. Note that the mooring line may go slack when the anchor strikes the seabed. If the line is not perfectly torque balanced, it is possible for loops and kinks to form in the line, and these will lead to early failure of the mooring. Building the Model The mooring is represented by a single Line, attached between the Buoy and the Anchor, each modelled for simplicity as 3D buoys. (A more detailed model would use 6D buoys allowing us to study the pitch and roll motions of these objects). The Anchor is attached to the Vessel using a Link, which is released as soon as the simulation starts (see the Link data file). This represents the action of cutting the anchor free. We find an initial static position for the mooring catenary, with the Buoy at a pre-selected position - i.e. it is not included in the static calculation. The Vessel motion is specified in the Vessel data: initially it accelerates to a steady forward velocity of 2 m/s (about 4 kts), then continues forward at constant velocity. Results Go to the default view, CTRL+T, and look at the animation for the Whole Simulation. Choose a refresh interval of 1 second, and a target speed of, say, 500%. See how the catenary shape develops, pulling the top end buoy down from the surface. Look at the time histories of Effective tension at End A (the Buoy) and End B (the Anchor). You will be able to identify the point where the buoy submerges, and the impact forces occurring when the anchor strikes the seabed. Look also at the time history of the Buoy Z coordinate. The buoy maximum depth is about 64m, compared with the static depth of about 42m. This is important when choosing the depth rating of the buoyancy unit. 3.8.9 G10 Lower with Bend Limiter See the G directory in the OrcaFlex Examples. Introduction This example shows the use of non-linear bending to represent a bend limiter on an umbilical termination. A seabed template is being lowered to the seabed, with an umbilical hanging in a loose bight. When the template has landed, the top end of the umbilical is paid out, laying the umbilical on the seabed. Building the model For illustration, the umbilical is attached to the top of the template. Without a bend limiter it would suffer severe overbending. The limiter protects against this over the first 12 m of the umbilical. 59 w Look at the Model Browser and select Variable Data / Structure / Bending Stiffness, and press the Profile button. This will show you the non-linear stiffness characteristic used to model the umbilical+bend limiter combination. It has the following characteristics: • Up to a curvature of 0.25 rad/m the bend stiffness is just that of the umbilical, since the limiter has not yet ‘locked out’. Bend moment = bend stiffness x curvature, so at 0.25 rad/m the moment due to the umbilical alone is 0.25 x (Umbilical Bend Stiffness) = 2.531 kN.m. At the 0.25 rad/m curvature limit the limiter locks and the stiffness rises sharply. This is modelled by the steep step in the bend moment profile. It is usually sufficient to model this with an arbitrary large stiffness, but if the limiter is a rigid plastic material then it may be worth getting an estimated figure for its stiffness to include in the model. The step goes up to a bend moment of 200 kN.m and then the slope reduces again. This helps the static analysis to converge, since it reduces the likelihood of extremely large outof-balance forces arising during iteration towards the static solution. It does not affect the solution itself since the bend moment will not be anything like that high in the solution. • • The non-linear stiffness is used in the Line Type Data for the Line Type called Bend Limiter. Look in the Stiffnesses tab to see where a Name has been substituted for the numerical value of stiffness. Finally, look at the Line Data for the Line called ‘Umb’, and choose the Structure tab. You will see that the Bend Limiter applies over a 12 m length at the termination. Results Run the replay for the whole simulation and see the whole operation on screen (press CTRL T to get the pre-set default view). If you press CTRL P you will get the plan view and see how the umbilical lays out on the seabed. Look at a range graph of umbilical curvature for the full simulation. The bend limiter is present for the first 12m, but there is overbending in the umbilical just beyond the end of the limiter. This indicates that the bend limiter is not long enough to protect the umbilical. 3.9 H - OFFLOADING SYSTEMS 3.9.1 H01 Stowed Line See the H directory in the OrcaFlex Examples. Introduction A floating hose, which is attached to the stern of an FSU (Floating Storage Unit), is stowed by curling it around and attaching the free end to the vessel side. Interaction with the vessel sides needs to be considered. Building the model The vessel sides are modelled as solids so that clashing can be considered. However note that the complex loads due to turbulence and water trapped between the vessel side and the approaching hose are not considered. The hull is modelled as a simple rectangular block attached to the vessel. The hose is attached to the stern of the vessel and on the port side, near the bow. It is modelled as three lines: Hose Top runs from the vessel stern to a clamp where a 'hold back' 60 w chain is attached. Hose Mid runs from the clamp to a Mid-line Connector (MBC). Hose Bot runs from the MBC to the vessel side. The clamp and MBC are modelled as 6D spar buoys, as bending moments need to be transferred between the hose lines. Note that this means the lines are attached to the buoys with Encastré ends, i.e. infinite bend stiffness, and line headings at the ends must be defined. At intervals, clump weights are attached representing flange connections. These are attached to nodes so the segment lengths must be arranged so that a node is present at each flange location. As the lines are not in a catenary shape and 'quick' statics would start off with the lines inside the solid, the best starting point for statics is a spline. Look in plan view, CTRL+P, to see the shape. It need only be approximate, as full statics convergence will refine the shape. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. The range graphs of solid contact force during the latest wave show that the first and last lengths, 'Hose Top' and 'Hose Bot', both contact the hull of the vessel. Looking at the time history of contact force at an arclength of 15m for 'Hose Top' and 35.7m for 'Hose Bot' shows more detail of the contact loads. 3.9.2 H02 Floating Line See the H directory in the OrcaFlex Examples. Introduction The same hose as in the previous example is now modelled trailing free from the FSU stern. During the analysis, the protective chain at the FSU breaks. Building the model The basic model structure is described in the example Stowed Line.sim. However in this case End B is free and the line extends behind the vessel. To assist in static convergence of the free-ended floating hose, a winch is attached. This applies a small tension to encourage the hose into a straight line. This winch releases at the start of dynamic analysis. The analysis is carried out with the following stages: Statics Stage 0 Stage 1 Stage 2 Winch applies 0.1kN tension Winch releases and wave builds up Simulation Chain releases -6sec to 0sec 0sec to 18sec 18sec to 36sec If you look at 'Temp Winch' data you will see it releases at the start of Stage 0. End B of 'Chain' releases at the start of Stage 2. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Look at the transverse waves being generated along the line due to compression. 61 w At 18 seconds the chain releases and can be seen hanging free. Look at the time history of tension in the chain and the hose at End A, the vessel. The chain protects the hose by taking 150kN of load in the first wave cycle. However after 18 seconds the chain is no longer connected and the hose connection must take the entire load itself, shown as a tension increase. 3.9.3 H03 Jacket to Semisub See the H directory in the OrcaFlex Examples. Introduction A cable catenary is suspended between a semi-submersible rig and fixed jacket. It is analysed in a random sea. Building the model Both the jacket and the semi-submersible are modelled as vessels. Although the jacket does not move, being a vessel allows the drawing facilities to be applied and objects to be attached to it. To ensure it does not move, the 'Jacket' RAOs are all set to zero. Circular symmetry is applied so the values are valid for all wave headings. From the Model Browser, select ‘Cable’. Note that the Semisub connect has the End Orientation Gamma angle set at 90º. When torsion is not applied, gamma can be used to define the orientation of End x and y about z. This is convenient if you want all x axes to be normal to the vessel side and all y axes to be parallel, so that result presentation follows one convention. In this example, setting gamma to 90º makes the x axis of the end connection normal to the semisub side, and y parallel to it. This matches the x and y orientations at the Jacket End. Select the view and press CTRL+Y. The end axes will appear in the view. Press CTRL+Y again to turn them off. The main concern in this example is clashing between the cable and the jacket structure. This is best assessed visually. A jacket strut has been made from a line. It has dummy properties with the diameter set to that for the strut. It has then been attached to the jacket. As it is to remain straight, it can be modelled as one segment. Keeping the length slightly shorter than the distance between End A and End B just makes the statics convergence a bit easier. A line is preferable to a solid for this clashing model. Solids only contact line nodes. The cable could slide and allow the solid to fall between nodes. This does not occur with line/line contact. For line/line contact to be modelled, the lines concerned require a contact stiffness in their properties. We have used 100 kN/m in this example, and have applied damping of 1 kN/(m/s). Contact stiffness values are rarely known for pipes so an arbitrary value can be applied. For a violent impact the contact impulse will be insensitive to contact stiffness. For a low speed contact the contact force will be insensitive. See Line Clashing. To turn the clashing routine on, say 'yes' to Clash check on the Structure tab in the data forms for the lines 'Structure' and 'Cable'. Note that the Clash check will result in slower runs so should only be applied where required. For 'Cable' it has only been selected for the last 100m of the line, i.e. the length expected to contact the jacket. A random wave train has then been applied. For details see Setting Up a Random Sea. 62 w Results Time histories and range graphs are available as usual but in these cases the view gives the answers we need. Go to the default view, CTRL+T and look at the full simulation. Note how the cable curves around the strut in the larger waves. 3.10 I - TOWED ARRAYS 3.10.1 I01 Streamer Array See the I directory in the OrcaFlex Examples. Introduction This is an example of a seismic streamer model. The model represents the Port half of the system only i.e. two hydrophone streamers plus one air gun towed from a ship. Building the model The diverter is modelled as a 6D buoy with wings attached. These generate the directional lift and drag from the diverter being towed through the water. See 'Prandtl199' on the Wing Types data form. Pressing the Graph button will show you the lift and drag coefficients versus incident angle. Select any item on the Wing Types data form and press F1 to get more details from the on-line help. Lines cannot be connected directly to lines in OrcaFlex. Branching is therefore achieved using 3D buoys. These are acceptable, as transfer of bending moment between lines is not important for this example. Rather than modelling the two streamers in full, most of each length is represented by a "sea anchor", a 3D buoy with area and drag coefficient set to generate a drag force equivalent to that of the streamer length it represents. Look at 'StrmTail A' data. Getting the initial static position for this type of system can be difficult. There are many buoys so the system has a large number of degrees of freedom. However OrcaFlex allows you to lock individual buoys in place during static analysis. Therefore as each buoy static location is found, it can be held in place and does not have to be recalculated in subsequent static analyses as you determine other buoy positions. The motion of the whole system through the water can be modelled within OrcaFlex in two ways. The vessel can be given a constant forward velocity. However this means that the system origins are constantly moving in relation to the global origin. Also the system will keep moving out of the view window. Alternatively, as the system is moving in a straight line, it can stay put and a current can be applied in the opposite direction of the same velocity and through the full water depth. In both methods the water velocity and heading relative to the system is the same. However applying the current is more convenient for analysis of results. This is the method applied here. Remember to take account of any actual current applied when using this method. Results Go to the default view, CTRL+T, and look at the animation through the latest wave. Look in elevation view, CTRL+E, as well as the default plan. 63 w Plot time histories of the lift, drag and incident angle for the diverter wings. To access these you need to select 'Diverter' for Object on the results page then turn on 'Results for wings'. Note how the lift is far greater than the drag and that the incident angle only varies by 3.5º. 3.10.2 I02 Deployment with Sub See the I directory in the OrcaFlex Examples. Introduction A submarine tows a sensor array. It releases components in turn to position them on the seabed. Building the model The system is to be installed using a submarine. This is modelled as a vessel with a slight response to the wave loading, see the RAO data. The shape is generated using solids attached to the vessel. A line extends behind the vessel with a 6D towed fish, best for horizontal cylinders, attached at the far end to represent the deployer. Lines connect each float to an anchor while, for towing, a short link holds each float close to its anchor. A line also connects the anchors together so that a required maximum separation is not exceeded. The anchors are then each attached to the deployer by a short link. The two floats are modelled as 3D buoys, i.e. translations only, as the detailed motions of the floats are not of interest. The two anchors are modelled as 6D buoys to better model interaction with the seabed, for example if one edge will contact first. The analysis is carried out in the following stages: Stage 0 1 2 3 4 Vessel Accelerates to 1.5m/s Proceeds at 1.5m/s Proceeds at 1.5m/s Proceeds at 1.5m/s Proceeds at 1.5m/s Links 1st anchor released so anchor and float sink towards seabed 1st float released so rises up Time -10sec to 0sec 0sec to 5sec 5sec to 30sec 2nd anchor released so anchor 30sec to 35sec and float sink towards seabed 2nd float released so rises up 35sec to 75sec Note that the vessel is allowed to accelerate to 1.5m/s during Stage 0, the build-up stage, see the Prescribed Motion tab on the 'Submarine'data form. At the same time the wave height is increasing to the required maximum. This means that the system has a gentler start, reducing or avoiding transient responses. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. Note how the deployer sinks at the start of the analysis unit then rises as it gets lighter, due to the release of the anchors. Look at the animation in plan view, CTRL+P, see how the line has moved out of plane as it falls, slack, onto the seabed. Look at the full tension time history for 'Sensor1' at any point. This is the line supported by the 1st float. You will need to amend the Y-axis scale to -1kN to 6kN as transient tension at the very start of the model has resulted in a large scale. Note the snatch load at 10sec as the float rises to the full extent of the line. 64 w 3.11 J - PRE AND POST PROCESSING 3.11.1 J01 Batch Script A simple example batch script is shown below. In addition the J01 directory in the OrcaFlex Examples contains some simple ready-to-run example batch script files. //Example batch script file to run 3 variations //on a pre-prepared base data file. load BaseData.dat select sea select wavetrain Primary WaveTrainHeight = 10 WaveTrainDirection = 150 run H10_D150.sim select sea select wavetrain Primary WaveTrainHeight = 12 WaveTrainDirection = 180 run H12_D180.sim select sea select wavetrain Primary WaveTrainHeight = 15 WaveTrainDirection = 210 run H15_D210.sim 3.11.2 J02 Results See the J02 directory in the OrcaFlex Examples. Introduction System optimisation is often achieved by running a set of OrcaFlex analyses varying one or more parameters systematically. As a simple example, we take a lazy wave riser configuration with distributed buoyancy. A batch script file is used to carry out a series of increases to the buoyed length of the riser and to generate simulation files. The results of these runs are then compared using an OrcaFlex Results spreadsheet within Excel. An optimum buoyed length can then be identified. Building the model Two files are needed. a) Basecase.dat: This is a standard OrcaFlex model of a lazy wave configuration. It is set up for one of the permutations to be considered. Modifying this file with Script.txt will generate the other cases. b) Script.txt: This is a text file containing instructions on what to do with the base case. First step is to load basecase.dat. It is then run to generate the first set of results, 70.sim. Note that saving of simulation files is automatic. The second section of 'Riser A' then has its length modified to 80m and is run and saves as 80.sim. This is then repeated for two further cases. 65 w The file Script.txt is run as an OrcaFlex batch. Open OrcaFlex and go to the Calculation menu. Select 'Batch Processing' then 'Add File'. The script file can be selected just as a data or simulation file would. See Batch Processing for further information. Results Open the spreadsheet Results.xls. This is an OrcaFlex Results spreadsheet that has been set up to automatically extract and summarise results from the simulation files generated by the batch script. The spreadsheet has six worksheets - an instructions worksheet, one worksheet for the results from each simulation file, and a worksheet giving a summary of all the results. The 'Instructions' worksheet has an instructions table that specifies which results to extract, plus two buttons that trigger macros to obey those instructions. The instructions in the table are in groups (highlighted using Excel formatting, but this is optional), each of which consists of a Load command to open one of the simulation files, followed by a series of other commands to retrieve various results from that file and place them in the appropriate worksheet. When you press the Process button the spreadsheet executes a macro that reads and obeys the instructions in order. The first group of instructions consists of a 'Load' command to open the simulation file 70.sim, followed by a series '70'. There are then similar blocks of instructions to extract the corresponding results from the other simulation files. Instructions are only carried out when you press one of the process buttons at the top of the 'Instructions' sheet. If any simulation files are modified, the button can be pressed again to generate updated results. Look at sheet '70' and 'Summary' to see how the results can be presented and an example of what can be done with them. 3.11.3 J03 Stress Analysis See the J03 directory in the OrcaFlex Examples. Introduction The stresses in steel risers due to wave loads are usually required. OrcaFlex obtains these in the post processing stage, using a Stress spreadsheet in Excel. This example obtains stress results for a simple steel catenary suspended from a vessel in two different wave conditions. Building the model An OrcaFlex model is set up with a steel riser hanging down from a vessel in a simple catenary. The riser properties are generated using the Line Type Wizard routine. Reset the simulation so the datafile can be accessed and open the Line Types data form. Select 'Pipe' then press the Wizard button and step through the pages to see how the properties were built. Note that OrcaFlex can cope with the load bearing wall thickness being less than the total wall thickness, due to linings and coatings. Look at the Stress tab on the Line Types data form. The outer and inner diameters to be used for stress analysis can be input here if they are different from the overall diameters. See Stress Diameters for details. If wall tension and maximum stress results are required then an internal pressure at End A of the line must be specified. See the Riser data form where pressure is set at 23.2x10^3 kN/m^2 (23.2MPa) for this case. See Line Pressure Effects for more details. 66 w For a comparison of results, the cases need the same segmentation. This means node 5 in Example1 is at the same arc length as node 5 in Example2. Similarly, they must have a sufficient simulation period. If you want results from 26sec to 39sec, both cases must have results to at least 39sec. The system is then analysed in two different wave conditions, generating two simulation files Example1.sim and Example2.sim. Results OrcaFlex comes with an Excel template called 'Stress'. This allows you to set up Excel spreadsheets that can access OrcaFlex simulation files and retrieve results. The results can then be manipulated on standard Excel sheets in the usual manner. Open the spreadsheet, Stress.xls, from the Examples directory using Excel and look at the three sheets. The first is the instruction sheet. This has been generated using the Stress template. The other two are where the retrieved results from the two simulation files have been placed. They have been generated by pressing the 'Add Load Case Sheet' button and inputting the filename and line name. Look at the first worksheet called 'Main Sheet'. In this example the spreadsheet will report radial, hoop and axial stress at an arc of 60m from End A. As only two theta values are to be reported, results will be at 0 degrees and 180 degrees about the inner circumference. Instructions are only carried out when the 'Collect Results' button is pressed on the first sheet. If any simulation file is modified, the spreadsheet can be run again to generate updated results. Look at the Case1 worksheet to see how the results are presented. The pathname for the simulation file needs to be input, as does the line name. This case will open Example1.sim and obtain the results for the line 'Riser'. To see the stress results being collected, check that the pathnames are correct for the Example locations on your machine then press 'Collect Results'. 3.11.4 J04 Fatigue analysis See the J04 directory in the OrcaFlex Examples. Introduction Rigid pipes are vulnerable to fatigue. OrcaFlex has a post-processing routine that extracts line load results from a series of pre-run regular simulation files, calculates the resulting pipe stress ranges and then calculates the fatigue damage. See Fatigue Analysis and related topics. This example is a steel catenary riser suspended from a semi-submersible FPSO as used offshore Brazil. The model contains three risers suspended from two semisubs so that each file generates results for Near, Far and Transverse cases using waves and current from 0 deg. Building the model A base case is built consisting of three steel risers suspended from two semisubs in simple catenaries. They are configured so that the Near, Far and Transverse results are generated from one wave and current heading (0 degrees); see Base.dat. As maximum stress results are required, an internal pressure at End A of the line must be specified, see any line page. See Line Pressure Effects for more details. 67 w Six simulations at different wave heights are then carried out using the OrcaFlex batch file Fatigue.txt (see example J01: Batch Script for information on batch language). This generates Case#02.sim, Case#04.sim, Case#06.sim, Case#08.sim, Case#10.sim and Case#12.sim. Note that the line segmentation must be the same for all the cases in the fatigue analysis. Results Open the fatigue analysis tool by selecting Fatigue Analysis on the Results menu. Open the example fatigue file Case#01.ftg. This shows a typical fatigue analysis, using the simulation files generated above. The Load Cases tab defines the pathname for each case, the line to get results for and specifies the number of wave cycles, of this particular set of load conditions, that the line will experience. These data are usually extracted from a wave scatter diagram for the area. The Analysis Data tab specifies the units to use in the analysis. These need not match those used in the simulation files. Note that a user-defined combination is used in our example. It will collect data over two arc lengths, End A to 80m (the top of the riser) and 400m to 800m (the touchdown zone). For each arc length a different stress concentration factor and S-N curve can be defined. In this example it will report results every 2m over the specified arc length at eight points around the pipe circumference, i.e. every 45 degrees. It will also highlight any total damage that exceeds the specified critical value of 0.02. The settings can be retained by selecting Save on the File menu. They are then saved as a *.ftg file. Before carrying out the analysis, it is advisable to perform a preliminary check of the fatigue analysis data, using Analysis / Check or the icon at the top of the window. This 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. To carry out the analysis, select Analysis / Calculate from the top menu or the icon at the top of the window. The fatigue analysis can take a long time if there are many load cases, or if there are many log samples in the load case simulations, or finally if there are a lot of segments in the arc length intervals specified. A progress window is displayed and you can cancel the analysis if desired. When the calculation is complete the results are displayed in a spreadsheet window. This needs to be exported to an Excel spreadsheet if they are to be saved. Either copy and paste into an open spreadsheet or click with the right mouse key and export into a *.xls file. Check the file pathnames are correct for your machine then run this example or look at the excel file, Damage.xls, which contains the results. Note that generating the results may take some time. 3.12 K - LINE ON LINE CONTACT 3.12.1 K01 Line on Line Impact See the K directory in the OrcaFlex Examples. 68 w Introduction OrcaFlex allows you to prevent lines passing through each other in the dynamic analysis. When the option is selected on both lines it generates a resistive force when one line contacts the other. This routine also takes account of line outer diameters when assessing contact. In this example a line free at one end is swung to hit a second held at both ends in a curve. Building the model Two lines are generated called 'Anvil, the line that is hit, and 'Hammer', the one that swings to hit the first. 'Hammer' is made to swing simply by releasing End A at the start of Stage 1, i.e. after the build-up period. To prevent one line passing through the other, both require contact stiffnesses to be set and clash check to be selected. Contact stiffness is specified in the Line Types data form on the 'Friction and Clashing' tab. This is rarely known for pipes so an arbitrary value can be applied. The stiffness should be sufficiently high that one line cannot push through the other. In this case 5MN/m is applied. Variations in stiffness will vary the magnitude of the contact force reported but the contact energy will be unchanged and can be derived from the results. See Line Results: Clashing. To turn the clashing routine on, say 'yes' to Clash check on the Structure tab in the data forms for both lines 'Anvil' and 'Hammer'. Note that the Clash check will result in slower runs so should only be applied where required. In this case it is applied along the full arc length for both lines but it can be applied to individual sections of the line. See the examples Jacket to Semisub and Line on line slide. Results Go to the default view, CTRL+T, and look at the animation through Stage 1, i.e. from the moment 'Hammer' is released. It swings across to 'Anvil' which it pulls with it before it swings back and away. Plot a range graph of Line Clash Force for 'Anvil' through the whole simulation. The maximum clash force occurs at an arc length of 52.5m. Look at time histories of Line Clash Force and Clearance at this arc length. They are in the Clashing variable set. Note the noise in the clash force plot where the lines have bounced against each other after the initial impact. Also notice that the clearance plot does not go to zero. Clearance is reported between centrelines. As clashing takes account of the outer diameters, clashing occurs when clearance is less than or equal to the total of each lines radius. 3.12.2 K02 Line on Line Slide See the K directory in the OrcaFlex Examples. Introduction The line clashing routine can be used to model one line sliding over another. However remember that friction is not included and this will only occur in dynamics. A fun example of this is given below. A boy scout slides down an aerial ropeway by holding onto the ends of a short rope wrapped over it. He then flies off the end to hit the ground. 69 w Building the model The system is submerged but the seawater density has been set at 1.28kg/m³, the density of air. A solid fixed in space makes the platform that the scout stands on at the start of the analysis. The scout is modelled as a 6D buoy, which is fixed in statics. Properties for a typical 10 year old scout have been applied but drag and added mass are ignored as he is moving in air, so generated loads will be negligible. The arms and legs are then drawn using the buoy drawing facilities. Solids are attached to the buoy to make the head and body shapes. Lines are attached along the spine and across the bottom to give a friction force when the scout hits the ground. By applying mass to these lines, the weight distribution is varied so that the scout will land on his back. The ropeway is a simple line inclined and held at both ends. The hanger is also a simple rope, however to model the effect of line/line friction, the central section in contact with the ropeway has a large normal drag coefficient applied. Both the ropeway and the central section of the hanger have a contact stiffness and clashing check running so they cannot pass through each other. See the Clashing example for more information on this. To prevent one line passing through the other, both require contact stiffnesses and 'Clash Check' selected. Contact stiffness is specified in the Line Types data form. It should be sufficiently high that one line cannot push through the other. To turn the clashing routine on, say yes to Clash check on the Structure tab in the data forms for both lines 'Ropeway' and 'Hanger'. Note that the Clash check will result in slower runs so should only be applied where required. In this case it is only applied along middle section for the hanger. Links A and B hold the hanger up above the ropeway during statics then release at the start of Stage 0. This is required as the statics needs to be told on which side of the ropeway the hanger is, and because the clashing routine only operates in dynamic analysis. Results Go to the default view, CTRL+T, and look at the animation through the whole simulation. The scout slides along the line then flies off the end to somersault on the ground. Look at the time history of line clash force on the hanger middle. Note how the hanger bounces on the ropeway as it slides down. Look at the Z time history for the boy scout. Note how he flies up after leaving the ropeway before descending to bounce on the ground. 3.13 L - RAO IMPORT 3.13.1 Example RAO Text File A simple example RAO text file is shown below. In addition the L directory in the OrcaFlex Examples contains a ready-to-import example file. ***OrcaFlex RAO Start Data*** Draught Transit Direction 0 WP XA XP YA YP ZA 0.0 0.0 0.0 0.0 0.0 0.0 ZP 0.0 RXA 0.0 RXP 0.0 RYA 0.0 RYP 0.0 RZA 0.0 RP 0.0 70 w 7.0 0.1 5.0 0.0 0.0 8.0 0.3 75 0.0 0.0 Infinity 1.0 90 0.0 0.0 ***OrcaFlex RAO End Data*** 0.3 0.3 1.0 -20 +80 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 1.2 0.0 46 90 0.0 0.0 0.0 0.0 0.0 0.0 0.0 71 w 4 4.1 USER INTERFACE INTRODUCTION 4.1.1 Program Windows OrcaFlex is based upon a main window that contains the Menus, a Status Bar, a Tool Bar and usually at least one 3D view of the model. The window caption shows the program version and the file name currently in use for either data (.DAT) or simulation files (.SIM). Within this main window, you can place a selection of subordinate windows which may be: 3D View Windows Graph Windows Spreadsheet Windows Text Windows showing 3D pictorial views of the model showing results in graphical form showing graph results in numerical form showing results in numerical form You can arrange windows as desired - they can be laid on top of each other (cascaded), or side-by-side (tiled), but are restrained within the bounds of the main window. Additional temporary windows are popped up, such as Data Forms for each object in the model (allowing data to be viewed and modified) and Dialogue Boxes (used to specify details for program actions such as loading and saving files). 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. The actions that you can perform at any time depends on the current Model State. Arranging Windows 3D Views, Graphs and Text Windows may be laid on top of each other (cascaded), or side-byside (tiled), but are restrained within the bounds of the main window. There is always at least one 3D View window but you may arrange other windows as desired, using commands from the menu and tool bar to build and run models, and then view the results. If Auto-Arrange is selected then the program rearranges the windows using the current scheme every time a new window is created. Otherwise you can pull the window borders to any locations that you desire. Tip: After creating or closing a window, press F4 or SHIFT+F4 for a quick tidy-up of your screen. You may drag windows around using the caption bar, and may even slide them off the edges of the screen - a scroll bar appears so that you can reach them. In this way you can lay even large windows out side-by-side. 4.1.2 The Model OrcaFlex works by building a mathematical computer model of your system. This model consists of a number of objects that represent the parts of the system - e.g. vessels, buoys, lines etc. Each object has a name, which can be any length. Note that the names are case-sensitive, so Riser and riser are two different names. 72 w The model always has two standard objects: • • General: contains general data, such as title, units etc. Environment: represents the sea, seabed, waves, current etc. You can then use the Model Browser or the toolbar to add other objects to represent the parts of you system. There is no limit, other than the capacity of your computer, to the number of objects you can add to the model. At any time, you can save your model to a data file - you can then reopen it at a later date to continue work. 4.1.3 Model Browser At any time you can use the Model Browser to see what objects you have in your model. To or the Model|Model Browser display the model browser, use the model browser button menu item, or use the keyboard shortcuts (F2 to open the model browser and ESC to close it). The Model Browser consists of a list of all the objects in the model, arranged into categories according to object type. Several symbols are used in the list of objects: Categories can be opened, to show their contents, or closed, to simplify viewing a complex model. Objects. Use double click to view or edit the object’s data. Types such as the Line Types, Vessel Types. Use double click to view or edit the data. Locked You can navigate the list and select the object required by clicking with the mouse, or using the arrow keys and return. If the list is longer than the window then you can either enlarge the window or use the scroll bar. Model Browser Facilities The model browser menus, and its pop-up menu, provide the following model management facilities. For details of keyboard shortcuts see Keys on Model Browser. Add Delete Cut/Copy Paste Add a new object to the model. Delete the selected object from the model. Cut or Copy the selected object to the clipboard. Paste an object from the clipboard into the model. If the object is the Variable Data then all the variable data tables are pasted in, with tables being renamed if necessary to avoid clashing with existing variable data names. You can use Cut/Copy and Paste to transfer objects between two copies of OrcaFlex running on the same machine. You can also use it to transfer objects between two OrcaFlex data files (open the source file and copy the object to the clipboard, then open the destination file and paste the object back from the clipboard), but the Library facility (see below) provides an easier way of achieving the same thing. Finds and highlights the object, by briefly flashing it on the currently selected 3D view. This is useful in complex models where many objects are on the 3D view. Note: Locate 73 w Edit Rename Open the object's data form. Rename the selected object. You can also rename by single-clicking the selected object. Lock/Unlock Lock or unlock the selected object. Hide/Show Control whether the selected object is drawn on 3D views. Reorder You can use drag+drop with the mouse to reorder objects in the model. 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, so that it will be tackled first when OrcaFlex does the static analysis. The Library menu facilities allow you to open a second data file. You can then Import objects from that second file into the current model, or Export objects from the current model into the second file. You can also do Import/Export using drag+drop with the mouse. For details see Libraries. The second data file is referred to as the library model, but in fact it can be any OrcaFlex data file. The library facilities therefore provide an easy way to move objects between different OrcaFlex data files. If the object being imported or exported is the variable data then all the variable data tables are transferred, with tables being renamed if necessary to avoid clashing with existing variable data names. Switch The browser's Window menu enables you to switch focus to the main form without closing the browser window. A corresponding command on the main form's Window menu switches focus back. Library Notes: 4.1.4 Libraries Libraries An OrcaFlex Library is a collection of OrcaFlex objects (line types, lines, buoys etc.) stored in an ordinary OrcaFlex data file. For example, a library may contain all the standard Line Types that you use regularly. 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. To open a library file, use the File|Libraries menu or the Library menu on the Model Browser. Note that any OrcaFlex data file can be opened as a library file, and this makes it easy to use the model browser to copy objects from one model to another. Building a Library To build a library file run OrcaFlex and select Libraries|New Library from the File menu. The model browser appears and looks like: 74 w The left hand pane is the model currently open in OrcaFlex and the right hand pane is the library. The library is simply another OrcaFlex model, except that instead of being a model of an actual system, it usually contains just a collection of objects. Note: Because they are OrcaFlex models, libraries contain General and Environment data, but these would not usually be used, except perhaps for the model title, which can act as a title for the library. To build up the library model, use the File|Open menu to open an existing data file that contains objects you want to add to the library. This model then appears in the left pane and you can now export objects from it into the library. To do this, select the object in the left pane (singleclick) and then use the Export button (>>). Alternatively, you can simply drag the object from the current model (left pane) and drop it into the library model (right pane). After adding the required objects, the model browser might look like: You can now open other data files and export objects from them to the library. When you have finished building up the library, you can save it to a library file using the Library|Save menu item. Note: Because the library file is just an ordinary OrcaFlex data file, it can also be opened using File|Open. This allows you to edit the data of the objects in the library. 75 w You can set up as many library files as you wish. For example you might have separate libraries for Line Types, Attachment Types, Vessel Types etc., or you may choose to use just one library for everything. The model browser's Library menu contains a list of the most recently used libraries. Using Libraries Once you have set up your library, you can very quickly import objects from it into your current model. To do this, use the Library menu to open the library, then select the object you want to import and click the Import button (<<). Alternatively, you can simply drag and drop the object from the library model (right pane) to the current model (left pane). When you have finished with the library file, close it using the Library|Close menu item. Finally, here are some other points about using library files. • Because library files are simply ordinary OrcaFlex data files, you can temporarily treat any OrcaFlex data file as a library. This allows you to easily import objects from one OrcaFlex data file to another. You can re-size the Model Browser by dragging its border. You can also control the relative sizes of its two panes, by dragging the right border of the left pane. You can view, but not edit, the data for a library model object, by double clicking it in the Model Browser or by selecting it and using the pop-up menu. You can rename objects in the current model or in the library model. To do this, either use the pop-up menu, or else single click the object twice. When an object is imported from or exported to a library, the destination model may already have an object of that name. In this case OrcaFlex automatically gives the object a new name based on the old name; you may wish to alter this name. If the object being imported or exported uses a type - e.g. a line type or vessel type - then OrcaFlex automatically imports or exports all the types that the object uses. If the names of any of those types match names already in the destination model, then OrcaFlex needs to know which ones to use - the ones already in the destination model or the ones in the source model. If this situation arises then OrcaFlex warns you and gives you the following options: Use Existing: The type is not transferred. Instead, the transferred object will use the type, of that name, that already exists in the destination model. Rename: This option transfers the used type, giving it a new name, and the transferred object uses the transferred type. Use All Existing: This option applies the Use Existing option to all remaining types used by the object. So for all remaining types used by the object, the types already in the destination model are used, whenever their names match the types used. Rename All: This option applies the Rename option to all remaining types used by the object. So all the remaining types used by the object are transferred, using new names where needed, and the transferred object uses the transferred types. • • • • • 4.1.5 Model States OrcaFlex builds and analyses a mathematical model of the system being analysed, the model being built up from a series of interconnected objects, such as Lines, Vessels and Buoys. For more details see Modelling and Analysis. 76 w OrcaFlex works on the model by moving through a sequence of states, the current state being shown on the status bar. The following diagram shows the sequence of states used and the actions, results etc. available in each state. RESET Calculate Static Position Calculating Statics Reset STATICS COMPLETE Run Simulating Edit or Reset Pause Run Reset SIMULATION PAUSED or STOPPED Figure: Model States The states used are as follows: Reset The state in which OrcaFlex starts. In Reset state you can freely change the model and edit the data. No results are available. Calculating Statics OrcaFlex is calculating the statics position of the model. You can abort the calculation by CLICKING the Reset button. 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. Simulating The dynamic simulation is running. The results of the simulation so far are available and you can examine the model data, but only make minor changes (e.g. colours used). You cannot store the simulation to a file while simulating - you must pause the simulation first. 77 w Simulation Paused There is a simulation active, but it is paused. The results so far are available and you can examine the model data. You can also store the part-run simulation to a file. Simulation Stopped The simulation is complete. The simulation results are available and you can store the results to a simulation file for later examination. You must reset the model, by CLICKING on the Reset button, before significant changes to the model can be made. 4.1.6 Using Model States To illustrate how model states work, here is an example of a typical working pattern: 1. In Reset state, open a new model from a data file or use the current model as the starting point for a new model. 2. In Reset state, add or remove objects and edit the model data as required for the new model. 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. 3. Run a static analysis (to get to Statics Complete state) and examine the static position results. Make any corrections to the model that are needed - this will automatically reset the model. Steps (2) and (3) are repeated as required. 4. Run a simulation and monitor the results during the simulation (in Simulating state). 5. If further changes to the model are needed then Reset the model and edit the model accordingly. Steps (2) to (5) are repeated as required. 6. Finalise the model, perhaps improving the discretisation (for example by reducing the time step sizes or increasing the number of segments used for Lines). Run a final complete simulation (to reach Simulation Stopped state) and generate reports using the results. 4.1.7 Toolbar The toolbar holds a variety of buttons that provide quick access to the most frequently used menu items. The selection of buttons available varies with the current Program State. Button Action Open Save Model Browser New Vessel New Line New 6D Buoy New 3D Buoy New Winch Equivalent Menu Item File | Open File | Save Model | Model Browser Model | New Vessel Model | New Line Model | New 6D Buoy Model | New 3D Buoy Model | New Winch 78 w New Link New Shape Calculate Statics Run Simulation Pause Simulation Reset Start Replay Stop Replay Step Replay Forwards Edit Replay Parameters Add New 3D View Examine Results Help Contents and Index Model | New Link Model | New Shape Calculation | Statics Calculation | Run Simulation Calculation | Pause Simulation Calculation | Reset View | Start Replay View | Stop Replay View | Step Replay Forwards View | Edit Replay Parameters Window | Add 3D View Results | Select Results Help | Contents and Index 4.1.8 Status Bar The Status Bar is divided into three fields: The Message Box At the left hand end. It shows information about the progress of the current action, such as the name of the currently selected object, or the current iteration number or simulation time. Error messages are also shown here. When a statics calculation is done messages showing the progress of the calculation are shown in the message box. To see all the messages from the statics calculation CLICK on the message box - the Statics Progress Window will then be opened. CLICKING here outside a statics calculation displays the Session Log. The Program State Indicator In the centre and shows which state the program is in (see Model States). The Information Box This is on the right. It shows additional information, including: • • The global coordinates of the position of the cursor, in the current view plane. Distances when using the measuring tape tool. 79 w 4.1.9 Mouse and Keyboard Actions As well as the standard Windows mouse operations such as selection and dragging OrcaFlex uses some specialised actions. Clicking the right mouse button over a 3D View, Graph or Text Window displays a pop-up menu of frequently used actions, such as Copy, Paste, Export etc. For 3D Views and Graph Windows the mouse can be used for zooming. Simply hold the ALT key down and using the left mouse button, drag a box over the region you want to view. All of the menu items can be selected from the keyboard by pressing ALT followed by the underlined letters - this is described in your Microsoft Windows Manual. Example: To exit from the program (menu: File | Exit) press ALT+F then X, or ALT then F then X A number of frequently used menu items may also be accessed by "hot keys", such as CTRL+R to start a replay. See the tables below. We suggest that as you become more familiar with the operation of OrcaFlex that you memorise some of the hot keys for actions that you use frequently. Keys on Main Window Help Print Show Model Browser Switch between Model Browser and Main Window Calculate static position Run simulation Pause simulation Reset simulation Open results selection form Go to next window Go to previous window Tile windows Cascade windows Close selected window Close program Keys on Model Browser Rename object Lock object Cut object Copy object Paste object Delete object Close browser Keys on Data Forms Help Go to next data form Go to previous data form F1 F6 SHIFT+F6 F2 CTRL+L CTRL+X CTRL+C CTRL+V DEL ESC F1 F7 F2 SHIFT+F2 F9 F10 F11 F12 F5 CTRL+F6 SHIFT+CTRL+F6 F4 SHIFT+F4 CTRL+F4 ALT+F4 80 w Display batch script names for currently selected data item or table. Close form Data Selection Keys Go to next data item or table Go to previous data item or table TAB SHIFT+TAB F7 ALT+F4 Go to data item or table labelled with underlined letter ALT+LETTER ← → ↑ ↓ Move around within a table Select multiple cells in table Go to first or last column in table Go up or down table several rows at a time Data Editing Keys Enter new value for selected cell Edit current value of selected cell Move around within new data value being entered Accept edit Accept edit and go to adjacent cell in table Cancel edit Cut selected cell(s) to clipboard Copy selected cell(s) to clipboard Paste from clipboard Fill selection from top (copy top cell down) Fill selection from left (copy leftmost cell to right) Fill selection from bottom (copy bottom cell up) Fill selection from right (copy rightmost cell to left) Insert new row in table Delete selected row of table 3D View Control Keys Elevation view Plan view Rotate viewpoint down (decrement view elevation angle) Rotate viewpoint right (increment view azimuth angle) Rotate viewpoint +90º Rotate viewpoint -90º Zoom In Zoom Out CTRL+E CTRL+P SHIFT + ← → ↑ ↓ SHIFT+HOME SHIFT+END HOME, END PGUP, PGDN Type new value F2 ←, →, HOME, END RETURN ↑, ↓ ESC CTRL+X CTRL+C CTRL+V CTRL+D CTRL+R CTRL+U CTRL+SHIFT+D CTRL+L CTRL+SHIFT+R INSERT DELETE Rotate viewpoint up (increment view elevation angle) CTRL+U CTRL+N CTRL+J Rotate viewpoint left (decrement view azimuth angle) CTRL+H CTRL+Q CTRL+SHIFT+Q CTRL+I CTRL+O 81 w Move view centre - fine adjustment Move view centre - coarse adjustment Edit view parameters for current 3D view Reset to default view Show / Hide local axes Undo most recent drag Lock/Unlock selected object Place new object Edit selected object Cut selected object to clipboard Copy selected object, or view if none selected, to clipboard ← → ↑ ↓ CTRL + ← → ↑ ↓ CTRL+W CTRL+T CTRL+Y CTRL+Z CTRL+L SPACE OR RETURN CTRL+F2 CTRL+X CTRL+C Paste object from clipboard (followed by mouse click CTRL+V or RETURN to position the new object) DELETE Measuring tape tool Replay Control Keys Start / Stop replay Replay faster Replay slower Step forwards one frame in the replay and pause Step backwards one frame in the replay and pause Edit replay parameters CTRL+SHIFT+DRAG CTRL+R CTRL+F CTRL+S CTRL+A CTRL+B CTRL+D 4.2 MENUS 4.2.1 Menus OrcaFlex has the following menus: • • • • • • • • The File menu has the file opening and saving commands, plus commands for printing or exporting data or results and managing libraries. The Edit menu has data and object editing facilities. The Model menu gives access to the model building facilities. The Calculation menu provides commands for starting and stopping analyses, including batch processing. The View menu provides view and replay control. The Results menu leads to the results facilities. The Tools menu allows you adjust preferences and to lock or unlock objects. The Window menu gives access to the various windows that are available, and allows you to adjust the layout of your windows. 82 w • The Help menu leads to the various help documentation that is available. 4.2.2 File Menu New Deletes all objects from the model and resets data to default values. Open Open a data or simulation file. You are offered the data files (.DAT) and simulation files (.SIM) in the latest directory used in OrcaFlex. 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, whereas if you select a simulation file then OrcaFlex reads in both the data and the simulation results. To read just the data from a simulation file, you can use the Open Data menu item. If you load a partially-run Calculation | Run Simulation. simulation then it can be completed by using OrcaFlex can read files that were written by previous Windows versions of the program. It can even read files written by more recent version of the program. If the file requires a facility that is not available in the version reading it then a warning is given. OrcaFlex cannot read files written by the old DOS version of OrcaFlex (version 5), but there are conversion utility programs available that convert the data from such files to the format now used by OrcaFlex. See the Convert directory on the OrcaFlex CD. Save Save the data, plus the simulation results if a simulation is active, to the currently selected filename, using extension .DAT (if there are no simulation results) or .SIM (if there are simulation results). If a file of that name already exists then it is overwritten. Note: Save As This is the same as Save but allows you to specify the filename to save to. If a file of that name already exists then you are asked whether to overwrite the file. Open Data Read the data from an existing data file (.DAT) or simulation file (.SIM), replacing the existing model. If a simulation file is specified then OrcaFlex reads just the data from it, ignoring the simulation results in the file. Note: To select a simulation file you first need to set "File of Type" to be "All Files (*.*)". You cannot save the simulation while it is running - you must pause the simulation first. 83 w Save Data Save the data into the currently selected filename, using extension .DAT. If a file of that name already exists then it is overwritten. Save Data As This is the same as Save Data but allows you to specify the filename to save to. If a file of that name already exists then you are asked whether to overwrite the file. Compare Data Compares the data of 2 OrcaFlex models. See Comparing Data for details. Libraries You can create new libraries of OrcaFlex objects, or open existing libraries. You can then import objects from the library into your existing model, or export objects from your existing model to the library. Export Display the Export Dialogue box, allowing you to export Data, 3D Views, Graphs, Spreadsheets or Text Windows. See also Copy. Print Display the Print Dialogue box, allowing you to print Data, 3D Views, Graphs, Spreadsheets or Text Windows. See Printing. Selected Printer Allows you to change the selected printer. Printer Setup Calls up the Printer Setup dialogue. This standard Windows dialogue is used to select which printer to use, and allows you to control the way that it is used - the details vary from printer to printer, and depend on the printer manufacturer's device driver currently installed. Please refer to the manuals for your printer as well as the Microsoft documentation. Most Recent Files List of the most recently used files. Selecting an item on the list causes the file to be loaded. The size of the list can be adjusted from Preferences. Exit Close OrcaFlex. 4.2.3 Edit Menu Undo Drag Undo the most recent drag. This is useful if you accidentally drag an object. 84 w Cut Copies the current selection to the clipboard and then deletes it. Copy If there is a currently selected object (see Selecting Objects), then that object is copied to the clipboard. You can then use Edit | Paste to create duplicate copies of the object. The data for the object is copied to the clipboard in text form, from where it can be pasted into a word processor document. Note: After pasting into a word processor, you will probably need to put the text into a fixed space font since much of the data is in tables. If there is no currently selected object then the currently selected 3D view, text window, graph or spreadsheet is copied to the clipboard. Paste Insert object from clipboard. This can be used to duplicate an object several times within the model. After selecting Paste, the object is inserted at the next mouse CLICK position in a 3D view. If the current window is a Spreadsheet then the contents of the clipboard are pasted into the spreadsheet. Delete If the active window is a 3D View then the currently selected object is deleted. Before the object is deleted, any connected objects are disconnected, and any graphs associated with the object are closed. If the active window is a Spreadsheet then the selected cells are cleared. Select All Selects all the text in a Text Window or all the cells in a Spreadsheet. Copy All Data Copy the whole model to the clipboard. The model data is copied to the clipboard in text form, from where it can be pasted into a word processor document. 4.2.4 Model Menu Model Browser The Model Browser button opens the Model Browser from which you can choose which object to edit or examine. Double click, press return or use the browser Edit menu to view the data form for that object. Data is drawn in grey if it cannot currently be changed (because a simulation is active, for example). You can move to other objects' data forms by CLICKING on the Next button on each data form (SHIFT+CLICK the Next button to go to the previous data form). 85 w New Vessel New Line New 6D Buoy New 3D Buoy New Winch New Link New Shape Create new objects. The mouse cursor changes to the New Object symbol . The object is placed at the position of the next mouse CLICK within a 3D view. 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 Default View Centre. Vessels are always placed initially at the sea surface, that is with their origin at Z = Sea surface Z (see Vessel Data). Truncate Object Names Old versions of OrcaFlex (before 7.4b) cannot read files that contain long object names, i.e. longer than 10 characters. This menu item truncates any long object names in the model. You should do this if you wish to send a file to another user whose version of OrcaFlex is older than 7.4b. Delete Unused Types Deletes any types (e.g. Line Types, Clump Types etc.) that are not in use. This is sometimes useful to simplify a data file, or to find out which types are in use. 4.2.5 Calculation Menu Single Statics Start the single statics calculation (see Static Analysis). Progress and any error messages that occur are reported in the Statics Progress Window, which is shown as a minimised window icon. The statics calculation can be interrupted by CLICKING the Reset button. Multiple Statics Starts the multiple offset statics calculation (see Multiple Statics). Progress and any error messages that occur are reported in the Statics Progress Window, which is shown as a minimised window icon. The statics calculation can be interrupted by CLICKING the Reset button. 86 w Run Simulation Start a full dynamic simulation (see Dynamic Analysis). automatically do a statics calculation first. If necessary, OrcaFlex will During the simulation, 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. The update interval is set in the Tools | Preferences dialogue box. The simulation can be interrupted by CLICKING the Pause button. Note: Documents and Results Tables are not updated and their contents become invalid. Pause Simulation Pause the simulation. To save the results of a part-run simulation you need to pause it first. The simulation can be restarted by CLICKING the Run button. Reset Reset the model, discarding any existing results. The model can then be edited or a new model loaded. Extend Simulation Adds another stage to the current simulation, without having to reset. You are asked to specify the length of the new stage. Other properties of the new stage (e.g. winch control) are set to the same as for the previous stage. You can then continue the simulation, without having to restart it from scratch. This is particularly useful if you have a simulation that has not been run for long enough. This facility is only available when the current simulation is either paused or completed. Batch Processing Run a batch of simulations automatically while the program is unattended. See Batch Processing for details. A Batch Mode dialogue box is presented, allowing you to select the data files to be included in the batch run and then start the batch run. The results are automatically written to simulation files with the same names as the data file, for later inspection. While running in batch mode the program does not require user input and does not request confirmation before overwriting simulation files. 4.2.6 View Menu Edit View Parameters Adjust the View Parameters for the highlighted 3D View. position, view size and direction. See View Parameters. You can adjust the view centre 87 w Rotate Up / Down / Left / Right Change the view direction, for the highlighted 3D View, by the view rotation increment (see Preferences). Plan Set the highlighted 3D View to a plan view (Elevation = +90º). Elevation Set the highlighted 3D view to an elevation view (Elevation = 0º). Rotate 90 / Rotate -90 Increase (or decrease) the view azimuth by 90º, for the highlighted 3D view. Zoom In / Zoom Out Click the zoom button to zoom in (decrease view size) or SHIFT+CLICK it to zoom out (increase view size). Applies only to the currently highlighted 3D View. Reset to Default View Reset the currently highlighted 3D view back to the default view for this model. Set as Default View Set the default view for this model to be the currently highlighted 3D view. Axes This submenu gives you control of the 3D View Drawing Preferences. Superimpose Times Allows model configurations for different times of the simulation to be superimposed in 3D Views. See Superimpose Times. Current Position Draws the model at the latest time. Edit Replay Parameters Adjust the Replay Parameters, such as the period of simulation to replay, the time interval between frames, the replay speed etc. For more information see Parameters. Start / Stop Replay Starts or stops the Replay. 88 w Step Replay Forwards, Step Replay Backwards CLICK Step the replay forwards or backwards one frame at a time. Click the button to step forwards; with SHIFT held down to step backwards. Replay Faster / Slower Increase/Decrease frame repetition rate (Replay speed). Export Video Exports the replay as a video clip in AVI file format. See Replays for more details. 4.2.7 Results Menu Select Results Display Results Selection dialogue box (see Results). This allows you to choose from the currently available selection of graphs and results tables. Graphs such as Time Histories, XY Graphs and Range Graphs may be created before a simulation has been run, thus allowing you to watch the variables during a simulation. Fatigue Analysis Opens the Fatigue Analysis form. Modal Analysis Opens the modal analysis form. 4.2.8 Tools Menu Lock / Unlock Selected Object Locking an object prevents it from being accidentally dragged or connected using the mouse on 3D views, for example if you nudge the mouse slightly while trying to DOUBLE CLICK. Lock / Unlock Selected Object toggles the lock on the currently selected object. If the lock is on, it will be switched off. If the lock is off, then it will be switched on. Locked Objects may still have their positions edited in the data Edit Forms. The status of the object locks is shown by symbols in the Model Browser. Lock / Unlock All Objects Locks or unlocks all objects in the model. Preferences Allows you to control various program settings so that you can customise the program to the way you prefer to work. See Preferences. 89 w 4.2.9 Window Menu Add 3D View Add another 3D View Window. Having multiple views on screen allows you to watch different parts of the system simultaneously, or to see different views at the same time (for example a plan and an elevation). Tile Horizontal / Vertical, Cascade Arrange windows in a stack, one above the other, or side-by-side. Using these commands is a good way of reorganising your screen after creating or deleting view or graph windows. The previously selected method is shown with a check mark. Auto Arrange If this is checked then the program automatically tiles or cascades windows every time a new window is created or deleted. Switch to Model Browser This command, and the corresponding command on the model browser's Window menu, enable you to switch focus between the main form and the model browser window. Session Log Displays the Session Log. Statics Progress Displays the Statics Progress Window. Window List This is a list of all currently open windows. If a window is hidden under others it can be selected easily from this list. 4.2.10 Help Menu Contents and Index Open the Contents / Index / Find in the on-line help. What's New Gives a list of recent improvements and alterations to OrcaFlex. Tutorial and Examples Displays an introduction to using OrcaFlex and descriptions of the example files. Keyboard Shortcuts Lists the keyboard shortcuts used by OrcaFlex. 90 w Technical Notes Displays the technical notes in the help file. Frequently Asked Questions Displays help giving common questions and answers about OrcaFlex. About OrcaFlex Displays a window giving the program version and details about Orcina Ltd. In addition, the window reports the amount of disk space, memory and Windows resources that are currently free. 4.3 3D VIEWS 4.3.1 3D Views 3D Views are windows showing isometric projections of the three-dimensional model, and they may be rotated, zoomed and panned to allow any aspect of the system to be viewed. 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, while a scale bar in the view indicates the current View Size. 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). This allows you to build non-in-plane models on screen with the mouse. Further 3D View windows are added by using the Window | New 3D View menu item or by CLICKING on the New 3D View button on the tool bar. Windows may be arranged by dragging their borders or using the Window | Tile and Window | Cascade menu items. 3D Views may be deleted by DOUBLE CLICKING the control box at the top left-hand corner. The objects in a 3D view are "live" in the sense that you can use the mouse pointer to select objects, drag them around in the view and make connections between objects. See Selecting Objects, Creating and Destroying Objects, Dragging Objects, Object Connections, for details. If you DOUBLE CLICK on an object then the data form for that object appears, so that you can examine or edit its data. After running a simulation, or loading a simulation file, a dynamic replay (animation) can be shown in one or more 3D View windows. A replay shows a sequence of snapshots of the model taken at specified intervals throughout part or all of the simulation. Replays may be played in just one 3D View window, or in all of them simultaneously - see Preferences. Finally, 3D Views may be printed by selecting the view desired and using the print menu. Also, the picture may be exported to a file or the windows clipboard. Measuring Tape Tool You can measure distance on a 3D view using the measuring tape tool. 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. Note that this is the distance in the plane of the 3D view. 91 w 4.3.2 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. View Centre Defines the 3D global coordinates of the point that is shown at the centre of the window. View Size The diameter of the view area. It equals the distance represented by the smaller of the 2 sides of the view window. This parameter must be greater than zero. Example: If the window on screen is wider than it is high, and View Size = 100.0 then an object 100 units high would just fill the height of the window. View Elevation and View Azimuth These determine the direction (from the view centre) from which the model is being viewed. The azimuth angle is measured from the global X direction towards the global Y direction. The elevation angle is then measured upwards (downwards for negative elevation angles) from there. The view shown is that seen when looking from this direction - i.e. by a viewer who is in that direction from the view centre. Example: View Elevation +90º means looking in plan view from above, and View Elevation = 0º, View Azimuth = 270º (or -90º) means a standard elevation view, looking along the Y axis. Default View Each model has its own Default View Parameters that are saved with the model data. Whenever a new 3D view is created, it starts with this default view. 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). To set the default view parameters, 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 pop-up menu). Window Size You can adjust the size of a 3D view window either by dragging the window border, or by setting its window size on the view parameters form. The latter is sometimes useful when exporting a view or a exporting a replay video, since it makes it easier to export two different cases and get matching sizes. 4.3.3 View Control You can adjust the view in a 3D view window using the view control buttons: Button Action Equivalent Menu Item Increase view elevation View | Rotate Up Increase view azimuth View | Rotate Left 92 w Zoom in Edit View Parameters CLICKING View | Zoom In View | Edit View Parameters these buttons while holding the SHIFT key down causes the action to be reversed. You can also use the mouse wheel button to change view. Turn the wheel to scroll the 3D view up and down. Turn it with the CTRL key held down to zoom in or out on the point that the mouse is currently pointing at. Note that this mouse wheel facility is not available in Windows 95. For more precise control you can set the view parameters explicitly using the View Parameters dialogue. Finally, 3D views can also be controlled using the View menu and various hotkeys - see Mouse and Keyboard Actions. Note: The view control keys only affect the currently selected 3D view window - the one with its caption highlighted. They have no effect if there is no currently selected 3D view window. To select a 3D view simply CLICK on it. 4.3.4 Zooming Views You can zoom in or out using the mouse wheel button with the CTRL key held down (not available in Windows 95). 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. To do this, hold the ALT key down, 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. When you release, the region selected will be expanded to fill the window. To zoom out, repeat the operation holding down the SHIFT and ALT keys - the region shown in the window will shrink to fit into the rectangle drawn. ALT+CLICK You can also zoom in and out by a fixed amount, keeping the same view centre, by using and SHIFT+ALT+CLICK. 4.3.5 How Objects are Drawn Each object in the model is drawn as a series of lines using the Pen Colour, Line Width and Style (solid, dashed etc.) 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. To change the pen colour, select and CLICK the colour button on the data form and then CLICK on the new colour wanted. You can also exclude (or include) individual objects from the 3D view, by opening the model browser, selecting the object and then using the Hide (or Show) command on the browser's Edit or pop-up menu. Notes: In Windows, a line width of zero does not mean "don't draw" - it means draw with the minimum line width. On some machines the display driver cannot draw the dashed or dotted pen styles and instead draws nothing. So on such machines only the solid and blank pen styles work. Warning: If you use thicker lines to draw objects, then the speed of drawing will be reduced. This may slow down the speed of replays. 93 w The various objects are drawn as follows: • The various coordinate systems can be drawn as small triplet of lines showing their origin and the orientation of their axes. Also, the wave, current and wind directions can be drawn as arrows in the top right hand corner of 3D views. You can control both what is drawn (see 3D View Drawing Preferences) and the drawing data used. • • The Seabed is drawn as a grid using the seabed pen. The Sea Surface is drawn as a grid or as a single line. This is controlled by the user's choice of Surface Type as specified on the drawing page on the Environment data form. If the Surface Type is set to Single Line then one line is drawn, aligned in the wave direction. If the Surface Type is set to Grid then a grid of lines is drawn. This line or grid is drawn using the sea surface pen. The density of the grid is specified in terms of the length of the scale bar on the 3D view; a density of d means that there are d lines per scale bar length, so higher density values give a finer grid (but takes longer to draw). • Shapes are drawn either as wire frames (Blocks and Cylinders) or as a grid (Planes). As well as controlling the pen colour, width and style, for shapes you can also control the number of lines used to draw the shape. Vessels are drawn as a wire frame of edges and vertices defined by the user on the Vessel and Vessel Types data forms. 3D Buoys are drawn as a single vertical line of length equal to the height of the buoy. 6D Buoys are drawn as a wire frame of edges and vertices. For Lumped Buoys, the vertices and edges are defined by the user on the buoy data form. For Spar Buoys the vertices and edges are automatically generated by OrcaFlex to represent the stack of cylinders that make up the buoy. Lines are drawn as a series of lines, one for each segment, joining points drawn at each node. Separate pens are used for the segments and nodes, so you can, for example, increase the pen width used for the nodes to make them more visible. There is also, on the Line Data form, a choice of which pen to use to draw the segments. Clumps are drawn as a thin vertical bar. Drag Chains are drawn using the colour and line style specified on the drag chain types form. The hanging part of the chain is drawn as a line, of length equal to the hanging length and at the angle calculated using the above theory. The supported part of the chain (if any is supported) is separately drawn as a blob at the seabed, directly beneath the node. The drag chain drawing therefore directly reflects the way in which the chain is modelled. Links are drawn as a single line joining the ends of the link. Winches are drawn as a line representing the winch wire. • • • • • • • • Lines, Links and Winches and Shapes are special slave objects that can be connected to other master objects - see Connecting Objects. To allow these connections to be made, each slave object has a joint at each end that you can connect to a master object or else leave Free. 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. The other joints are drawn as small squares. This distinguishes which end of a Line, Link or Winch is which. If the joint is connected to a master object, then it is drawn in the colour of the master object to which it is connected. If the joint is Free, then it is drawn in the colour of the Line, Link or Winch to which it belongs. 94 w 4.3.6 Selecting Objects A single CLICK on or near an object in a 3D View selects it ready for further operations. The currently selected object is indicated in the Status bar. All objects have a "hot zone" around them, the width of which is set in the Preferences dialogue box (see Preferences). If several objects have overlapping hot zones at the mouse position, they will be selected in turn at subsequent CLICKS. To deselect the object (without selecting another object) CLICK on the 3D view away from all objects. CLICK on an object to open its data form. 4.3.7 Creating and Destroying Objects When the model is in Reset or Statics Complete state then you can create and destroy objects using the mouse. To create a new object, CLICK on the appropriate new object button on the tool bar or select the Model | New Object menu item. The mouse cursor changes to show this. A new object of that type is created at the position of the next CLICK on a 3D View. You can also create a new object by copying an existing one. To do this select the object and press CTRL+C to take a copy of it. 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. 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. To destroy an object, simply select it and then press the DELETE key. You will be asked to confirm the action. 4.3.8 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. When the mouse button is released, then the object will be positioned at the new location. The current coordinates of the object are shown in the Status Bar during the drag operation. Note: Objects must be dragged a certain minimum distance (set in the Preferences dialogue box - see Preferences) before the drag operation is started. This prevents accidental movement of objects when DOUBLE CLICKING etc. The drag operation is denoted by the mouse cursor changing to Objects may be locked to prevent unintended drag operations moving them (see Locking an object). Their coordinates may still be edited on their data form. Note: Slave objects that are connected are moved relative to their master's local origin. Other objects are moved in the global coordinate frame. Dragging is only available in Reset or Statics Complete states, and when the object is not locked. 4.3.9 Connecting Objects Unlocked slave objects (e.g. Lines, Links, etc.) can be connected to master objects using the mouse in a 3D View (see Object Connections). First select the end of the slave that you want to connect by CLICKING on or near its end joint. Then hold down the CTRL key while CLICKING on 95 w the master object - the two will then be connected together. This operation is only permitted for master-slave object pairs, for example connecting a line to a vessel. 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. To Free a joint - i.e. to disconnect it - select it and then CTRL+CLICK on the sea surface. To connect a joint to a Fixed Point, select it and then CTRL+CLICK on the global axes. 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. If the object is close to the seabed then the program snaps it onto the seabed. This allows an object to be placed exactly on the seabed. If you require an anchor coordinate close to, but not on the seabed, connect it to the seabed at a distance and then drag it nearer or edit the coordinate in the Data Form. Note: At present you cannot connect a slave object to a shape. 4.3.10 Printing, Copying and Exporting Views 3D Views may be printed, copied to the windows clipboard, or exported to a windows graphics metafile, so that the pictures may be used in other applications such as word processors and graphics packages. First select the view and adjust the viewpoint as desired. Then to print the view click the right mouse button and select Print (if needed, you can first adjust the printer setup using the File|Printer Setup menu item). To copy or export the view, ensure no object is selected (by clicking on the 3D view away from all objects) and then to copy to the clipboard press CTRL+C (or click the right mouse button and select Copy) and to export to a file click the right mouse button and select Export. If you are printing the view on a black and white printer (or are transferring the view into a document which you intend to print on a black and white printer) then it is often best to first set OrcaFlex to output in monochrome (use the Tools|Preferences|Output menu item). This avoids light colours appearing as faint shades of grey. After a 3D view has been transferred to another application you should be careful not to change its aspect ratio, since this will produce unequal scaling in the vertical and horizontal directions and invalidate the scale bar. In Word you can maintain aspect ratio by dragging the corners of the picture, whereas if you drag the centres of the sides then the aspect ratio is changed. 4.4 REPLAYS 4.4.1 Replays A Replay is a sequence of 3D views shown one after another to give an animation. A replay is therefore like a short length of film, with each frame of the film being a snapshot of a model as it was at a given time. There are various controls and parameters that allow you to control a replay. You can also view a series of snapshots all superimposed onto a single view - see Superimpose Times. There are two types of replay: • Active Simulation Replays show the model as it was at regularly spaced times during the currently active simulation. This type of replay is therefore only available when a simulation is active and can only cover the period that has already been simulated. If you have a time 96 w history graph window open when the replay is run, then the replay time is indicated on the graph by a vertical line that moves across the graph in time with the replay. • Multiple File Replays are replays where each frame can be from a separate data or simulation file. See Multiple File Replays for details. Export Video Replays can be exported as a video clip in AVI file format, using the Export Video button on the replay parameters form. An AVI file is generated containing the replay using the most recently selected 3D view window and using the same period, frame interval and speed as the replay. AVI is a standard video format, so the file can then be imported into other applications, for example to be shown in a presentation. Notes: AVI files can be very large if the window size is large or there are a lot of frames in the replay. Also, re-sizing video clips (after pasting into your presentation) will introduce aliasing (re-digitisation errors), so it is often best to set the 3D View window size to the required size before you export the video. 4.4.2 Replay Parameters The replay can be controlled by the following parameters that can be set in the Replay Parameters dialogue window, accessed using the Replay Parameters button. Replay Period The part of the simulation that the replay covers. You can select to replay the whole simulation, just one simulation stage (an asterisk * denotes an incomplete stage), the latest wave period or else a user specified period. If you select User Specified then you can enter your own Start and End Times for the replay period. Interval The simulation time step size between frames of the replay. Using shorter intervals means that you see a smoother animation (though the extra drawing required may slow the animation). Example: For a simulation with stages of 8 seconds each, selecting stage 2 and a replay time step of 0.5 seconds causes the replay to show 16 frames, corresponding to t=8.0, 8.5, 9.0 ... 15.5. Target Speed Determines how fast the replay is played. It is specified as a percentage of real time, so 100% means at real time, 200% means twice as fast etc. As a special case, the fastest allowable target speed (10000% at the moment) is taken to mean "as fast as possible". Note: The specified target speed is not always achievable because the computer may not be able to draw each frame quickly enough. When this happens, the replay will be played as fast as possible. Replays may be slow if you specify thick lines (line width>1) for objects in the model, since this can increase the drawing time. 97 w Continuous Continuous means replaying like an endless film loop, automatically cycling back to the first frame after the last frame has been shown; this is suitable for replays of whole cycles of regular cyclic motion. Non-continuous means that there will be a pause at the end of the replay, before it starts again at the beginning; this is more suitable for non-cyclic motion. All Views If this is selected, then the replay is shown in all 3D Views simultaneously, allowing motion to be viewed from several different viewpoints. Otherwise the replay is played in the currently selected view window only. Note: Show Trails If this is selected, 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. Replaying in several 3D views simultaneously may be slow on some machines. 4.4.3 Replay Control The replay can be controlled using the following menu items, toolbar buttons and their corresponding hot keys. Button Menu Item View | Start Replay View | Stop Replay View | Step Replay Forwards View | Step Replay Backwards + SHIFT Hot Key CTRL+R CTRL+R CTRL+A CTRL+B CTRL+F CTRL+S CTRL+D Action Start replay Stop replay Step to next frame and pause Step to previous frame and pause Speed up replay Slow down replay Edit replay parameters View | Replay Faster View | Replay Slower View | Replay Parameters 4.4.4 Superimpose Times Allows model configurations for different times of the simulation to be superimposed in 3D Views. Use View | Current Position to undo the superimposed view. The data items are: List of Times The simulation times which will be superimposed. The times listed may be slightly different from those entered. This is because the only times that can be drawn are at log samples. If you need finer resolution then you may have to increase the number of log samples. 98 w Add Time Adds a simulation time to the list. Remove Removes the selected time from the list. Clear Removes all times from the list. All Views If this box is checked then the superimposed view is drawn in all 3D View windows. If not then it is drawn in the selected 3D View. 4.4.5 Multiple File Replays A multiple file replay is a replay in which each frame can be from a separate OrcaFlex file. Each frame of the replay can be either the static position for a specified data file, or a snapshot of a specified time in a specified simulation file. The former allows you to string together a series of static analyses 'snapshots' to give an animation of an installation procedure, for example. The latter allows you to create replays where the frames are from one or more simulations, and control in detail the time intervals between frames. Replay Specification File A multiple file replay is specified by setting up a replay specification file. This is a text file that can have any name, but which has the structure of Windows .INI files (files that are commonly used to store program configuration information). Here is an example replay specification file: ; Example Replay Specification File [General] Interval = 0.3 ; Frame 1 [Starting Point] File = Case#01.dat ; Frame 2 [Intermediate position] File = Case#02.sim Time = 27.5 ; Frame 3 [Final Position] File = Case#03.sim The structure of the file is that it contains a number of 'sections', each section being a line of the form [<SectionName>] followed by a number of 'value' lines of the form 99 w <ValueName> = <Value> The section ends at the beginning of the next section, or at the end of the file. So, in the above example there are 4 sections, called 'General', 'Starting Point', 'Intermediate Position' and 'Final Position'. General section The General section, if present, must be called 'General'. It can contain a 'value' line of the form Interval = 0.3 that specifies the real time interval (in seconds) between drawing successive frames of the replay. If this Interval value line, or the whole General section, is not present then the default interval is 0.1s. Note that you can adjust the actual replay speed relative to this nominal real time speed. Frame Sections All other sections in the file are assumed to specify the individual frames in the replay. You can choose the names of the frame sections yourself, but they must be distinct and not equal to 'General'. When you run the replay the frame section names are displayed in the OrcaFlex status bar, to identify the current frame. Each frame section must contain a value called File that specifies the name of the file for that frame. This is the filename of an OrcaFlex data or simulation file. If a full path is not specified then the filename is assumed to be relative to the directory containing the replay specification file. If the file is a data file then the frame is a static position frame - it calculates and displays the static configuration of that model. If the file is a simulation file then the frame is a simulation snapshot frame - it displays the configuration of that model at the simulation time specified by the Time value. Each frame section may optionally also contain a value named Time. This value is only used if the File value specifies a simulation file. It specifies, in seconds, the simulation time to be used for this frame. If the value is not specified then the frame displays the configuration of the model at the end of the specified simulation. Comments You can put comment lines in a replay specification file by starting the comment line with a semi-colon character. Such lines are ignored, as are any blank lines in the file. Running the Multiple File Replay Whenever the replay is started OrcaFlex first has to prepare all the frames of the replay. For static position frames this involves opening the specified data file and calculating the static position of the model. For simulation snapshot frames the simulation file is opened and read to find the position of the model at the specified simulation time. 4.5 DATA FORMS 4.5.1 Data Forms Each object in the model has data items that define its properties. The data are examined and edited in the object's Data Form, which can be accessed by various methods: 100 w • • • use the Model Browser DOUBLE CLICK RIGHT CLICK the object in a 3D view the object in a 3D view and use the pop-up menu. If a simulation is active then most data items cannot be changed since they affect the calculation, but you can change things like the object's colour. Control Buttons OK Accepts the data changes made and then closes the form. Cancel Cancels the data changes made and then closes the form. Next Accepts the data changes made and then displays the next form in sequence. Holding the key down while CLICKING the Next button accepts the changes and then displays the previous data form in sequence. SHIFT Pop-up Menu The pop-up menu on a data form provides various facilities, including: • • • • The data form can be printed, copied to the clipboard or exported to a file. The data for the whole model may be printed using the File | Print menu item. Access to the next and previous data form and to the Variable Data form. The batch script names for the currently-selected block of data items. On data forms of some model objects, a report of the properties of that object. The report displays properties like weight in air, displacement, weight in water etc. 4.5.2 Data Fields Data items on each Data Form are displayed in Fields, generally with related fields organised into Groups or Tables. You can select a field with the mouse, or use the keyboard to navigate around the form. TAB moves from group to group, and the arrow keys move across the fields in a group. Where data are complex the form has pages of a tab index that choose between a number of distinct sections of the data. Where tabular data are shown on the data form, there is usually a separate field that specifies the number of entries in the table, and if necessary scroll bars are shown - use these to navigate through the whole table. Please note that if scroll bars are present, then only part of the data is currently being displayed. The following types of fields are used: Text A general string of text, used for example for titles and comments. 101 w Name Each object is given a name, which you can edit. Object names must be unique - you can not have two objects with the same name. Certain names are reserved for special purposes: Fixed, Anchored and Free (see Connecting Objects). Numeric Numbers can be entered in a number of formats such as 3, 3.0, 0.3, .3 or 3.0 E6. It is possible to enter more digits than those shown in the field, but beware that it will not be possible to see them again without editing again and using the arrow keys to examine the rest of field. For some numeric data items the value '~' is permitted. For example this is sometimes used to mean 'default value'. Details are given in the descriptions of the relevant data items. Spin Buttons These are small buttons with up and down arrows, used for incrementing and decrementing the associated field (such as the number of entries in a table). Using the mouse, CLICK on the upper or lower parts of the button to increment or decrement the associated counter. Multi-choice Buttons These are used when a number of options are available. Activate the button to step on to the next available option. Check Boxes These show a tick, meaning selected, or are blank, meaning not selected. CLICK or press RETURN to change. Colour Selection These show as a block of colour. DOUBLE CLICK or press RETURN to open the Colour Selection dialogue box. The desired colour may now be selected. List Boxes These show the current selection, such as the name of another object that this object is connected to. DOUBLE CLICK or press RETURN to show a List Box, and then select another item and RETURN to accept the new choice. 4.5.3 Data Form Editing The TAB, SHIFT+TAB, HOME, END and ARROW keys and the mouse can be used to navigate around the Edit Form. Editing mode is entered by DOUBLE CLICKING a cell with the mouse, or by starting to type alphanumeric characters, which are entered into the field as they are typed. 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, and the new value takes effect, when you press RETURN or select another field or button on the form. To end editing mode but reject the edit (and so keep the old value) press ESC. Many numeric fields have limits on the range of values that can be entered, for example an object's mass must always be greater than zero. Warnings are given if invalid values are typed. 102 w Input can also be from the Windows clipboard. CTRL+C copies the selected field or block of fields to the clipboard whilst CTRL+V pastes from the clipboard into the selected field. In this way data can be easily transferred to and from Spreadsheets, Word Processors, etc. Mouse Actions CLICK CLICK+DRAG, SHIFT+CLICK DOUBLE CLICK SECONDARY BUTTON CLICK Select Field Select a block of fields Start Edit Mode in this field (please also see Data Fields) Context sensitive pop-up menu for copying, exporting and printing the form and, for some model objects, viewing additional properties Next Group Previous Group Move to the group with this letter underlined in its heading Go to adjacent row or column Go to leftmost column Go to rightmost column Go to top row Go to bottom row Insert or delete a row of a table Edit (replace) Move within field Cancel edit Accept edit and move to previous/next row Accept edit Copy selected field/block to clipboard Paste from clipboard into selected field Fill selection from top (copy top cell down) Fill selection from left (copy leftmost cell to right) Fill selection from bottom (copy bottom cell up) Fill selection from right (copy rightmost cell to left) Group Movement TAB SHIFT+TAB ALT+... Field Movement ←↑↓→ HOME END PAGE UP PAGE DOWN Table Editing INS, DEL Start Editing 0..9, A..Z During Editing ←→,HOME,END End Editing ESC ↑↓ RETURN Copy / Paste CTRL+C CTRL+V CTRL+D CTRL+R CTRL+U CTRL+SHIFT+D CTRL+L CTRL+SHIFT+R 103 w 4.5.4 Variable Data Most OrcaFlex data is constant - i.e. its value, y say, is a fixed specified value. But for some numerical data items you can choose to instead specify variable data. The data item's value y is then specified as being a function of some other value x, and the actual value y(x) used by OrcaFlex then depends on the value of x at the time. If x varies during the simulation then y varies accordingly. As an example consider the drag coefficient of a line. In the real world this isn't a fixed constant value - it depends on the Reynolds number. For many application this variation is not significant so a fixed constant drag coefficient is sufficient. But sometimes the Reynolds number variation is important, so you can then specify the drag coefficient to be a function of Reynolds number. Then, 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). Note that for some data items use variable data in a slightly different way. For example the axial stiffness of a line type is the slope of the tension-strain curve, so in this case constant data specifies dy/dx, rather than y, where y is tension and x is axial strain. In this context 'constant' means constant slope, i.e. linear, and the constant value you specify is dy/dx, 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. Using Variable Data Variable data can only be used for certain data items. These are the numerical data items that have a small down-arrow button to the right of the data item value. For these you can either specify a fixed constant numerical value in the usual way. Or you can specify the name of a variable data set, either by typing the name in or by selecting it using the down-arrow button. The named data set must already have been set up - see the next section. Setting Up Variable Data All the variable data tables are specified on the Variable Data form. This form can be opened using the model browser or using the pop-up menu on any data form. Each table on the Variable Data form is given a name and the tables are grouped according to the type of data they contain. For example data for drag coefficients is kept separate from data for axial stiffness. This structure is indicated by the layout of the form, which is designed to be used from left to right. So first select the type of data you want, using the tree view in the left hand section of the form. The centre section of the form then shows how many tables have already been defined for that selected type of data, and their names. To add a new table, increment the Number of Data Sets. To edit the name of a table double click the name or select the name and then press F2. To delete a data set select it and press the DELETE key. The right hand section of the form displays the variation of y against x for the data set currently selected in the centre section. It is specified by giving a table of corresponding values (x1,y1), (x2,y2), .., (xn,yn), where the table's left hand column is the independent variable x and its right hand column is the dependent variable y. The data will be automatically sorted into order of increasing x when the data is used or when you use the Profile button. For intermediate values of x OrcaFlex interpolates. For values of x outside the range specified OrcaFlex either extrapolates or else truncates. Truncation means that OrcaFlex uses y1 for all x <= x1 and yn for all x >= xn (the table already having been sorted so that x1 is the lowest x- 104 w value specified and xn is the highest). The variable data form reports the method of interpolation and whether extrapolation or truncation is used. Profile Graph The Profile button displays a graph of the currently-select data. This is useful for data checking purposes. Where appropriate, log scales are used. 4.5.5 Data in Time History Files For certain data you can use time history files to specify time-varying values. This is available for wave elevation, wind speed and vessel motion, and it allows you full control over how the variable changes with time. If you want to specify time-varying data for more than one object (e.g. for both the wave and wind, 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. To use a time history file you must specify the following information. Input File This is the name of the Time History input file that contains the data. The filename can either be typed in or else set by using the Browse button. If you type it in you can either specify the full path or a relative path. Columns You must tell OrcaFlex which columns in the time history file contain the relevant data. To allow you to do this OrcaFlex provides an Import Wizard that displays the time history data in a spreadsheet window that has list boxes at the top of each column. The list boxes allow you to specify what data is in each column, or alternatively that a column is not used (i.e. contains data that is not relevant). The import wizard is automatically opened when you select a new time history file; or you can open it yourself by clicking the button provided. Time Origin The time origin data item gives you control of how the times given in the time history file relate to the times in OrcaFlex. The time origin is specified relative to the OrcaFlex global time origin, so it specifies the global time that corresponds to zero time in the time history file. The simulation time origin is also specified relative to global time, so you can simulate different periods of the time history by adjusting either the time history origin or the simulation time origin. So, for example, if the time history file's time origin is set to 100s and the simulation time origin is set to 400s, then a simulation consisting of 40s of build-up (i.e. simulation time -40 to 0) followed by 200s of simulation (simulation time 0 to 200) will cover time history time from 260s to 500s. Note that the time history file must contain data to cover the whole of the simulation. Note: If you are using more than one time history file (e.g. one for a wave train and one for motion of a vessel) then they each have their own time origins, which you can use to time shift each time history independently of the others. Time History File Format Time History files must conform to the following formatting rules: 105 w • The file must be a tab-delimited text file; in other words it must be a text file in which the time history data columns are separated by single tab characters. Files of this format can easily be produced with commercial spreadsheet programs by using "Save As" and selecting tabdelimited text form. The data values must be in standard decimal or scientific form. One column must contain the time values and these must be given in ascending order. The data must be given in the same units as used in the OrcaFlex model. For a wave time history the time values must be equally spaced (since a fast Fourier transform is used). But for wind velocity or vessel motion time history files variable time intervals can be used (since cubic spline interpolation is used). • • • • The data is assumed to start at the first numeric entry in the time column and blank rows are not allowed once the data has started. This means that textual information about the file (titles etc.) can precede the data but once the data begins it cannot be interrupted with any more text. 4.6 RESULTS 4.6.1 Results You can access results by either CLICKING on the Results button on the toolbar or by using the Select Results menu item; the Select Results form then appears. There is a Keep Open switch on the form's context menu, which allows you to choose whether the form automatically closes when you select a result, or alternatively stays open (and on top) until you explicitly close it. The Select Result form allows you to select the results you want by specifying: • The type of results required. Results are available as text tables (summary results, full results, offset tables, statistics or linked statistics) or as graphs (time histories, range graphs, offset graphs or XY graphs). The types of results available depend on the current program state. The object for which you want results (selected in the same way as in the Model Browser) and for some objects which point in the object. For the Environment you must specify the global X,Y,Z coordinates of the point for which you want results. For 6D Buoys that have wings attached, results for the buoy and for each wing are available separately. For lines you must specify the arc length along the line - see Line Results. For time histories, XY graphs and range graphs you must specify the period of the simulation to be included. This can be one of the stages of the simulation, the Whole Simulation or a User Specified Period. If the wave is regular then you can select the Latest Wave Period. For Range Graphs you can also select Static State - this option is only available after a statics calculation. The desired variable(s). • • • Graphs and Tables can be sent straight to the printer by CLICKING the Print button. If the values of a graph are required in text form then CLICK the Values button - this give the values in a Spreadsheet window, which can handle multiple variables if desired. The summary and full results are taken directly from the current state of the model. All the other results are derived from a temporary simulation log file which OrcaFlex creates automatically when a simulation is run. As the simulation progresses, OrcaFlex samples the variables for 106 w each object at regular intervals and stores the sampled values in the log file. All time histories, statistics and range graphs are derived from this simulation log file. You can control the number of samples taken during the simulation, and hence the time resolution of the results, by setting the Number of Log Samples data item on the general data form. This must be done before the simulation is started. Increasing the number of samples taken will improve the time resolution of the results, but will both slow the program down a bit and use more disk space for the simulation log and for any simulation files that are created. Note: A special algorithm is used for logging tensions (and other results that might vary rapidly) to ensure that any spikes that may occur between samples are recorded. Compression Warning If any lines have, during the simulation, gone into greater compression than their segment Euler load then a warning note is added to the Results form. Such lines are also marked with the symbol § in the Model Browser. See Line Compression. Offset Warning If any of the multiple statics calculations have failed then a warning note is added to the Results form. 4.6.2 Selecting Variables Each object has associated with it: • • A currently selected variable that will be used for graphs. A set of statistics variables that will be included in statistics reports. For the currently selected object, the currently selected variables are shown in a list on the results selection form. If Statistics results are selected, then the list shows the set of variables that will be included in the statistics report and you can add or remove variables by CLICKING on them in the list. If a Time History is selected, the list shows the (single) currently selected variable and you can select a different variable by CLICKING on it in the list. You can also multi-select variables, using: CLICK DRAG SHIFT+CLICK CTRL+CLICK CTRL+DRAG select one variable select a range of variables select a range of variables add / remove one variable add / remove range of variables If more than one variable is selected, then the Values button will give a single Spreadsheet Window with a time history column for each selected variable, and the Graph button will give a separate Graph Window for each variable. New columns can be appended to existing time history spreadsheet windows, as follows: • • Select the spreadsheet window to which you want to append, by clicking on it. Then open the Select Results form and select the variables that you want to append. 107 w • • Then hold the CTRL button down and click the Values button. Provided that the selected spreadsheet window is a time history values table and that the time periods for both sets of histories match, then the new time histories will be appended to the active window. This allows you to have a single window containing results from different objects. 4.6.3 Summary and Full Results These spreadsheet windows give the current state of an object or of the whole model. For example, in Statics Complete state the full results tables show the position of objects in their static position. If a simulation is active, then they show the positions of objects at the latest time calculated. To obtain one of these results tables: • • • Select Summary Results or Full Results on the Results form. Select the object require. Click the Table button. The summary results are simply an abbreviated form of the full results, in which the results for lines only include the end nodes, not all of the intermediate nodes. The summary and full results include estimates of the shortest natural periods of objects or of the whole model. These can be used to determine suitable simulation time steps. The simulation inner time step should normally be no more than 1/20th 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. 4.6.4 Statistics The Statistics report provides, for each statistics variable: • • The minimum and maximum values and the simulation times when they occurred The mean and standard deviation (i.e. the root mean square about the mean). These statistics are reported for each of a number of periods of the simulation. If Statistics by Wave Period is selected then these periods are successive wave periods; otherwise they are the stages of the simulation. To obtain a Statistics report: • • • Select Statistics. Select the object and the variables of interest (see Selecting Variables). CLICK the Table button. The report is presented in a Spreadsheet. Warning: The samples in a time history are not independent. They have what is called 'serial correlation', which often affects the accuracy of statistical results based on them. 4.6.5 Linked Statistics The Linked Statistics table relates a group of variables for a given object. For a specified group of variables and a specified period of simulation, OrcaFlex finds the minimum and maximum of 108 w each variable and reports these extreme values, the times they occurred and the values that all the other variables took at those times. To obtain a Linked Statistics report: • • • • Select Linked Statistics. Select the required object and period. Select the variables of interest (see Selecting Variables). CLICK the OK button. The report is presented in a Spreadsheet. 4.6.6 Offset Tables These Text Windows are available only after multiple statics calculations and only for vessels. For a given offset direction they report the total load on the vessel and show how it varies with offset distance. The worst tension in any segment of any line connected to the vessel is also reported for each offset. To obtain an Offset Table: • • • • Select Offset Table on the Results form. Select the offset vessel. Select the offset direction required. CLICK the Table button. The report is presented in a Text Window. 4.6.7 Time History and XY Graphs Time History graphs are of a single variable against time. XY graphs are of one time dependent variable against another. The period of simulation covered by the graph is chosen from a list. To obtain a Time History or XY Graph: • • • Select Time History or XY Graph on the Results form. Select the object required. Select the variable required (see Selecting Variables). selected for time histories. More than one variable can be For XY graphs the above 2 steps need to be done for both axes. Do this by CLICKING on one of the options labelled X-axis or Y-axis, which are located at the bottom of the results form, and then repeating the above 2 steps. • • Select the period required. CLICK the Graph button. Time history and XY graphs are displayed in Graph Windows and they are "live" - i.e. they are regularly updated during the simulation. You can therefore set up one or more graph windows 109 w at the start of a simulation and watch the graphs develop as the simulation progresses. If you reset the simulation then the curves will be removed but the graphs will remain, so you can adjust the model and re-run the simulation and the graphs will then be redrawn. Graphs are automatically deleted if the object that they refer to is removed, for example by loading a new model. Range Jump Suppression For time histories of some angles OrcaFlex chooses the angle's range so that the time history is continuous. For example consider vessel heading, which is normally reported in the range -180 to +180 degrees. If the vessel's heading passes through 180 then without range jump suppression the time history would be: .., 179, 180, -179, .. i.e. with a 360 degree jump. To avoid this jump OrcaFlex adds or subtracts multiples of 360 degrees to give the best continuation of the previous value. So in this example it adds 360 to the -179 value and hence reports: .., 179, 180, 181, .. This addition is valid since 181 and -179 are of course identical headings. Note that this means that angle time history results can go outside the range -360 to +360. Empirical Cumulative Distribution From any time history graph you can use the pop-up menu to obtain the empirical cumulative distribution graph for that time history. This graph shows what proportion of the samples in the time history are less than or equal to a given value. These graphs are sometimes referred to as an 'Exceedence Plots' since they can sometimes be used to estimate the probability that the variable will exceed a given value. Warning: The samples in a time history are not independent. They have what is called 'serial correlation', which often affects the accuracy of statistical results based on them. 4.6.8 Range Graphs Range graphs are only available for a selection of variables and they are only available for Lines. They show the values the variable took, during a specified part of the simulation, as a function of arc length along the Line. In particular: • Range graphs show the minimum, 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 shows the minimum value. Effective tension range graphs have extra curves showing the segment Euler load and the Maximum Tension value (as specified on the Line Types data form). 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). 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). Stress range graphs show the Allowable Stress (as specified on the Line Types data form). • • • • 110 w • 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). Two curves are then drawn, at Mean ± xσ, where x is a user chosen value and σ is the standard deviation. The standard deviation is calculated from all the samples that lie in the simulation period chosen for the graph. Warning: Be careful not to assume that 95% of the data lie in the interval Mean ± 2σ. This common guideline is based on the assumption that the data are sampled from a Normal (i.e. Gaussian) distribution. To obtain a Range Graph: • • • • • Select Range Graph on the Results form. Select the object required. Select the variable required (see Selecting Variables). Select the period required. CLICK the Graph button. Range graphs are displayed in Graph Windows and they are "live" - i.e. they are regularly updated during the simulation. 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. If you reset the simulation then the curves will be removed but the graphs will remain, so you can adjust the model and re-run the simulation and the graphs will then be redrawn. Graphs are automatically deleted if the object that they refer to is removed, for example by loading a new model. 4.6.9 Offset Graphs These graphs are available only after a multiple statics calculation has been done and only for the offset vessel. 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. Note that this force is not necessarily in the offset direction. Vertical Force The vertically downwards component of the total force applied to the vessel by the attached Lines or other objects. Yaw Moment The moment, about the vertical, applied to the vessel by the attached Lines or other objects. Worst Tension The largest tension in any segment of any Line connected to the vessel. To obtain an Offset Graph: • • Select Offset Graph on the Results form. Select the offset vessel. 111 w • • • Select the offset direction required. Select the variable required. CLICK the Graph button. 4.6.10 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. Here are some tips on how this can be done. Graphs Graphs can be transferred from OrcaFlex to presentation programs by simple copy + paste. Note: In PowerPoint, instead of using Paste, it is better to use Paste Special (from the Edit menu) and then select the Enhanced Metafile. This gives better resolution. Replays Replays can be transferred by exporting to an AVI file and then importing that video clip file into the presentation program. 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. Video Clips of OrcaFlex in Use Your presentation can even show video clips of OrcaFlex in use, illustrating how the program is used. However, it is rather harder to generate the required AVI files. Here is a method that we have used successfully at Orcina. • The process uses HyperCam, a shareware program for capturing and manipulating video sequences. This program writes video clips in AVI format which can then be imported into your presentation. For details of how to obtain HyperCam see internet website http://www.hyperionics.com. Run OrcaFlex and set it up to be ready for the first frame of the video you want. Run HyperCam and define the screen area in OrcaFlex that you want to record. To do this use either the Select Region or Select Window button on HyperCam's Screen Area form. The HyperCam window disappears and you have either a cross hair cursor with which to define the corners of the recording area (Select Region) or a blinking frame around the selected window (Select Window). If necessary use ALT+TAB to bring up OrcaFlex, then make your selection. The HyperCam menu reappears automatically. On HyperCam's AVI File tab, set the file name and path where you want the recorded AVI file to be stored. Press HyperCam's Start Paused button. This prepares to record, but waits for a key press before starting. In OrcaFlex, ensure it is ready for the first frame and move the cursor out of the recording area. Then press F4 to record a single video frame. Allow a short interval for recording (typically ½ -1 second) before proceeding. • • • • • 112 w • • Set up OrcaFlex for the next frame, press F4 to record it and allow recording time again. Continue in this way until you have recorded the last frame and then press F2 to stop. You should now have an AVI file of the OrcaFlex sequence you want which can be imported into and replayed by packages such as PowerPoint. The recording process is quite quick and easy, but some practice may be required to get exactly the result you want. Specific problems we have encountered include: • • Aliasing where the final screen area in the presentation differs from the screen area used for recording - this can result in continuous lines appearing broken on replay. Recording of unwanted parts of the screen, cursors, Help bubbles, etc. If you don’t want the cursor to appear, then move it out of the recording area before pressing the F4 key. If you are recording the full OrcaFlex window including control buttons, then move the cursor off the screen edge. Leaving the cursor over a button may bring up the help bubble which will then be recorded with everything else. 4.7 GRAPHS 4.7.1 Graphs When you request results in graphical form, they are presented in Graph Windows. You can open several simultaneous graph windows, showing different results, and tile them on the screen together with 3D views and text results windows. To adjust the graph's properties (range of axes, colours, etc.) see Modifying Graphs. Graphs have a pop-up menu that provides the following facilities. • • • • Undo Zoom (only available after using Zoom) returns the graph axes to their original ranges of values. Copy copies the graph to the clipboard, from where you can paste it into other applications. Values displays a spreadsheet containing the numerical values on which the graph is based. Spectral Density (only available for time history graphs) opens a new graph showing the frequency spectrum of the time history. The function shown on the graph is the one-sided power spectral density per unit time of the sampled time history, obtained using a Fourier transform. Note: the sampling inevitably introduces 'noise' to the spectrum and this is often very noticeable on the graph. Export enables you to export the graph to a metafile or bitmap file. Print facilities and the Monochrome Output preference. Properties opens the graph properties form (which can also be opened by double clicking the graph). • • • Graphs of simulation results are "live" - i.e. they are updated automatically as the simulation progresses. Also, they are kept even if you reset the simulation, 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. You can also set up results graphs when in reset state, prior to running a simulation - the graph will be empty initially and will grow as the simulation progresses. Note that we do not recommend this for graphs of line clearance, however, since updating them can significantly slow down the simulation. 113 w To print a graph, use the File | Print menu item. 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. From the clipboard you can then paste it into another application, for instance into a word processor document. Graphs can also be exported as Windows metafiles, use the File | Export menu item. Metafiles can be imported into many Windows programs, such as word processors, spreadsheets, graphics packages etc. When copying a graph to the clipboard, the size of the graph on screen has an effect on how the fonts appear when the graph is pasted into another application. For example, if you are copying a graph to a Word Processor and want the graph to be full page size then the graph should be made large on screen (i.e. maximised). If you are wanting a number of graphs on one page of a document then the graph should be smaller on screen - try tiling or cascading the windows (use the Window menu). By experimenting with various differently sized graphs it should be possible to arrange for the fonts to appear as you wish. Note: You will get the best results when printing to a monochrome printer by setting the Monochrome Output preference - this is set by default when the program is first installed. 4.7.2 Modifying Graphs You can zoom in a graph by holding down the ALT key and dragging a box around the area that you want the graph to display. When you release the mouse button the region selected will be expanded to fill the graph. If you want to reverse this process then right click the mouse and choose "Undo Zoom" from the pop-up menu. You can also change the appearance of a graph by double clicking on the graph or by selecting properties from the graph's pop-up menu. A dialogue box then appears, allowing you to change various aspects of the graph, as follows: Axes You can set the range, the tick spacing and the number of small ticks. Labels You can alter the text and fonts of the axis and tick labels. Curves You can control the line properties and visibility for each curve on the graph. Legend The legend is a key showing which curve is which. It only appears on graphs that have multiple curves, e.g. range graphs. You can control whether the legend is shown and if so where and using what font. Note that the legend includes all the curves, even if some of them may not be visible at the time. Intercepts Intercepts are lines, like the axes, that go right across the graph. In fact the X and Y axes themselves are considered to be intercepts. You can add more intercepts, for example to mark things like stage start times, and you can control their position and style. 114 w Save As Default Changes to a graph’s properties normally only apply to that graph. But for general settings (fonts etc.) you can also click the Save As Default button. OrcaFlex then remembers the current settings for use with future graphs. 4.8 SPREADSHEETS 4.8.1 Spreadsheets Some numerical results (e.g. obtained with the Values button on the Results form) appear in an Excel compatible spreadsheet. All the usual spreadsheet operations are provided (including all the standard floating point functions), so you can easily do simple post-processing calculations without having to copy+paste the results over to your full spreadsheet program. Formula entry is identical to that of Excel and all the standard mathematical formulae are available. The more sophisticated spreadsheet facilities (for example cell formatting, graphs, multiple sheets) are not provided, but of course when you need these you can easily use export of copy+paste to get the results into your favourite spreadsheet program. Printing, Copying and Exporting Spreadsheets To print the spreadsheet right click and select Print, but remember that OrcaFlex time histories are normally quite long and will therefore produce many pages. If necessary, you can first adjust the printer setup using File|Printer Setup. 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. Saving to file. Right click the mouse and choose Export. Note: When copying to the clipboard only the values of the cells are copied. If you have entered any formulae and want these transferred you must save to file (using Excel format) and then load into your spreadsheet application. 4.9 TEXT WINDOWS Simple text windows are used for some reports - see below. To print a text window, use the File | Print menu. 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). From the clipboard you can then paste it into another application, for instance into a word processor document. Alternatively, you can export the text to a file by using the File | Export menu item. The resulting text file can then be imported into your word processor. Statics Progress Window During a Statics Calculation, the progress of the calculation is shown in the message box on the status bar. However the messages are also sent to a text window that is normally minimised. This window may be viewed by clicking on the message box during statics, or by selecting the Window | Statics Progress menu item if you wish to watch the process more closely. Like other text windows it may be printed, copied or exported, as described above. 115 w Session Log This is a text window giving details of file actions, calculations etc. It can be viewed from the Window | Session Log menu or by clicking the message box. It is particularly useful for batch calculations. If one of the simulations of a batch run fails then information about the failure is written to the Session Log and can be displayed when the batch run is complete. 4.10 COMPARING DATA The Compare Data menu item opens the Compare Data form, which allows you to find differences between the data in 2 OrcaFlex files. The comparison is done using a user-provided compare program, so when you first use this facility you need to configure OrcaFlex to tell it which compare program that you want to use; see Configuration below. You can then compare files as follows: • • • On the Files tab, specify the 2 files that you wish to compare. These can be data or simulation files. Click the Compare button. OrcaFlex then saves the data from the 2 files to 2 temporary text files and then runs the user-specified compare program to compare those 2 text files. Configuration On the Configuration tab you need to tell OrcaFlex the text file compare program that you want to use, and how to use it. The compare program must be a program that can compare 2 text files passed to it through the command line. Various such programs are available on the web; examples are WinDiff, Compare It! and Araxis Merge. Compare Program This is the compare program's executable filename. You can specify either the full path, or just the filename if the executable file resides in a directory which is on your system path. Command Line Parameters This defines the command line parameters that are passed to the compare program. OrcaFlex replaces the special strings %1 and %2 with the filenames of the temporary text files. For most compare programs the default setting of "%1 %2" will be sufficient. Otherwise you will need to consult the documentation of your compare program. 4.11 PREFERENCES OrcaFlex has a number of settings that can be customised to suit the way that you work. The majority of settings can be adjusted in the Preferences dialogue box, which is accessed by using the Tools | Preferences menu item. 116 w 3D View Preferences Mouse Selection Zone This is the distance (in pixels) of the "hot zone" around each object. Larger values require less accuracy in pointing at objects with the mouse, but increase the chance of selecting a nearby object instead. Minimum Drag Distance Object positions are not updated until the mouse has been dragged at least this distance (in pixels). This prevents accidental changes to object positions. To make a small movement, drag away and then back again, or edit the coordinate directly in the object's Edit Form. View Rotation Increment The default is 5º. Each CLICK on a Rotate View button increments or decrements View Azimuth or Elevation by this amount. Refresh Rate During a simulation calculation all 3D View and Graph windows are updated at this rate. Selecting a faster rate allows you to see the behaviour of the simulation more clearly at the expense of performance. Set a slow Refresh Rate to give the numerical calculation more processor time. Background Colour This sets the background colour of all 3D View windows. 3D View Drawing Preferences Draw View Axes The view axes show the same directions as the global axes, but are drawn in the top right hand corner of 3D views, rather than at the global origin. Draw Scale Bar Determines whether a scale bar is drawn in 3D views. Draw Global Axes Determines whether the global axes are drawn, at the model's global origin (0,0,0). Draw Environment Axes Determines whether the wave, current and wind directions are drawn in the 3D view. When multiple wave trains are present the first wave train is taken to be the dominant one and is drawn using sea surface pen, whereas the other wave trains' directions are drawn in the secondary wave direction pen. 117 w Draw Local Axes Determines whether the local axes for vessels, buoys and lines are shown. Drawing the local axes on the 3D view helps you check the orientations of these objects. Can also be set from the View menu or by pressing CTRL+Y. Draw Out Of Balance Forces If selected, then in the static analysis (not during the simulation) there are extra lines drawn on the 3D view, representing the out of balance force acting on each vessel and buoy. This preference is sometimes useful for static analysis, since it enables you to see how far a buoy or vessel is from being in equilibrium. The force is drawn as a line, starting at the force’s effective point of application, and whose length represents the size of the force. The scaling is piecewise linear and based on the View Size of the 3D view. 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. Video Preferences Codec This specifies the method used to encode and compress exported video. You can choose between the following options. We recommend using Run Length Encoding unless you have problems playing the AVI files it produces. • Run Length Encoding: This is the default and is usually the best choice. This codec offers good compression rates for OrcaFlex video. The AVI files produced using this codec can be played on most Windows PCs. Uncompressed: This codec stores each frame of the video as an uncompressed bitmap. This means that the AVI file produced can be extremely large. Other: Should you wish to use a different codec you must also specify the four character code which identifies the codec. For more details see the documentation of the particular codec you wish to use. • • Output Preferences Printer Margins These set the Left and Top margins used on printouts. Monochrome Output If this is checked then external output (copying to the clipboard, exporting metafiles and printing) is in black and white. This is useful with black and white printers, since otherwise pale colours may be drawn in very light grey and may be hard to see. General Preferences Auto Backup Batch Runs If this is switched on then simulations run in batch mode are automatically stored to simulation files at the specified regular Auto Backup Interval. 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, rather than having to re-run the whole simulation from scratch. The 118 w Auto Backup Interval should be neither too short, since then the program will then waste a lot of time repeatedly storing away the results, nor too long, since then a lot of simulation work will be lost if a failure occurs. Number of Recent Files The number of recently used files displayed in the File menu. Set this to 0 if you want to disable this feature. 4.12 • PRINTING AND EXPORTING The Print / Export dialogue is accessed using either the File | Print or the File | Export menu item and allows you to choose one or more of the following items to be printed or saved to file: The model data. Vessel Types often have very large amounts of data, much of which may not apply to the current model, so OrcaFlex offers you the option of printing all the vessel type data or only the data that is in use. Any 3D Views, Graphs, Spreadsheets and Text Windows currently on display. Note: Spreadsheets cannot be printed directly from OrcaFlex. To print a spreadsheet you must first export as an Excel spreadsheet and then print from Excel. Graphs are printed as large as possible whilst maintaining aspect ratio. • Note: 119 w 5 5.1 • BATCH AND POST-PROCESSING INTRODUCTION OrcaFlex provides several important facilities for automating and post-processing work: The Batch Processing facility enables you to run a set of simulations in unattended mode, for example as an overnight job. The simulations can either be of pre-prepared data files, or else can be specified by a batch script file that specifies the simulation as variations on a base data file. The fatigue analysis tool provides in-built fatigue analysis for pipes. OrcaFlex is supplied with two special Excel spreadsheets which enable you to automate the extraction of simulation results into your own spreadsheet. You can then use the normal Excel calculation facilities to do your own customised post-processing and graphing. OrcaFlex includes a programming interface. This is a Windows dynamic link library (DLL) called OrcFxAPI (short for OrcaFlex Application Program Interface) and it is installed when you install OrcaFlex. The interface includes facilities for setting data, calculating static positions and extracting results from those calculations or from pre-run simulation files. For example you can write programs to automate post-processing or that use OrcaFlex as a 'statics calculation engine'. One important example application of this is for real-time monitoring of pipe, moorings etc. For details of the OrcFxAPI programming interface see the file OrcFxAPI.hlp (this help file can be found in the OrcaFlex directory on the OrcaFlex CD). For further information or to discuss possible applications of OrcFxAPI, please contact Orcina. • • • 5.2 BATCH PROCESSING 5.2.1 Batch Processing Simulations, script files and fatigue analyses can all be run in unattended mode, by using the Calculation|Batch Processing menu item. This command opens a form that allows you to set up a list of files that are to be run. Then, when you run the job, OrcaFlex opens and runs each file in turn. The list of files can include any number and mixture of the following types of file: 1. Pre-prepared OrcaFlex data files (*.dat). OrcaFlex opens the data file, runs the static analysis followed by the simulation, and then saves the results in a file with the same name as the data file, but with a .SIM extension. 2. Part-run OrcaFlex simulation files (*.sim). OrcaFlex opens the part-run simulation file, finishes the simulation and then saves the completed simulation results back to the same file. 3. A batch script file (*.txt). This is a text file which contains OrcaFlex script commands that specify what OrcaFlex should do. OrcaFlex opens the script file and obeys the commands in turn. A common use of script files is to run a number of variations on a base data file. 4. A fatigue analysis file (*.ftg). OrcaFlex performs the fatigue analysis and saves the results to an Excel compatible spreadsheet of the same name but extension *.xls. 120 w Note: You can also ask OrcaFlex to store the partial results to file at regular intervals during the batch job. 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, rather than having to re-run the whole simulation from scratch. See Preferences. Batch Form Buttons Close Dismisses the Batch form. Add File Files are added to the file list by CLICKING on the Add button. The Open File dialogue box is displayed, where you select one or more files to be entered in the Batch File list. To select a group of files, use SHIFT+CLICK and CTRL+CLICK. You can add data files, batch script files, or part-run simulation files. Remove File This button removes any files highlighted in the file list. Check Files OrcaFlex opens each file in the batch list in turn, checks that they contain valid OrcaFlex data or script commands, and reports any errors. The files are not changed, and no calculations are performed. The Check Files command does not take long, so we recommend you use it before starting your batch job. Run Batch Start running the listed files. Each file is opened and run in turn, and the file that is currently being run is highlighted in the file list. If any file fails due to errors then that file is abandoned and the batch job continues with the next file. Errors are recorded in the Session Log (which can be viewed from the Session Log item on the Window menu) and are also reported at the end of the batch job. Stop Batch Terminate the batch job. Note: Calculations run faster if there are fewer 3D View windows and Graphs open, and if the Refresh Rate in the Preferences dialogue box is set to a slower value. So to optimise performance consider closing all windows. 5.2.2 Script Files OrcaFlex provides special facilities for running a series of variations on a base data file, using a script file. This contains a sequence of commands to read a data file, make modifications to it, and run the modified file, storing the results for later processing. The file can also include comments. The syntax for the instructions is described in the next topic. For examples see the Batch Script Examples. 121 w To run a batch script file, specify the script file name in an OrcaFlex batch files list. To add a script file to the list, click the "Add File" button on the OrcaFlex batch form and then click on "Files of Type" and select *.txt, and then select your script file. When OrcaFlex processes the files included in the batch list, it checks the type of each file in turn: OrcaFlex data and .sim files are loaded and the simulation run and stored, text files are read in and expected to contain batch script commands. You can therefore run a single batch job containing several script files, or you can even mix 'ordinary' simulations and scripts in the same batch job. 5.2.3 Script Syntax An OrcaFlex batch script is made up of commands, which are obeyed sequentially, and comments, which are ignored. A comment is a line that is either blank or on which the first non-blank characters are "//". A command can be: 1. A directive followed by one or more arguments, optionally separated by white space (one or more spaces or tabs). For example: load c:\temp\test.dat where load is the directive and c:\temp\test.dat is the argument. 2. An assignment of the form VariableName=value, again with optional white space separators. For example: Length = 55.0. Note that: • • • • Directives and variable names are case independent. Model object names are case dependent, so tanker and Tanker are not the same object in an OrcaFlex model. If your script includes a relative filename then it is taken to be relative to the directory from which the script was loaded. Filenames, arguments, 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. For example '6" pipe' and "200' riser" are valid, but the following are not valid: 6 inch pipe - contains spaces, so needs to be enclosed in quotes; 6"pipe - contains a double quote, so needs to be enclosed in single quotes; '6' pipe' - contains a single quote, so needs to be enclosed in double quotes instead of single. 5.2.4 Script Commands The following batch script commands are currently available. You need to put quotes round filenames or other parameters that include spaces or non-alphanumeric characters. Load <FileName> Opens an OrcaFlex data file. The model defined in the data file becomes the current model. Run <FileName> Run the current model and save the resulting simulation to <FileName>. 122 w Save <FileName> Save the current model (data only) to <FileName>. Note: In the Load, Run and Save commands, if <FileName> is a relative path then it is taken to be in the directory from which the script file was loaded. Select [<Object Type>] <ObjectName> Specify the model object to which subsequent assignment commands will apply. It will only remain selected until the next non-assignment command is encountered. The <ObjectType> argument is optional, and by default is 'object', meaning select the named model object. <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' or 'Sea' (for the Environment data form). Other <ObjectType> values only need to be specified in the following special cases: • If the sea has been selected and there is more than one wave train, then before you can specify any wave train data you must give another select command to select the wave train. This second select command has the form Select wavetrain <WaveTrainName> So for example: Select Sea Select wavetrain Primary WaveDirection = 30.0 Note that you must also give this extra select command if you alter the number of wave trains in a script file. • If a vessel type has been selected and it has more than one draught, then before specifying any draught-dependent data you must give another select command that selects the draught. This second select command has the form Select draught <DraughtName> Similarly, before specifying vessel type data for a given wave direction you must give another select command to select that direction. This takes the form Select direction <Direction> So for example: Select "VType A" Select draught "Transit" Select direction 22.5 RAOYawAmplitude[2] = 0.1 Note that you must also give these extra select commands if you alter the number of draughts or directions in a script file. See the file Example2.txt for a more extensive example. Note that indentation with spaces or tabs is optional, but makes scripts more readable. Warning: In general, selecting a model object in a script is equivalent to opening that object's data form. The only exception to this rule is that wings on 6D Buoys are model objects in their own right, but are edited via the 6D Buoys data form: to set their data in a batch script you must select the wing you wish to edit, not the buoy to which it is attached. 123 w 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 model object. The Value on the right hand side must be in the appropriate form for that variable (i.e. numeric or text) and it must be given in the same units as used in the current model. For example: select 'Vessel A' length = 100 draught = 'Operating' If VariableName is the name of a variable that appears in a check box in OrcaFlex then the Value should be True or False. For example: select Sea CurrentRamp = True If VariableName is the name of a variable that appears in a table in OrcaFlex, then its row number must be given. The row number is given as an index enclosed by either square or round brackets (don't mix them on the same line), and is always 1-based - i.e. [1] is the first row of the table. Note that this sometimes requires care, since in OrcaFlex the table might not be 1based. For example, when setting the prescribed motion for a vessel, the command PrescribedMotionVelocity[2] = 4.8 sets the velocity in the 2nd row of the table, 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. 5.2.5 Handling Script Errors As with other computer programs, OrcaFlex batch script files can easily contain errors. It is therefore wise to check your script file for errors before running it as a batch job. To check for errors in your scripts, use the "Check Files" button on the OrcaFlex batch form. This will read and obey all the commands in the script files except those that perform calculations or write files. It will then report any errors it finds, including the line number on which the error occurs. You can then correct the problem before running the script. Example3.txt is an example containing various errors, so to see how errors are reported use the "Check Files" button with this example. Warning: If you misspell a variable name in an assignment statement then "Check Files" will report an error. But if you incorrectly specify a variable name which is nevertheless valid then OrcaFlex cannot detect the error. So you need to be very careful that you use the correct variable names for the data items that you want to change. 5.2.6 Obtaining Variable Names Each OrcaFlex data item has its own name that is used to specify it in a script file. The names of the data items are based on the corresponding labels used on the data form. To find out the name of a data item, open the appropriate data form, select the data item, and then open (e.g. by right click) the pop-up menu and select the Batch Script Names command. This displays the variable name of the selected data item and you can select and copy+paste the name directly into your batch script. 124 w If the data item is in a table (or group) of data items then the Batch Script Names form displays the names of all the data items in the table. The different columns in the table each have their own names; you then need to add an index to specify which row you want. The exceptions to this are the 'Connections' data controls for Lines and Links, which consist of two rows, one for End A and one for End B. For these, the Batch Script Names form lists the names for End A only: those for End B may be obtained by simply replacing 'EndA' with 'EndB' in the name. Finally, note that Batch Script Names are not available for an empty table - e.g. if you want the names for the attachments table on the line data form, but there are currently no attachments. In this case you must add a row to the table before you can use the Batch Script Names form. 5.3 FATIGUE ANALYSIS 5.3.1 Fatigue Analysis The OrcaFlex fatigue analysis carries out a deterministic fatigue analysis based on regular or irregular wave simulations. It extracts line load results from a series of pre-run simulation files, calculates the resulting pipe stresses and then calculates the fatigue damage. Warning: The fatigue analysis uses the stress results which assume a pipe made of a uniform, homogeneous, linear material. Two types of analysis can be performed - simple regular wave analysis or irregular wave analysis using the rainflow cycle counting method. The fatigue analysis tool is run by selecting the Fatigue Analysis command from the OrcaFlex Results menu. It is essentially a self-contained sub-program within OrcaFlex, with its own menus, data and results. Any OrcaFlex process active in the main window is paused until the Fatigue Analysis data form is closed. The Fatigue Analysis has no effect on existing OrcaFlex data. The steps involved in doing a fatigue analysis are: 1. Use the normal OrcaFlex facilities to set up and run simulations that model the various load cases that the line will experience. 2. Open the fatigue analysis tool and set up the data. This fatigue analysis data is held separately from the other OrcaFlex data and can be saved in a separate Fatigue Analysis File (.ftg). Note: An example file can be found in the PostProc sub-directory of the OrcaFlex installation directory. The filenames in this example data may need editing, since they assume that OrcaFlex has been installed to the default installation directory. 3. Check the data for errors. 4. Calculate the stresses and damage. Note: The Calculate stage of a fatigue analysis can take a long time , especially a rainflow analysis using a lot of large simulation files. To help with this there is an Estimate Calculation Time facility and fatigue analyses can be run in batch mode. 125 w 5.3.2 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. The approach is to divide the range of sea states that the system will experience into a number of wave classes. A typical way of doing this is to use a wave scatter diagram. One OrcaFlex simulation file can then be created for each wave class. 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. This simulation is then one Load Case. Each load case is assigned an exposure level. For regular load cases this is the total number of occurrences of waves within the class and for rainflow load cases this is the total time exposed to waves within the class. Warning: The included arc lengths must be the same in each load case, so the line to be analysed should have the same number and distribution of segments in each of the load case simulations. 5.3.3 Commands File Menu The file menu commands use the latest directory used in OrcaFlex, but you can browse directories as required. New Clears previously entered Fatigue Analysis data and results, and, where relevant, resets data to default values. Open Open a Fatigue Analysis file (.ftg) from the current directory. Save Save the data to the currently selected filename (shown in title bar of the window) If a file of that name already exists then it is overwritten. Save As This is the same as Save, but allows you to specify the filename to save to. If a file of that name already exists then you are asked whether to overwrite the file. Most Recent Files List List of the most recently used files. Selecting an item on the list causes the file to be loaded. The size of the list can be adjusted from the Preferences form. 126 w Analysis Menu Estimate Calculation Time Gives an estimate of how long it will takes to do the fatigue analysis and present the results. This is useful for long analyses, e.g. rainflow analyses involving a lot of cases or long simulations. Check The Check command performs a preliminary check of the fatigue analysis data. 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. The Check command is generally much quicker that the fatigue analysis itself, so we recommend that the Check command is used before the Fatigue Analysis is run, 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. 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. Calculate The Calculate command starts the Fatigue Analysis. The fatigue analysis can take a long time if there are many load cases, or if there are many log samples in the load case simulations, or finally if there are a lot of segments in the arc length intervals specified. A progress window is displayed and you can cancel the analysis if desired. When the calculation is complete the results are displayed in a spreadsheet window. 5.3.4 Data Title Used to label all output of the fatigue analysis. Analysis Type Two types of fatigue analysis are available: • A Regular analysis must be based on a series of regular wave simulations that represent the various load cases that will occur. For each of these load cases a single-occurrence damage value is calculated based on the last wave cycle in the simulation. This damage value is then scaled up by the specified number of cycles expected to occur during the structure's life, and this gives the total load case damage value. Finally these total load case damage values for each load case are then summed to give the overall total damage. A Rainflow analysis is normally based on a series of random wave simulations. It uses a cycle counting technique to break down each random wave case into a series of half cycles, and then sums the damage from each half cycle according to the Palmgren-Miner law (for details see the book by Maddox and the paper by Rychlik). This gives the single-occurrence damage value for that load case, which is then scaled up to the specified total exposure time for that load case, and this gives the total load case damage value. Finally these total load case damage values for each load case are then summed to give the overall total damage. • 127 w Units The units to be used for the fatigue analysis, for both the fatigue analysis data and for its results. The units are specified in the same way as elsewhere in OrcaFlex. Note that the units specified for the fatigue analysis need not match the units that were used in the various load case simulation files. If they do not match, then the stress results from that simulation file will automatically be converted to the units specified for the fatigue analysis. This is useful, since it allows the fatigue analysis to be done using mm and N as the length and force units (giving stresses in N/mm^2 = MPa), for example, even if the simulation load cases use m and kN (which corresponds to stresses in kN/m^2 = kPa). Similarly, in US units, the fatigue analysis can use inches (giving stresses in ksi) even if the simulation files use feet as the length unit. If you change units, then all existing fatigue analysis data is automatically changed to match the new units. This is useful if you want to enter data in some other set of units, since you can simply change to the units of the new data, then enter the new data, and then change back to the original units again. Load Case Data Add Load Case The Add Load Case button is used to add load cases to the Fatigue Analysis; it adds an extra row in the load case table. Remove Load Case Removes the currently-selected load case from the load case table. Simulation File Name The name of the load case simulation file. The filename can either be typed in or else set by using the Add Load Case button. If you type it in you can either specify the full path or a relative path. Line Name The name, in this load case simulation file, of the line to be analysed. Note: Normally the line name will be the same in all of the load cases (though this is not necessary). However the named lines in the various load cases must, of course, all represent the same physical line. And they must also have the same segmentation in the areas being analysed. Number of Cycles (regular analysis only) The number of wave cycles, of this particular set of load conditions, that the line will experience. Simulation Period and Exposure Time (rainflow analysis only) Simulation Period specifies the period of the pre-run simulation file that defines the load case. The exposure time is the total time the system is exposed to this load case. 128 w Analysis Data The Analysis Data page contains the following data items, which specify the parts of the line to be analysed, and their stress properties. Critical Damage Is a warning level. If the total damage at any fatigue point exceeds the Critical Damage then that damage figure will be highlighted in the results. Number of Thetas The number of theta values around the pipe circumference, at which fatigue analysis will be performed. There will be Number of Thetas fatigue points uniformly distributed around the pipe outer circumference, and the same number similarly distributed around the inner circumference. A larger number of thetas gives a more comprehensive analysis, but takes a little longer. Arc Length Intervals You define the parts of the line that are to be analysed by specifying a number of nonoverlapping Arc Length Intervals in the form of From and To arc length values. OrcaFlex will analyse cross-sections at each line end and mid-segment whose arc length S is in the range From <= S < To. Note that OrcaFlex therefore won't a line end or mid-segment whose arc length S that exactly equals To; to include it specify an arc length a little beyond. For simple cases you can use just one arc length interval covering the whole line. However it is often clear which part, or parts, of the line are liable to fatigue problems, and it is then useful to be selective and only analyse those parts of the line. This both speeds up the analysis and also reduces the quantity of results that you need to examine. Warning: The included arc lengths must be the same in each load case, so the line to be analysed should have the same number and distribution of segments in each of the load case simulations. Stress Concentration Factor (S.C.F.) When the maximum stress range is used with the S-N curve to calculate damage, that maximum stress range is first scaled by the Stress Concentration Factor. If no stress concentration is required then the S.C.F. should be set to 1. This factor enables you to allow for special situations, where the assumption that the line is a simple pipe made of a homogeneous material does not hold. For example, at weld joints the stress tends to be more concentrated than for the rest of the pipe and so fatigue failure is more likely in such areas. The default value is 1. Notes: The stresses reported in the results have not been scaled by the S.C.F. This factor is only applied when the maximum stress range S is used with the S-N curve to calculate damage. To use different stress concentration factors for different parts of the line, you will need to specify separate arc length intervals for those parts. S-N Curve Specifies which S-N curve is used for damage calculations in this arc length interval. 129 w 5.3.5 S-N Curve Data An S-N curve defines the number of cycles to failure, N(S), when a material is repeatedly cycled through a given stress range S. OrcaFlex uses the S-N curve to calculate the damage in a fatigue analysis. If needed you can define a number of different S-N curves and use them at different arc lengths along a line. This enables you to handle cases where different parts of the line are made up of different materials. With each S-N curve you must also specify an associated stress fatigue limit, FL, which is the stress range below which no damage occurs. This is sometimes referred to as the endurance limit. The S-N curve itself can be specified either by parameters or by a table. When the curve is defined by parameters the user specifies two parameters, A and b, and the curve is then given by either of the following equivalent formulae: N = 10^A / S^b Log10(N) = A - b Log10(S) When the curve is specified by a table the user gives a table of corresponding values of S and N. For other values of S we use log linear interpolation or extrapolation to find the value of N. The Graph button displays the selected S-N curve on a log-log graph. S-N Curve Units The S-N curve parameters entered must be consistent with the fatigue analysis units. S-N curve parameters are typically quoted with respect to stresses in Mpa, but you might be doing the fatigue analysis using some other stress units. You can handle this problem as follows. First change the fatigue analysis units and set the units system to be 'User', the length units to be 'mm' and the force units to be 'N'. This corresponds to stresses in Mpa, so you can then enter the S-N parameters in terms of Mpa. Finally, restore the units to those that you want for the fatigue analysis. The parameters will automatically be converted to allow for the change in units. Note: The way the S-N curve parameters A and b alter when you change units is not intuitively obvious. If you need to know the formulae, then recall that the S-N curve for deriving N (the number of cycles to failure) is given by: Log10(N) = A - b.Log10(S) (1) If we now change units then the stress value S changes to S' = c.S, where c is how many new stress units equal one old stress unit. Let A' and b' be the new S-N curve parameters, using the new units. Then equation (1) becomes: Log10(N) = A' - b'.Log10(S'). which leads to: Log10(N) = A' - b'.Log10(c.S) = [A' - b'.Log10(c)] - b'.Log10(S) (2) Comparing equations (1) and (2) we see that b'=b and A'=[A+b.Log10(c)]. For details of how the S-N curve is used to calculate the damage see How Damage is Calculated. 130 w 5.3.6 Results The Fatigue Analysis results are presented in a spreadsheet that has one Damage Tables worksheet, plus one Load Case worksheet for each load case. There is also a worksheet echoing the S-N curve data. Load Case Worksheets The Load Case worksheets contain the derived stress results for each fatigue point that has been analysed, together with general information such as the environmental data that applied to that load case. There is one table of stress results for each arc length covered by the specified arc length intervals. Each such table contains a row of results for each fatigue point in that arc length cross-section. These results are the stress ranges (for each of the stress components), the maximum stress range and the resulting single-occurrence load case damage values. The maximum von Mises stress is also reported, but note that this value has no effect on the damage calculation. Damage Table Worksheet The Damage Tables worksheet starts with an Excessive Damage table, which lists any fatigue points at which the overall total damage has exceeded the specified critical damage value (which is displayed in the table title). There then follows a table summarising the Other Stresses table, which reports the maximum and minimum direct stress (i.e. any of the diagonal terms in the stress matrix) and the maximum and minimum shear stress (i.e. the off-diagonal terms) at any of the fatigue points. The largest off-diagonal stress values should be checked to ensure that they are small compared to the direct (i.e. diagonal) stresses - see the note in How Damage is Calculated. This table also reports the maximum von Mises stress. Finally, the Damage Tables worksheet provides damage tables for each arc length crosssection analysed. These report, for each fatigue point in the cross-section, the total exposure damage value from each load case and the overall total damage. In all of the damage tables, overall total damage values that exceed the specified critical damage value are highlighted in red. Printing and Exporting To save the results you will need to export the spreadsheet as an Excel worksheet. If you want to print the results then for best results you should first export them and then use Excel to do the printing. Note: There is no facility to print the fatigue analysis data, but the data is echoed in the fatigue results spreadsheet. 5.3.7 Fatigue Points Fatigue is analysed at a number of line end and mid-segment cross-sections along the line, as specified by defining Arc Length Intervals in the Analysis Data. Each included arc length defines a cross-section through the pipe. Each such section is then discretised, in polar coordinates (R, Theta), using a user-specified Number of Theta angles, and using two r-values - one at the line's stress ID and one at the line's stress OD. Theta is 131 w measured from the line's local x-axis towards its y-axis, as indicated in the figure below, which shows the fatigue points that will be analysed when the number of theta angles is set to 8, giving fatigue points at theta = 0, 45, 90, 135, 180, 225, 270 and 315 degrees. y C R Theta x (Theta=0) Fatigue Points Stress ID Stress OD Figure: Fatigue Points at an arc length cross-section This therefore defines a total of (Number of included arc lengths) x (Number of Theta Angles) x 2 fatigue points at which the damage will be analysed. 5.3.8 How Damage is Calculated For each fatigue point OrcaFlex calculates damage values that are reported in the fatigue results. Here is a summary of how the calculation is done: • For each of the 3 principal stress directions (axial, radial and circumferential), OrcaFlex calculates the time history of the stress component that occurred in that principal direction, at that fatigue point, in that load case. See Principal Stress Calculation below for details. OrcaFlex then calculates the damage values that correspond to each of these 3 principal stress component time histories. See Component Damage Calculation below for details. OrcaFlex then chooses the largest of those 3 principal damage values and this is taken to be the damage value at that fatigue point due to one occurrence of that load case. The load case worksheets in the fatigue results report these single-occurrence load case damage values for each fatigue point. Note: • This worst damage is usually due to the axial stress, since that includes the effects of both tension and bending. • • OrcaFlex then scales the above single-occurrence load case damage values to allow for the exposure associated with that load case. For regular analysis this means multiplying by the number of cycles specified for this load case. For rainflow analysis this means multiplying by the exposure time divided by the simulation period analysed for that load case. This gives the total exposure damage value from that load case at this fatigue point. These totalexposure load case damage values appear in the Damage Tables worksheet in the fatigue results. 132 w • Finally, OrcaFlex then sums these total-exposure load case damage values to obtain the give the final total damage value at that fatigue point. These total damage values are again reported in the Damage Tables worksheet in the fatigue results. Principal Stress Calculation At each fatigue point, and for each load case, OrcaFlex calculates the stress matrix RRStress RCStress RZStress RCStress CCStress CZStress RZStress CZStress ZZStress from the various loads that acted on the pipe during the load case simulation. See Pipe Stress Calculation. Here the 3 diagonal entries RRStress, CCStress and ZZStress are the principal radial, circumferential (or hoop) and axial (or longitudinal) stresses, respectively, and the 3 off-diagonal terms are the shear stresses. Note: Strictly speaking, the principal stresses are the eigenvalues of this matrix. But in practice the principal axes of stress are almost always very close to the natural axes of the pipe, in which case the diagonal terms are very good estimates of the principal stresses. The fatigue analysis assumes that this holds and therefore treats the diagonal terms as being the principal stresses. The validity of this assumption can be confirmed by checking that the peak values of any of the shear stresses are small compared to the peak values of the diagonal terms. All these peak values are reported in the fatigue analysis results. Component Damage Calculation The S-N curve defines the number of cycles to failure, N(S), for a given stress range S, and also defines a fatigue limit, FL, below which no damage occurs. 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. Note: If the S-N curve is defined by parameters then for S > FL we have Log10(N) = A - b Log10(S) so D(S) can be expressed in the following form: D(S) = 10^-(A - b Log10(S)) = (10^-A) x (S)^b. OrcaFlex uses this damage definition to calculate the component damage value that is associated with a given principal stress component in a given load case. This calculation depends on whether a Regular or Rainflow fatigue analysis is done, as follows: • For regular analysis the minimum and maximum values that the stress component took over the last simulated wave cycle are used to give a stress range S. The associated single-occurrence load case damage value is then given by D(κS) where κ is the stress concentration factor specified in the fatigue analysis data. For rainflow analysis the stress component time history is analysed using the rainflow cycle counting method. This gives a number of stress ranges for half cycles, say S(i) where i runs from 1 to the number of stress ranges. The associated single-occurrence load case • 133 w damage value is then given by 0.5*(Sum of D(κS(i)) where the summation is over all the half cycles and κ is the stress concentration factor. Note that the factor 0.5 is present because the rainflow algorithm counts half cycles. 5.4 POST-PROCESSING RESULTS 5.4.1 Post-processing Results OrcaFlex users often use spreadsheets to post-process their OrcaFlex results. This can be done manually by transferring the results from OrcaFlex into the spreadsheet using copy + paste. However, this is laborious and error prone if a lot of results need transferring, so we have developed special facilities to automate the process. This automation is done by creating a special Excel spreadsheet that has special buttons that trigger automatic extraction of specified results from one or more OrcaFlex files into nominated cells in the spreadsheet. You can then use the normal spreadsheet facilities to calculate other post-processed results from those OrcaFlex results. Note: The post-processing spreadsheets work with Excel 97 or later and require OrcaFlex to be installed on the machine. Creating Post-Processing Spreadsheets You can create post-processing spreadsheets from Excel templates that are supplied with OrcaFlex. There are two types available: • • Results.xlt is a general purpose spreadsheet template for extracting results from OrcaFlex simulation files. Stress.xlt is a more specialised spreadsheet template, for extracting detailed stress results from OrcaFlex simulation files. You should base your own post-processing spreadsheets on these templates, which are installed in the OrcaFlex installation directory when you install OrcaFlex is on your machine. To create your own post-processing spreadsheet, open the Windows Start menu, select Programs|Orcina Software and then select New Results Spreadsheet or New Stress Spreadsheet. (These are convenient shortcuts to the above template files and when used Excel starts up and creates a new spreadsheet based on that template.) Before you try to use the new spreadsheet you need to save it to a file; it can be given any valid filename. It is usually most convenient to save it to the directory containing the OrcaFlex files from which you want to extract results, since you can then specify the names of those files in the spreadsheet using relative paths. This makes it easier if you later need to rename the directory or move the spreadsheet and OrcaFlex files to some other directory. For example post-processing spreadsheets, see J02 Results and J03 Stress Analysis. 5.4.2 Results Spreadsheet A Results spreadsheet is a post-processing spreadsheet that enables you to automate the extraction of results from OrcaFlex files into Excel. For an example see J02 Results. To create your own see Creating Post-Processing Spreadsheets. Note: For extracting detailed stress results a Stress spreadsheet may be suitable. 134 w A Results spreadsheet consists of an Instructions worksheet, plus other worksheets to receive the OrcaFlex results and for any derived results. The Instructions worksheet consists of an instructions table and two buttons that run Excel macros that read and obey those instructions. Do not change the name of the Instructions worksheet, since the macros use that name to find that worksheet. Instructions Table Each row in the instructions table is a separate instruction. Each instruction has 2 parts - the first part specifying a label cell to be written and the second part specifying some associated results cells to be written. Each part is optional, so you can have an instruction that has a blank command cell and so only writes a label, or one that has a blank label cell and so only writes results. The end of the table is taken to be the first row that has both its label and command columns blank, so you cannot have an instruction that has no label and no command. In particular, you cannot have a blank row in the middle of the instruction table. Also, the macros assume that the first instruction is row 5 of the worksheet, so do not insert or delete rows above this. The macros ignore the formatting of the spreadsheet, so you can use things like bold, italic, background colours etc. to make the worksheets easy to read, and you can also re-size columns or rows to suit. This applies to all the worksheets, including the Instructions worksheet. Process Buttons The Process All button runs a macro that obeys all the instructions in the table, starting at the top of the table and working down. The Process Selected button tells the spreadsheet to process only the instructions in the currently selected cell or block of cells, again in top to bottom order. If the currently selected cell(s) are not in the table then this button does nothing. The example instruction table illustrates how the instructions work: • Click the Process All button. You should see the Example1 worksheet being filled in and then a new worksheet called Example2 being created and filled in. If you look at the instructions table on the Instructions sheet then you will see how this was specified. The first block of instructions in the table specifies that the simulation file Example1.sim should be loaded and then various results extracted from it and written to various cells in a worksheet called Example1. Note that the example instructions are set up to work with example simulation files that are installed with the Results.xls spreadsheet. The Example1 worksheet already existed, and it was already set up with suitable column widths and cell properties (e.g. a larger font size, right alignment for some cells). So the instructions simply "filled in" various cells in that sheet. The second block of instructions in the table specifies that the simulation file Example2.sim should be loaded and then various results extracted from it and written to a worksheet called Example2. No such sheet existed, so one was created. Because the worksheet Example2 was newly created it has default properties and so it not yet properly formatted. You can now format it (resize the columns, change cell font sizes etc.) as you wish. Next time you click the Process All button the worksheet will retain the formatting you set up. Now go back to the Example1 worksheet and try setting a new cell to calculate a "derived" result. For instance you could calculate the tension range by setting cell H4 to "=G4-F4". Now delete the contents of cells G4 and F4 on the Example1 worksheet - cell H4 will become zero. Now go back to the Instructions worksheet and in the top half of the • • • • • • 135 w instruction table select the block of 6 cells in the column headed 'Command' that contain Min or Max. Now click the Process Selected button - this button obeys just the instructions in the currently selected block, so cells G4 and F4 on the Example1 worksheet will be rewritten and your derived cell H4 will be automatically updated (assuming you have recalculation switched on in Excel). You should now have a good idea of how the spreadsheet works and you can now modify the spreadsheet to suit your own purpose. To do this, delete the example instructions from the table and set up your own instructions to specify the results you want and where you want them. Details of the instruction format follow. 5.4.3 Instruction Format In the results spreadsheet, each instruction consists of the following cells. See also Tips and Tricks. Sheet Specifies the name of the worksheet in which cells are to be written. If a worksheet with this name already exists then the specified label and output cells will be overwritten, but other cells will be left unchanged. If no sheet of that name exists then one will be created. Label Cell Specifies the cell, in the specified worksheet, to which the label (if not null) will be written. Label Specifies the label string to be written to the label cell. This cell can be left empty, in which case the label cell is ignored. Output Cell Specifies the cell, in the specified worksheet, to which results should be written. Some commands specify multiple-value results - for example a time history consists of a column of results. In this case the Output Cell specifies the top left cell of the block of cells to be written. Note: Command This should be one of the pre-defined commands or else empty. If the command cell is empty then the output cell is ignored. One pre-defined command, Load, is special - it causes a simulation file to be loaded, ready for subsequent commands to extract results from that simulation. Object Name The name of the object, in the OrcaFlex simulation file, for which results are wanted. Node Number, Arc Length These are only used if Object Name specifies a Line in the simulation file. In this case you must specify the position on the line for which results are wanted. You can either specify the position in either the Node Number column or in the Arc Length column but not both. In the Node Number column you can specify an actual node number, but alternatively you can specify 136 The Output Cell (or Label Cell) can be specified directly, e.g. B7, but can also be specified indirectly - see Tips and Tricks. w 'A' or 'B' (meaning end A or B) or 'Touchdown' (meaning the touchdown point). The results are given for the nearest appropriate result point; see Line Results for details. For the Range Graph and Range Graph Summary commands you can specify a range of arc lengths, e.g. "20 to 50". Simulation Period The period of simulation for which results are wanted. This can be Whole Simulation, Latest Wave or a stage number (0 for the build-up, 1 for stage 1 etc.). It can also be a specified period of simulation, given in the form "t1 to t2" where t1 and t2 are numeric time values that are in the simulation and Simulation Start Time <= t1 <= t2 <= Simulation End Time. For example "20 to 30" or "-12.5 to +35.7". Note: This specified period format can be used to extract results at a single time point; for example the period "27.4 to 27.4" will give the results at the nearest log sample to time 27.4. Variable The results variable that you want. This should be set to the same name (not case sensitive) as is used for the results variable in OrcaFlex. For example Effective Tension, curvature, surge, etc. 5.4.4 Pre-defined Commands In the results spreadsheet, the Command Cell can contain one of the following commands: LOAD <FILENAME> This command tells OrcaFlex to open the specified simulation file. extraction commands then apply to that file. You can either specify the full path of the file, for example: Load c:\Project100\Case1.sim or else use a relative path (relative to the directory containing the spreadsheet). The latter is often more convenient. For example if the file Case1.sim is in the same directory as the spreadsheet then you can use the command: Load Case1.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. SAMPLE TIMES Returns the time values that apply to the time history results. This command returns a column of N numbers, where N is the number of OrcaFlex log samples that are in the specified Simulation Period. So if Output Cell is set to G5 and there are 500 log samples in the Simulation Period, then the time values for those log samples will be written to cells G5..G504. TIME HISTORY Returns the time history values of the specified variable. This command returns a column of N numbers, as with the Sample Times command. Subsequent results 137 w MIN, MAX, MEAN and STANDARD DEVIATION Min return a single number, equalling the minimum value of the specified time history variable during the specified simulation period. Similarly for Max, Mean and Standard Deviation (which can be abbreviated to Std Dev). LINKED STATISTICS The Linked Statistics command outputs the same information as the Linked Statistics command on the OrcaFlex results form. In the Variable column of the instruction you should specify two or more results variable names, separated by commas. The command outputs a table of statistics for those variables, occupying 2N+3 rows by N+2 columns, where N is the number of variables specified. RANGE GRAPH and RANGE GRAPH SUMMARY These commands output tables containing either the full set of range graph results, or a summary, for the specified variable of a line. They are available for any line variable for which a range graph is available in OrcaFlex. The Range Graph command gives a table having 7 columns, containing Arc Length, Minimum, Maximum, Mean, Standard Deviation, Upper Limit, and Lower Limit. 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 Range Graph Summary command gives a table having two rows, one for the overall minimum and one for the overall maximum. Each row has 4 cells; 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, and the arc length at which it occurred. To use these commands you must specify, in the Simulation Period column of the instruction, the period of simulation for which you want results. If the Arc Length column in the instruction is left blank then the results will apply to the whole line. Alternatively, you can restrict these commands to only cover part of the line, by specifying a range of arc lengths, e.g. "20 to 50", in the Arc Length column. The table will then only include results for points whose arc length is within the specified range. The length units used must be the same as those used in the OrcaFlex simulation file. Note that the Node Number column of the instruction is not used for either of these commands. 5.4.5 Tips and Tricks Here are some useful tips for setting up the instructions table of a Results spreadsheet. Use Excel's "=" facility If you have several instruction table cells that are equal to some other cell, A9 say, then set them to "=A9". That way when you alter A9 then the other cells will automatically alter to match. For example if you have a block of 10 instructions that all output their result to sheet "Load Case 3" then set the first instruction's Worksheet cell, cell A9 say, to "Load Case 3" and then set the other Worksheet cells to "=A9". You can now change the destination sheet for all the instructions by simply altering cell A9. Use OffsetCell to specify output cells indirectly You can do a similar thing with the Output Cell (and Label Cell) by using the special spreadsheet function OffsetCell(PointerCell, ColOffset, RowOffset). 138 w Suppose that, on your instruction sheet, the output cell D9 contains the address "C12"; i.e. D9 points to C12 (on the output sheet). Then you can now use C12 as an Origin and set up some other output address relative to it. To do this set the other output cell to "=OffsetCell(D9, 3, 4)", which means "the cell 3 columns right and 4 rows down from the cell referenced in D9". The output will therefore be placed in cell F16 on the output sheet. The advantage of this is that you can now easily redirect the output of a whole set of instructions by simply changing the first one's output cell. The other instructions' output destinations stay fixed relative to the first's. Here's the formal definition of OffsetCell. It takes 3 parameters: PointerCell is the address of a cell that contains the address of an OriginCell, and ColOffset & RowOffset are integers specifying an offset from that OriginCell. The function returns the address of the cell that is ColOffset columns right and RowOffset rows down from the cell that PointerCell points at. 5.4.6 Error Handling In the results spreadsheet, errors in instructions are handled by either displaying an error message window or by writing an error message to the specified output cell. So when setting up new instructions: • • • Check carefully that you have set all the instruction cells correctly. Then test the instructions by selecting them and using the Process Selected button. Then check that the specified Label Cells and Output Cells have been set correctly. 5.4.7 Stress Spreadsheet The file Stress.xls is an Excel spreadsheet for extracting detailed stress components from OrcaFlex simulation files. You can then add your extra worksheets to it to do whatever postprocessing of results you require. The stress spreadsheet consists of one main worksheet, called Main Sheet, and then a number of load case worksheets into which the OrcaFlex stress results will be written. Each load case worksheet corresponds to one Line in one OrcaFlex simulation file, so if you want to extract results from 3 simulation files then you need to set up 3 load case worksheets. To create a new stress results worksheet click the Add Load Case Sheet button on the main worksheet. The load case worksheets are characterised by the fact that their top-left cell contains "Stress results for single case", so do not alter this cell. However, on each load case worksheet there are two cells that you must set up - the simulation file name (including its path) and the name of the line for which results are to be extracted. You must not alter any other cells on the load case worksheets, but you can rename the load case worksheets with suitable names. When you have set up the load case worksheets that you require you must then set up, on the main worksheet, the following cells specifying the points and the stress results required. Again, you should not alter any other cells on the main worksheet. • • Simulation Period is the period of simulation for which time history stress results are wanted. The points for which results are wanted are specified using cylindrical polar coordinates (r, theta, z), where: z is the unstretched line length from end A to the point r is the radial distance from the centreline to the point 139 w theta is the circumferential angle, measured positive clockwise from the local line Lx direction towards the Ly direction. • Arclength is the arc length, z, from end A, to the points (r, theta, z) on the line for which stress results are wanted. The results will be for the mid-segment point of the OrcaFlex segment that contains that arclength. Radial Positions specify whether results are wanted at the line's StressID or StressOD, or both. Number of Theta values is the number of points, around the line circumference, for which results are wanted. So if 4 theta values are requested then results will be extracted for theta=0, 90, 180 and 270 degrees. Stress Components specify which components of the stress tensor are required. The stress tensor is a 3 by 3 matrix of stress components, with respect to a local RCZ set of right-handed Cartesian axes at the result point. R points radially outwards from the point, C is circumferential and Z points axially along the line towards end B. So "RR Stress" is the radial stress, "CC Stress" is the hoop stress and "ZZ Stress" is the axial or longitudinal stress. • • • When you have set up the load case worksheets you require and set up the main worksheet to specify the stress results you want then you are ready to extract results. To do this simply click the Collect Results button on the main worksheet. For each load case worksheet, the specified stress results are then read from the specified OrcaFlex simulation file and time history columns containing the results are created on the load case worksheet. When the Collect Results button is clicked the results are extracted from the OrcaFlex simulation files and written into the load case worksheets. If the OrcaFlex cases are later rerun, for example because of a change in the model, then your spreadsheet can simply be reopened and the Collect Results button clicked to refresh the spreadsheet with the new results. 140 w 6 6.1 THEORY COORDINATE SYSTEMS OrcaFlex uses one global coordinate system GXYZ, where G is the global origin and GX, GY and GZ are the global axes directions. In addition, there are a number of local coordinate systems, generally one for each object in the model. All the coordinate systems are right handed, as shown in the following figure, which shows the global axes and a vessel with its own local vessel axes Vxyz. In general we use Lxyz to denote a local coordinate system. Another coordinate system that we make widespread use of is the Line End orientation which we denote Exyz. z Sea Surface y x V Z Vessel Axes Y Global Axes G Figure: X 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. 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 local coordinate systems for each type of object are described in the section about that object, but typically the origin is at a selected fixed point on the object and the axes are in special fixed directions, such as the surge, sway and heave directions for a vessel. The seabed also has its own seabed origin and local axes, with respect to which the seabed shape is defined. The local axes are distinguished from the global axes by using lower case; for example the local object direction is referred to as the "x-direction" whereas the global direction is referred to as the "X-direction". Whenever data or results are coordinate system dependent, they are referred to as being either global-relative (and are labelled in upper case) or object-relative (and are labelled in lower case). You can ask OrcaFlex to draw the local axes on the 3D view. This enables you to see the local axes and check that they are as wanted. Most of the data and results are given relative to the global axes, including: • data defining the sea, such as the mean sea surface Z level and the current and wave direction. 141 w • the positions of objects; for example the position of the vessel is defined by giving the global coordinates of the vessel origin V The most common object-relative items are: • • the coordinates of points that move with the object, such as the vertices of a vessel or the connection point when something is connected to a buoy the direction-dependent properties of objects, such as drag and added mass coefficients, moments of inertia, etc. 6.2 DIRECTION CONVENTIONS Directions and Headings Wave, current and wind directions are specified in OrcaFlex by giving the direction in which the wave (or current or wind) is progressing, measured positive from the global X-direction towards the global Y-direction, as shown in the following figure: 90 150 GY 180 GX 0 30 210 270 330 Direction relative to global axes Figure: Directions and Headings This convention is also used when specifying vessel headings and slope directions: • • The vessel heading is the direction in which the vessel Vx-axis is pointing. The slope direction for the seabed or a shape is the direction that points up the slope. For the slope of a plane shape that is connected to another object, the slope direction is specified relative to that object's axes. Vessel response to waves (similarly for current and wind) depend on the wave direction relative to the vessel, so vessel type properties are given for a specified relative wave direction (= Wave Direction - Vessel Heading). So a relative wave direction of 0 means a wave coming from astern and a relative direction of 90 means one coming from starboard. Azimuth and Declination Directions are defined in OrcaFlex by giving two angles, azimuth and declination, that are broadly similar to those used in navigation, gunnery, etc. As with positions, directions are sometimes defined relative to the global axes and sometimes relative to the local object axes. For directions defined relative to the object axes Oxyz, the azimuth and declination angles are defined as follows: 142 w • Azimuth is the angle from the x axis to the projection of the direction onto the xy plane. The positive x axis direction therefore has Azimuth = 0, and the positive y axis direction has Azimuth = 90 degrees. Declination is the angle the direction makes with the z axis. Therefore Declination is 0 for the positive z-direction, 90 degrees for any direction in the xy plane, and 180 degrees for the negative z-direction. When Declination is 0 or 180 degrees, Azimuth is undefined (OrcaFlex reports Azimuth = 0 in these cases). • Directions relative to the global axes are defined in just the same way, simply replacing the local xyz directions above with the global XYZ directions. A global declination of 0 therefore means vertically upwards, 90 means horizontal and 180 means vertically downwards. When a direction is being defined, the "sign" of the direction must also be defined. 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. The "sign" conventions used in OrcaFlex for directions are: • • For Lines, axial directions are always defined in the A to B sense, in other words from end A towards end B. Thus a vertical line with end A at the top has declination 180 degrees. For Winches and Links, axial directions are defined in the sense 'from first end towards second end'. Thus a link with end 1 directly above end 2 has declination 180 degrees. 6.3 OBJECT CONNECTIONS Lines, links, winches and shapes are special objects that can be connected to other objects. First consider connecting a line to another object. To enable connections to be made each line has two joints, one at each end, which are drawn as small blobs on the ends of the line, when the model is in Reset state. To distinguish the two ends, the joint at end A is drawn as a triangle and the joint at end B as a square. Each of these line end joints can either be Free or else be connected to a Vessel, 3D Buoy, 6D Buoy, the Global Axes or the seabed. Lines cannot be connected to themselves, to other lines, nor to a Link or Winch. When a line's joint is Free, 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. When the joint is connected to another object, that end of the line becomes a slave and the object to which it is connected becomes its master. The connection is then indicated by the joint being drawn in the colour of its master. 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, but with the following exceptions. • • Link and winch joints cannot be Free - they must always be connected to some master. Link and winch joints can be connected to nodes on a line, as well as to Vessels, 3D Buoys, 6D Buoys, the Global Axes or the seabed. This allows, for example, a winch to be attached to the end node of a line so that winching in or out can be modelled. Shapes have a single joint which can be connected to Vessels, 3D Buoys, 6D Buoys, the Global Axes or the seabed. When a joint is connected to a master, 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. 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. Because neither the Global Axes nor the seabed move, a joint connected to either of them is simply fixed in one position. The difference between them lies in how the connection point is 143 w specified. For a connection to the Global Axes, the X, Y and Z coordinates of the connection point are specified relative to those axes and the joint is called Fixed. For a connection to the seabed the X and Y coordinates are specified relative to the global axes, but the Z coordinate is specified relative to the seabed Z level at that X,Y position; the joint is then referred to as being Anchored. So for an Anchored joint, Z=0 means that the connection is exactly on the seabed and Z=1 means it is 1 unit above the seabed. By using anchored joints you can therefore avoid the need to calculate the seabed Z level at the given X,Y position (not simple with sloping seabeds). 6.4 • INTERPOLATION METHODS These methods are OrcaFlex use a number of different methods for interpolating data. described below: Linear. The data is assumed to follow a straight line between each (X,Y) pair. Linear interpolation is said to be piecewise linear. Curves that are linearly interpolated are continuous but their first derivative is discontinuous at each X data point. Cubic spline. Cubic spline interpolation fits a cubic polynomial over each interval in the data - that is the fitted curve is piecewise cubic. These cubics are chosen so that both first and second derivatives are continuous at each X data point. Cubic Bessel (also known as Parabolic Blending). Cubic Bessel interpolation is similar to cubic spline in that it is also piecewise cubic. However, for this method the cubics are chosen so that the first derivative at each data point equal to the unique parabola passing through 3 consecutive data points. The fitted curve has continuous first derivative but discontinuous second derivative. • • Choosing interpolation method Sometimes OrcaFlex provides a choice of interpolation method. In general we would recommend that you use the default interpolation method, but in some cases it may be appropriate to use a different method. To decide you need to take into account what the interpolated data is used for and the different properties of the interpolation methods. If continuity of first derivative is not required then linear interpolation is often appropriate. It has the advantage that it is very simple. The other 2 methods are piecewise cubic and they produce smooth curves, but they can sometimes produce curves that have overshoots. For example the following graphs show how each method interpolates a particular set of data. Although the greatest Y value in the data is 8, the interpolated curves for cubic spline and cubic Bessel both exceed this value (although the effect is much smaller for cubic Bessel). 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. 144 w 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. If it does not then you usually need to supply more data points. The main difference between the two is that cubic spline interpolation has a continuous second derivative whereas cubic Bessel does not. However, in many cases this is not important, and one attractive feature of cubic Bessel interpolation is that it is less prone to overshoot than cubic spline. 145 w 6.5 STATIC ANALYSIS 6.5.1 Static Analysis There are two objectives for a static analysis: • • to determine the equilibrium configuration of the system under weight, buoyancy, hydrodynamic drag, etc. to provide a starting configuration for dynamic simulation. In most cases, the static equilibrium configuration is the best starting point for dynamic simulation and these two objectives become one. However there are occasions where this is not so and OrcaFlex provides facilities for handling these special cases. These facilities are discussed later. Static equilibrium is determined by a series of linked iterative calculations. At the start of the calculation, the initial positions of the vessels and buoys (3D and 6D) are defined by the data: these in turn define the initial positions of the ends of lines connected to them. The equilibrium configuration for each line is then calculated, which determines the forces applied by the lines to the other free bodies. The out of balance force vector acting on each free body (3D or 6D buoy) is then calculated together with the associated stiffness matrix, and a new position for the body is estimated by a Newton-Raphson technique. The calculation is then repeated from this new starting position. The process is repeated until the net force vector on each free body is zero (within a small tolerance). For details see Statics of Buoys and Vessels. For simple systems, the static analysis process is very quick and reliable. For very complex systems with multiple free bodies and many inter-connections, however, convergence may be difficult to achieve. To help overcome this problem, 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. See Statics of Buoys and Vessels. Finally, the static analysis can also be turned into a steady state analysis by specifying non-zero starting velocity on the General Data form. This is useful when modelling towed systems or other systems that have a steady velocity. 6.5.2 Statics of Lines Statics of Lines When you do a static analysis OrcaFlex does a static analysis of each line in the model. Note: The lines are analysed in the order they appear in the model browser. So if you are having a problem with the static analysis of a particular line, and there are a lot of lines in the model, then you can make investigation of the problem easier by dragging the line up to the top of the list in the model browser. The static analysis of a given line has two stages: • • The first stage calculates an initial position of all the nodes on the line, using the Statics Method specified on the line data form. The second stage, which is optional, is called Full Statics. If Full Statics is included, then it calculates the true equilibrium position of the line, starting from the initial position found by stage 1. If Full Statics is not included, then the line is simply left in the initial position found by stage 1, which (depending on the Statics Method chosen) may not be an equilibrium position. 146 w Catenary Statics The Catenary method calculates the equilibrium position of the line, but it ignores the effects of bending and torsional stiffness of the line or its end terminations. The Catenary method also ignores contact forces between the line and any solid shapes in the model, but it does include all other effects, including weight, buoyancy, axial elasticity, current drag and seabed touchdown and friction. Note: For technical reasons, seabed effects are only included if end B is exactly on the seabed - see Seabed Touchdown. Because bend stiffness (and other) effects are not included in the Catenary method, the position found is not, in general, an equilibrium position. Therefore Full Statics. should normally be included unless it is known that the omitted effects are unimportant. Nevertheless, the Catenary position is often quite close to the true equilibrium position, especially when bend stiffness is not a major influence. The Catenary algorithm is robust and efficient for most realistic cases but it cannot handle cases where the line is in compression. This is because, when bending stiffness is ignored, compression means the line is slack and there is no unique solution. The algorithm is an iterative process that converges on the solution. If necessary; you can control the maximum number of iterations that are attempted, as well as other aspects of the convergence process - see Catenary Convergence. Spline Statics The Spline method gives the line an initial shape that is based on a user-defined smooth Bezier spline curve. It is therefore not, in general, an equilibrium position, and so when it is used Full Statics should be included if you want the equilibrium position to be found. 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. The smoothness of the spline can be controlled using the spline order. The Spline method puts the line into a position that, as far as possible, follows the Bezier curve. However the Bezier curve may often have the wrong length (depending on how accurately you have set up the control points), so the Spline method scales the Bezier spline curve up or down until the resulting line shape has the correct pre-tension, as specified on the line data form. Quick Statics The Quick method simply leaves the line in the position that it was drawn when in Reset state. This is a crude catenary shape that (for speed reasons) ignores most effects, including buoyancy, drag, bending and torsional stiffness, and interaction with seabed and solids. In fact the position set by the Quick method only allows for the line's average weight per unit length and axial elasticity, so it is not usually an equilibrium position (though for simple cases it may be quite close). The Quick method should usually be used only as a preliminary to Full Statics. Prescribed Statics The Prescribed method is intended primarily for pull-in analyses. It provides a convenient way of setting the line up in the as laid (i.e. pre pull-in) starting position, ready for a time simulation of the pull-in. The starting shape of the line is specified by defining a track on the seabed (see Track Data). 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. See Laying Out the Line. 147 w Y Start of track Track Section 1 Length = 150 Turn = 0 X Track section 2 Length = 100 Turn = -90 10° End A Azimuth = 10° Track section 3 Length = 100 Turn = 90 Track Section 4 Length = 150 Turn = 0 Continuation of last track section Figure: Plan View of Example Track Full Statics The Full Statics calculation is a line statics calculation that includes all forces modelled in OrcaFlex. In particular it includes the effects of bend stiffness and interaction with shapes. These effects are omitted from the Catenary calculation, and this sometimes results in significant shock loads at the start of the simulation, when the effects of bend stiffness and shapes were introduced. Because the Full Statics calculation includes these effects, no such shock loads should occur when it is used. We therefore recommend using Full Statics for most cases. To use Full Statics set the Full button on the Line data form to "Yes". Full statics needs a starting shape for the line, and it uses the specified Statics Type to obtain this; it then finds the equilibrium position from there. You must therefore also set the Statics Type to give a reasonable starting shape, choosing from one of the four other statics methods: Catenary, Prescribed, Quick or Spline. Which Statics Type you should choose for the starting shape depends on the model in question. In general you should choose the statics type that gives the best initial estimate of the line's static position. For lines with no buoyant sections and no interaction with shapes or the seabed, the Quick statics type may well suffice. If there is seabed interaction or a buoyant section then Catenary might be better. For lines that interact with a shape, the Spline starting shape is perhaps best since it enables you to ensure that the line starts on the correct side of the shape. Which Line Statics method to use The settings to use for the line data items Statics Method and Full Statics depend on the type of system being modelled and the type of static position wanted. The default settings (for a new line) are the Catenary method followed by Full Statics. This is often a good choice, since the Catenary method is fast and in many case gives a good initial estimate of the equilibrium position. It therefore often provides a good starting point for the Full Statics calculation, which then refines the position to take into account the effects that the Catenary omits, such as bending and torsional stiffness and interaction with solids. There are situations where you may need to use other settings. Some specific cases are described below, but first here are some general points to bear in mind. 148 w Full Statics should be included if you want the true equilibrium position to be found. When Full Statics is included, the first stage Statics Method is only used to give the initial starting shape for the Full Statics. The choice of Statics Method is then, in principle, not important, since the final position found will be the equilibrium position, irrespective of the initial starting position. However it is normally best to choose the Statics Method that gives the best initial estimate of the desired equilibrium position, since this will give the best starting position for the Full Statics to work from. There are some cases where the choice of Statics Method is important. Firstly, in cases where there may be more than one equilibrium position, the Full Statics calculation will tend to find the one that is closest to the initial starting position found by the Statics Method. Secondly, 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 form the true equilibrium position. In both these situations, it is generally best to choose the Statics Method that gives the best initial estimate of the desired equilibrium position. Catenary convergence failure The Catenary method is iterative and may fail to converge. It may be possible to solve this by adjusting the Catenary Convergence Parameters on the line data form. If this proves difficult, then an alternative is to use one of the other statics methods. The Quick method may suffice, or alternatively the Spline method may be needed. Providing Full Statics is included then the final static position found will be the same. Full Statics Convergence Failure Full Statics is also an iterative calculation and may sometimes fail to converge. 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, the problem may be due to the initial starting position obtained by the specified statics method being a long way from the equilibrium position. 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. Note: When setting up the spline control points, it is often useful to first set Full Statics to "No". This allows you to examine and refine the spline shape, by running the static analysis and adjusting the control points until the spline shape is close to the desired shape. You can then set Full Statics back to "Yes" in order to find the true 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. As a result the Full Statics calculation may fail to converge, or else converge to the wrong equilibrium position (e.g. one in which the line is on the wrong side of the solid). In both these cases it may be better for the user to select the Spline method and then specify control points that give an initial shape that is close to the desired equilibrium position. Pipeline Pull-In For a pipe lying on the seabed there are usually many equilibrium positions, since seabed friction will often be able to hold the pipe in the shape it was originally laid. For pull-in analysis this originally-laid shape is generally known, and the Prescribed method can be used to define this shape. 149 w It is then optional whether Full Statics is included or not. Normally, it would not be included. If it is included then it will have no effect if the Prescribed position is already in equilibrium - i.e. if friction is sufficient to hold the pipe in that position. But if friction is not sufficient then Full Statics will tend to find a nearby position that is in equilibrium. 6.5.3 Statics of Buoys and Vessels Each buoy and vessel can be either included or excluded form the static analysis. This is controlled by the data item Included in Static Analysis on the object's data form. Notes: You can also use the Buoy Degrees of Freedom Included In Static Analysis. data item, on the General data form, to include or exclude all buoys with a single setting. Also, for 6D buoys, you can include just the translational degrees of freedom (X,Y,Z) and exclude the rotational degrees of freedom. This is sometimes useful as an aid to convergence. If a buoy is excluded from the static analysis, then when the static analysis is done OrcaFlex will simply place the buoy in the Initial Position specified on the buoy data form. This will not, in general, be the equilibrium position. The same applies to vessels. If any buoys or vessels are included in the static analysis, then the static analysis finds the equilibrium position of those buoys and vessels, using an iterative procedure, as follows: 1. OrcaFlex first places all of the buoys and vessels in their Initial Position, as specified on their data forms. Buoys or vessel that are excluded from the analysis are then simply left in that position. 2. OrcaFlex then calculates the forces and moments acting on each of the buoys and vessels that are included in the analysis. This takes into account weight, buoyancy, drag, applied load etc., and also loads from any attached links, winches or lines. The calculation therefore involves calculating the statics of any lines that are attached, which is often itself an iterative calculation. 3. Next, OrcaFlex moves the included buoys and vessels by an amount that is aimed at balancing the forces and moments acting on them. Note that this movement and load balance is only done with the degrees of freedom that are included in the analysis. For vessels these are surge, sway and yaw only. For 6D buoys you can specify whether to include just the translational degrees of freedom or the rotational degrees of freedom as well. 4. Steps 2 and 3 are then repeated until all included buoys and vessels are in equilibrium. This iterative procedure usually converges successfully, but in some cases there can be difficulties. To give the best chance of convergence you should specify buoy and vessel initial positions that are good estimates of the true equilibrium position. 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. There is a button on the general data form for this purpose - see Use Static Positions. Note: As an aid to static analysis, the out-of-balance forces on buoys and vessels can be drawn on the 3D view. If necessary, you can also control the buoy convergence process using the statics convergence parameters on the general data form. 150 w 6.5.4 Multiple Statics for Vessels You can use the Multiple Statics command on the Calculation menu to perform a series of static analyses for an array of different position of a vessel. This feature is mainly intended for use in mooring analyses. 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 the these vessel positions. Key results, for example load-offset curves, are then made available in the form of tables and graphs as a function of the offset distance. The vessel positions are specified by a series of offsets about the vessel's initial position (see Vessel Multiple Statics Data). 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. See Vessel Data. 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. No results are given for offsets with failed statics. When the calculation is completed the program enters Multiple Statics Complete state. Results can only be viewed in this state and are lost upon Reset. Results cannot be saved. A dynamic simulation cannot be carried out after multiple statics - you must Reset first. 6.6 DYNAMIC ANALYSIS 6.6.1 Dynamic Analysis The dynamic analysis is a time simulation of the motions of the model over a specified period of time, starting from the position derived by the static analysis. The period of simulation is defined as a number of consecutive stages, whose durations are specified in the data. Various controlling aspects of the model can be set on a stage by stage basis, for example the way winches are controlled, the velocities and rates of turn of vessels and the releasing of lines, links and winches. This allows quite complex operational sequences to be modelled. Before the main simulation stage(s) there is a build-up stage, during which the wave and vessel motions are smoothly ramped up from zero to their full size. Ramping of current is optional (see Current Data). 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 build-up stage is numbered 0 and its length, which is specified in the data, should normally be at least one wave period. The remaining stages, simply numbered 1, 2, 3..., are intended as the main stages of analysis. Time is measured in OrcaFlex in seconds. To allow you to time-shift one aspect of the model relative to the others, different parts of the OrcaFlex model have their own user-specified time origins. See the diagram below. For example, simulation time is measured relative to the simulation time origin, which is specified on the Wave tab on the environment data form. The simulation time origin is at the end of the build-up stage, so negative simulation time is the build-up stage and the remaining stages are in positive simulation time. The figure below shows a simulation using a build-up of 10 seconds, followed by two stages of 15 seconds each. 151 w Each wave train also has its own time origin, and similarly for time-varying wind and any time history files that you use. All of these time origins are defined relative to the global time origin (which is not user-specified), so if necessary you can use the time origins to time-shift one aspect of the model relative to the others. By default all of the time origins are zero, so all of the time frames coincide with global time. For most cases this simple situation is all you need, but here is an example where you might want to adjust a time origin. • You might want to arrange that a wave crest, or a particularly large wave in a random sea, arrives at your vessel at a particular point in the simulation. If you use the View Profile facility and find that the wave arrives at the vessel at global time 2590s, then you can arrange that this occurs at simulation time 10s (i.e. 10 seconds into stage 1) by either setting the simulation time origin to 2580 or else setting the wave train time origin to -2580. The former shifts the simulation forwards to when the wave occurs, whereas the latter shifts the wave back to the period the simulation covers. Static Starting Position Build-up -10 0 Stage 1 15 Stage 2 30 Wave Train Time 0 Time-history Time 0 T=0 Global Time Origin Wave Train Time Origin Global Time T Simulation Time Origin Time-history Time Origin End of Simulation Simulation Time t Figure: Time and Simulation Stages 6.6.2 Calculation Method The OrcaFlex dynamic analysis is a time-domain simulation that uses an explicit Euler integration technique with a constant timestep that is specified in the data. At the start of the time simulation, the initial positions and orientations of all objects in the model, including all nodes in all lines, are known from the static analysis. The forces and moments acting on each free body and node are then calculated. Forces and moments considered include: • • • weight buoyancy hydrodynamic drag 152 w • • • • • • hydrodynamic added mass effects, calculated using the usual extended form of Morison's equation with user-defined coefficients tension and shear bending and torque seabed reaction and friction contact forces with other objects forces applied by links and winches {M}.{x"} = {F} where {M} is the mass matrix for the node or body, including added mass terms, {x"} is the acceleration vector, and {F} is the total force vector. The equation is solved for the acceleration vector which is then integrated. At the end of each timestep, the positions and orientations of all nodes and free bodies are again known and the process is repeated. The timestep required for stable integration is very short - typically around 0.001s. OrcaFlex gives guidance on an appropriate timestep. Hydrodynamic forces typically change little over such a short time interval, and are time-consuming to compute. To save computing time, hydrodynamic loads are updated only over a longer "outer" timestep. Both time steps are userdefined (see Inner and Outer Time Steps) and may be set equal for critical cases. Simulation time is further reduced by the use of a build up time at the beginning of the simulation. During the build-up time the wave amplitude and vessel motions are increased smoothly from zero to the full amplitude specified in the data. This gives a gentle start to the simulation which reduces transient responses and avoids the need for long simulation runs. The build-up time is specified in the data, and normally should be at least one wave period. Negative time is shown during the simulation to indicate the build-up time; so time before time zero is build up time, time after time zero is normal simulation with the full specified excitation. Since the system geometry is recomputed at every timestep, the simulation takes full account of geometric non-linearities, including the spatial variation of both wave loads and contact loads. Note that the method of solution does not involve the construction and inversion of a stiffness matrix for any part of the system. An important consequence is that the program has no difficulty in dealing with the transition between tension and compression in lines, e.g. at seabed touchdown. Of the various objects available in OrcaFlex, Lines are the most computationally demanding. For most models that include lines, 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. If the time step is maintained at the maximum level recommended value (see Inner and Outer Time Steps) and nodes are distributed uniformly along the lines, then the run time is approximately proportional to the square of the number of nodes. The simulation can be interrupted using the Pause button. OrcaFlex will pause when it reaches the end of the current outer time step, so if the outer step size is long you will have to wait a few seconds. Whilst the simulation is interrupted, you can use most of the normal commands. So, for example, you can examine the results obtained so far and examine the data. The equation of motion (Newton's law) is then formed for each free body and each line node: 153 w 6.6.3 Ramping During the build-up stage of the simulation the wave dynamics, vessel motions and optionally the current (see Current Data) are built up smoothly from zero to their full level. The ramping factor is calculated as follows: Ramping Factor = 3r² -2r³ where r is the proportion of the build-up stage completed, given by: r = (Time + Length of Stage 0) / (Length of Stage 0) Note: Time is negative throughout the build-up stage. 6.7 BUOYANCY VARIATION WITH DEPTH The buoyancy of an object is normally assumed to be constant and not vary significantly with depth. But the buoyancy is equal to ρ.V.g, where ρ is the water density, V is the volume and g is the acceleration due to gravity. So in reality the buoyancy does vary with depth, due to two effects: • • Firstly, if the object is compressible then its volume V will reduce with depth due to the increasing pressure. Secondly, the water density ρ can vary with depth, either because of the compressibility of the water, or else because of temperature or salinity variations. Normally the density increases with depth, since otherwise the water column would be unstable (the lower density water below would rise up through the higher density water above). For buoys and lines these effects can be modelled in OrcaFlex. Compressibility of Buoys and Lines All things are compressible to some extent. The effect is usually not significant, but in some cases it can have a significant effect on the object's buoyancy. To allow these effects to be modelled, you can specify the compressibility of a 3D Buoy, 6D Buoy or Line Type by giving the following data on the object's data form. Bulk Modulus The bulk modulus, B, specifies how the object's volume changes with pressure, according to the following formula. Volume at pressure P = V0.(1 - P/B) where V0 is the uncompressed volume at atmospheric pressure, and P is the pressure excess over atmospheric pressure. The bulk modulus has the same units as pressure (F/L²) and the above formula can be thought of as saying that the volume reduces linearly with pressure, and at a rate that would see the object shrink to zero volume if the pressure ever reached B. For an incompressible object the bulk modulus is infinity, and this is the default value in OrcaFlex. Note: The above formula breaks down when P ≥ B and would become inaccurate well before that pressure was reached. However, B is normally very large, so the object normally only experiences pressures that are small compared to B. 154 w 6.8 CURRENT THEORY Extrapolation In the presence of waves, the current must be extrapolated above the still water level; in OrcaFlex we adopt the convention that the surface current applies to all levels above the still water level. If a sloping seabed is specified, the boundary is inconsistent with a horizontal current. This effect is not usually important and is uncorrected in OrcaFlex. The current at the greatest depth specified is applied to all greater depths. Interpolated Method Horizontal current is specified as a full 3D profile, variable in magnitude and direction with depth. The profile should be specified from the still water surface to the seabed. Linear interpolation is used for intermediate depths. If the specified profile does not cover the full depth then it is extrapolated (see Extrapolation above). Power Law Method Current direction is specified and does not vary with depth. Speed (S) varies with position (X,Y,Z) according to the formula: S = Sseabed + (Ssurface - Sseabed) x ((Z-Zseabed) / (Zsurface-Zseabed)) ^ (1/Exponent) where Ssurface and Sseabed are the current speeds at the surface and seabed, Exponent is the power law exponent, Zsurface is the water surface Z level, all as specified in the data, Zseabed is the Z level of the seabed directly below (X,Y). Note: If Z is below the seabed (e.g. has penetrated the seabed) then the current speed is set to Sseabed and if Z is above the surface (e.g. in a wave crest) then current speed is set to Ssurface. 6.9 WAVES 6.9.1 Wave Theory Each wave train can be a regular wave, a random wave or specified by a time history file. Regular Waves OrcaFlex offers a choice of a long-crested, regular, linear Airy wave (including seabed influence on wave length) or nonlinear waves using Dean, Stokes' 5th or Cnoidal wave theories (see Nonlinear Wave Theories). Waves are specified in terms of height and period, and direction of propagation. 155 w Random Waves OrcaFlex offers three standard spectra, JONSWAP (see below), ISSC (based on PiersonMoskovitz) and Ochi-Hubble. The program synthesises a wave time history from a userdetermined number of wave components, whose amplitudes and periods are selected by the program to match the specified spectrum. The phases associated with each wave component are pseudo-random: a random number generator is used to assign phases, but the sequence is repeatable, so the same user data will always give the same train of waves. Different waves from the same spectrum can be obtained by shifting the simulation time origin relative to the wave time origin. OrcaFlex provides special facilities to assist in selecting an appropriate section of random sea. The first lists all the waves in a selected time interval whose height or steepness is large by comparison with the reference wave Hs, Tz. The second allows the wave elevation for a selected period to be drawn to screen. JONSWAP Spectrum Five parameters are required for a complete definition. Two of these, the spectral width parameters Sigma 1 and Sigma 2, are set to standard values of 0.07 and 0.09 respectively. Alpha, fm and gamma are then calculated by the program for the given values of Hs and Tz (using the formulae given by Isherwood, Applied Ocean Research, September 1987). You may select a different value of gamma if required. The program then recalculates alpha and fm to correspond to the required Hs and Tz. 6.9.2 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. It only applies to Airy waves and to random waves (which are made up of a number of Airy waves). Linear wave theory in principle only applies to very small waves, so it does not predict kinematics for points above the mean water level since they are not in the fluid. The theory therefore needs to be 'stretched' to cover such points, and OrcaFlex offers a choice of three published methods: Vertical Stretching, Wheeler Stretching and Extrapolation Stretching (see below). Consider, for example, the horizontal particle velocity u. In Airy wave theory the formula for u at position (x,z) at time t is: u = E(z) a ω cos(ωt - φ + kx) ........................ (1) where a, ω, φ and k are the wave amplitude, angular frequency, phase lag and wave number, respectively, and z is measured positive upwards from the mean water level. The term E(z) is a scaling factor given by E(z) = cosh(k(d+z))/sinh(kd), where d = mean water depth. It is an exponential decay term that models the fact that the fluid velocity reduces as the point goes deeper. However for z>0 (i.e. above the mean water level) E(z) is greater than 1 so it amplifies the velocity. This can give particle velocity predictions that are unrealistically large (the problem being worst for high frequency waves). The various stretching methods deal with this problem by replacing E(z) with a more realistic term. Note that all the stretching methods apply not only to the scaling factor E(z) in the horizontal velocity formula (1), but also to the scaling factors in the corresponding Airy wave theory formulae for the vertical velocity and the horizontal and vertical acceleration. 156 w Vertical Stretching This is the simplest of the 3 methods. E(z) is left unchanged for z<=0, but for z > 0 (i.e. above the mean water level) E(z) is replaced by E(0). This has the effect of setting the kinematics above the mean water levels to equal those at the mean water level. Wheeler Stretching This method stretches (or compresses) the water column linearly into a height equivalent to the mean water depth. This is done by replacing E(z) by E(z') where z’ = d.(d+z)/(d+ζ) - d and ζ is the z-value at the instantaneous water surface. This formula for z' essentially shifts z linearly to be in the range -d to 0. 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. In other words, for z<=0 equation (1) is left unchanged, but for z>0, E(z) is replaced by E(0) + z.E'(0), where E' is the rate of change of E with z. 6.9.3 Ochi-Hubble Spectra The Ochi-Hubble Spectrum allows 2-peaked spectra to be set up, enabling you to represent sea states that include both a remotely generated swell and a local wind generated sea. Example of Ochi-Hubble Spectrum 6 5 S(r) [m^2] 4 3 2 1 0 0 1 2 Relative Frequency r 3 4 The Ochi-Hubble wave spectrum is the sum of 2 separate component spectra - the example graph shows the 2 components and their sum. 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. This is why the Ochi-Hubble spectrum is often called a 2-peaked spectrum; however in practice, 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. The two component spectra are each specified by a set of three parameters - Hs1, fm1, Lambda1 for the lower frequency component and Hs2, fm2, Lambda2 for the higher frequency component. See Data for Ochi-Hubble Spectra. 157 w In OrcaFlex you can either specify all these 6 parameters explicitly, 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. In the latter case, OrcaFlex uses ‘most probable’ parameters based on formulae given in the Ochi-Hubble paper (table 2b). 6.9.4 Non-linear Wave Theories OrcaFlex models two types of waves, periodic regular waves and random waves. A regular wave is a periodic wave with a single period. A random wave in OrcaFlex is a superposition of a number of regular linear waves of differing heights and periods. We shall not discuss random waves here. For very small waves in deep water, Airy wave theory (also know as linear wave theory) is valid. Many waves in practical engineering use do not fall into this category, hence the need for nonlinear wave theories. These include Stokes' 5th order theory, Dean's stream function theory and Fenton's cnoidal theory which are all available in OrcaFlex. We shall give an outline of these theories here in the form of concise abbreviations of the relevant papers. For an overview of all the theories considered here see Sobey R J, Goodwin P, Thieke R J and Westberg R J, 1987. To fix notation we use the following conventions throughout. These conventions are different from those used in OrcaFlex but we use them here in order to agree with the literature. We assume that the wave is long-crested and travels in the x direction and we shall work only in the (x,z) plane. The seabed has z = 0 and the mean water level is given by z = d, where d is the water depth (at the seabed origin). The wave is specified by wave height (H) and wave period (T) and the wavelength (L) will be derived. The horizontal and vertical particle velocities are denoted by u and v respectively. We assume a moving frame of reference with respect to which the motion is steady and x = 0 under a crest. See Stokes' 5th, Dean's stream function theory and Fenton's cnoidal theory for a brief overview of each of the non-linear wave theories available in OrcaFlex and for guidance on how to decide on which wave theory to use in practice. 6.9.5 Stokes' 5th The engineering industry's standard reference on 5th order Stokes' wave theory is Skjelbreia and Hendrickson (1961). 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. The length a has no physical meaning and by choosing ak as expansion parameter, convergence for very steep waves cannot be achieved. 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. Thus it is Fenton's theory which we recommend, although both theories have been implemented in OrcaFlex. It is worth noting that the linear theory of Airy is a 1st order Stokes' theory. Assuming that the user supplies wave train information comprising water depth, wave height and wave period then the wave number k must be computed before the theory can be applied. In order to do this a non-linear implicit equation in terms of k is solved using Newton's method with derivative calculated by perturbation. This equation is known as the dispersion relationship. Once k is known, a number of coefficients are calculated and these are used for power series expansions in order to find surface profile and wave kinematics. Accuracy of method Inherent in the method is a truncation of all terms of order greater than 5. Thus if the terms which are discarded are significant then this theory will give poor results. See Ranges of 158 w applicability for the waves for which Stokes' 5th theory is valid, but essentially this is a deep water, steep wave theory. 6.9.6 Dean's Stream Function Theory A typical approach to wave theory makes use of the idea of a velocity potential. This is a vector field φ (x,z) whose partial derivatives are the particle velocities of the fluid. That is: ∂φ / ∂x = u and ∂φ / ∂z = v. Chappelear devised a wave theory based on finding the best fit velocity potential to the defining wave equations. This was quite complicated and Dean's idea was to apply the same idea to a stream function. A stream function is a vector field ψ(x,z) which satisfies ∂ψ / ∂x = -v and ∂ψ / ∂z = u. Dean's original paper (1965) was intended to be used to fit stream functions to waves whose profile was already known, for example a wave recorded in a wave tank. For the purpose of OrcaFlex the user provides information on the wave train in the form of water depth, wave height and wave period and we wish to find a wave theory which fits this data. 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). This method is also known as Fourier approximation wave theory. The problem is to find a stream function which: • • • • satisfies Laplace's equation ∂²ψ / ∂x² +∂²ψ / ∂z² = 0, which means that the flow is irrotational is zero at the seabed, that is ψ( x,0 ) = 0 is constant at the free surface z = η( x ), say ψ( x , η ) = -Q satisfies Bernoulli's equation ½ [ (∂ψ / ∂x)² + (∂ψ / ∂z)² ] + η = R, where R is a constant. and In these equations all variables have been non-dimensionalised with respect to water depth d and gravity g. By standard methods, equations (a) and (b) are satisfied by a stream function of the form ψ(x,z) = B0 z + Σ Bj [sinh (jkz) / cosh (jk)] cos (jkx) where k is the wave number which is as yet undetermined, and the summation is from j = 1 to N. The constant N is said to be the order of the stream function. The problem now is to find coefficients Bj and k which satisfy equations (c) and (d). Implementing stream function theory requires numerical solution of complex non-linear equations. The number of these equations increases as N increases and there is a short pause in the program while these equations are solved. The default value is 10 and for most purposes it is not necessary to alter this. However, for nearly breaking waves the solution method sometimes has problems converging. If this is the case then it might be worth experimenting with different values. 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. For these methods, power series expansions are obtained and then truncated at an arbitrary point. If the terms which are being ignored are not small then these methods will give inaccurate answers. In theory, Dean's method should cope well in similar circumstances as it is finding a best fit to the governing equations. This 159 w means that stream function wave theory is very robust. However for finite waves in deep water, Stokes' 5th is preferred as the ignored terms are indeed small and the computation is faster than that for Dean. In very shallow water Fenton believes that his high order cnoidal wave theory is best, although we would recommend stream function theory here. It is possible that, by their very nature, Stokes' 5th and the cnoidal theories may give inaccurate results if applied to the wrong waves. In all circumstances the stream function method, if it converges, will give sensible results. Hence it can be used as a coarse check on the applicability of other theories. That is if your preferred wave theory gives significantly different results from Dean's, applied to the same wave, then it is probably wrong! 6.9.7 Fenton's cnoidal theory This is a steady periodic water wave theory designed to be used for long waves in shallow water. 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. 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. This work has been superseded by Fenton (1990 and 1995). Fenton's original paper gave formulae for fluid velocities based on a Fourier series expansion about the term ε = H / d In his later works Fenton discovered that much better results could be obtained by expanding about a "shallowness" parameter δ. We follow this approach. A 5th order stream function representation is used but instead of terms involving cos the Jacobian elliptic function cn is used, hence the term cnoidal. The function takes two parameters, x as usual, and also m which determines how cusped the function is. In fact when m = 0, cn is just cos and the Jacobian elliptic functions can be regarded as the standard trigonometric functions. The solitary wave which has infinite length corresponds to m = 1 and long waves in shallow water have values of m close to 1. 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. The initial step of the solution is to determine m and an implicit equation with m buried deep within must be solved. As in the Stokes' theory this equation is the dispersion relationship. The solution is performed using the bisection method since the equation shows singular behaviour for m ≈ 1 and derivative methods fail. After m has been determined Fenton gives formulae to calculate surface elevation and other wave kinematics. In practice m is close to 1 and Fenton takes advantage of this to simplify the formulae. He simply sets m = 1 in all formulae except where m is the argument of an elliptic or Jacobian function. This technique is known as Iwagaki approximation and proves to be very accurate. 6.9.8 Ranges of Applicability Regular wave trains are specified in OrcaFlex by water depth, wave height and wave period. Which wave theory should one use for any given wave train? For an infinitesimal wave in deep water then Airy wave theory is accurate. For finite waves a non-linear theory should be used. 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. If U < 40 then the waves are said to be short and Stokes' 5th may be used. For U > 40 we have long waves and the cnoidal wave theory can be used. The stream function theory is applicable for any wave. The boundary number 40 should not be considered a hard and fast rule. In fact for Ursell number close to 40 both the Stokes' 5th theory and the cnoidal theory have 160 w inaccuracies and the stream function method is recommended. In regions well away from Ursell number 40 then the relevant analytic theories (Stokes' 5th or cnoidal) perform very well. Our recommendations are: Ursell number << 40 ~ 40 >> 40 Recommended wave theory Dean or Stokes' 5th Dean Dean or Cnoidal In general then, we would recommend the stream function wave theory in most cases. If another theory is being used then it should be compared against the stream function theory to check its validity. This is a very important point. OrcaFlex has no way of telling if a theory has been misapplied, 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! 6.9.9 Breaking waves All the regular wave theories are suspect for breaking or near breaking waves. In shallow water then the height of a breaking wave, HB, is around 0.8d and for deep water HB = 0.14L. An expression which covers all depths, due to Miche, is HB = 0.88k¯¹ tanh ( 0.89 kd ) where k is the local wave number as calculated by Airy wave theory. OrcaFlex reports a warning if the wave height exceeds HB. 6.9.10 Particle velocities and accelerations An important consideration for computing the wave kinematics is whether to use apparent or real quantities. That is, do we compute velocities and accelerations relative to a fixed point in the fluid (Eulerian) or relative to an individual water particle (Lagrangian). For velocities there is no confusion as the two concepts coincide but there is an issue for accelerations. 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. 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, which is based on the assumption that the wave is very small, then apparent and real accelerations are effectively equal and OrcaFlex computes apparent accelerations for Airy wave theory. For the non-linear theories, real accelerations are used in all cases. 6.9.11 Currents Each of the theories implemented allows for a uniform Eulerian current but none is designed to deal with current profiles. 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, as we do for Airy waves. So we have to reach some compromise. 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. Call this current component CW. To calculate the fluid velocity V at any given point in time we must take into account the fluid velocity VW containing uniform current CW together with the current C at the point in question, as specified by the current profile. The formula is: 161 w V = VW - CW + C A similar formula is used during the build up. If the wave factor is λ then V = λ (VW - CW ) + C 6.9.12 Seabed Slope In the case of a sloping seabed in OrcaFlex, we adopt the following convention for wave theories. We assume that the water depth is that at the seabed origin for the purpose of deriving the wave information (wave number, stream function etc.) We define the fluid motion for a point (x,y,z) where z < 0 to be the fluid motion for the point (x,y,0). 6.9.13 Physically implausible solutions The non-linear wave theories implemented in OrcaFlex each have their own ranges and limitations as previously discussed. However, it is sometimes possible to obtain a solution for a particular wave train which is physically implausible. For example if the stream function or Stokes' 5th theories are misapplied then they may predict wave profiles with multiple crests. Whilst these are valid solutions to the mathematical problem, they are not realistic. Also it is sometimes predicted by each theory that the horizontal fluid velocities under a crest increase with depth. This also is physically implausible. OrcaFlex warns if such unrealistic solutions occur. It is then up to the engineer to judge the validity of the results. It has not been possible to guard against all such anomalies, in particular the Stokes' 5th theory can predict wave profiles with points of inflection other than at crest and trough. 6.10 SEABED THEORY The seabed is modelled as a sprung surface whose properties are specified in the seabed data. Objects Affected Only 3D buoys and 6D buoys, lines and drag chains interact with the seabed; other objects are not affected by it. A line interacts when one of its nodes penetrates the seabed. The node then experiences the seabed stiffness force and damping force, applied at the node centre. The node may also experience a friction force - see Seabed Friction. A 3D buoy interacts when the buoy origin penetrates the seabed. The seabed stiffness and damping forces are then applied at the buoy origin. No seabed friction force is applied. A 6D buoy interacts when its vertices penetrates the seabed. (A 6D buoy with no vertices is treated as if it had one vertex at the buoy origin.) Each penetrating vertex experiences the seabed stiffness and damping forces, applied at the vertex. No seabed friction force is applied. Drag chain interaction with the seabed is slightly different; see drag chain seabed interaction. Seabed Stiffness Force The seabed reaction force is in the outwards normal direction and has magnitude R = K.A.d where K is the seabed stiffness A is the area of contact 162 w d is the depth of penetration into the seabed. For details on how the area of contact values are calculated see 3D Buoy Theory, 6D Buoy Theory and Line Interaction with Seabed and Solids. Seabed Damping Force The seabed damping force is only applied when the object is travelling into the seabed, not when it is coming out of the seabed. It is in the outwards normal direction and has magnitude D given by: D = λ.2√(M.K.A).Vn D=0 where λ is percentage of critical seabed damping / 100 M is the mass of the object K is the seabed stiffness A is the area of contact Vn is the component of velocity normal to the seabed, +ve when travelling into the seabed and -ve when coming out. We recommend using 100% critical damping for seabeds. if Vn > 0 if Vn <= 0 6.11 LINE THEORY 6.11.1 Overview OrcaFlex uses a finite element model for a line as shown in the figure below. 163 w Actual Pipe End A Node 1 Discretised Model Segment 1 Segment 1 Node 2 Segment 2 Segment 2 Node 3 Segment 3 End B Segment 3 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. The model segments only model the axial and torsional properties of the line. The other properties (mass, weight, buoyancy etc.) are all lumped to the nodes, as indicated by the arrows in the figure above. Nodes and segments are numbered 1,2,3,... sequentially from end A of the line to end B. 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. The exception to this is end nodes, which have only one half-segment next to them, and so represent just one half-segment. Each line segment is divided into two halves and the properties (mass, weight, buoyancy, drag etc.) of each half-segment are lumped and assigned to the node at that end of the segment. 164 w Forces and moments are applied at the nodes - with the exception that weight can be applied at an offset. Where a segment pierces the sea surface, all the fluid related forces (e.g. buoyancy, added mass, drag) are calculated allowing for the varying wetted length up to the instantaneous water surface level. Segments Each model segment is a straight massless element that models just the axial and torsional properties of the line. 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. The bending properties of the line are represented by rotational springs+dampers at each end of the segment, between the segment and the node. The line does not have to have axial symmetry, since different bend stiffness values can be specified for two orthogonal planes of bending. This section has given only an overview of the line model. See structural model for full details. 6.11.2 Structural Model Details The following figure gives greater detail of the line model, showing a single mid-line node and the segments either side of it. The figure includes the various spring+dampers that model the structural properties of the line, and also shows the xyz-frames of reference and the angles that are used in the theory below. 165 w Sx1 Sy1 Sz Sx1 τ Axial spring + damper Sy2 Sz Sx2 Torsion spring + damper α2 Ny Node Nx Nz (axial direction) Bending springs + dampers α1 End B Figure: Detailed representation of OrcaFlex Line model As shown in the diagram, there are 3 types of spring+dampers in the model: • The axial stiffness and damping of the line are modelled by the axial spring+damper at the centre of each segment, which applies an equal and opposite effective tension force to the nodes at each end of the segment. The bending properties are represented by rotational spring+dampers either side of the node, spanning between the node's axial direction Nz and the segment's axial direction Sz. 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, which applies equal and opposite torque moments to the nodes at each end of the segment. 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. • • 6.11.3 Calculation Stages We now describe the calculation sequence that OrcaFlex uses to calculate the forces and moments on the mid-node shown in the diagram Line Model Detail. 166 w Stage 1: Tension Forces Firstly the tensions in the segments are calculated. To do this, OrcaFlex calculates the distance (and its rate of change) between the nodes at the ends of the segment, and also calculates the segment axial direction Sz, which is the unit vector in the direction joining the two nodes. The tension in the axial spring+damper at the centre of each segment can then be calculated; it is the vector in direction Sz and whose magnitude is given by: Te = EA . [(L - L0)/L0+ (e . dL/dt)/L0)] where Te = effective tension L = instantaneous length of segment L0 = unstretched length of segment dL/dt = rate of increase of length EA = axial stiffness of line, as specified on the line types form (= effective Young's modulus x cross-section area) e = damping coefficient of the line, in seconds. Note that the effective tension Te can be negative, indicating compression. For the relationship between effective tension and pipe wall tension see Line Pressure Effects. The damping coefficient e represents the structural damping in the line. It is calculated automatically based on the Axial Target Damping value specified on the general data form. e = e(critical) . (Target Axial Damping) / 100 where e(critical) = √ (2.SegmentMass.L0 / EA) is the critical damping value for a segment and SegmentMass includes the mass of any contents but not the mass of any attachments. This tension force vector is then applied (with opposite signs) to the nodes at each end of the segment. Each mid-node therefore receives two tension forces, one each from the segments on each side of it. Stage 2: Bend Moments The bend moments are then calculated. There are bending spring+dampers at each side of the node, spanning between the node's axial direction Nz and the segment's axial direction Sz, and 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. These axial directions are associated with the frames of reference of the node and segment. The node's frame of reference Nxyz is a Cartesian set of axes that is fixed to (and so rotates with) the node. Nz is in the axial direction and Nx and Ny are normal to the line axis and correspond to the end x- and y-directions that are specified by the Gamma angle on the line data form (see End Orientation). The segment has two frames of reference - Sx1 y1 z at the end nearest end A, and Sx2 y2 z at the other end. These two frames have the same Sz-direction, which was calculated in step 1 above, so the bend angle α2 between Nz and Sz can now be calculated. The effective curvature vector C is then calculated - it is the vector whose direction is the binormal direction, which is the direction that is orthogonal to Sz and Nz, and whose magnitude is α2 / (½ L0), where L0 is the unstretched length of segment. 167 w The bend moment, M2, generated by the bending spring+damper is then calculated. If the bend stiffnesses for the x and y-directions are equal then it is the vector in the binormal direction whose magnitude is given by M2 = EI.|C| + D.d|C|/dt where EI = bending stiffness, as specified on the line types form D = (λ/100).Dc. Dc = the bending critical damping value for a segment = L0.√(SegmentMass.EI.L0) λ = target bending damping, as specified on the general data form. If the bend stiffnesses for bending about the x and y-directions are different, then the above equation is separated into its components in the Sx2 and Sy2 directions, giving component of M2 is the Sx2 direction = EIx.Cx + Dx.dCx/dt component of M2 is the Sy2 direction = EIy.Cy + Dy.dCy/dt where EIx, EIy = bending stiffnesses of segment, as specified on the line types form Cx, Cy = components of the curvature vector C in the Sx2 and Sy2 directions Dx = (λ/100).L0.√(SegmentMass.EIx.L0) Dy = (λ/100).L0.√(SegmentMass.EIy.L0). The curvature used in the calculation of bending moments is the value in the true plane of bending, taking full account of the 3D motions of the adjacent nodes. The bending damping term D represents the effect on bending of the structural damping in the line; its level is set by the Target Bending Damping data item on the general data form. The bend angle (α1) and bend moment vector (M1) on the other side of the node are calculated similarly, so the node experiences two bend moments, one each from the segments on each side of it. Stage 3: Shear Forces Having calculated the bend moments at each end of the segment, the shear force in the segment can be calculated. Each model segment is a straight stiff rod in which the bend moment vector varies from M1 at one end (the end nearest end A of the line) to M 2 at the other end, where these bend moments are calculated as described in Step 2 : Bend Moments above. Because the model segment is stiff in bending, 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. The shear force is therefore given by: Shear Force Vector = (M 2 - M1) / L where L is the instantaneous length of the segment. Note that M1 and M2 are vectors, so this is a vector formula that defines both the magnitude and direction of the shear force. This shear force vector is applied (with opposite signs) to the nodes at each end of the segment. 168 w Stage 4: Torsion Moments The torsion is then calculated (providing torsion has been included). To do this, the directions Sx1, Sy1, Sx2 and Sy2 must first be calculated, since so far only the segment axial direction Sz has been found. The directions Sx2 and Sy2 at the end of the segment are determined from the orientation Nxyz of the adjacent node, by rotating Nxyz until its z-direction is aligned with Sz. This rotation is therefore through angle α2 and it is a rotation about the binormal direction (i.e. the direction that is orthogonal to both Nz and Sz). (Note that rotations about the binormal direction are bending rotations only - i.e. they involve no twisting.) The directions Sx1 and Sy1 at the other end of the segment are derived in the same way, but starting from the orientation of the node at that other end of the segment. The twist angle τ in the segment can then be calculated - it is the angle between the directions Sx1 and Sx2. Note that this twist angle is also the angle between Sy1 and Sy2 - in other words the orientations Sx1 y1 z and Sx2 y2 z, at the two ends of the segment, differ by just a twist through angle τ. 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.τ / L0 + C.(dτ/dt) + A.Te where K = torsional stiffness, as specified on the line types form τ = segment twist angle (in radians), 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 A = torque per unit tension, as specified on the line types form Te = effective tension in the segment The damping coefficient C represents the torsional effect of structural damping in the line. It is calculated automatically based on the Target Torsional Damping value specified on the general data form using the formula C = C(critical).(Target Torsional Damping) / 100 where C(critical) is the critical damping value for a segment, given by C(critical) = √ (2.Iz.K/L0). Here, Iz is the rotational moment of inertia of the segment about its axis, allowing only for the structural mass of the line, not the mass of any contents (since the contents are assumed to not twist with the pipe). This torque moment vector is then applied (with opposite signs) to the nodes at each end of the segment. Stage 5: Total Load As described above, each mid-node experiences two tension forces, two bend moments, two shear forces and two torque moments (one each from the segments either side of the node). These loads are then combined with the other non-structural loads (weight, drag, added mass etc.) to give the total force and moment on the node. OrcaFlex then calculates the resulting 169 w translational and rotational acceleration of the node, and then integrates to obtain the node's velocity and position at the next time step. See Calculation Method. 6.11.4 Line End Orientation At line ends, we usually need to define not only the axial direction of the end fitting but also the twist orientation about that axial direction. 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. Together, the 3 angles azimuth, declination and gamma fully define the rotational orientation of the end fitting. To define how this is done we need to define a frame of reference Exyz for the end fitting, where: • • • E is at the connection point. Ez is the axial direction of the fitting, using the "A to B" convention - i.e. Ez is into the line at end A, but out of the line at end B. Ex and Ey are perpendicular to Ez. The 3 angles, Azimuth, Declination and Gamma, specify the orientation of Exyz relative to the local axes Lxyz of the object to which the end is connected, as follows. (If the line end is not connected to another object, then it is either Fixed, Anchored or Free. In these cases the angles define Exyz relative to the global axes GXYZ.) • • • • Start with Exyz aligned with Lxyz. Then rotate Exyz by Azimuth degrees about Ez (= Lz at this point). Now rotate by Declination degrees about the resulting Ey direction. Finally rotate by Gamma degrees about the resulting (and final) Ez direction. In all these rotations, a positive angle means rotation clockwise about the positive direction along the axis of rotation, and a negative angle means anti-clockwise. Three-dimensional rotations are notoriously difficult to describe and visualise. When setting the azimuth, declination and gamma, it is best to check that the resulting Exyz directions are correct by drawing the local axes on the 3D view. Here are some examples of the effect of various values of (Azimuth, Declination, Gamma) for a Fixed end. For ends connected to other objects, replace GXYZ by Lxyz in these examples. • • • • • (0,0,0) sets Exyz to be aligned with GXYZ. (0,30,0) sets Ex at 30° below GX (in the GXZ plane), Ey along GY, Ez at 30° to GZ, towards GX. (0,180,0) sets Ex along -GX, Ey along GY, Ez along -GZ. (90,90,0) sets Ex along -GZ, Ey along -GX, Ez along GY. (90,90,90) sets Ex along -GX, Ey along GZ, Ez along GY. End Direction Results If the end orientation Exyz is defined, then OrcaFlex offers various results relative to those axes. 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). The angles offered are as follows: 170 w • • • • The "Ez-Angle" is the angle between V and the Ez-direction (i.e. axial direction). measures how far V is away from the end fitting axial direction. This The "Ezx-Angle" is the angle from Ez to the projection of V onto the Ezx plane (measured positive from Ez towards Ex). This is the angle V makes with Ez when viewing the zx-plane. The "Ezy-Angle" is the angle from Ez to the projection of V onto the Ezy plane (measured positive from Ez towards Ey). This is the angle V makes with Ez when viewing the zy-plane. 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). This is the angle V makes with Ex when viewing the xy-plane. 6.11.5 Line Local Orientation At any point P, the line orientation is defined by its local axes Pxyz. Pz is in the axial direction, towards end B, and is reported by the azimuth and declination angles. Px and Py are normal to the line axis. At the ends of the line, these local axes are referred to as the end axes Exyz, and their directions are specified by the end orientation angles on the line data form. 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. 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. In more detail, 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, using the no-twist assumption at each step to calculate the next node's local orientation. Note that this method is not used if end A is free (or if it is released), so currently for such lines torsion must be included if the line has non-isotropic properties, in order to properly calculate the local orientation. 6.11.6 Morison's Equation OrcaFlex calculates hydrodynamic loads on lines, 3D buoys and 6D buoys using an extended form of Morison's Equation. See Morison, O'Brien, Johnson and Schaaf. Morison’s equation was originally formulated for calculating the wave loads on fixed vertical cylinders. There are two force components, one related to water particle acceleration (the ‘inertia’ force) and one related to water particle velocity (the ‘drag’ force). For moving objects, the same principle is applied, but the force equation is modified to take account of the movement of the body. The extended form of Morison’s equation used in OrcaFlex is: Fw = (∆.aw + Ca.∆.ar) + ½.ρ.Vr|Vr|.CD.A where Fw is the wave force ∆ 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 171 w 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, the other is the drag force. The drag force is familiar to most engineers, but the inertia force can cause confusion. The inertia force consists of two parts, one proportional to fluid acceleration relative to earth (the ‘Froude-Krylov’ component), and one proportional to fluid acceleration relative to the body (the ‘added mass’ component). To understand the Froude-Krylov component, imagine the body being removed and replaced with an equivalent volume of water. This water would have mass ∆ and be undergoing an acceleration aw. It must therefore be experiencing a force ∆.aw. Now remove the water and put the body back: the same force must now act on 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, undisturbed by the presence of the body. (Note the parallel with Archimedes’ Principle: in still water, the integral of the fluid pressure over the wetted surface must exactly balance the weight of the water displaced by the body.) The ‘added mass’ component is due to the distortion of the fluid flow by the presence of the body. A simple way to understand it is to consider a body accelerating through a stationary fluid. The force required to sustain the acceleration may be shown to be proportional to the body acceleration and can be written: F = (m + Ca.∆).a where F is the total force on the body m is the mass of the body (Ca.∆) is a constant related to the shape of the body and its displacement a is the acceleration of the body. Another way of looking at the problem is in terms of energy. The total energy required to accelerate a body in a stationary fluid is the sum of the kinetic energy of the body itself, and the kinetic energy of the flow field about the body. These energies correspond to the terms (m.a) and Ca.∆.a respectively. Trapped Water The term (Ca.∆) has the dimensions of mass and has become known as the ‘added mass’. This is an unfortunate name which has caused much confusion over the years. It should not be viewed as a body of fluid trapped by and moving with the body. Some bodies are so shaped that this does occur, but this trapped water is a completely different matter. Trapped water occurs when the body contains a closed flooded space, or where a space is sufficiently closely surrounded to prevent free flow in and out. Trapped water should be treated as part of the body: the mass of the trapped water should be included in the body mass, and its volume should be included in the body volume. For a more complete description of Morison’s equation and a detailed derivation of the added mass component see Barltrop and Adams, 1991 and Faltinsen, 1990. 172 w 6.11.7 Treatment of Compression A segment is said to experience compression if the effective tension is negative. OrcaFlex has two modes for handling this, depending on the setting of the Limit Compression data item on the line types form. Limit Compression: No The segment is treated as a strut which can support unlimited elastic compression. This is the preferred model except where the bend stiffness is insignificant. Limit Compression: Yes The segment is treated as an elastic Euler strut; the compression is limited to the segment Euler load value for the segment π²EI/L0², where EI is the bending stiffness of the pipe and L0 is segment unstretched length. This correctly models a chain or very flexible rope, which can support little or no compression. In the case of a chain, the bending stiffness is set to zero, and the segment Euler load limit is also zero. The segment Euler load provides a check on the ability of the model to represent compressive loads and the deformations which result. Compression causes the line to deform laterally, the deformation being controlled by bending. Given adequate segmentation, OrcaFlex will correctly represent this deformation. If compression exceeds the segment Euler load of an individual segment, this indicates that the wavelength of deformation is shorter than can be represented by the chosen segmentation and the results may be unreliable. The model should be re-run with shorter segments in the affected area. The segment Euler load is shown on tension range graphs and infringement warnings are given on the result form and in the statistics tables. For more details see Modelling Compression in Flexibles and "Limit Compression" Switch. 6.11.8 Contents Flow Effects Introduction Contents flow effects are normally neglected when modelling pipes in OrcaFlex. However for pipes carrying high contents density at rapid flow rates the flow effects can be significant. The published literature show that there are three extra forces introduced by contents flow - a centrifugal force, a Coriolis force and a flow friction force. OrcaFlex includes the facility to specify the contents mass flow rate on the line data form. If this is non-zero then the resulting centrifugal and Coriolis effects are included. Note that the flow friction effects are not included in OrcaFlex. Note that these flow effects apply only to the dynamic simulation, not to any of the static calculations performed by the program. The mass flow rate is increased smoothly through the build-up period of the simulation, using the same algorithm employed for 'ramping' wave height. Since the duration of the build-up period is under the user's control, this feature can be used to determine the transient effect of different start-up rates. Theory This section documents the theory behind the modelling of the centrifugal and Coriolis forces in OrcaFlex. This theory is technical and specific to the way pipes are modelled in OrcaFlex. 173 w Notation ρ r a l p v u ω dx/dt x' contents density mass flow rate internal cross-sectional area segment length position of node relative to fixed axes velocity of node relative to fixed axes unit vector in downstream direction of line angular velocity of moving frame relative to fixed frame rate of change of any variable x relative to fixed axes rate of change of any variable x relative to moving axes The contents mass per unit length is aρ so the flow velocity is r/(aρ). Centrifugal force on a node due to flow through a node First consider a node with flow arriving from one direction, uin say, and leaving in another direction, uout. For a mid-node uin and uout are simply the unit vectors in the directions of the segments before and after the node. For the first node uin is the end direction - this is taken to be the same as uout if the end is free and otherwise is taken to be the no-moment direction. Similar treatment is applied to uout at the last node. Similarly let ain and aout denote the internal cross sectional areas on the input side and output side, respectively. ain for the first node, and aout for the last node, are taken to be the same as the internal cross section area of the end segment - i.e. we assume no change in internal cross sectional area at the line ends. Then contents flow into the node at mass flow rate r and velocity r/(ainρ)uin so the rate of input of momentum is r²/(ainρ)uin. The output mass flow rate is also r but the output velocity is r/(aoutρ)uout so the rate of output of momentum is r²/(aoutρ)uout. 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, i.e. r²/(aoutρ)uout - r²/(ainρ)uin The resulting centrifugal force on the node must be equal and opposite to this, so Centrifugal Force on Node = (r²/ρ)( uin / ain - uout / aout ). We can check this result in two ways. Firstly, it has the correct units: Units = [(M/T)² ] / [(M/L³).(L²)] = ML/T² = F. Secondly, it matches the centrifugal term included in equation 10 - see Gregory & Paidoussis, 1996. Coriolis force due to movement of a segment Now consider a segment between two nodes n1 and n2 and consider two frames of reference - a fixed global frame and a moving local frame whose origin moves with node n1 and whose z-axis always points in direction u = unit vector from n1 towards n2. Consider the contents of a segment. Its velocity relative to the moving axes is 174 w p' = (r/aρ)u So its velocity relative to the fixed axes is v1 + dp/dt = v1 + p' + ω x p Therefore its acceleration relative to fixed axes is d( v1 + p' + ω x p) )/dt = (v1 + p' + ω x p)' + ω x (v1 + p' + ω x p) = 0 + 0 + ω' x p + ω x p' + ω x v1 + ω x p' + ω x (ω x p) = ω' x p + 2ω x p' + ω x v1 + ω x (ω x p) and of these terms the only new one, i.e. that is dependent on the rate of flow p' rather than p, is the term 2ω x p' = 2ω x (r/aρ)u. When multiplied by the mass of contents in the segment, laρ, this gives the Coriolis force on the segment, i.e. 2lr (ω x u). But ω is given by ω = u x (v2 - v1) / l so the Coriolis force is given by 2r (u x (v2 - v1)) x u = 2r ( (u.u)(v2 - v1) - (u.(v2 - v1))u ) = 2r ( (v2 - v1) - (u-direction component of (v2 - v1)) ) = 2r . (component of (v2 - v1)) normal to u). We then apportion this total Coriolis force on the segment into two equal parts - i.e. a force of r . (component of (v2 - v1)) normal to u) on each of the two nodes at the ends of the segment. 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. The above result has the correct units: Units = (M/T) . (L/T) = ML/T² = F. and it agrees with the Coriolis term included in equation 10 - see Gregory & Paidoussis, 1996. Other references: Paidoussis M P, 1970 Paidoussis M P & Deksnis E B, 1970. Paidoussis M P & Lathier B E, 1976. 6.11.9 Line Pressure Effects OrcaFlex reports two different types of tension - the effective tension (Te) and the wall tension (Tw). These two tensions are related by the formula Tw = C1.(Te + Pi.Ai - Po.Ao) where 175 w • Pi = internal pressure. Pi at end A is the Contents Pressure specified in the data and it is assumed to remain constant during the simulation. Internal pressure elsewhere in the line is calculated from this value by allowing for the static pressure head due to the current height difference between the point and end A. Po = external (i.e. surrounding fluid) pressure. Po is assumed to be zero at and above the mean water level. Below there it is calculated allowing for the static pressure head due to the current height difference between the point and the mean water level. Ai, Ao = internal and external stress cross section areas, respectively. Ai = π.StressID²/4 and Ao = π.StressOD²/4, where StressID, StressOD are the stress diameters. C1 = tensile stress loading factor. By default this equals 1. • • • Explanation of Wall Tension Formula To understand this formula and the difference between effective tension and wall tension, consider the forces acting axially at the mid-point of a segment. The nodes either side represent a length of pipe plus its contents. More importantly, 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. The diagram below illustrates this and shows the tension and pressure forces present; the equation above is simply the force balance equation for this diagram. Te Tw Pi.Ai Po.Ao Te Pi.Ai Po.Ao Tw node n segment mid-point node n+1 Figure: Tension and Pressure forces This is the standard method of handling internal and external pressure when modelling pipes. The effect is that the spring tension calculated by OrcaFlex is the effective tension, rather than the wall tension. OrcaFlex then derives the wall tension, using the above equation, and offers both effective and wall tension in the results. This method of modelling lines introduces a small error, since the axial stiffness specified by the user is being stretched by the effective tension Te, rather than by the wall tension Tw. But if the axial stiffness is high then the resulting change in extension is negligible, and this is so for most practical applications. To reduce this error further, we recommend that the unstretched length you specify for the line is the unstretched length at normal working pressure. Notes: Both effective tension and wall tension are relevant to the question of pipe buckling. For buckling of the pipe as an Euler strut, effective tension is the governing parameter - when it is negative the strut is in compression. On the other hand, local buckling of the pipe wall is determined by wall tension. (Note that OrcaFlex does not model local buckling, which depends critically on details of the pipe construction and is therefore beyond the scope of the program.) For cables, umbilicals and ropes, the internal pressure term PiAi does not apply. However, the external pressure term PoAo is still applicable, and the actual tension in the cable is the wall tension as defined above. 176 w For chains, which are inherently discontinuous, the pressure terms do not apply and the effective tension is the true tension in the chain. 6.11.10 Pipe Stress Calculation OrcaFlex provides stress results that apply only to simple pipes. More precisely, 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. It also assumes that the cylinder is made of a uniform material. The pipe stress results are therefore only valid for things like steel or titanium pipes - they do not apply to composite structure flexible pipes. Note that the fatigue analysis uses the pipe stresses, so these restrictions also apply to the fatigue analysis. Consider a cross-section through a mid-segment point, as shown in the following diagram. The diagram shows the frame of reference used for the cross-section, which has origin O is at the pipe centreline, 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). y R P C r End A Stress ID y (Theta=90) Theta x (Theta=0) O z Stress OD O Side View Cross-Section Figure: Frame of Reference for Stress Calculation The OrcaFlex simulation calculates the following loads that are acting at the cross-section: • • • • • • • • • • Internal and external pressures, Pi and Po respectively. Effective tension and resulting wall tension. These are both vectors in the z-direction, with magnitudes Te and Tw respectively. Bend Moment, which is a vector in the xy-plane, with magnitude M and components Mx and My in the Ox and Oy directions, respectively. Shear force, which is also a vector in the xy-plane, with magnitude S and components Sx and Sy in the Ox and Oy directions, respectively. Torque, which is a vector in the z-direction with magnitude τ. StressOD and StressID = stress diameters, as specified on the line types form. A = cross-sectional stress area = (π/4).(StressOD² - StressID²) Ixy = 2nd moment of stress area about Ox (or Oy) = (π/64).(StressOD^4-StressID^4) Iz = 2nd moment of stress area about Oz = 2.Ixy C1, C2, C3, C4 = stress loading factors (C1 = tensile, C2 = bending, C3 = shear, C4 = torsional), as specified on the line types form. 177 In addition we define the following terminology: w The stress generated by the above loads varies across the cross-section. Consider the point P in the cross-section shown as a black dot in the diagram, which can be identified by its polar coordinates (r, θ). At P, we define a local set of axes (R,C,Z) where R is radially outwards, C is in the circumferential direction (positive in the direction of Theta increasing) and Z is parallel to Oz. With respect to these axes, the stress at P is a symmetric 3x3 matrix of stress components (see Pipe Stress Matrix). OrcaFlex calculates this matrix and then derives stress results from it. 6.11.11 Pipe Stress Matrix The pipe matrix at point P (see Pipe Stress Calculation) can be written as: RRStress RCStress RZStress RCStress CCStress CZStress RZStress CZStress ZZStress For terminology see Pipe Stress These stress components are calculated as follows. Calculation. Diagonal Terms The 3 diagonal entries of the stress matrix, RRStress, CCStress and ZZStress, are the radial, circumferential (or hoop) and axial (or longitudinal) stresses, respectively. Radial and Hoop Stresses RRStress and CCStress are due to the internal and external pressure. They are calculated using Lame's equation for a thick-walled cylinder whose internal and external diameters are StressID and StressOD, as specified on the line types form. This gives: RRStress = Radial Stress = a - b/r² CCStress = Hoop Stress = a + b/r² where a and b are the values that satisfy a - b / (StressID/2)² = -Pi a + b / (StressOD/2)² = -Po. Notes: StressID and StressOD are by default equal to the ID and OD specified on the line type form. However, they can be set to be different to ID and OD. In this case the above calculation is equivalent to assuming that the material in between ID and StressID, and between StressOD and OD, is transparent to pressure. The internal pressure therefore applies right through to the StressID and the external pressure applies right through to StressOD. If StressID is zero, then OrcaFlex assumes that external pressure applies throughout the structure - i.e. that RRStress = CCStress = -Po. Axial Stress ZZStress is the axial stress and is given by: ZZStress = 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. The wall tension is assumed to be uniformly distributed across the stress area, so its contribution is given by: 178 w Direct Tensile Stress = Tw / A The bend moment contribution varies across the cross-section and is given by: Bending Stress = (C2.Mx.r.sinθ - C2.My.r.cosθ) / Ixy Off-Diagonal Terms The 6 off-diagonal terms are the shear stresses, but there are in fact only 3 independent terms, since the matrix is symmetric. They are given by: RCStress = 0 RZStress = (C2.Sx.cosθ + C2.Sy.sinθ) / A CZStress = C3.τ.r / Iz + (C2.Sy.cosθ - C2.Sx.sinθ) / A The contribution C3.τ.r / Iz in the above equation is the shear stress contribution due to torque. If torsion is not included in the model, then it is zero. The other contributions are both due to the shear force, which is assumed to be uniformly distributed across the stress area. Finally, for two useful references on this subject, see Sparks (1980) and Sparks (1983). 6.11.12 Hydrodynamic Loads Drag The drag forces applied to a line are calculated using the "cross flow" principle. That is, the fluid velocity relative to the line is split into its components Vn normal to he line axis, and Vz parallel to the line axis. The components of drag force normal to the line axis are then based on Vn, and its x and y-components Vx, Vy. The component of drag force parallel to the line axis is based on Vz. The drag force formulae use drag coefficients, Cdx, Cdy and Cdz (specified on the line type data form) and the drag areas appropriate to each direction. For the directions normal to the line axis (x and y) the drag area is taken to be the projected area D.L where D is the outside diameter and L is the length of line represented by the node. For the axial direction (z) the drag area is taken to be the skin surface area π.D.L. If Cdx or Cdy vary with Reynolds number then OrcaFlex calculates the Reynolds number using the normal component of relative velocity, Vn. This Reynolds number is then used to find Cdx or Cdy (or both) using the specified variable data table. OrcaFlex uses linear interpolation for Reynolds numbers between those specified in the table, and truncation for Reynolds numbers beyond those specified in the table. There is a choice of the following three possible drag formulations for the drag force components (Fx, Fy, Fz) in the local line directions. The formulations differ in how the drag force components vary with the incidence angle φ between the flow and the line axial direction. The formulations are reviewed in Casarella and Parsons. In the formulae below, ρ is the sea water density and PW is the proportion wet. Standard Formulation Fx = PW.( ½.ρ.(D.L).Cdx.Vx.|Vn| ) Fy = PW.( ½.ρ.(D.L).Cdy.Vy.|Vn| ) Fz = PW.( ½.ρ.(πD.L).Cdz.Vz.|Vz| ) 179 w This formulation is the most commonly-used and was the formulation used by versions of OrcaFlex before a choice of formulation was introduced. It has been proposed or used by various authors, including Richtmyer, Reber and Wilson. It is appropriate for general flow conditions. Pode Formulation Fx = same as standard formula for Fx, above Fy = same as standard formula for Fy, above Fz = +/- PW.( ½.ρ.(πD.L).Cdz.|V|² ) where the sign of Fz, i.e. whether it is towards end A of the line or towards end B, is the same as the axial component of the relative flow vector. This formulation is preferred by some analysts for systems with near-tangential flow. Warning: The Pode formula for Fz is discontinuous at φ = 90, since then the axial component of the flow vector is zero and so the direction of Fz is undefined. In this case OrcaFlex sets Fz to zero. Eames Formulation for bare cables Fx = PW.( ½.ρ.(D.L).Cdx.Vx.|Vn| + ½.ρ.(πD.L).Cdz.Vx.(|V| - |Vn|) ) Fy = PW.( ½.ρ.(D.L).Cdy.Vy.|Vn| + ½.ρ.(πD.L).Cdz.Vy.(|V| - |Vn|) ) Fz = PW.( ½.ρ.(πD.L).Cdz.Vz.|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. Consider the case where the line is axially symmetric, i.e. Cdx = Cdy = Cdn say, and let φ be the incidence angle between the flow vector V and the line axis. Then Vz = V.cosφ and Vn = V.sinφ. Also, let: R = PW.( ½.ρ.(D.L).Cdn.|V|² ) µ = π.Cdz/Cdn. Fn = the normal component of the drag force. Then the formulations can be expressed as follows. Standard: Pode: Eames: |Fn| = R.sin²φ |Fn| = R.sin²φ |Fn| = R.( (1-µ).sin²φ + µ.sinφ ) |Fz| = R.µ.cos²φ |Fz| = R.µ |Fz| = R.µ.cosφ Added Mass The added mass effects on a line are calculated separately for the local x, y and z-directions. For each of these directions, the line is subject to two added mass effects: 1. Its effective mass is increased by Ca.(Displaced Mass) 180 w where Displaced Mass is the mass of the fluid displaced (taking into account the proportion wet) and Ca is the added mass coefficient specified for that direction. As a result, if the line accelerates then it experiences an extra inertial force (due to added mass) given by -Ca.(Displaced Mass).AL where AL is the component (in that direction) of the acceleration of the line (relative to the earth). 2. If the fluid is accelerating then the line experiences a fluid acceleration force given by (1+Ca).(Displaced Mass).AF where AF is the component (in that direction) of the acceleration of the fluid (relative to the earth). Note: The fluid acceleration force is sometimes written as Cm.(Displaced Mass).AF where Cm = 1 + Ca. It can also be split into two terms: (Displaced Mass).AF + Ca.(Displaced Mass).AF where the first term is called the Froude Krylov force and the second term is called the added mass force. 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. 6.11.13 Drag Chains A drag chain is an attachment to a line that applies a force to the node to which it is attached. The force consists of the tension in the drag chain and so is in the direction in which the chain is hanging. 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. This is now described in more detail. θ A Connection to Line Vn V Va α =θ-90 Drag Chain Wn W Wa 180-θ Figure: Drag Chain 181 w Consider the drag chain shown in the above diagram. 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). Then the incidence angle α between the horizontal relative velocity vector V and the drag chain is α = θ - 90 and the normal and axial drag forces are given by: Fn = normal drag force = 0.5.ρ.L.D.Cdn(α).Vn.|Vn| Fa = axial drag force = 0.5.ρ.π.L.D.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), 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, so we assume that the drag chain is always in equilibrium under the action of 3 forces: • • • the chain's wet weight (W) the fluid drag on the chain the tension being applied by the line at the top of the chain. Because the tensile force being applied by the line is axial to the chain, the components of wet weight and drag normal to the chain must balance. In other words, 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. The remaining net force on the chain in the axial direction, Fa, is then applied to the line. 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. Drag Chain Seabed Interaction Drag chains, in OrcaFlex, interact with the seabed in a fairly simplistic way that is designed to achieve the following two primary effects of seabed interaction: • • Firstly, that as the chain is lowered down onto the seabed, the wet weight of the chain is steadily reduced as the chain becomes supported by the seabed. Secondly, that if the chain is dragged across the seabed then an opposing friction force µR is generated, where µ is the friction coefficient and R is the seabed reaction. At any given time, OrcaFlex first calculates how much of the drag chain would be supported by the seabed if the chain hung straight vertically down from the line. The drag chain is then The seabed interaction model used is as follows: • 182 w considered as being made up of two parts - the supported part and the remaining hanging part. • • The hanging part of the chain is then analysed as described above. The supported part of the chain is modelled as if it lying on the seabed directly beneath the node to which the chain is attached. As the node moves laterally, the supported chain also moves laterally (but below the node) and so generates a friction force that is then applied to the node. Note that the division of the drag chain into a hanging length and a supported length is done before the hanging length is analysed, and so is done with the chain vertical. 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. This is an inaccuracy that cannot easily be avoided at the moment. 6.11.14 Line End Conditions Except for Free Ends, the connection at the line end is modelled as an isotropic 'ball-joint' with a rotational stiffness and a preferred 'no-moment' direction. A rotational stiffness of zero simulates a freely rotating end, and a value of Infinity simulates a clamped end. The inclusion of end stiffness allows the program to calculate the curvature and bending moment at the termination. If the curvature is large, the calculated value is accurate only if sufficiently short segments have been used to model the line near its end. OrcaFlex reports a value for End Force and End Ez-Angle. These are the magnitude of the end force, and the magnitude of the angle between the end force vector and the no-moment direction. Vessel motion is automatically accounted for. The end force and angle values provide the basis for the design of end fittings such as bend stiffeners. See Modelling Line Ends. 6.11.15 Line Interaction with the Sea Surface OrcaFlex Lines are subdivided into segments, and the various forces are attributed to nodes at each end. For a partially submerged segment, the hydrostatic and hydrodynamic forces are proportioned depending on how much of the segment is submerged - the Proportion Wet. (The Proportion Wet is available as a line result variable.) For a segment whose axis is normal to the surface, the Proportion Wet could be calculated from the intersection of the segment centreline axis with the free surface. However, this simple approach breaks down when the segment is tangent to the surface. For this reason, OrcaFlex uses a simple but effective modification of this concept. Instead of using the centreline axis, we use the diagonal line joining the highest point on the segment circumference, at the 'dry' end, with the lowest point at the 'wet' end; see the diagonal line in the figure below. As the segment passes through the tangent position, the diagonal line switches corners but the proportion wet varies continuously. The intersection of the diagonal line with the surface continues to give the appropriate Proportion Wet result, and the hydrostatic and dynamic forces are attributed to the appropriate node. 183 w 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, containment booms and wave suppression systems. However please note the following points when modelling such systems: • A consequence of this model is that a hose floats in still water as a wall-sided body; 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 cases of practical dynamics, this simplification is of minor importance, 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, or just awash. When modelling floating hoses, it is important to have enough segments to model the local curvature. If your hose is flexible, and the waves are short, then you will need at least ten and preferably twenty segments per wave to model the curvature properly. However a stiff hose tends to bridge the wave troughs, and fewer segments are required. The program uses constant drag and added mass coefficients for the floating hose, and the user has to select appropriate values based on the average immersion depth. Unfortunately the literature is of limited help - if you know of any good data source, we would be very pleased to hear of it. • • 6.11.16 Seabed Touchdown and Friction Seabed Touchdown The Catenary algorithm for calculating the static position of a line has facilities for including seabed touchdown, but for technical reasons it has the following limitations: • • Seabed touchdown can only be included at end B of the line, not at end A. Therefore, if you want touchdown then you should arrange it to be at end B. Touchdown is only included if end B is anchored exactly on, or else below, the seabed. If end B is above the seabed, even if only by a small amount, then no touchdown will be modelled and the line may hang below the seabed. This will be corrected when the simulation starts, since the nodes below the seabed will be pushed back up by the seabed reaction forces. Alternatively, you should use the Full statics option, which can handle this case. If end B is below the seabed, then the Catenary algorithm models touchdown by assuming that the line 'levels out' at the level of end B. This will result in part of the line being below the seabed, but again this will be corrected when the simulation starts, since the nodes below the seabed will be pushed back up by the seabed reaction forces. • 184 w Seabed Friction OrcaFlex provides a simple friction model that can give an approximate representation of seabed interaction. 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, accumulation of soil in front of the line, etc. To model seabed interaction accurately would require much more information about the soil structure and would involve modelling the soil itself. This is beyond the scope of OrcaFlex. Statics Friction can be included in the static analysis only if the Statics Method specified is Catenary or if Full Statics is used. There is a problem in deriving a static position for a line with seabed friction present, since in general a range of static solutions exist, depending on how the line was originally laid and on its subsequent loading history. The particular approach we have chosen in OrcaFlex is to apply friction so that the resulting static position is as near as possible to an assumed "originally laid" position. This is done by applying, to each node in contact with the seabed, a friction force with: • • • Magnitude less than or equal to µR, where µ is the friction coefficient and R is the normal component of the reaction force. Direction chosen so that the resulting static position of the node is as near as possible to the "originally laid" position. If the Statics Type is Prescribed, then the originally laid position is taken to be the position given by the Prescribed track, allowing for the specified Pre-Tension. Otherwise, the line is assumed to have originally been laid, with the specified Pre-Tension, leading away from end B in the Lay Azimuth direction. See Line Data:Statics. Dynamics Seabed friction is modelled as Coulomb friction in the seabed plane. If a node is stationary and in contact with the seabed then the friction force opposes the in-plane component, Fi, of the resultant force on the node. The value of the friction force is set equal to Fi or µ.R, whichever is the less, where R is the seabed reaction force on the node and µ is the friction coefficient in the direction Fi. If the node is sliding across the seabed, the friction force has magnitude µ.R, where µ is the friction coefficient in the direction of sliding. The direction of the applied friction force depends on the specified friction coefficients and bias power (see Friction Coefficients and Bias Power). If the normal and axial friction coefficients are equal then the friction force is applied directly opposing the direction of sliding. But if the normal and axial friction coefficients differ then the bias power can be used to bias the friction direction towards the direction of larger coefficient. For example if µn > µa then the larger the bias power the more the friction direction is turned towards opposing sliding in the normal direction. Note: Friction Model We now give the friction model in detail. Consider one node of a line that is lying on the sea bed. Denoting vectors by underline, we let: This friction direction bias is not (yet) available with profile seabeds. µn, µa = normal and axial friction coefficients, as specified on the line types form 185 w C = friction bias power, as specified on the line types form R = magnitude of the sea bed reaction force D = unit vector in the plane of the sea bed, in the direction of motion Dn, Da = the vector components of D in the normal and axial directions F = magnitude of the vector (µn.Dn + µa.Da).R V = - { (µn^C).Dn + (µa^C).Da } Then for a moving node the friction force applied by OrcaFlex has magnitude F and is applied in the direction of vector V. For a stationary node the friction force has magnitude up to F and is applied in the direction directly opposing the force attempting to move the node. This model has the following characteristics: • • • For pure axial motion the friction force is µaR axially and for pure lateral motion it is µnR laterally, as required. As D varies from the axial to the normal direction, the friction force varies smoothly and monotonically from µaR to µnR. For a moving node the friction direction (given by the vector V) varies from axial when D is axial, to normal when D is normal, but in between its direction is "biased" towards the direction of the larger friction coefficient. For moving nodes, the model described above "biases" the direction of the friction force towards the direction of the larger friction coefficient. So, for example, if µn > µa (and C>0) then motion at an angle to the line axis is resisted by an opposing force at a larger angle to the line axis, tending to make the line move axially, as expected. • The amount of direction bias for a moving node depends on the ratio (µn/µa)^C, so the friction bias power C provides a way of controlling the amount of direction bias in the model. Note that C only affects the direction in which friction is applied for moving nodes. It has no effect on the magnitude of the friction force, nor on its direction for a stationary node. The direction bias in this model has the following properties: • • • If µn = µa then there is no direction bias and a standard isotropic friction model results. In this case C has no effect. If C=0 then again there is no direction bias - the friction force on a moving node then simply opposes the direction of motion. If µn > µa and C>0 then C controls the amount of direction bias. Increasing C increases the direction bias and hence increases the tendency of the line to slide axially. 6.11.17 Interaction with Seabed and Shapes Nodes are also subjected to reaction forces from the seabed and any Shapes with which they come into contact, given by: Reaction = K A d where K is the Stiffness of the seabed or shape d is the depth of penetration A is the contact area, which is taken to be Outside Diameter multiplied by the length of line represented by the node. 186 w In addition, nodes experience a damping force. For details see Seabed Theory and Shapes Theory. 6.11.18 Clashing OrcaFlex includes the capability to model clashing between lines. To include clash modelling between two lines, you must set Clash Check to "Yes" and set the Contact Stiffness to a nonzero value, for both lines. You can also specify the Contact Damping value. The facility to suppress clash modelling (by setting Clash Check to "No") has been included because the clashing algorithm is time consuming. It is therefore best to suppress clash modelling on all sections that will never clash with other lines, or if you are not interested in the effects of clashing. OrcaFlex assumes constant spring stiffness and damping values, and neglects friction. The force algorithm is described below. It pushes lines apart again if they try to pass through another, and it permits lines to separate again after contact. Multiple contact points along the line length are allowed for, but clashes of one part of a line with another part of the same line are not modelled at present. 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. This is a developing area and we would appreciate feedback from users. The following notes expand on the way the calculations are carried out by the software and give our suggestions on interpretation. Calculating the Clash Force OrcaFlex checks for clashing between each line segment and every segment in every other line in the OrcaFlex model (providing check checking is enabled and the contact stiffness is nonzero, for both segments involved). Note that OrcaFlex does not check for clashing between two segments of the same line, so it does not model clash contact of a line with itself. The clash check between segment S1 (on line L1) and segment S2 (on a different line L2) is done as follows. Let the radii of the two segments be r1 and r2 (as defined by the line type outer diameter). First OrcaFlex calculates the shortest separation distance, d, between the centrelines of the two segments. If d >= (r1 + r2) then the lines are not in contact and no contact force is applied. If d < (r1 + r2) then the lines are in contact. In this case OrcaFlex applies equal and opposite clash contact forces to the 2 segments to push them apart, as follows. Let p1 and p2 be the two points of closest proximity - i.e. p1 is on the centreline of segment S1 and p2 is on the centreline of segment S2, and these are the two points that are minimum distance d apart. Also, let u be the unit vector in the direction from p1 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 S1, 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 k1 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 187 w damping force is applied. If v>0 then the penetration is increasing and the damping term is then given by: Damping Term = c.v 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 Clashing 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 clash. Impact In the case of a violent impact, the contact forces arrest the relative movement of the lines over a very short time interval. Kinetic energy is extracted from the system and transformed into strain energy at the point of contact, with some energy loss to damping. This sort of clash is probably best quantified in terms of the clash impulse rather than the clash force. Numerical experiments show that the clash impulse is relatively insensitive to changes in contact stiffness or model discretisation. Since the line contact formulation is based on a linear spring, then if the damping is low the energy of impact can be estimated from the peak clash force: Estimated Contact Energy = Fmax²/(2.k) where Fmax is the peak clash force and k is the combined contact stiffness. Note that in the case of an exactly symmetric collision with a line node, the reported clash force will be shared between the two adjacent segments. In this case, the energy should be calculated using the clash force reported for the other line involved in the collision. Low Speed Contact Where one line drifts quite slowly against another as a result of weight or drag forces, then the energy of impact is negligible, and the clash force at the point of contact is the best measure of what is happening, and will be insensitive to changes in modelling. 188 w 6.12 VESSEL THEORY 6.12.1 RAOs and Phases Vessel motions in waves are defined by Response Amplitude Operators (RAOs). Each RAO consists of a pair of numbers that define the vessel response, for one particular degree of freedom, to one particular wave direction and period. The two numbers are an amplitude, which relates the amplitude of the vessel motion to the amplitude of the wave, and a phase, which defines the timing of the vessel motion relative to the wave. Example: A surge RAO of 0.5 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; a pitch RAO of 0.5° per metre in the same wave means that the vessel pitches from -1° to + 1°. The vessel has 6 degrees of freedom: 3 translations (surge, sway, heave) and 3 rotations (roll, pitch, yaw), so the RAO data consist of 6 amplitude+phase pairs for each wave period and direction. The RAO amplitude and phase vary for different types of vessel, and for a given vessel type they vary with draught, wave direction, forward speed and wave period (or frequency). It is important to obtain accurate values for the RAO amplitude and phase if the dynamics of the system are to be correctly modelled. RAOs can be obtained either from model tests or from specialist computer programs. 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 Import RAOs from Text Files). There are many different conventions for defining RAOs. 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. The only safe course is to obtain a complete description of the system used for the data in each case. The Orcina convention is to use the amplitude of response (in length units for surge, sway, heave, in degrees for roll, pitch, yaw) per unit wave amplitude, 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, the phase origin being at the RAO origin). Mathematically, this is given by: x = R.a.cos (ωt - φ) where x is the vessel displacement (in length units for surge, sway, heave, in degrees for roll, pitch, yaw) a, ω are wave amplitude (in length units) and frequency (in radians/seconds) t is time (in seconds) R, φ are the RAO amplitude and phase. However, OrcaFlex can accept RAO data using a wide range of different conventions - see Conventions Data - so you can input your RAO data in its original form and simply tell OrcaFlex what conventions apply to that data. In addition to the actual RAO data you therefore also need to know: • The coordinates of the RAO origin and of the phase origin. 189 w • The system used to define wave direction. In OrcaFlex 0° means waves approaching the vessel from astern and 90° means waves coming from the starboard side, but if a different convention applies to your data then you must allow for this when entering the data. The coordinate system used to define vessel motions and, in particular, which direction is positive (e.g. is surge positive forward or aft? is heave positive up or down? is pitch positive bow up or bow down?). OrcaFlex allows the RAO input data to use a wide range of systems, but 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 • • Whether the rotational RAO data are in degrees (or radians) of rotation per metre (or foot) of wave height, or in degrees (radians) per degree (radian) of wave slope or wave steepness. The reference time for phase angles, and the reporting convention used (e.g. whether phases are reported as lags or leads). Again, OrcaFlex allows a range of options. • 6.12.2 RAO Quality Checks RAOs (particularly the phases) are difficult, abstract concepts for which few users have a natural, intuitive understanding. This makes them difficult to check, but it also makes it all the more important to check them, since the same difficulty applies to the people who derived the data in the first place. RAOs and phases, even from the most respected sources, are notoriously error-prone! Fortunately, there are a few natural points of reference where we know what must be going on. The most obvious and useful ones are response at very short and very long wave periods. In very short period waves, the vessel inertia suppresses response, so the expected RAO amplitudes are zero (and phase is then irrelevant). 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. The tables below give the expected RAO amplitudes and phases (using the Orcina standard conventions) for a freefloating vessel in very long waves. 190 w Expected RAOs for a vessel in very long waves From ahead (180º) Amp. Surge Sway 1 0 -90º ~ 0º ~ +90º ~ From astern (0º) 1 0 1 0 1 0 +90º ~ 0º ~ -90º ~ From port (270º) 0 1 1 1 0 0 ~ -90º 0º -90º ~ ~ From starboard (90º) Phase ~ +90º 0º +90º ~ ~ 0 1 1 1 0 0 Phase Amp. Phase Amp. Phase Amp. Heave 1 Roll Pitch Yaw 0 1 0 Towards direction θ Amp. Surge Sway | cos(θ) | | sin(θ) | Phase +90º if cos(θ)>0 -90º if cos(θ)<0 +90º if sin(θ)>0 -90º if sin(θ)<0 0 +90º if sin(θ)>0 -90º if sin(θ)<0 -90º if cos(θ)>0 +90 if cos(θ)<0 180º if sin(2θ)>0 0º if sin(2θ)<0 Heave 1 Roll Pitch Yaw | sin(θ) | | cos(θ) | | ½ sin(2θ) | Warning: The expected yaw RAOs given in the above table only apply to slender ships. Notes: In these tables, the translational amplitudes are non-dimensionalised against wave amplitude and the rotational amplitudes are non-dimensionalised against maximum wave slope. The phases given are lags relative to the wave crest. I.e. +90 means that the maximum positive motion occurs 90 degrees after the wave crest passes the vessel (where positive surge is forward, positive sway is to port, positive heave is up, positive roll is starboard down, positive pitch is bow down and positive yaw is bow to port. When the amplitude is zero the phase value is irrelevant; this is indicated in the tables by '~' . You can check RAOs in two ways. First, OrcaFlex provides RAO graphs that help spot errors see Checking RAOs. Second, you can run quick simulations with only the vessel in the model and then check that the motions you see are sensible. Consider a ship in waves coming from ahead. Set up a simple OrcaFlex model with the vessel only - nothing else - and run a short simulation (say 10 seconds build up plus 2 wave periods). Use a large wave height (20m) and long time step - say 0.05 seconds for both inner and outer 191 w time steps. 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 best view direction is horizontal, normal to the direction of travel of the waves. With the waves coming from the right on screen, then in the wave crest the ship should be at maximum heave up and moving to the left, and vice versa in the trough. At the point of maximum wave slope as the crest approaches, the ship should be at maximum surge forwards into the wave and maximum pitch angle with the bow up. If the phase convention has been misunderstood (e.g. leads have been read as lags) then the motion is obviously wrong and you should go back and re-examine the data, or confirm your interpretation with the data source. This is an excellent check for phases, which are usually the most troublesome to get right. It is not quite so good for amplitudes, but it is nevertheless worth pursuing. If the wave is very long compared to the ship, then the ship should move like a small particle in the water surface. Heave amplitude should be equal to wave amplitude and pitch motion should keep the deck of the ship parallel to the water surface. Surge amplitude should also be equal to wave amplitude in deep water, but will be greater in shallow water in which the wave particle orbits are elliptical. The check can be extended to other wave directions. Broadly speaking, we may expect the motion to be predominantly in the wave direction, with the phasing of surge and sway such that the components in the wave direction reinforce each other. Similarly, roll and pitch phasing should be such that the components of rotation about an axis normal to the wave direction reinforce each other. 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. Generally speaking, if it looks right in long waves, it probably is right. If not, then think again! 6.12.3 Drag Loads Drag loads on a vessel are an important source of damping when modelling vessel slow drift. For a discussion of the various damping sources see Damping Effects on Vessel Slow Drift. The hydrodynamic and aerodynamic drag loads on a vessel are calculated using the data specified on the Hydrodynamic and Wind Drag tabs on the vessel type data form. The drag loads are split into those due to translational relative velocity and those due to yaw rate. 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, which is outlined below. For further details see Oil Companies International Marine Forum, 1994. The OCIMF method is for calculating the surge, sway and yaw drag loads on a stationary vessel. OrcaFlex extends the method to cover a moving vessel by replacing the current (or wind) velocity used in the OCIMF method by the relative translational velocity of the current (or wind) past the vessel. More precisely, the relative velocity used is the current (or wind) velocity, relative to the primary motion of the vessel, at the specified current (or wind) load origin. In other words the relative velocity includes the current but not the waves, and it includes the primary motion of the vessel, but not the superimposed motion. Note that the OCIMF method does not include any drag due to yaw angular velocity of the vessel, since there are none for a stationary vessel. OrcaFlex's extension of OCIMF does not add these yaw rate drag terms, since the OCIMF method has no framework for them. They are therefore calculated separately in OrcaFlex - see Drag Loads due to Yaw Rate below. Note: The OCIMF method is intended for tankers, but could be applied to other vessel types providing suitable data is obtained. 192 w Warning: The current and wind loads are based on theory for surface vessels and are not suitable for submerged vessels. The drag loads due to surge and sway relative velocity are calculated as given by the following OCIMF formulae. Surge Force = ½.C(surge).ρ.V².A(surge) Sway Force = ½.C(sway).ρ.V².A(sway) Yaw Moment = ½.C(yaw).ρ.V².A(yaw) where A(surge), A(sway) and A(yaw) are the surge and sway areas and the yaw area moment, as specified in the data. For current these correspond to the exposed areas below the waterline, and for wind to the exposed areas above the waterline. C(surge), C(sway) and C(yaw) are the surge, sway and yaw coefficients for the actual current or wind direction relative to the vessel. ρ is the water density (for hydrodynamic drag) or air density (for wind drag). V is the magnitude of the relative velocity of the sea or air past the vessel. For wind loads, V is based on the wind velocity specified in the data (i.e. the wind velocity at 10m above mean water level). For hydrodynamic drag, V is based on the current velocity relative to the vessel at the instantaneous position of the load origin (if this is above the water surface, then the current velocity at the surface is used). In both cases V includes allowance for the translational velocity of the load origin due to any primary motion of the vessel, but does not include any superimposed motion. These surge force, sway force and yaw moment act at the current or wind load origin. The surge and sway forces act in the vessel Vx and Vy-directions, respectively, and the yaw moment acts about the vessel Vz-direction. Notes: The OCIMF standard method uses L² x D for the yaw area moment for current loads, and L x A(sway) for the yaw area moment for wind loads, where L is the length between perpendiculars and D is the draught. For current loads (not wind loads) the OCIMF standard method uses L x D for both the surge and sway areas. Drag Loads due to Yaw Rate A vessel rotating in yaw will generate a drag moment resisting the yaw rate, but the OCIMF method described above does not include this drag load (since the OCIMF method is designed for stationary vessels). For wind drag these yaw rate terms are insignificant and so are omitted by OrcaFlex. But for hydrodynamic drag they are important, so OrcaFlex models them using the following formulae. Surge Force = (½.ρ.ω²).SurgeFactor Sway Force = (½.ρ.ω²).SwayFactor Yaw Moment = (½.ρ.ω²).YawFactor .................. (1) where SurgeFactor, SwayFactor, YawFactor are the yaw rate drag factors (specified on the Hydrodynamic Drag tab on the vessel type data form). ω is the vessel yaw rate, in radians per second, due to any primary motion of the vessel ρ is the water density. 193 w These yaw rate drag loads are then applied at the hydrodynamic load origin. 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, as given by Wichers (1979). Consider the simplest situation where the vessel centre is stationary but the vessel is yawing at rate ω about that centre. 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), and that for simplicity we choose to put the load origin at the centre of that area. We now divide the drag area into vertical strips of width dx and consider the sway drag load on the strip at distance x forward of the centre. The strip's area is D.dx and its sway velocity due to the yaw rate is ω.x, so we can estimate the sway drag load on it by ½.ρ.Cd.D.dx.(ω.x).|ω.x|. where Cd is the drag coefficient, which we assume to be the same for all the strips. These sway drag loads from each strip, and their moments about the centre, are then integrated to give the total sway force and a contribution to yaw moment. When we do this integral the sway forces from corresponding strips forward and aft of centre have the same magnitude but opposite direction, so they cancel and the total sway drag force is therefore zero. However the yaw moment terms from forward and aft of centre have the same magnitude and same direction, so they reinforce, giving a significant yaw drag moment. In fact the integral gives the following yaw moment. Yaw Moment = (½.ρ.ω²).(Cd.D.L^4/32) ................. (2) The same argument can be applied to the drag forces in the surge direction, with length L being replaced by width W. But for a slender vessel W is much less than L, so the surge force contribution to yaw moment is generally negligible. Comparing equations (1) and (2) we see that the YawFactor corresponds to the bracketed term (Cd.D.L^4/32) in equation (2). This is in fact a combination of a drag coefficient and the 3rd moment of drag area about the centre. This strip theory argument therefore concludes that for a slender ship, with the hydrodynamic drag load origin at the centre, then we can estimate the yaw rate drag factors by: SurgeFactor = SwayFactor = 0 YawFactor = (Cd.D.L^4/32) where Cd is some appropriate drag coefficient. However, there are a lot of questionable assumptions in the strip theory argument. Indeed Wichers (1979) found that the strip theory results significantly underestimated the actual yaw drag measured in model tests, unless the Cd value was increased to about 5, which is rather high for a drag coefficient. So if more specific data is available, e.g. from model test, then we recommend setting the yaw rate drag factors to values that best fit your data. Interaction with sway rate Further complications arise if the vessel is swaying as well as yawing. In this case the integral in the above strip theory argument turns out to give an extra term involving v.ω. This is an interaction between sway velocity and yaw rate and its effect is to significantly increase the yaw moment. OrcaFlex does not yet include this interaction effect. The reason for this is that it is difficult to model. Wichers (1979) included them in his strip theory model, but as described above the model's results did not match experimental results particularly well. He returned to the problem in his PhD thesis (Wichers, 1988) and developed a more accurate empirical approach based on 194 w model test data. However the method has some theoretical difficulties, since the formulae break down when ω is zero. Orcina is studying this, with a view to implementing a more accurate yaw rate drag model in a future release of OrcaFlex. In the meantime we recommend that you specify yaw rate drag factors that are appropriate to the conditions prevailing in the case being modelled. See the papers by Wichers for further information. 6.12.4 Added Mass and Damping The added mass and damping loads are calculated using the formulae given below. Waverelated fluid motion is not included in the damping load, since wave frequency motion is assumed to be completely prescribed by the vessel RAOs. Damping Load The damping loads are calculated by multiplying the damping matrix by the primary velocity of the vessel centre of gravity, using the formulae: Surge damping force = - (C[surge,surge].V[surge] + C[surge,sway].V[sway] + C[surge,yaw].V[yaw]) Sway damping force = - (C[sway,surge].V[surge] + C[sway,sway].V[sway] + C[sway,yaw].V[yaw]) Yaw damping moment = - (C[yaw,surge].V[surge] + C[yaw,sway].V[sway] + C[yaw,yaw].V[yaw]) where: C is the damping matrix, specified on the vessel type data form. For example C[surge, yaw] is the entry in the surge row and yaw column of that matrix. V[surge/sway] are the components, in the primary x/y axes directions, of the primary velocity of the vessel CG relative to global axes. V[yaw] is the primary yaw angular velocity of the vessel, in radians/sec, relative to global axes. The units of the damping matrix elements are therefore as follows: surge surge sway yaw F/(L/T) F/(L/T) (F.L) / (L/T) sway F/(L/T) F/(L/T) (F.L) / (L/T) yaw F/(1/T) F/(1/T) (F.L) / (1/T) where F, L and T denote the units of force, length and time, respectively. Added Mass Load The added mass load is calculated by multiplying the added mass matrix by the primary acceleration of the vessel CG, using the formulae: Surge added mass force = - (M[surge,surge].A[surge] + M[surge,sway].A[sway] + M[surge,yaw].A[yaw]) Sway added mass force = - (M[sway,surge].A[surge] + M[sway,sway].A[sway] + M[sway,yaw].A[yaw] Yaw added mass moment = - (M[yaw,surge].A[surge] + M[yaw,sway].A[sway] + M[yaw,yaw].A[yaw]) where M is the added mass matrix, specified on the vessel type data form. For example M[sway, surge] is the entry in the sway row and surge column of that matrix. A[surge/sway] are the components, in the primary x/y axes directions, of the primary acceleration of the vessel CG relative to global axes. 195 w A[yaw] is the primary yaw angular acceleration of the vessel, in radians/sec^2, relative to global axes. The units of the added mass matrix elements are therefore as follows: surge surge sway yaw M M M.L sway M M M.L yaw M.L M.L M.L^2 where M and L denote the units of mass and length, respectively. 6.12.5 Wave Drift Loads The wave drift load on a vessel is only calculated if the vessel's primary motion is set to Calculated. For a detailed description of the theory see Faltinsen's book. Here we give a summary and the formulae used in OrcaFlex. The wave loads on a vessel can be expressed as a sum of first order, second order and even higher order terms. The linear first order terms are the largest. The second order terms are non-linear effects that are much smaller, but they can be significant in some cases. The higher order terms are even smaller and are neglected. The first order terms generate the vessel's first order motion and this is modelled in OrcaFlex by the vessels RAOs. The first order wave loads are therefore not calculated by OrcaFlex. The second order terms are quadratic terms and they are made up of three terms: • • • Difference frequency terms, which have frequencies given by the differences between combinations of different wave component frequencies. A constant term, called the mean wave drift force. This term is really the limiting case of the difference frequency term when the two frequencies are equal. Sum frequency terms, which have frequencies given by the sums of combinations of wave component frequencies. The constant and difference terms are collectively known as the wave drift loads; these are both included in OrcaFlex. The constant term is called the mean wave drift load and this is applied in OrcaFlex in both the static and dynamic analyses; it can cause significant mean offset. The difference frequency terms are only included in the dynamic analysis; they can cause significant slow drift motion if their frequencies are near to a vessel surge, sway or yaw natural frequency. The sum frequency terms are not included in the OrcaFlex calculation, since they are high frequency terms whose effect on a massive moored vessel is normally negligible. Wave Drift Load Theory Wave drift loads are calculated based on the Quadratic Transfer Functions (QTFs) specified in the user's wave drift data. QTFs are similar to RAOs in so far as they are scaling factors that are applied to wave components. But whereas an RAO is applied to a single component and gives a displacement, a QTF is applied to a pair of wave components and gives a wave drift force or moment. The full QTF is a complex-valued function Q(ω1, ω2) of a pair of wave angular frequencies ω1 and ω2. There are separate QTFs for each of the 6 vessel degrees of freedom, so we use the following notation: Q1(ω1, ω2) = Surge QTF 196 w Q2(ω1, ω2) = Sway QTF Q6(ω1, ω2) = Yaw QTF where the digits 1, 2 and 6 refer to the surge sway and yaw degrees of freedom. OrcaFlex does not calculate slow drift for heave (3), roll (4) and pitch (5), since those degrees of freedom are constrained by buoyancy effects. Consider a vessel exposed to a pair of wave components, of angular frequencies ω1 and ω2, and let the wave elevation at the vessel's QTF origin due to those components be: Z1 = A1.Cos(ω1.t - φ1) = Real part of A1.Exp[ω1.t - φ1] Z2 = A2.Cos(ω2.t - φ2) = Real part of A2.Exp[ω2.t - φ2] Then the wave drift load due to the difference term from those 2 components is given by: Surge force = Real part of (ρ.g.L).Q1(ω1, ω2).A1.A2.Exp[(ω1-ω2).t - (φ1-φ2)] Sway force = Real part of (ρ.g.L).Q2(ω1, ω2).A1.A2.Exp[(ω1-ω2).t - (φ1-φ2)] Yaw moment = Real part of (ρ.g.L^2).Q6(ω1, ω2).A1.A2.Exp[(ω1-ω2).t - (φ1-φ2)] The first bracketed term on the right hand side of each equation is a dimensionalising factor that gives a non-dimensional definition of Q. The factors involve the water density ρ, the acceleration due to gravity g, and the vessel type length L. The total wave drift load is then the sum of these loads, over all pairs of frequencies (ω1, ω2) present in all the wave trains specified. This terms involved in this sum can be viewed as being made up of two types: • The 'diagonal' terms (i.e. those where ω1 and ω2 are equal) each give a constant load. The sum of these terms is the mean wave drift load, and this is applied in both the static and dynamic analysis in OrcaFlex. The off-diagonal terms (i.e. those where ω1 and ω2 differ) each give a harmonically timevarying load. The sum of these terms is the dynamic wave drift load and this is only calculated and applied in the OrcaFlex dynamic analysis. These terms are not included in the static analysis since their time-average value is zero. • OrcaFlex uses Newman's Approximation to Calculate the Wave Drift Loads There are 2 significant implementation problems with the above theory. The first problem is that it is not practical for the user to specify the QTF values for all possible pairs of frequencies (ω1, ω2). Instead, in the OrcaFlex QTF data, the user only specifies the 'diagonal' values of the function, Q(ω, ω), for a range of discrete frequencies ω = ω1..ωn. For intermediate frequencies OrcaFlex uses linear interpolation to obtain the diagonal QTF value. These diagonal values must be real and they are the terms that give the constant term - i.e. the mean wave drift load. However we also need to calculate the difference terms that arise from the off-diagonal terms. To do this, Newman approximated the off-diagonal terms from the diagonal terms by taking the off-diagonal term Q(ω1, ω2) to equal the geometric mean of the 2 diagonal terms Q(ω1, ω1) and Q(ω2, ω2). The justification for this approximation is twofold. Firstly, the important difference terms are those with low frequency, which arise from the near-diagonal terms in Q. The far-from-diagonal values give much higher frequency difference terms which have little effect of a vessel of sufficiently large inertia. Secondly, on theoretical grounds, the function Q should be continuous in both ω1 and ω2, so the near-diagonal term Q(ω1, ω2) should be well-approximated by the mean of Q(ω1, ω1) and Q(ω2, ω2). 197 w The second implementation problem is the amount of computation required to do the full calculation. To calculate and sum the difference terms due to each pair of frequencies is a double summation that requires computation time proportional to N^2, where N is the number of wave components. When N is large this double summation calculation is much too slow to be practical. To reduce the computation Newman therefore proposed a further approximation in which the double sum is estimated by a difference of squares of single sums; see Newman's paper for details. OrcaFlex uses Newman's 'difference of squares' formula to calculate the wave drift loads from the QTF data specified by the user. The formula incorporates the geometric mean approximation (described above) to estimate the off-diagonal terms. It also introduces spurious high-frequency terms that have no physical basis. However numerical tests confirm that these high frequency terms have little effect on the vessel providing the vessel's inertia is large enough. 6.13 3D BUOY THEORY The effects included for a 3D Buoy are weight, buoyancy, drag, added mass and reactions from shapes. All of the fluid related effects are calculated allowing for what proportion of the buoy is currently immersed in the sea. This is done by calculating a proportion wet, PW, and then scaling all of the fluid related forces by this proportion. In the following equations, the water density is denoted by ρ. The forces applied are: Weight = Mass . g vertically downwards Buoyancy = ρ . g . PW . Volume vertically upwards Drag forces are calculated separately for each of the global X, Y and Z directions. For the X direction (and similarly for the Y and Z directions) the drag force applied is PW . ½ . ρ . CdX . AX . VrX . |Vr| where CdX and AX are the Drag Coefficient and Drag Area, respectively, specified in the data 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. Fluid acceleration force = (1+Ca) . ρ . PW . Volume . A, in each of the global axes directions where Ca is the Added Mass Coefficient specified in the data 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. The Froude-Krylov force: ρ . PW . Volume . A 2. The added inertia force: Ca . ρ . PW . Volume . A. In addition, the inertia of the buoy in each of the global axes directions is increased by: Added mass = ρ . Ca . PW . Volume where Ca is the Added Mass Coefficient specified in the data for that direction. 198 w Finally, 3D Buoys are also subjected to a reaction force from the seabed and any elastic solid with which they come into contact, given by: Reaction = K . A . d where K is the Stiffness of the seabed or elastic solid A is the contact area, which is taken to be Volume/Height d is the depth of penetration of the buoy origin B. In addition to this reaction force, 3D Buoys receive a damping force. For details see Seabed Theory and Solids Theory. 6.14 6D BUOY THEORY 6.14.1 6D Buoy Theory Hydrodynamic Loads Hydrodynamic loads are calculated using Morison's equation with additional components as discussed below. Hydrodynamic Damping (linear) For Lumped Buoys, additional damping forces and moments may be applied which are directly proportional to the fluid velocity and angular velocity relative to the buoy. 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 by reference to the local angular velocity and acceleration of the fluid, defined as the angular velocity and acceleration of the local water isobar. The resulting moments are correct for rotational motions of the body itself, and give a good representation of moments due to waves where the moments derive from vertical-facing areas, e.g. discus buoys. However, the formulation gives a poor representation of waveinduced moments which derive from horizontally-facing areas. The difficulty arises because there is no unique definition of fluid angular velocity and angular acceleration at a point. 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. 199 w Interaction with Shapes Interactions with shapes and the seabed are calculated as if the buoy consists of a series of lumps, one at each vertex. Notes: For a lumped buoy you can specify the number and location of the vertices. If you specify none then, for seabed and solid contact purposes, OrcaFlex behaves as if there was just one vertex, located at the buoy origin. For a spar buoy or towed fish, OrcaFlex automatically generates the vertices and edges that are visible on the 3D view. There are eight vertices per cylinder, placed at the extremities of a box whose length, width and centre are all the same as the cylinder. Whenever a vertex penetrates a shape, it then experiences a reaction force from the shape given by Reaction = K . A . d Because the vertices are (in general) offset from the buoy origin, this reaction force gives a reaction moment about the buoy origin. Here K is the Stiffness of the Solid, A is the contact area associated with each vertex and d is the depth of penetration of the vertex into the solid. The contact area associated with each vertex is derived by assuming that the total contact area for the buoy is (Volume/Height) and then dividing this equally between all the vertices. A damping force is also included - see Solids Theory for details. Note: For a lumped buoy with no vertices Interaction with the Seabed Interaction with the seabed is treated in exactly the same way as with shapes. The seabed reacts to penetration by the vertices of the buoy and applies a reaction force at the vertex, giving a moment about the buoy origin. See Seabed Theory for details. 6.14.2 Lumped Buoy Theory Weight and Buoyancy The weight and buoyancy forces applied to the buoy are given by: Weight Force = g . Mass Buoyancy Force = PW . ρ . g . Volume where PW is the proportion wet for the buoy, g is the acceleration due to gravity and ρ is the water density. Damping The damping force applied in each local axis direction is given by: Force = PW . UnitDampingForce . Vr where UnitDampingForce is the Unit Force specified in the data for that direction and Vr is the component, in that direction, of the water velocity relative to the buoy. Similarly, the damping moment applied about each local axis direction is given by: Moment = PW . UnitDampingMoment . Wr 200 w where UnitDampingMoment is the Unit Moment specified in the data for rotation about that direction and Wr is the component in that direction, of the angular velocity of the local water isobar relative to the buoy. Drag The drag force applied in each local axis direction is given by: Force = PW .½ .ρ . Cd . A .Vr.|Vr| where A and Cd are the Drag Area and Drag Coefficient specified in the data for that direction and Vr is the component, in that direction, of the water velocity relative to the buoy. The drag moment applied about each local axis direction is given by: Moment = PW . ½ .ρ . Cd . AM . Wr.|Wr| where AM and Cd are the Moment of Area and drag coefficient specified in the data for rotation about that axis and Wr is the component, in that direction, of the angular velocity of the local water isobar relative to the buoy. Fluid Inertia Loads 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 specified in the data for that direction, and A is the component, in that direction, of the local water particle acceleration. The fluid inertia moment applied about each local axis direction is given by: Moment = PW . Cm . HydroInertia . B where HydroInertia and Cm are the reference inertia and Cm coefficient specified in the data for rotation about that direction, and B is the component, in that direction and in radians/s², of the rotational acceleration of the local water isobar. Added Mass and Inertia 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 specified in the data 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 specified in the data for rotations about that direction. 6.14.3 Spar Buoy and Towed Fish Theory The fluid related 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, PW, is calculated for each cylinder according to its level of immersion). 201 w Drag Forces The drag forces are calculated using the "cross-flow" assumption. 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 specified in the data for the normal direction Cdn is the drag coefficient specified in the data for the normal direction Vrx and Vry are the x and y-direction components of the water velocity relative to the buoy | 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 specified in the data for the axial direction Cda is the drag coefficient specified in the data for the axial direction Vrz is the z direction component of the water velocity relative to the buoy |Vrz| is its absolute magnitude. In the local x and y 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 . Wrx .|Wrxy| y Moment = PW . ½ . ρ . Cdn . An . Wry .|Wrxy| where An is the drag area moment specified in the data for the normal direction. Cdn is the drag moment coefficient for the normal direction Wrx and Wry are the x and y components of the angular velocity of the local water isobar relative to the buoy |Wrxy| is the absolute magnitude of the component in the xy plane of the angular velocity of the local water isobar relative to the buoy. And about the local z direction the drag moment is given by: z Moment = PW . ½ . ρ . Cda . Aa . Wrz .|Wrz| where Aa is the drag area moment specified in the data for the axial direction. Cda is the drag moment coefficient specified for the axial direction Wrz is the z component of the angular velocity of the local water isobar relative to the buoy 202 w |Wrz| is its absolute magnitude. Drag Area Moments The drag area moments in the above equations are the rectified 3rd moments of drag area about the axis of rotation. I.e. 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 L^5. 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.W^4) / 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.L^4) / 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 = (D^5) / 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. • • Calculation of Sea Angular Velocity In order to calculate the relative angular velocity, OrcaFlex has to determine a local angular velocity for the water. This is not defined by standard wave theory, so OrcaFlex uses the angular velocity of the local isobar (at the surface this is the angular velocity of the water surface). The resulting drag moments due to waves are approximately correct for a buoy with large horizontal extension - e.g. a discus shape. For a long vertical SPAR buoy, the calculated pitch/roll drag area moment is actually in the wrong direction. Instead the buoy should be divided into several cylinders and the required moments are generated by distributing the hydrodynamic loading between them. The drag area moments for the individual cylinders should be set to zero. For an object which has significant dimensions both vertically and horizontally, the drag area moments are a mix of roughly correct and incorrect parts. The problem relates only to drag moments due to waves - moments resulting from body angular velocity in still water are correctly calculated. Added Mass The components, relative to buoy axes, of the added mass force and moment applied to a cylinder are given by: x Force = PW . (DM . Ax + Can . DM . Arx) y Force = PW . (DM . Ay + Can . DM . Ary) z Force = PW . (DM . Az + Caa . DM . Arz) 203 w x Moment = PW . (DIn . Wx + AIn . Wrx) y Moment = PW . (DIn . Wy + AIn . Wry) z Moment = PW . (DIa . Wz + AIa . Wrz) where PW is the proportion wet for this cylinder DM is the displaced mass of the cylinder when it is fully submerged (= WaterDensity . (π/4 . CylinderDiameter² . CylinderLength)) DIn and DIa are the normal and axial moments of inertia of the displaced mass of the cylinder, when fully submerged Can and Caa are the normal and axial added mass coefficients (specified in the data) AIn and AIa are the normal and axial added moments of inertia (specified in the data) Ax, Ay, Az are the components, in buoy axes directions, of the local water particle acceleration relative to global axes Arx, Ary, Arz are the components, in buoy axes directions, of the local water particle acceleration relative to the buoy Wx, Wy, Wz are the components (in buoy axes directions) of the angular acceleration of the local water isobar relative to global axes Wrx, Wry, Wrz) are the components (in buoy axes directions) of the angular acceleration of the local water isobar relative to the buoy. Notes: In the above equations, the first term is known as the Froude Krylov force (or moment) and the second term is the added mass force (or moment). If the added inertia (AIn or AIa) is zero, then the Froude Krylov moment term is omitted for that direction, so no moment is applied about that direction. This does not apply to the Froude Krylov force terms - they are still applied even if the added mass coefficient for that direction is zero. Damping Forces and Moments The components, relative to buoy axes, of the damping force and moment applied to a cylinder are given by: x Damping Force = PW .UDFn. Vrx y Damping Force = PW .UDFn. Vry z Damping Force = PW .UDFa. Vrz x Damping Moment = PW .UDMn. Wrx y Damping Moment = PW .UDMn. Wry z Damping Moment = PW .UDMa. Wrz where PW is the proportion wet for this cylinder UDFn and UDFa are the Unit Damping Forces specified in the data for the normal and axial directions, respectively UDMn and UDMa are the Unit Damping Moments specified in the data for the normal and axial directions, respectively Vrx, Vry and Vrz are the components (in local buoy axes directions) of the water velocity 204 w relative to the buoy Wrx, Wry and Wrz are the components (in local buoy axes directions) of the angular velocity of the local water isobar, relative to the buoy. 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 M is the mass of water currently displaced. If the buoy is surface-piercing then this allows for the proportion of the buoy that is in the fluid. However, note that the value of Cmm is ill defined for a partially submerged body. Moreover, the true effects of breaking surface, for instance planing and slamming, are much more complex than this and are not modelled. V is the flow velocity relative to the buoy, at the point on the stack axis that is half way between the ends of the stack. α is the angle between the relative flow velocity V and the buoy axis. The moment is applied about the line that is normal to the plane of the buoy axis and the relative flow vector, in the direction that tries to increase the angle α. 6.15 SHAPE THEORY Elastic Solids The reaction force on an object penetrating an elastic solid is in the direction of the outward normal of the nearest surface of the shape with magnitude equal to K.d.A where K = stiffness of the material, d = depth of penetration, A = contact area. Also there is a damping force D, in the same direction, given by: D = λ.2√(M.K.A).Vin where λ is percentage of critical damping / 100, M is the mass of the object, 205 w Vin is the normal component of object velocity. The damping force is only applied when the object is travelling into the shape (i.e. when Vin is positive). For details of the way the contact area is calculated, see: Line Interaction with Seabed and Solids, 3D Buoy Theory and 6D Buoy Theory. Care is needed when using elastic solids - some of the issues involved are listed below: • • Elastic solids are only taken into account in the static analysis for those lines with the Full Statics calculation. Elastic solids are intended only for modelling the overall limitation on movement that a physical barrier presents; they are not intended to model an object's interaction with the barrier in detail. For example no friction forces are included and the calculation of the contact area and penetration depth are very simplistic and do not allow for the detailed geometric shape of the object. The value given for Stiffness is therefore not normally important, providing it is high enough to keep penetration small. On the other hand, although the actual stiffness of real barriers is usually very high, 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. Friction is not calculated for elastic solids in the current version, so you must check that a physically realisable configuration is modelled. Lines only interact with elastic solids by their nodes coming into contact, so elastic solids that are smaller than the segment length can "slip" between adjacent nodes. 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. Where elastic solids intersect with each other, it is sometimes necessary to "overlap" them. If the overlap is zero or small, a line may slip along the interface. • • • Trapped Water Inside a trapped water shape the fluid motion is modified as follows: • The fluid translational velocity and acceleration are calculated on the assumption that the trapped water moves and rotates with the shape. So if the trapped water shape is Fixed or Anchored then no fluid motion occurs inside the shape. But if the shape is connected to a moving vessel, for example, then the trapped water is assumed to move and rotate with the vessel. The fluid angular velocity and acceleration of the local water isobar are both taken to be zero. (These angular motions are only used for calculating moments on 6D buoys.) 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. We make this assumption because of the difficulty in predicting, for realistic cases, how the surface will behave inside the trapped water volume. For example, a moonpool with an open connection at the bottom will suppress most of the wave and current action. However there will be some flow in and out of the moonpool, depending on the size of the opening to the sea, pressure difference effects and the local geometry. The surface elevation in the moonpool therefore does respond to the wave outside, but it is attenuated to some extent and lags behind the surface outside. • 206 w 6.16 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, L0, is set to the Value specified, the wire tension t is then set to: Equation (1) t = (L-L0) . (Wire Stiffness)/L0 where L is the total length of the winch wire path, Wire Stiffness is specified in the data, the winch drive force f is set to equal t. Alternatively, if the Statics winch control mode is set to Specified Tension then for the static analysis the winch drive force f and the wire tension t are both set to the given Value, and the unstretched length paid out, L0, is then set to match this wire tension according to equation (1) above. Dynamic Analysis If Specified Payout is specified (length control mode) for a stage of the simulation, then the unstretched length of winch wire paid out, 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, negative Value means haul in. The winch wire tension t (which is applied to each point on the wire) is then given by Equation (2) t = [(L-L0) + (Wire Damping).(dL/dt - dL0/dt)]. (Wire Stiffness) / L0 where L i the total length of the winch wire path Wire Damping and Wire Stiffness are as specified in the data. Note: The winch wire is not allowed to go into compression, 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. If Specified Tension mode is specified for a stage of the simulation, the Value specified in the data is used as a target nominal constant tension that the winch drive attempts to achieve. In Simple winches the winch drive is always assumed to achieve the target tension, so the Value specified is used for the actual winch wire tension. In Detailed winches the winch drive tries to achieve the target tension by applying a drive force to one side of the winch Inertia, opposing the wire tension being applied to the other side. The drive force f applied is then given by: Equation (3) if dL0/dt < 0: f(V) = f(0) - Deadband + A.V - C.V² 207 w if dL0/dt = 0: f(V) = f(0) if dL0/dt > 0: f(V) = f(0) + Deadband + B.V + D.V² where V = rate of payout = dL0/dt Deadband = the winch drive deadband data item A, B = the winch drive damping term data items C, D = the winch drive drag term data items. f(0) = Value + Stiffness.(L0 - 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) Drive Force f f(V) = f(0) + Deadband 2 + B.V + D.V Deadband Deadband f(0) = Nominal Tension + Stiffness × (Payout since simulation started) 0 Payout Speed V (-ve = hauling in) f(V) = f(0) - Deadband 2 + A.V - C.V Figure: Force Control Mode for Detailed Winches If the winch Inertia is non-zero, 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: d²(L0)/dt² = t - f so the wire tension therefore tends towards the winch drive force and is hence controlled by the given Value. If the winch inertia is set to zero, then the winch is assumed to be instantly responsive so that Equation (4) f = t at all times. Given the current value of L0, the common value of f and t is then found by solving the simultaneous equations (2), (3) and (4) for the payout rate dL0/dt. The unstretched length of winch wire out, L0, is then altered at the calculated rate dL0/dt as the stage progresses. 208 w Note: If the winch inertia is set to zero then at least one of the damping and drag terms A, B, C, D should be non-zero, since otherwise the simultaneous equations (2), (3) and (4) may have no solution. A warning is given if this is attempted. 209 w 7 7.1 SYSTEM MODELLING - DATA AND RESULTS INTRODUCTION To analyse a marine system using OrcaFlex, you must first build a mathematical model of the real-world system, using the various modelling facilities provided by OrcaFlex. The model consists of the marine environment to which the system is subjected, plus a variable number of objects chosen by the user, placed in the environment and connected together as required. The objects represent the structures being analysed and the environment determines the current, wave excitation, etc. to which the objects are subjected. The following types of objects are available in OrcaFlex. (Detailed descriptions of each type of object are given later.) Vessels are used to model ships, floating platforms, barges etc. They are rigid bodies whose motions are prescribed by the user. The motion can be specified either by a time history motion data file, or else by specifying Response Amplitude Operators (RAOs) for each of 6 degrees of freedom (surge, sway, heave, roll, pitch and yaw). They can also be driven around the sea surface, at user specified velocities and headings, during the course of the simulation. 3D Buoys are simple point bodies with just 3 degrees of freedom - the translational degrees of freedom (X,Y and Z). Unlike a vessel, whose response to waves is defined by the data, the motion of a buoy is calculated by OrcaFlex. 3D buoys are not allowed to rotate and are intended only for modelling objects that are small enough for rotations to be unimportant. 6D Buoys are much more sophisticated than 3D buoys - they are rigid bodies with the full 6 degrees of freedom. That is, OrcaFlex calculates both their translational and rotational motion. Several different types of 6D Buoy are available, for modelling different sorts of marine object. Note: Although called buoys, 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. Lines are catenary elements used to represent pipes, flexible hoses, cables, mooring lines, etc. Line properties may vary along the length, for example to allow a buoyant section to be represented. Line ends may be fixed or free, or attached to other objects such as Vessels or Buoys, and ends can be disconnected in the course of a simulation. Each line can also have a number of attachments. These are elements attached to lines at user-specified locations, and provide a convenient way of modelling items such as floats, clump weights, or drag chains. 210 w Links are mass-less connections linking two other objects in the model. Two types are available: Tethers are simple elastic ties, Spring / Dampers are combined (linear or non-linear) spring + damper units. Winches are also mass-less connections linking two (or more) objects in the model. The connection is by a winch wire, which is fed from and controlled by a winch drive mounted on the first object. The winch drive can be operated in either constant speed mode, in which it pays out or hauls in the winch wire at a user-specified rate, or else in constant tension mode, in which it applies a user-specified tension to the winch wire. Shapes are geometric shapes and two types are available - Solids or Trapped Water. Trapped Water Shapes can be used to model parts of the sea, such as moonpools, that are shielded from the waves. Solids can be used to act as physical barriers to restrict the movement of the other objects in the system; they are made of an elastic material and so apply a reaction force to any object that penetrates them. However, by specifying zero stiffness, you can also use a solid purely for drawing purposes, for example to see on the 3D view the position of a piece of equipment. Several different elementary shapes (cuboids, planes and cylinders) are available and a number of shapes may be placed together to build up more complex compound shapes. They may be fixed or attached to other objects such as Vessels or Buoys. Of these various object types, the lines, links and winches have the special property that they can be used to connect together other objects. Assembling the model therefore consists of creating objects and then using the lines, links and winches to connect the other objects together, as required. See Object Connections for details. The number of objects in the model is only limited by the memory and other resources available on the computer being used. Similarly, there are no built-in limits to the number of lines, links or winches that are attached to an object. As a result very complex systems can be modelled, though of course the more complex the model the longer the analysis takes. Example files are provided with OrcaFlex. Computer programs cannot exactly represent every aspect of a real-world system - the data and computation required would be too great. So when building the model you must decide which are the important features of the system being analysed, and then set up a model that includes those features. The first model of a system might be quite simple, only including the most important aspects, so that early results and understanding can be gained quickly. Later, the model can be extended to include more features of the system, thereby giving more accurate predictions of its behaviour, though at the cost of increased analysis time. Once the model has been built, OrcaFlex offers three types of analysis: Modal Analysis is only available for lines. It calculates and reports the undamped natural modes of a line. Static analysis in which OrcaFlex calculates the static equilibrium position of the model; current drag loads can be included but not waves. 211 w Dynamic analysis in which OrcaFlex carries out a time simulation of the response of the system to waves, current and a range of user-defined inputs. 7.2 GENERAL DATA 7.2.1 General Data The General Data form gives data that applies to the whole model. Comments A free form multi-line text field that can be used to store notes about the model. OrcaFlex does use this text. Units Data This may be SI, US or User Defined (multiple choice). Units are defined for length, mass, force, time and temperature. Selecting SI gives length in metres, mass in tonnes, force in kN, time in seconds and temperature in Celsius. Selecting US gives length in feet, mass in kips, force in kips, time in seconds and temperature in Fahrenheit. If neither of these systems meets your requirements then select User Defined. You may then select individually from the length, mass, force, time and temperature units on offer. The program displays the units selected and the corresponding value of g (gravitational acceleration). If the units are changed, then OrcaFlex converts all the data in the model into the new units. 7.2.2 Statics Buoy Degrees of Freedom Included in Static Analysis Buoys can either be included or excluded from the static analysis. When a buoy is included OrcaFlex calculates the static equilibrium position of the buoy; when it is excluded OrcaFlex simply places the buoy at the position specified by the user. 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, together with individual settings on each buoy's data form. This data item should normally be set to All, in which case the static analysis will attempt to find the static equilibrium position of all the buoys in the model, as well as finding the static equilibrium position of the other objects. When this data item is set to None, OrcaFlex does not find the true static equilibrium position of the buoys in the model, but instead simply places the buoys at the initial starting position specified in the data. The final option for this data item is Some. In this case you can specify individually for each buoy, on the buoy data form, whether that buoy should be included in the static equilibrium calculation. For 6D Buoys you can also choose whether the rotational degrees of freedom are included or excluded. 212 w There are several cases where this data item should be set to None. The first is if the you are not using Catenary Statics or Full Statics for any lines in the model (see Static Analysis). In this case, the line is not in true static equilibrium and so OrcaFlex cannot find the static equilibrium position of any buoy to which such lines are attached. If any such lines exist then all the buoys must be excluded from the static analysis by setting this data item to None. The second case where this item may need to be set None is if the model is statically indeterminate, for example a free floating buoy, or if the static analysis fails to converge. The static analysis is an iterative calculation and for some complex systems this calculation may fail to converge, especially if the initial estimated position given in the data is far from being an equilibrium position. If this happens you can exclude some or all buoys (or, for 6D buoys, just the rotational degrees of freedom) from the static analysis; this simplifies the static analysis and should enable convergence. Although the simulation then starts from a non-equilibrium position, it does allow the simulation to proceed and the initial non-equilibrium errors will normally be dissipated during the build-up stage of the simulation, provided a reasonable length build-up stage is specified. In fact the simulation can then often be used to find the true static equilibrium position, by running a simulation with no waves; once it is found, the true static equilibrium positions of the buoys can then be input as their starting positions for subsequent runs. Finally, you may specifically want the simulation to start from a non-equilibrium position. One example of this is to use the simulation to determine the damping properties of the system, by running a simulation with no waves and starting from a non-equilibrium position. Use Calculated Positions This button is available after a successful static iteration or when the simulation is finished or paused. If the model is in the statics complete state then clicking the button sets the initial positions of buoys, vessels and free line ends to be the calculated static position. This can be desirable when setting up a model, since the positions found are likely to be good estimates for the next statics calculation. If the model is in the simulation paused or stopped state, then clicking the button sets the initial positions of buoys and free line ends to be the latest position in the simulation. This is useful when the statics calculation is failing to converge and you are using dynamics with no wave motion to find the static equilibrium position. Use Static Line End Orientations This button is only available after a successful static analysis. Clicking the button sets the line end orientation data, for all line ends in the model that have zero connection stiffness, to the orientations found in the static analysis. This is done as follows. • • For any line end with zero bend connection stiffness, the end azimuth and end declination will be set to the azimuth and declination of the end node, as found by the static analysis. If the line includes torsion and the line end connection twist stiffness is zero, then the end gamma will be set to the gamma of the end node, as found by the static analysis. This button 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. To do this first set the end connection stiffness values to zero, then run the static analysis and then click the Use Static Line End Orientations button. You can then set the end connection stiffness to their actual values. 213 w Starting Velocity Specifies the velocity of the whole model for the static analysis and for the start of the simulation. It is defined by giving the speed and direction. Normally the starting speed is zero. If a non-zero speed is specified (e.g. 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 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 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. 7.2.3 Statics Convergence Convergence 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. The Set To Default button restores the parameters to their default values. For further details contact Orcina or your Orcina agents. 7.2.4 Dynamics Inner and Outer Time Steps For efficiency of computation, OrcaFlex uses 2 integration time steps 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 most hydrodynamic forces) are only recalculated every Outer time step. This reduces the calculations needed and so increases the speed of simulation. Both time steps must be short enough to give stable and accurate simulation. Experience indicates that the inner step should not exceed 1/20th of the shortest natural period of motion of the model, the value of which is reported in the Static Analysis results. The outer step can usually be set to 100 times the inner time step; this gives a good saving in computing time without risking instability. Occasionally it may be necessary to use a shorter outer time step, for example where the velocity of part of the system changes very rapidly (perhaps as part of a transient during build-up). 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). 214 w Note: When a simulation is started OrcaFlex checks the time steps specified. If the criteria outlined above are infringed OrcaFlex gives you the option of setting the time steps automatically - according to these criteria. 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. See also the effects of seabed stiffness. 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: Seabed stiffness will shorten the natural period of parts of the system lying on it, and this in turn requires a smaller simulation inner time step. Beware that the shorter natural periods will not be reported in the statics results table if touch-down does not occur until dynamics are run. 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. 7.2.5 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 inner time step. You can obtain more information about the logging by using the Properties command on the pop-up 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. 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 certain cases. We therefore recommend that you use single precision logging unless you see signs of precision problems in the results. The 215 w 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. 7.2.6 Target Damping Target Damping The percentage of critical damping to be assumed for tension, bending and torsion in all Lines. All practical systems include some internal (structural) damping, but how much is rarely known, even approximately. 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 critical damping is usually assumed. For details on the use of this data, see the documentation of tension, bending and torsion in the Line Theory: Calculation Stages section. 7.3 ENVIRONMENT 7.3.1 Environment The environment defines the conditions to which the objects in the model are subjected; it consists of the sea, current, waves and seabed. Z Still water surface Surface Z-level Datum Current Direction Wave Direction Y G X Global Axes Seabed Direction of Slope Water Depth Seabed Origin 216 w Figure: Environment As shown above, the environment is defined relative to the global axes. So for example the seabed and the current and wave directions are specified relative to the global axes. 7.3.2 Sea Data Sea Surface Z Specifies the global Z coordinate of the mean (or still) water level. Kinematic Viscosity This data is used to calculate the Reynolds number. The viscosity can either be a constant or vary with temperature. In the latter case the user can either input their own table of viscosity variation against temperature, or else use one of the tables supplied in the OrcaFlex default data. The tables supplied in the OrcaFlex default data are for 0% (freshwater) and 3.5% salinity, as given on page 337 of the book Principles of Naval Architecture (PNA). For other salinity values that book recommends using interpolation between the freshwater and 3.5% salinity tables. If variation with temperature is specified then OrcaFlex uses linear interpolation for temperatures between those specified in the table, and truncation for temperatures beyond those specified in the table. Temperature The temperature of the water can either be constant or vary with depth below the mean water level. If variation with depth is specified then OrcaFlex uses linear interpolation for depths between those specified in the table, and truncation for depths beyond those specified in the table. The temperature can affect the viscosity (if that is specified as varying with temperature), which in turn affects the Reynolds number, which in turn can affect the drag coefficient used for a line (if the drag coefficient is specified as varying with Reynolds number). Sea Density Water Density Variation specifies whether, and how, the water density varies with depth. It is normally set to Constant, allowing you to specify a single density value that applies everywhere in the sea. This is the most common value to use, since in most models the effects of density variation with depth are not significant. For some systems, however, density variation with depth is important because it causes buoyancy variation with depth. For such cases, two other settings for Water Density Variation with depth are available: Interpolated allows you to specify a density profile as a table giving the density at a series of depth levels. Linear interpolation is used to obtain the density at intermediate levels, and at levels beyond the ends of the table the density value at the end of the table is used. Bulk Modulus specifies that the density varies with depth purely because of the compressibility of the water. You must specify the water's Surface Density and Bulk Modulus. The water's bulk modulus specifies how a given mass of water shrinks under pressure, using the same volume formula as for buoys and line types - see Bulk Modulus. OrcaFlex then derives the density 217 w variation with depth on the assumption that the water column has the given bulk modulus and is at uniform temperature and salinity. For the Interpolated and Bulk Modulus options, you can check that the density variation is as expected by using the View Profile button to display a graph showing the density variation that will be used. Note: Density variation with depth only affects the buoyancy of objects. OrcaFlex does not allow for density variation with depth when calculating hydrodynamic effects such as drag and added mass. For these effects the water density value at the still water surface is used. A dry land system can be modelled by using Constant density and setting the density to zero. Seabed Data Seabed Type Two types of seabed shape are available. A Flat seabed is a simple plane, which can be horizontal or sloping. A Profile seabed is one where the shape is specified by a 2D profile in a particular direction; normal to that profile direction the seabed is horizontal. Seabed Origin and Depth The seabed origin is a point on the seabed and is the point to which the seabed data refer. It can be chosen by the user and is specified by giving its coordinates with respect to global axes. For a profile seabed the seabed origin Z-coordinate is not specified directly, but is determined by the Z values specified in the profile table. The seabed origin Z-coordinate and the specified Sea Surface Z together determine the water depth at the seabed origin, which is displayed on the data form (but cannot be edited directly). The seabed origin Z-coordinate must therefore be less than the specified Sea Surface Z. Warning: The depth at the seabed origin is used for all the wave theory calculations, so if the water is shallow and the depth varies then the seabed origin should normally be chosen to be near the main wave-sensitive parts of the model. Direction The direction in which the depth varies, measured positive anti clockwise from the global X-axis when viewed from above. For a flat seabed the direction specified is the direction of maximum upwards slope. For example, 0 degrees means sloping upwards in the global X direction and 90 means sloping up in the in the global Y direction. For a profile seabed the direction specified is the direction in which the 2D profile is defined. Slope (flat seabed only) The maximum slope, in degrees above the horizontal. The flat seabed is modelled as a plane, inclined at this angle, passing through the seabed origin. The model is only applicable to small slopes. The program will accept slopes of up to 45 degrees but the model becomes increasingly unrealistic as the slope increases because the bottom current remains horizontal. Profile (profile seabed only) The profile table defines the seabed shape in the vertical plane through the seabed origin in the seabed direction. The shape is specified by giving the seabed Z coordinate, relative to global 218 w axes, at a series of points specified by their Distance From Seabed Origin, which is measured from the seabed origin in the seabed direction (negative values can be given to indicate points in the opposite direction). The resulting depths at the points are reported in the table. The seabed also has its own seabed origin and local axes, with respect to which the seabed shape is defined. Seabed Z-values in between profile points are obtained by smooth cubic spline interpolation, and beyond the ends of the table the seabed is assumed to be horizontal. The seabed is assumed to be horizontal in the direction normal to the seabed profile direction. Interpolation Method (profile seabed only) Determines how OrcaFlex interpolates between values in the specified profile. Warning: Linear interpolation can cause difficulties for static and dynamic calculations. If you are having problems with static convergence or unstable simulations then you should try one of the other interpolation methods. 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. However you can specify a near-vertical cliff. If you do this, note that to avoid interpolation overshoot you may need to specify several extra points just either side of the cliff, or else use linear interpolation. See Choosing Interpolation Method. View Profile The View Profile button provides a graph of the seabed profile. The specified profile points are shown, together with the interpolated shape in between profile points. The seabed is horizontal beyond the ends of the graph. You should check that the interpolated shape is satisfactory, in particular that the interpolation has not introduced overshoot - i.e. where the interpolated seabed is significantly higher or lower than desired. Overshoot can be solved by adding more profile points in the area concerned and carefully adjusting their coordinates until suitable interpolation is obtained. Seabed Stiffness and Damping The seabed is normally modelled as a sprung and damped surface with a spring reaction force that is proportional to the depth of penetration and the contact area, plus a damping force that is proportional to the rate of penetration. See Seabed Theory. The seabed stiffness is the constant of proportionality of the spring force and equals the sprung reaction force per unit area of contact per unit depth of penetration. A high value models a surface such as rock; a low value models a soft surface such as mud. The seabed damping is the constant of proportionality of the damping force, and is percentage of critical damping. Warning: A high seabed stiffness will shorten the natural periods of parts of the system lying on it, which may require the use of a smaller simulation time step. Beware that the shorter natural periods will not be reported in the statics results table if touchdown only occurs during the simulation. 219 w 7.3.3 Current Data Current Method Can be Interpolated or Power Law. The Interpolated method uses a full 3D profile with variable magnitude and direction. The Power Law method uses an exponential decay formula. This enables modelling of boundary layer effects. Ramp During Build-Up If selected then the static position will be calculated without the effects of current and during the build-up stage of dynamics the current is ramped up to its full value. If not selected (the default) then the current is used in calculating the static position and full current is applied throughout. 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. For example, consider a case where a flexible line is to the left of a stiff pipe but current pushes the flexible up against the pipe. Since the OrcaFlex static analysis does not include the effects of contact between lines, 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 simulation would then start with the flexible on the wrong side of the pipe. This problem can be overcome by setting the current to ramp during build up and setting clash checking for the two lines. The static position will exclude the effect of current and so will leave the flexible to the left of the pipe. The build-up stage will then introduce the current effects but will also include the effect of contact between the two lines. View Profile Draws a graph of current speed against depth. Data for Interpolated Method Speed and Direction The magnitude and direction of a reference current, generally taken as a surface current. The actual current at a given Z level is then defined relative to this reference current by a current profile. The direction specified is the direction the current is progressing - for example, 0 and 90 degrees mean currents flowing in the X and Y directions, respectively. The speed and direction can either be fixed or vary with simulation time. If they are variable then linear interpolation is used for times between those specified in the variable data table, and truncation is used for times beyond those specified in the table. Profile A current profile may be defined by specifying factors and rotations at various depths, relative to reference. At each Depth in the table the current speed is the reference current speed multiplied by the Factor for that depth; the Direction is the reference direction plus the rotation specified. Current speed and direction are interpolated linearly between the specified levels. The current at the greatest depth specified is applied to any depth below this, for example when a sloping seabed is specified. Similarly, the current at the least depth specified is applied to any depth above this. 220 w If you prefer to enter current speeds and directions directly, rather than using a reference current and reference-relative profile, simply set the reference current speed to 1 and the reference direction to 0. Data for Power Law Method Speed at Surface and at Seabed The current speed at the still water level and at the seabed level. Note: Direction When using the power law current method, the current direction is the same at all levels. The direction specified is the direction the current is progressing, measured positive from the global X-axis towards the global Y-axis. For example, 0 and 90 mean currents flowing in the X and Y directions, respectively. Exponent This determines how the current decays. With a smaller value, the decay is spread more evenly across the water depth. With a higher value, the decay mostly occurs close to the seabed. Speed at Seabed cannot be greater than Speed at Surface. 7.3.4 Wind Data The Wind tab on the Environment data form contains the following data for modelling wind. Note that this wind data is only currently used to calculate the wind loads on vessels - see Vessel Theory: Drag Loads. Air Density The air density is assumed to be constant and the same everywhere. Wind Direction The direction specified is the direction in which the wind is progressing - see Direction and Headings. In all cases the wind is unidirectional. Wind Speed Wind speed is assumed to be the same everywhere. The speed specified should be the value at an elevation of 10m (32.8 ft) above the mean sea surface, since that is the height used by the OCIMF vessel wind load model. If you have the wind speed V(h) at some other height h (in metres), then the wind speed V(10) at 10m can be estimated using the formula: V(10) = V(h) (10/h)^(1/7). You can choose to specify wind speed in various ways, by setting the Wind Type to one of the following. Constant The wind speed is then constant in time. 221 w Random The wind speed varies randomly in time, using a choice of either the American Petroleum Institute spectrum (API) or the Norwegian Petroleum Directorate spectrum (NPD). In both cases: • The spectrum is determined by specifying the Mean Speed and the spectrum then determines the statistical variation about that mean. The View Spectrum button shows a graph of the spectrum. The wind speed is modelled by a sum of a number of components. The components are sinusoidal functions of time whose amplitudes and frequencies are chosen by OrcaFlex to match the spectral shape. OrcaFlex uses a 'equal energy' algorithm to choose the amplitudes and frequencies. This gives all the components the same energy, and therefore the same amplitude, but their frequencies are chosen so that the components are more closely spaced where the spectral energy density is high, and more widely spaced where the spectral energy is low. You can specify the Number of Components to use. You should specify enough to give a reasonable representation of the spectrum. The phases of the components are chosen using a pseudo-random number generator that generates phases which are uniformly distributed. The phases generated are repeatable i.e. 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. This can be any integer in the range -2^32 to +2^32-1. The View Components button gives a report of the components that OrcaFlex has chosen. The View Profile button shows the resulting wind speed time history, as a function of global time. If you want to simulate a particular section of that time history then you can use the wind Time Origin to time shift that section into the simulation period. See Time Origins for details. • • • • • Time History The wind speed variation with time is then specified explicitly in a file. For details see Data in Time History Files. Linear interpolation is used to obtain the wind speed at intermediate times. View Profile The View Profile button displays a time history graph showing the wind speed that will be used. The graph covers the specified Duration, starting at the specified Start time. This Start time, and the graph's time axis, are both global times. 7.3.5 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. In most cases a single wave train is sufficient, but multiple wave trains can be used for more complex cases, such as a crossing sea (i.e. a superposition of locally generated waves in one direction and distant storm-generated swell in a different direction). 222 w Each wave train can be given a name and a specified direction. And each wave train can be either a regular wave (with a choice of wave theory) or a random wave (with a choice of spectrum), or else be specified by a time history file. Simulation Time Origin The simulation time origin allows you to control the period of time that the dynamic simulation covers. It defines the global time that corresponds to simulation time t = 0, so changing the simulation time origin allows you to shift the period of global time that is simulated. Altering the simulation time origin shifts the simulation time relative to all of the wave trains; alternatively, you can also time shift an individual wave train by altering its wave time origin. See Dynamic Analysis for details of the time frames used in OrcaFlex. Data for a Wave Train Each wave train is specified by the following data. Wave Direction For both regular and random waves, the wave Direction is the direction that the wave is progressing, measured positive anti-clockwise from the global X-axis when viewed from above. So, for example, 0 degrees means a wave travelling in the positive X-direction, and 90 degrees means a wave travelling in the positive Y-direction. 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. Wave Type Each wave train can be any of the following types: • • • Airy, Dean, Stokes' 5th or Cnoidal. These are various different wave theories for regular waves. See Data for Regular Waves. JONSWAP, ISSC (also known as Pierson-Moskowitz), Ochi-Hubble, or User Defined Spectrum. These are various different spectra for random waves. Time History allows you to specify the wave in the form of a time history input file. See Data for Time History Waves. For regular waves we recommend the Dean wave - this is a nonlinear wave theory using a Fourier approximation method and it is suitable for all regular waves. The Airy wave theory is a simple linear wave theory that is only suitable for small waves. The Cnoidal wave theory is only suitable for long waves in shallow water. The Stokes' 5th wave theory is only suitable for short waves in deep water. There are two Stokes' 5th order theories implemented in OrcaFlex which we have called Stokes' 5th (SH) and Stokes' 5th. The former is the standard method of Skjelbreia and Hendrickson whilst the latter theory is due to Fenton. We consider Fenton's work to be an improvement on the original, primarily because it deals with currents more accurately. If the specified wave is not suitable for the selected wave theory, OrcaFlex will give a warning or may report that the wave calculation has failed. If this happens please check that the wave theory selected is suitable. For further details see Ranges of Applicability. 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. OrcaFlex 223 w offers a choice of three methods: Vertical Stretching, Wheeler Stretching and Extrapolation Stretching. For details see Kinematic Stretching Theory. Note: Random waves are modelled by combining a number of linear Airy waves, so kinematic stretching also applies to random waves. The Horizontal Velocity preview graph can be used to see the effect of the different kinematic stretching methods. Wave Time Origin Each wave train has its own Wave Time Origin, which is specified relative to the global time origin. The wave train's data specify the wave train relative to its own time origin, so you can time-shift a given wave train, independently of the other wave trains, by adjusting its wave time origin. For a regular wave train the wave time origin is the time at which a wave crest passes the global origin. You can therefore use the Wave Time Origin to arrange that a wave crest passes a particular point at a particular time during the simulation. For a random wave train, the phases of the wave components that make up the wave train are randomly distributed, but they are fixed relative to the wave time origin. You can therefore arrange that the simulation covers a different piece of the random wave train by changing the wave time origin. This can be useful for two purposes: • • You may want to select a particularly significant event in the wave train, such as a large wave. OrcaFlex has special facilities to make this easy - see Wave Preview. Secondly, you may want to do a series of runs with the same wave train data but different random phases for the wave components. This can be done by specifying randomly chosen wave time origins for the different runs, since randomly selecting different periods of the wave train is statistically equivalent to choosing different random phases for the wave components. Stream Function Order For the Dean wave theory only, you can set the order of stream function to be used. The default value is 10 and for most purposes it is not necessary to alter this. However, for nearly breaking waves the method sometimes has problems converging. If this is the case then it might be worth experimenting with different values. Data for Regular Waves A regular wave is a single wave component defined by wave Direction, Height and Period. Wave height is measured from trough to crest. Data for Random Waves Random waves are specified by giving the energy spectrum of the random sea. The Wave Type specifies the type of spectrum and the spectral data then defines the actual spectrum within that type. You can use the View Spectrum button to view a graph of resulting energy spectrum. For the JONSWAP and Ochi-Hubble spectra (see Data for Ochi-Hubble spectra) you have a choice of using Auto or User settings for some of the spectra data. 224 w Number of Components and Seed Random wave trains are represented by a user-defined number of component waves, all in the specified wave direction, whose amplitudes and periods are selected by the program to give a sea state having the specified spectrum and spectral parameters. The phases associated with each wave component are pseudo-random. OrcaFlex uses a random number generator and the used-defined seed to assign phases. The sequence is repeatable, so the same seed will always give the same phases and consequently the same train of waves. For a given spectrum, sea state and simulation time origin, different wave conditions can be obtained by shifting the wave time origin. For more information, see Setting up a Random Sea. You can use the View Wave Components command (on the Waves tab of the environment data form) to get a spreadsheet that gives details of the wave components that OrcaFlex has used to represent a random or time history wave train. For a random wave train the spreadsheet also reports the spectrum's: • • Mean period T1. This equals m0/m1 where mi denotes the i'th moment of the spectrum. Peak period and frequency Tp and Fm. These are the period and frequency at which the spectrum has the highest spectral density. Spectral Data for JONSWAP and ISSC Spectra The following spectral parameters are available. For the JONSWAP spectrum you have a choice of using Auto or User settings. Auto sets standard spectral parameter values, based only on the specified Hs and Tz. User allows you to specify individual parameters of the spectrum. Hs, Tz, fm, Tp Hs is the significant wave height. Tz is the zero crossing period. Tp and fm are the spectral peak period and peak frequency, i.e. those with largest spectral energy. Note that Tz, Tp and fm are tied together, so setting any one of them sets the other two to match. If you change some other parameter that affects the relationship between Tz, Tp and fm, then Tz is taken as the master data and Tp and fm are updated accordingly. Gamma The peak enhancement factor. For the ISSC spectrum Gamma is determined by Hs and Tz. For the JONSWAP spectrum you have the choice of Auto setting or User setting for Gamma. If Auto is selected then Gamma is automatically calculated by the program using formulae given by Isherwood, 1987. If User is selected then you can specify the value. Sigma1 and Sigma2 The spectral width parameters are reported. These only apply to the JONSWAP spectrum and are fixed at the standard values of 0.07 and 0.09 respectively. Alpha Alpha is the spectral energy parameter. It is calculated by the program to give a sea state with the specified Hs and Tz. 225 w Spectral Data for Ochi-Hubble Spectrum The Ochi-Hubble formulation allows 2-peaked spectra to be set up, enabling you to represent sea states that include both a remotely generated swell and a local wind-generated sea. See Data for Ochi-Hubble Spectra. Spectral Data for User-Defined Spectrum A user defined spectrum is specified by giving a table of values of S(f), where S(f) is the spectral energy as a function of frequency f in Hertz. The values of f specified do not need to be equally spaced. For intermediate values of f (i.e. 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. 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. OrcaFlex reports on the data form the significant wave height and zero-crossing period that correspond to the user-defined spectrum specified. 7.3.6 Drawing Data This data allows you to control the drawing of the various components which make up the OrcaFlex Environment. For a more general discussion of drawing in OrcaFlex see How Objects Are Drawn. Sea Surface Pen Determines how the sea surface, current direction arrow and wave direction arrows are drawn. The current direction arrow is an arrow next to the view axes which points in the direction of the current. This arrow is only drawn if the current speed is not zero and if the Draw Environment Axes preference is ticked. The wave direction arrows are explained below. Secondary Wave Direction Pen When the Draw Environment Axes preference is ticked a wave direction arrow is drawn in the direction of the wave. 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. The first wave train uses the sea surface pen since it is regarded as the dominant one for drawing purposes. All subsequent wave trains' direction arrows are drawn in the Secondary Wave Direction Pen. Wind Direction Pen Determines how the wind direction arrow is drawn. This is an arrow next to the view axes which points in the direction of the wind. This arrow is only drawn if the wind speed is not zero and if the Draw Environment Axes preference is ticked. Seabed Pen The seabed grid is drawn in this pen. 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. This can be used to emphasise the seabed profile data. 226 w 7.3.7 Data for Ochi-Hubble Spectra The Ochi-Hubble formulation allows 2-peaked spectra to be set up, enabling you to represent sea states that include both a remotely generated swell and a local wind generated sea. Hs and Tz Hs is the significant wave height and Tz is the zero crossing period. Their values depend on whether you specify Auto or User. Auto: In this case Hs is specified by the user and the program selects the most probable spectral parameters for that value of Hs. The resulting Tz is then derived and displayed, but cannot be edited. User: In this case the user specifies the spectral parameters explicitly. The resulting Hs and Tz values are displayed, but neither can be edited. Hs1, fm1, Lambda1, Hs2, fm2 and Lambda2 The Ochi-Hubble spectrum is the sum of 2 component spectra, each of which is specified by a set of three parameters: Hs1, fm1, Lambda1 for the lower frequency component and Hs2, fm2, Lambda2 for the higher frequency component. Parameters Hs1 and Hs2 are the significant wave heights of the component spectra; the overall significant wave height Hs is given by Hs = √(Hs1² + Hs2²). Parameters fm1 and fm2 are the modal frequencies of the two components. Finally, Lambda1 and Lambda2 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. You can specify these spectra parameters in two alternative ways: Auto: In this case the program calculates the parameters of the most probable spectrum, based on the overall significant wave height Hs that you have specified. The parameters used are as given in the Ochi-Hubble paper, table 2b. User: In this case you must specify all 6 parameters. The program then derives and displays the corresponding overall Hs and Tz values. Notes: The modal frequency of the first component, fm1, must be less than that of the second, fm2. It is also recommended that fm2 is greater than 0.096. The significant wave height of the first component, Hs1, should normally be greater than that of the second, Hs2, since most of the wave energy tends to be associated with the lower frequency component. 7.3.8 Data for Time History Waves 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. To use this you need to do the following: • Create up a suitable time history text file defining the wave elevation as a function of time. The time values in the file must be equally spaced and in seconds. The elevation values must be the elevation at the global origin used in the OrcaFlex model, measured positive upwards from the still water level specified in the OrcaFlex model, and using the same units as those in the OrcaFlex model. 227 w • • Set the Input File to refer to your time history file. See Data in Time History Files. Set the Minimum Number of Components. This affects the number of Fourier components that will be used to model the time history wave. It should be set high enough to give desired accuracy, but note that using a very large number of components may significantly slow the simulation. See How Wave Time History Data is Used for details. Set the Wave Time Origin to position the required section of wave time history within the simulation period. You can use the View Profile button (on the Waves Preview tab on the environment data form) to see the wave elevation as a function of situation time. • How Wave Time History Data is Used Briefly, OrcaFlex uses a Fast Fourier Transform (FFT) to transform the data into a number of frequency components. 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. 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. Here are the steps in more detail. 1. 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. These will be the time samples from time (T0 - BuildUpDuration) to (T0 + SimulationDuration) where BuildUpDuration is the length of the build-up stage of the simulation, SimulationDuration is the length of the remaining stages and T0 = SimulationTimeOrigin - WaveTimeOrigin. These time origin settings allow you, if you want, to shift the simulation relative to the time history. 2. OrcaFlex then includes more samples, if necessary Let n be the number of samples selected in step 1. In order to achieve the specified minimum number of components, m say, OrcaFlex needs at least 2m samples. So if n is less than 2m then OrcaFlex selects more samples from the file (taken equally from earlier and later in the file) until it has 2m samples. If OrcaFlex runs out of samples in the file while doing this then an error message is given; you must then either provide more samples in the time history file or else reduce the minimum number of components requested. However OrcaFlex also needs the number of samples to be a power of 2, since that is needed in order to use a fast Fourier transform. 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) until the number of selected samples is a power of 2. If OrcaFlex runs out of samples in the file while doing this then it zero-pads (i.e. it adds extra samples of value zero); you will be warned if this happens. 3. OrcaFlex uses a fast Fourier transform to obtain Fourier components The selected time history samples, N of them say, are converted into frequency domain form using a Fast Fourier Transform (FFT). This gives N/2 sinusoidal Fourier components. The View Wave Components button reports their numerical values and the View Spectrum shows their spectrum. 228 w 4. OrcaFlex models the time history wave as the superposition of Airy waves N/2 Airy waves are created, with periods, amplitudes and phases that match the Fourier components. The time history wave is then modelled as the superposition of these Airy waves. Warning: This last step effectively uses Airy wave theory to extrapolate from the global origin, where the surface elevation has been defined, to derive surface elevation at other points and to derive fluid kinematics from the surface elevation readings. This extrapolation introduces errors, which become worse the further you go from the global origin. It is therefore recommended that the global origin (= the point the time history file data applies to) is placed close to the main wave-sensitive parts of the model. 7.3.9 Wave Preview When using a random wave or a time history wave, OrcaFlex provides two preview facilities to aid selection of the wave, namely List Events and View Profile. These are provided on the Waves Preview tab on the environment data form and are documented below. Notes: These commands work in terms of global time, rather than simulation time. 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. If you are using multiple wave trains then these commands report the combined sea state from all of the wave trains. See also Setting up a Random Sea. Position This is the point to which the List Events, View Profile and Horizontal Velocity commands apply. 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, such as a riser top end position. View Profile This plots a time history of wave elevation at the specified Position over the specified interval of global time. An example of the use of these commands is to use List Events to scan over a long period of global time (e.g. 10000 seconds or more), look for large waves and then use View Profile to look in more detail at short sections of interest. Having decided which part of the wave train to use, the simulation time origin can then be set to just before the period of interest, so that the simulation covers that period. Horizontal Velocity This plots how the water horizontal velocity (due to current and waves) varies with depth, at the specified (X,Y) Position and specified global time. List Events This command lists all "severe" wave events in the specified interval of global time and at the specified Position. "Severe" here means that either there is a rise or fall that exceeds the specified height H, or (providing there is only a single wave train) that the wave steepness exceeds the specified steepness S. 229 w Note: The steepness criterion S is not used if there is more than one wave train specified. This is because steepness is measured in the wave direction and when multiple wave trains are present there is not necessarily a unique wave direction. For each event, the height (total rise or fall) is given and an equivalent period is derived from the time interval between the peak and trough. These are then used to calculate, for this water depth, an Airy wave of the same height and period, and the length and steepness of this equivalent Airy wave are given. If there is only one wave train then, for comparison purposes, a reference wave is reported at the top of the table. This reports the Airy wave whose height and period match the Hs and Tz of that single wave train. Finally, various wave elevation statistics are reported for the position and period of time specified. These include the largest rise and fall, the highest crest and lowest trough, the number of up and down zero-crossings and the sample's estimated Hs and Tz values. These statistics enable you to measure how "typical" this wave elevation sample is, compared with the overall parent spectrum. 7.3.10 Setting up a Random Sea Setting up a Random Sea This section gives information on how to set up a random sea using OrcaFlex's modelling facilities. For a detailed description of these, see Wave Data. The most common requirement is to produce a realistic wave train which includes a "design wave" of specified height Hmax and period Tmax. However alternative requirements are possible and it is sometimes useful to impose additional conditions for convenience in results presentation, etc. The height and period of the maximum design wave may be specified by the client, but on occasion we have to derive the appropriate values ourselves, either from other wave statistics (for example a wave scatter diagram, giving significant wave heights Hs and average periods Tz) or from a more general description of weather (such as wind speed). See Wave Statistics for guidance. Having decided what values of Hmax and Tmax are required, we select an appropriate wave train as follows, using the facilities available in OrcaFlex. • Set the significant wave height (Hs) and average period (Tz) for the design storm, and the wave spectrum - ISSC, JONSWAP and Ochi-Hubble options are available. See Setting the Sea State Data for details. Set the number of wave components (typically 100). Components for details. See Setting the Number of • • 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. If no wave of the required characteristics can be found, then adjust Hs and Tz slightly and repeat. See Finding a Suitable Design Wave Event for details. When the required design wave has been located, you can set the simulation time origin and duration so that the design wave occurs within the simulation time, with sufficient time before and after to avoid starting transients and collect all important responses of the system to the design wave. 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 • 230 w of 10 seconds. If the system is widely dispersed in the wave direction, then the simulation may have to be longer to allow time for the principal wave group to pass through the whole system. Since short waves travel more slowly than long ones, this affects simulations of mild sea states more than severe seas. Setting the Sea State Data The ISSC spectrum is a generalised form of the Pierson-Moskowitz spectrum and is appropriate for fully-developed seas in the open ocean. The JONSWAP spectrum is a variant of the ISSC spectrum in which a "peak enhancement factor", γ, is applied to give a greater concentration of energy in the mid-band of frequencies. The Ochi-Hubble spectrum enables you to represent sea states that include both a remotely generated swell and a local wind generated sea. JONSWAP is commonly specified for the North Sea. 2 parameters are sufficient to define an ISSC spectrum - we use Hs and Tz for convenience. For the JONSWAP spectrum, 5 parameters are required, Hs, Tz, γ, and 2 additional parameters σa and σb, (denoted σ1 and σ2 in OrcaFlex), which define the band width over which the peak enhancement is applied. If you choose JONSWAP then you can either specify γ or let the program calculate it (see formulae given by Isherwood (1987). The 2 band width parameters are set automatically to standard values). For the North Sea it is common to set γ = 3.3. If you have to do a systematic series of analyses in a range of wave heights, there are advantages in keeping γ constant. Note that a JONSWAP spectrum with γ = 1.0 is identical to the ISSC spectrum with the same Hs and Tz. Choice of wave spectrum can cause unnecessary pain and suffering to the beginner. For present purposes, the important point is to get the "design wave" we want embedded in a realistic random train of smaller waves. The spectrum is a means to this end, and in practice it matters little what formulation is used. The one exception to this sweeping statement may be 2peaked spectra (e.g. Ochi-Hubble). 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. The phases associated with each wave component are pseudo-random. OrcaFlex uses a random number generator and the used-defined seed to assign phases. The sequence is repeatable, so the same seed will always give the same phases and consequently the same train of waves. The wave components are added assuming linear superposition to create the wave train. Ship responses and wave kinematics are also generated for each wave component and added assuming linear superposition. OrcaFlex currently allows you to specify the number of wave components to use; more components give greater realism but a greater computing overhead. 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, a further infinite set from 101 components and so on. Strictly speaking, 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). This is prohibitively expensive in computing time so we use a much reduced number of components, as noted above. However, this does involve some loss of randomness in the time history generated. For a discussion of the consequences of this approach, see Tucker et al (1984). 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". OrcaFlex provides "preview" facilities for this purpose. If you are looking for a large wave in a random sea, say Hmax = 1.9Hs, then use the 231 w List Events command (on the Waves Preview tab of the environment data form) to ask for a listing of waves with height > H=1.7Hs, say. It is worth looking over a reasonably long period of time at first - say t = 0 to 50,000 or even 100,000 seconds. OrcaFlex will then search that time period and list wave rises and falls which meet the criterion you have specified. Suppose that the list shows a wave fall at t = 647s which is close to your requirement. Then you can use the View Profile command to inspect this part of the wave train, by asking OrcaFlex to draw the sea surface elevation for the period from t = 600 to t = 700s, say. You will then see the large wave with the smaller waves which precede and follow it. Note that when you use the "preview" facility you have to specify both the time and the location (X,Y coordinates). A random wave train varies in both time and space, so for waves going in the positive X direction (wave direction = 0°), the wave train at X = 0 differs from that at X = 300m. You can use the "preview" facility to examine the wave at different critical points for your system. For example, you may be analysing a system in which lines are connected between Ship A at X = 0 and Ship B at X = 300m. 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, then you will usually have to do the analysis twice, once with the design wave at Ship A and once at Ship B. If necessary, adjust Hs and Tz and repeat. If no wave of the required characteristics can be found, then adjust Hs and Tz slightly and repeat. As we noted above, the important point is to get the "design wave" we want embedded in a realistic random train of smaller waves. This is often conveniently done by small adjustments to Hs and Tz. We need make no apology for this. In the real world, even in a "stationary" sea state, the instantaneous wave spectrum varies considerably and Hs and Tz with it. For further discussion see Tucker et al (1984). If you are using an ISSC spectrum, or a JONSWAP spectrum with constant γ, then you can make use of some useful scaling rules at this point. In these 2 cases, provided the number of wave components and the seed are held constant, then: • For constant Tz, wave elevation at any time and any location is directly proportional to Hs. For example, if you have found a wave at time t which has the period you require but is 5% low in height, increasing Hs by 5% will give you the wave you want, also at time t. For constant Hs, the time between successive wave crests at the origin (X = 0, Y = 0) is proportional to Tz. For example, 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, increasing Tz by 5% will give you the wave you want, but at time 1.05t. Note: This rule does not apply in general except at the origin of global coordinates. • These scaling rules can be helpful when conducting a study of system behaviour in a range of wave heights. We can select a suitable wave train for one wave height and scale to each of the other wave heights. This gives a systematic variation in wave excitation for which we may expect a systematic variation in response. If the wave trains were independently derived, then there would be additional scatter. Wave Statistics The following is based on Tucker (1991). Deriving Hmax from Hs Hmax/Hs = K.√[(loge N)/2] 232 w where N is the number of waves in the period under consideration and K is an empirical constant. Since wave statistics are usually based on measurements made every 3 hours, N is usually taken as the number of waves in 3 hours: N = 10800/Tz For extreme storms, K may be taken as 0.9, but for moderate wave conditions as used for fatigue analysis, K = 1 is usually assumed. In extreme storm conditions, it is common to assume a "significant wave steepness" of 1/18, i.e. S = (2π.Hs)/(g.Tz²) = 1/18 hence Tz = √[(2π.Hs)/(g.Ss)] = 3.39√(Hs) for Ss = 1/18 ( Hs in metres, Tz in seconds.) Deriving Tmax from Tz Generally, it can be assumed that 1.05Tz < Tmax < 1.4Tz A common assumption is Tmax = 1.28Tz 7.3.11 Results Summary and Full Results Results tables are available for the Environment reporting Wave length, Wave number, Ursell number and theoretical Breaking wave height. Time History, Statistics and Linked Statistics For details on how to select results variables see Selecting Variables. For Environment results you must specify the global X,Y,Z coordinates of the point for which you want results. Note that the results given are for the sea conditions that apply during the simulation - they therefore include the build-up of wave motion that is done during the build-up stage. The available variables are as follows. Elevation The global Z-coordinate of the sea surface at the specified global X,Y position. Velocity, X, Y, Z-Velocity Acceleration, X, Y, Z-Acceleration 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 specified global X,Y,Z position. If the specified Z position is above the water surface then zero is reported. If the specified Z is below the seabed then the value applicable at the seabed is given. 233 w Current Speed and Current Direction The speed and direction of the current at the specified global X,Y,Z position. Wind Speed The wind speed. Note that this does not depend on the specified global X,Y,Z position. Static Pressure The pressure due to the static head of water at the specified global X,Y,Z position. 7.4 SHAPES 7.4.1 Shapes Shapes are simple 3 dimensional geometric objects that can be used to model two distinct things: 1. elastic solids to model physical obstacles, 2. trapped water to model moonpools or other areas where fluid motion is suppressed. Note: In older versions of OrcaFlex elastic solids were referred to simply as solids. 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 basic shapes available are planes, blocks and cylinders. Elastic solids An elastic solid represents a physical barrier to the motion of lines and buoys. 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 and speed of penetration of the object into the elastic solid. Note: Elastic solids do not resist penetration by Vessels, Links, Winches or other Shapes. Each elastic solid has an associated stiffness, 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. The stiffness is the force per unit area of contact per unit depth of penetration. Where an object interacts with more than one elastic solid simultaneously, the force acting on it is the sum of the individual forces from each elastic solid. Note: A elastic solid with zero stiffness has no effect on the rest of the model. Such shapes can be useful for drawing reference marks on the 3D views, without affecting the behaviour of the model. Trapped water Trapped water can be used to model hydrodynamic shielding - i.e. areas such as moonpools, the inside of spars or behind breakwaters, where wave and current effects are suppressed. Inside a trapped water shape the fluid motion is calculated as if the fluid was moving with the shape. So if the trapped water shape is fixed then no fluid motion occurs in the shape - this could be used to model a breakwater. But if the shape is connected to a moving vessel, for 234 w example, then the trapped water is assumed to move with the vessel - this could be used to model a moonpool. Note: Objects ignore any trapped water shapes which are connected to that particular object. 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, which in turn would affect the fluid forces on the buoy and hence its motion). Such feedback is undesirable so the buoy ignores any trapped water shapes that are connected to it. 7.4.2 Shape Data Name Used to refer to the shape. Type Either Elastic Solid or Trapped Water. Shape Can be one of Block, Cylinder or Plane. Connection Can be Fixed, Anchored or connected to another object (Vessels, 3D Buoys or 6D Buoys). Pens and Number of Lines Each surface of the solid is drawn as a wire frame using one the specified pens. To aid visualisation, the Outside pen is used if the surface is being viewed from the outside of the solid, and the Inside pen is used if it is being viewed from the inside. The Number of Lines determines how many lines are used in the wire frames - a larger value gives a more realistic picture, but takes a little longer to draw. Data for Elastic Solids Stiffness This is the reaction force that the solid applies per unit depth of penetration per unit area of contact. Stiffness may be set to zero, giving a solid that is drawn but which has no effect on the other objects in the system. Damping The percentage of critical damping for the elastic solid. 235 w 7.4.3 Blocks z y Block Position B x-size z-size x y-size A Block shape is a rectangular cuboid, defined by giving: Origin This is the position of one of the block's vertices, defined relative to the connection. This point is taken as the origin of the block's local x,y,z axes. For Fixed connections this is the global position of the point. For Anchored connections the object-relative x,y coordinates given are the global X,Y coordinates of the anchor point, and the z-coordinate is the distance of the anchor above (positive) or below (negative) the seabed at that X,Y position. For connections to other objects, the coordinates of the connection point are given relative to the object local frame of reference. Size This defines the block's dimensions in its local x, y and z directions. With respect to its local axes, the block occupies the volume x=0 to Size(x), y=0 to Size(y), z=0 to Size(z). Orientation This is defined by giving three rotation angles, Rotation 1, 2 and 3, that define its orientation relative to the object to which the block is attached, or else relative to global axes if it is not attached to another object. For example, if the block is attached to an object with local axes Lxyz, then the 3 rotations define the orientation of the block axes Bxyz as follows. First align the block with the local axes of the object to which it is attached axes, so that Bxyz are in the same directions as Lxyz. Then apply Rotation 1 about Bx (=Lx), followed by Rotation 2 about the new By direction, and finally Rotation 2 about the new (and final) Bz direction. 236 w 7.4.4 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 Radii. Length. Object-relative coordinates of one end point of the axis. For Fixed connections the coordinates are relative to global axes. For Anchored connections the object-relative x,y coordinates given are the global X,Y coordinates of the anchor point, and the z-coordinate is the distance of the anchor above (positive) or below (negative) the seabed at that X,Y position. For connections to other objects, the coordinates of the connection point are given relative to the object local frame of reference. • Azimuth and Declination of the axis. The azimuth and declination define the direction of the axis relative to the local axes of the object to which the end is connected. For objects that rotate, such as vessels and 6D buoys, the axis direction therefore rotates with the object. For Fixed or Anchored ends it is defined relative to global axes. Cylinders are drawn using circles to represent the end faces and a number of rectangular facets to represent around the curved surfaces. The number of facets used is the Number of Lines specified; 2 gives a very simple wire frame profile of the cylinder, whilst a very large number gives a pseudo-opaque cylinder at the expense of drawing speed. If the Inner Radius is zero then a solid disc is formed. If the Outer Radius is very large then it is treated as infinite. 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, radially outwards if an object comes into contact with the outer curved surface, normally outwards if an object comes into contact with one of the end faces. 237 w 7.4.5 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. The position of the plane is defined by specifying a Point on Plane through which it passes. The coordinates are object-relative. • • For Fixed connections the point is relative to global axes. For Anchored connections the object-relative x,y coordinates given are the global X,Y coordinates of the anchor point, and the z-coordinate is the distance of the anchor above (positive) or below (negative) the seabed at that X,Y position. For connections to other objects, the coordinates of the connection point are given relative to the object local frame of reference. The angle of the plane is then specified by giving its (maximum) Slope Angle and Slope Direction, relative to the object to which it is connected. • • Consider for the moment a Fixed or Anchored shape. The angle of the plane is specified by giving its (maximum) Slope Angle relative to horizontal (90° is therefore a vertical plane) and Slope Direction. The Slope Direction is the azimuth direction of the line of maximum slope upwards, relative to global axes. 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. A plane with zero slope angle is horizontal with the inside underneath. For a sloping plane, to determine the position and which side is which, begin with a horizontal plane through the Point on Plane. The inside is then on the under side of the plane. Now turn to look along the specified Slope Direction and tilt up to the maximum Slope Angle. Now consider shapes connected to other objects. In this case the Slope Angle and Slope Direction are relative to the object's local x,y plane. 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 object's local x,y plane. Planes are drawn as a rectangular grid, with the specified Number of Lines, centred on the reference point and with a spacing determined by the 3D View Size. Only a part of the infinite plane local to the View Centre is shown. 7.4.6 Drawing Representation of shapes in full on the screen can give a confusing display. OrcaFlex does not provide hidden-line removal as it would be too slow for practical use of the program, so objects are displayed by simple wire-frame drawings. You may exercise control over the display by 238 w selecting the number of lines drawn for each object, and the sequence in which they are drawn. For pen details, see How Objects Are Drawn. Where it is necessary to keep the display simple you should set Number of Lines to 2 for blocks and cylinders, 5 or 7 for planes. If the number of lines is set large for blocks or cylinders they appear as solid objects, although they may take a long time to draw. Please note also that the Number of Lines only affects the drawing, and not the calculations (which are correctly performed with curved geometry). Planes and Blocks are drawn first, and then Cylinders, but otherwise the solids in the model are drawn in the sequence that they were created. You can sometimes take advantage of this, by defining background shapes before foreground ones, to obtain a pseudo-hidden line effect. You are encouraged to experiment, but simplicity is best. Hint: Although the program provides 'depth clues' to the eye by drawing rear faces in a different colour, the eye can sometimes be fooled by the picture - try rotating the view back and forth a few times. 7.4.7 Results For details on how to select results variables see Selecting Variables. Contact Force The magnitude of the total force applied by an elastic solid to other objects in the model. This variable is only available for elastic solids. 7.5 VESSELS 7.5.1 Vessels A Vessel is used to model a ship, floating platform, barge, or any other rigid body whose motion can either be prescribed by a Time History file or else by a set of Response Amplitude Operators (RAOs) or other harmonic motions, superimposed on prescribed motion. vertex 3 edge joining 3 to 5 vertex 5 z (heave) yaw y (sway) pitch V roll x (surge) 239 w Figure: Vessel Model Each vessel has a Vessel Type that determines its RAO and drawing data. To illustrate this, consider a model of a pipe being towed by two identical tugs. This is modelled by creating a vessel type called ‘Tug’ and then creating two vessels, each of type ‘Tug’. The drawing data (defining the tug outline) are data of the Tug vessel type, since they apply to both tugs. Similarly, the RAOs are data of the vessel type, since again they are the same for both tugs. On the other hand the two tugs differ in their positions and prescribed motion, so these are properties of the individual vessel objects. Note: The vessel also has extra drawing data - this is to allow you to set up vesselspecific drawing. For example the lead tug may have a special tow-point fitting that you want to draw. When the vessel is drawn, OrcaFlex first draws the vessel type wire frame and then draws the vessel wire frame. These two wire frames can have different colours, so you can highlight applicationspecific drawing. The vessel is defined relative to a right-handed system of local vessel axes Vxyz, where: • V is the vessel origin for this vessel type. This is chosen by the user when the vessel type is set up. However note that if you specify that the vessel type has symmetry then the vessel origin must be placed on the plane of symmetry or at the centre of circular symmetry; see Vessel Type Data: Symmetry for details. Vx, Vy and Vz must be the directions of surge, sway and heave, respectively, for this vessel type. Note that these directions must therefore be the directions to which the RAOs apply. • Points on the vessel, for example where cables or risers are connected, are then defined relative to these vessel axes. These points then move with those axes as the vessel moves and rotates relative to the global axes, and OrcaFlex calculates these motions automatically. The vessel is drawn, in 3D views of the model, as a "wire frame" of user-specified vertices and edges. This allows a simple visual check that amplitudes, phases etc. are consistent with the applied wave. The vessel wire frame can also be used to do a visual check for interference between lines and vessel structure. As with all points on the vessel, the vertices are defined relative to the vessel axes Vxyz. 7.5.2 Vessel Data Overview The upper part of the vessel data form contains data that specifies the vessel type, geometry and initial position and the lower part contains various tabs containing other data. On the Calculation tab you must choose how the vessel motion is to be obtained. Your choice then determines which of the following other tabs of data are visible: • • • • • • Prescribed Motion. Harmonic Motion Time History Applied Load Multiple Statics Drawing. 240 w Type and Geometry Name Used to refer to the Vessel. Type Specifies the Vessel Type. The Vessel Types button allows you to view and edit the Vessel Type Data. Draught Specifies which set of RAOs to use from the specified vessel type. See Draughts. Length Specifies the length of this vessel. The default value '~' means that this vessel is the same length as the vessel type. If you specify a length that differs from the vessel type length, then OrcaFlex will scale all the vessel type's data to allow for the scaling factor VesselLength / VesselTypeLength. This is useful if you have RAO and drawing data for a 70m ship, for example, but want to use a 50m ship that is otherwise very similar. Note: The RAO scaling is done using Froude scaling (see Rawson and Tupper). Warning: The scaling is done assuming that all dimensions are scaled by the same factor VesselLength / VesselTypeLength. It is therefore only valid if the vessel is an exact scale model of the vessel type. If this is not the case, then scaling introduces errors and should not normally be used. Instead, accurate data specific to this vessel should be obtained. However, for ships in head and stern seas the RAO scaling errors may be acceptable, since the RAOs for these wave directions depend mainly on vessel length. For other cases the RAO scaling is likely to be poor, so OrcaFlex issues a warning if scaling is used and the wave direction is not close to a head or stern sea. Initial Position and Orientation These specifies the vessel's static position relative to the global axes. The Initial Position defines the position of the vessel origin V. The Initial Orientation defines the orientation of the vessel axes Vxyz as three rotations, Heading, 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, then the Trim rotation about Vy and finally the Heel rotation about Vx. If the vessel is not included in the static analysis then this Initial Position is taken to be the static position of the vessel. If the vessel is included in the static analysis, 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. Note: The vessel Z coordinate can only be changed by editing on the vessel data form. Dragging in the Z direction with the mouse is prevented. 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, so if you change the Initial Position you may need to change the harmonic motion phases accordingly. 241 w For other vessel data see Vessel Data: Overview. Calculation Data The following settings (on the Calculation tab on the vessel data form) control how the vessel's static position and dynamic motion are determined. Included in Static Analysis You can control whether the OrcaFlex static analysis calculates the static equilibrium position of the vessel, or simply places the vessel in the user-specified initial position. OrcaFlex first places the vessel at the initial position and orientation specified by the user. If Included in Static Analysis is set to No then OrcaFlex leaves the vessel in this user-specified position. This is not necessarily an equilibrium position. If Included in Static Analysis is set to Yes then OrcaFlex starts from the user-specified position and adjusts the vessel's X, Y and Heading until an equilibrium position is reached. Note that only these 3 free degrees of freedom of the vessel (X, Y and Heading) are included in the calculation. The other three degrees of freedom (Z, Heel and Trim) are assumed to be constrained and so are left at the values specified by the user. Note: 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. Other vessels in the model are included in the static analysis as specified by their own data. Dynamic Analysis The motion of a vessel during the dynamic analysis can be specified in a variety of ways. OrcaFlex allows the vessel motion to be made up of two parts, called the Primary motion and the Superimposed motion. Broadly, the Primary motion is aimed at modelling the steady or low frequency motion of the vessel, whereas the Superimposed motion is aimed at modelling the higher frequency motion, such as that generated by waves. As an example, consider a ship being driven under power along a specified course. In the absence of waves it moves steadily along its course and this would be modelled by the 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 RAOs. OrcaFlex superimposes this latter motion on the primary motion to give the total combined motion of the vessel. You can specify both the Primary and Superimposed motions in a choice of ways, as follows. Primary Motion The Primary motion determines what OrcaFlex refers to as the primary position of the vessel. It can be one of the following options. • • None. 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. Prescribed. This option allows you to drive the vessel around the sea surface, for example to model the vessel moving station during the simulation. The vessel's speed and course is specified using the data on the Prescribed Motion tab on the vessel data form. Calculated. In this option the OrcaFlex calculates the wave drift loads and the vessel slow surge, sway and yaw motion that results from these and other loads. The other loads • 242 w included are those from hydrodynamic and wind drag, damping, applied loads and loads from any lines or other objects that are attached to the vessel. Note: If the primary motion is not Calculated, then OrcaFlex does not calculate the wave drift or damping loads, so those loads will be omitted from the vessel results. • Time History. In this option the user specifies the primary motion in a time history file that defines the vessel Primary X, Primary Y, Primary Z, Heel, Trim, Heading as a function of time. See the vessel's Time History data. Superimposed Motion The Superimposed motion is applied as an offset from the position given by the primary motion. It can be one of the following options. • • None. In this option there is no offset and the vessel position is equal to the primary position at all times. RAOs + Harmonic. In this option the vessel's position oscillates harmonically about the primary position. The harmonically varying offset comes from two sources. Firstly, if waves are present and you specify non-zero RAOs for the vessel type, then the offset will include the wave-generated harmonic motions specified by those RAOs. Secondly, the vessel's superimposed offset also includes any harmonic motions that you specify on the Harmonic Motions tab on the vessel data form. Time History. In this option the user specifies the offset in a time history file that defines the vessel Surge, Sway, Heave, Roll, Pitch and Yaw as a function of time. See the vessel's Time History data. • Report RAOs The Report RAOs button is only available if you set the superimposed motion to RAOs + Harmonic. It provides a spreadsheet showing the RAOs that will be used for this vessel for any given direction. Note that these RAOs may differ from those specified on the vessel type form since they include any scaling and interpolation that OrcaFlex uses when deriving this vessel's RAOs from those of its vessel type. The spreadsheet has a highlighted cell into which you should type the wave direction (relative to the vessel) for which you want to see the RAOs. The spreadsheet then displays the RAOs that OrcaFlex will use, using the RAO conventions specified for this vessel's type. The table covers the wave periods specified on the vessel type data form, plus (if appropriate) the regular wave period specified on the environment data form. For other vessel data see Vessel Data: Overview. Prescribed Motion The prescribed motion data only applies if the vessel's Primary Motion is set to Prescribed. It enables you to drive the vessel around the sea surface along a predetermined path, by specifying how the vessel's primary position and heading change during the simulation. The vessel is driven by specifying, for each stage of the simulation, the forward velocity of the mean position and the rate of turn (the rate of change of the heading). For each simulation stage the velocity of the mean position can be either 1. set to a Constant Velocity that applies throughout the stage. 243 w Warning: This may cause an abrupt change at the beginning of the stage, which may cause transients in the system or 2. specified as a Velocity Change to be applied smoothly throughout the stage. For example, an increment of 1m/s during a stage of length 10 seconds causes an acceleration of 0.1 m/s² to be applied throughout the stage, so that if the vessel starts at rest then at the start of the next stage the vessel is travelling at 1m/s. In addition to changing the velocity of the mean position, you can specify a Rate of Turn for each stage. This is the angle change per second to be applied to the vessel's heading throughout the stage. For other vessel data see Vessel Data: Overview. Harmonic Motion The Harmonic Motion tab (on the vessel data form) only applies if the vessel's superimposed motion is set to RAOs + Harmonic. It allows you to specify a number of harmonic motions of the vessel. The harmonic motions are in addition to any wave-generated motion specified by the RAO data, 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, specified by giving: • • the Period of the harmonic motion; this applies to all 6 degrees of freedom, the Amplitude and Phase of the motion for each of the 6 degrees of freedom of the vessel. If you are modelling slow drift, then note that slow drift normally only applies to surge, sway and yaw, in which case the amplitudes for heave, roll and pitch should be set to zero. Note: 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, sway and heave) or degrees (for roll, pitch and yaw). Similarly, 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. More precisely, 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. Warning: Harmonic motions can be used to model pre-calculated vessel slow drift. If you do this, then if you move the vessel’s Initial Position in the wave direction, or if you change the data for the waves (other than changing the simulation time origin), then you will normally also then 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. For other vessel data see Vessel Data: Overview. 244 w Time History The Time History tabs (on the vessel data form) only apply if the vessel's primary or superimposed motion, or both, are set to Time History. It allows you to specify the motion by giving a time history file. To do this: • • • On the Calculation tab set the primary motion or superimposed motion data item (or both) to Time History. Create a tab-delimited text file containing the time history motion you want. See below for details. On the appropriate Time History tab, set the Input File to the name of the time history file and specify which columns in the file contain the data. The Browse button allows you to specify the file by finding it, and the Import Wizard button then provides a visual way of specifying which column is which. See Time History Files for details. Set the time history's time origin and the simulation time origin (on the Waves tab of the environment data form) so that the simulation covers the period you want. Choose which interpolation method you want OrcaFlex to use when it needs the vessel position and orientation for times between those specified in the time history file. Note: For most purposes we recommend using Cubic Spline interpolation, since it gives continuity of vessel velocity and acceleration. Cubic Bessel interpolation typically gives step changes in acceleration at the specified time samples, and Linear interpolation gives zero acceleration between the times specified and then an infinite acceleration when the velocity changes at a specified time sample. Such acceleration effects can manifest themselves as steps or spikes in the inertial forces on any objects attached to the vessel. • • 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. For primary motion these are Primary X, Primary Y, Primary Z, Heel, Trim and Heading, measured relative to the global axes. For superimposed motion the degrees of freedom that must be specified are Surge, Sway, Heave, Roll, Pitch and Yaw. They are measured relative to the primary position of the vessel, as specified by the vessel's primary motion. The time values in a vessel time history file need not be equally spaced. The units used for all the columns must be the same as those used in the OrcaFlex model, so the time values must be in seconds and angles in degrees. For further details of the file format see Time History Files. 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. If you have suitable data for the wave elevation then you can use that to specify the wave by time history. 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. The position and velocity specified by a time history file for the start of the simulation (i.e. for SimulationTime = -BuildUpDuration) will not, in general, match the static state from which OrcaFlex starts the simulation. 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. 245 w For other vessel data see Vessel Data: Overview. Applied Load You can apply to the vessel an external Global Load that does not rotate if the vessel rotates. This is specified by giving the components of Applied Force and Applied Moment relative to global axes. These components remain constant, so if the vessel rotates then the load does not rotate with it. In addition, you can specify an external Local Load that does rotate with the vessel. This is specified by giving the components of Applied Force and Applied Moment relative to vessel axes. Again these components remain constant, so if the vessel rotates then the load does rotate with it. This is suitable for modelling thrusters, for example. In both cases the Point of Application of the load is specified by giving its x,y,z coordinates relative to vessel axes. Notes: Applied loads will only affect vessel position in the static analysis and only when the vessel is included in the static analysis. Otherwise the vessel position is determined (e.g. by RAOs) and the applied loads are simply reported. The vessel's heave, roll and pitch degrees of freedom are not included in the static analysis, so the components of these loads in these degrees of freedom are ignored. For other vessel data see Vessel Data: Overview. Multiple Statics The offsets for multiple statics calculations are specified here. Offsets are from the vessel's initial position and are specified by giving a range of azimuth and offset values. For example: Azimuths From (deg) 0.0 Offsets From (m) 0.0 To (m) 100.0 Number of Steps 5 To (deg) 180.0 Number of Steps 4 The Azimuths table determines which directions are to be analysed. The Offsets table specifies how far in the given direction the vessel is to be placed. With the above data, the offsets analysed by the multiple statics calculation are as illustrated by the dots in the diagram below: 246 w Y 90 deg X 135 deg 45 deg 180 deg 0m 0 deg 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, to help visualise which offsets will be analysed. For other vessel data see Vessel Data: Overview. Drawing Vessels are drawn as wire frames defined in the data as a set of Vertices and Edges. The Vertices are defined by giving their coordinates relative to the vessel axes Vxyz. The Edges are lines drawn between two vertices. You can define wire frame drawing data in two places - for the vessel and also for its vessel type. The vessel is drawn by first drawing a wire frame based on the vertices, edges and pen specified for its vessel type (see the vessel types data form). Then a further vessel-specific wire frame may be drawn, using any vertices, edges and pen that you specify on the vessel's data form. This allows you to specify a wire frame drawing of the basic vessel type, and then optionally add to it (possibly in a different colour) a wire frame drawing of some equipment that is specific to that vessel. If the vessel length differs from the vessel type length, then the vessel type wire frame is scaled accordingly. Note that either, or both, of these wire frames can be empty (i.e. no edges) if desired. The drawing data do not affect the mathematical model in any way - they are purely for drawing 3D views. The vertices and edges follow the motions of the vessel, and thus may be used to improve understanding of the motion of the model. They can also be used to represent a spar or other equipment attached to the vessel, so that you can then look for clashing with other parts of the system. For example during a simulation replay you can adjust the viewpoint to look exactly along the edge of interest, and check visually if other parts of the model pass through it. For other vessel data see Vessel Data: Overview. 247 w 7.5.3 Vessel Types Vessel Types Each vessel has a vessel type that determines a lot of its data and which is defined on the vessel types form. You can define a number of different vessel types and each type is given a name, which is then used on the vessel data form to specify the type of that particular vessel. Two different vessels can have the same type. To illustrate this, consider a model of a pipe being towed by two identical tugs. This is modelled by creating a vessel type called ‘Tug’ and then creating two vessels, each of type ‘Tug’. The RAOs, for example, are data of the 'Tug' vessel type, since they apply to both tugs. On the other hand the two tugs differ in their positions and any prescribed motion, so these are properties of the individual vessel objects. You don't have to use all, or even any, of the vessel types you define. For example you can set up a data file that defines a number of vessel types but has no vessels. Such a file can then act as a library of vessel types that can be imported into other OrcaFlex data files. Vessel Type Data For each Vessel Type you can enter data for several different draughts, each draught having a user-specified Name. Each vessel in the model must specify (on its vessel data form) which draught to use. It is not possible to use different draughts at different times during the same simulation. Some of the vessel type data apply to all draughts, but a lot of the data is draught-dependent and so separate data is defined for each defined draught. See the following list of the main classes of vessel type data. • • • • • • Geometry and drawing data. Applies to all draughts. Conventions define the meaning of any RAO and wave drift QTF data. The conventions apply to all draughts. RAO data. Separate RAOs are specified for each different draught. Check RAOs facility that provides RAO graphs that help detect errors. Hydrodynamic and Wind Drag data. draught. There is a Separate values are specified for each different Wave Drift data. Separate values are specified for each different draught. Inertia and Damping data. The mass, moments of inertia and centre of mass apply to all draughts, but separate added mass and damping data can be specified for each different draught. Geometry and Drawing Vessel Type Length The length to which the vessel type RAO and drawing data apply. This may be left unspecified ('~'). If a value is specified, then it may be used to scale the vessel type data to the length of the vessel. See Vessel Length for details. Drawing Data Each vessel of this type is drawn as a wire frame, based on vertices and representing the vessel type, plus a wire frame representing vessel-specific features. See Drawing. 248 w Conventions The conventions tab (on the vessel types form) contains settings that define the meaning of both the RAO and QTF data. This enables you to enter RAO and QTF data directly from many other programs without having to convert the values into OrcaFlex conventions. Instead you can tell OrcaFlex the conventions that apply to that data and OrcaFlex will then automatically allow for those conventions when it uses the data. Although RAOs are simple enough in principle, a number of complications make them notoriously error-prone and difficult to check in practice. The main issues are: • • • Different coordinate systems. Different definitions of phase angle and rotational RAOs. Use of vessel symmetry, e.g. to obtain motions in seas from the port side given data for seas from the starboard side. OrcaFlex provides easy ways of handling these problem areas. The use of differing coordinate systems and conventions by different suppliers of data is the main source of confusion. It is vital that you know the conventions that apply to the RAO tables that you are using. Unfortunately, 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. Symmetry You can specify symmetry of the vessel type. 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. The Symmetry can be set to: • • None: The vessel type has no symmetry. The directions specified must cover all the wave directions used in the simulation. XZ plane (or YZ plane): This specifies that the XZ (or YZ) plane through the vessel origin is a plane of symmetry. For each direction given OrcaFlex uses symmetry to derive tables for the reflected direction on the other side of the plane. XZ & YZ planes: This specifies that both the XZ and YZ planes through the vessel origin are planes of symmetry. For each direction given OrcaFlex uses symmetry to derive tables for the reflected directions in the other 3 quadrants. Circular: This specifies that the vessel has circular symmetry about the vessel origin. RAO/QTF tables can only be given for one wave direction, and OrcaFlex uses symmetry to derive tables for all other directions. Warning: If you specify some planes of symmetry then your vessel origin must be on all the planes of symmetry. Or if you specify circular symmetry then you must place your vessel origin at the centre of symmetry. Rotational RAOs Roll, pitch and yaw RAOs may be specified in degrees or radians, relative to a wave of unit amplitude (e.g. degrees/metre), or to a wave of unit steepness or unit maximum slope (e.g. degrees/degree) Wave steepness ( = Waveheight / Wavelength ) is a commonly used angular measure of a wave and maximum wave slope ( = π.Waveheight / Wavelength ) is the true maximum slope of the sea surface. • • 249 w Warning: If rotational RAOs are given relative to wave slope or steepness, then OrcaFlex (internally) converts them to be relative to wave amplitude using the deep water wavelength, not the wavelength for the water depth specified in the model. Note: The translational RAOs are always non-dimensional (e.g. metres/metre or feet/foot). Waves referred to by The RAO and QTF data can be specified by period in seconds, or by frequency in radians/second or Hertz (cycles per second). Note: If you import RAO or QTF data from a text file, the setting specified here will be overridden by that defined in the text file - see Importing RAO Data and Importing QTF Data for details. Phases You can specify phases as leads or lags, in degrees or radians. The phase defines the time at which the maximum positive value of the motion occurs, relative to the time at which the wave crest or trough passes the phase origin. Directions Positive You must specify the directions that correspond to positive motion in the RAO data and positive load in the QTF data. 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. RAOs The vessel type RAOs are only used if the vessel's superimposed motion is set to "RAOs + Harmonic". In this case, in the dynamic analysis the vessel moves harmonically, in all 6 degrees of freedom, about its mean position. These harmonic motions are specified by giving the RAO (response amplitude operator) amplitudes and phases, for all six degrees of freedom, usually for a range of wave periods and directions. For further information see RAOs and Phases. RAO Origin The RAO origin is the point on the vessel whose motion is defined by the RAOs. The RAO origin is specified by giving its coordinates relative to the vessel axes. It is commonly, but not always, at the centre of gravity. Different draughts can use different RAO origins. RAO Phase Origin The RAO phase origin is the point on the vessel that the RAO phase values are relative to; it is specified by giving its x and y-coordinates with respect to vessel axes. The phase values given in the RAOs must be relative to the time that the wave crest or trough (depending on the RAO phase conventions specified) passes the specified RAO phase origin. Often the phase origin is the same as the RAO origin, i.e. the phases are relative to the time the crest or trough passes the point whose motion the RAOs define. In this case the phase origin can be set to '~', meaning 'same as RAO origin'. But some programs (one example being Moses) generate RAOs where the phase origin is not necessarily the same as the RAO origin. 250 w RAO Data RAOs are defined as the ratio of the motion amplitude to the wave amplitude. RAO data can be specified for a number of different wave directions, relative to the vessel. This relative wave direction is labelled on the tab at the bottom of the RAO table. It is the direction in which the wave is progressing, measured positive from the vessel x-direction towards the vessel y-direction. To change the wave direction for one of the RAO tables, select that table and edit the Selected Direction. To insert a new wave direction after an existing direction, select the existing direction's tab and click the Insert Direction button. Similarly, the Delete Direction button deletes the currently selected direction. For each direction, the RAO table covers a range of wave periods or frequencies, as specified in the conventions data. The periods/frequencies need not be entered in order - they will be sorted before use. In the case of a circular symmetric vessel, RAOs are specified for only one wave direction OrcaFlex will derive RAOs for all other directions. RAO Interpolation/Extrapolation You must provide RAO tables that include or span the wave direction(s) involved in the simulation. If RAOs are required for a wave direction for which an RAO table has not been supplied, then OrcaFlex will use linear interpolation to obtain an RAO table for that direction. For regular wave analysis, RAO data is only needed for the appropriate wave period, or for wave periods either side of that period. For random sea simulations, RAO data should be specified for a wide enough range of wave periods to cover the spectrum. The View Wave Components button (on the Waves tab of the environment data form) reports the wave frequencies that OrcaFlex will use to represent the spectrum. Note: If the vessel length differs from the vessel type length then the RAO periods specified on the vessel type form are Froude scaled, and it is these Froude scaled periods that must cover the actual wave period(s). Linear interpolation is used if RAOs are required for a period that is between the periods given in the table. 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. However if RAOs are required for a period outside the range of periods given then OrcaFlex will use linear extrapolation; a warning is given if this occurs. You can avoid the need for extrapolation by providing RAOs for periods zero and Infinity. The RAOs for the zero period limit must be all zero (since no object can respond to an infinite frequency wave). For the Infinity period limit the RAOs of a free-floating vessel can be derived from the knowledge that the vessel must surface follow in a sufficiently long wave. See RAO Quality Checks for details. Warning: Interpolation is likely to be poor if the interval involved is large. We therefore recommend that the RAO directions defined cover all the wave directions that will be used and in steps of 30 degrees or less. Note that RAO interpolation and extrapolation is done using the complex value representation of the RAOs, in which the RAO with amplitude A and phase lag P is represented by the complex number: C(A,P) = A.(cos(P)+i.sin(P)). So given RAOs (A1,P1) at period T1 and (A2,P2) at period T2, the interpolated RAO at period (T1+T2)/2 is (A,P) where: 251 w C(A,P) = ( C(A1,P1) + C(A2,P2) ) / 2 This gives better results than interpolating the amplitude and phase separately. Drag Loads Hydrodynamic and wind drag loads on a vessel are square law loads due to the relative velocity of the fluid past the vessel. They can be modelled using the data on the Hydrodynamic Drag and Wind Drag tabs on the vessel type data form. If the length of the vessel differs from that of the vessel type then the vessel type data will be scaled accordingly. Drag loads are an important source of damping when modelling vessel slow drift. discussion of the various damping sources see Damping Effects on Vessel Slow Drift. For a The velocity used to calculate the drag loads is the relative velocity of the fluid past the vessel. This includes any current or wind velocity and the vessel due to any primary motion. The drag forces and moments due to translational motion are modelled using the standard OCIMF method. The drag forces and moments due to any vessel rate of yaw are modelled using yaw rate drag load factors. For details of how the loads are calculated, see Vessel Theory: Drag Loads. Warning: The current and wind loads are based on theory for surface vessels and are not suitable for submerged vessels. Load Origin The coordinates (relative to vessel axes) of the point on the vessel at which the hydrodynamic or wind drag loads are calculated and at which they will be applied. This need not be at the vessel origin. It is normally best to place the load origin at the centre of the vessel. The velocity used in the hydrodynamic drag load calculation is the relative current velocity at the load origin, allowing for any velocity of the load origin due to prescribed motion of the vessel. The velocity used in the wind load calculation is the wind velocity at 10m above mean water level, minus any velocity of the wind load origin due to prescribed motion of the vessel. Load Symmetry Specifies what symmetry the vessel type has below (for hydrodynamic drag) or above (for wind drag) the water line. For XZ and YZ symmetry, OrcaFlex will use the symmetry to derive load coefficients for extra directions generated by reflection in the specified vessel axes planes. For circular symmetry, you must specify coefficients for one direction only and OrcaFlex will use symmetry to derive coefficients for all other directions. Note: The symmetry for hydrodynamic drag, wind drag and RAOs (see RAO Symmetry) need not be the same, though of course the symmetry for hydrodynamic drag would normally be the same as that for RAOs. 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: Drag Loads. Coefficients Load coefficients are specified for the vessel surge, sway and yaw directions. They depend on the direction of the current or wind, relative to the vessel (direction 0 meaning from astern, 90 meaning from starboard, etc.). 252 w OrcaFlex uses any symmetry specified to derive coefficients for other directions and then uses linear interpolation to derive coefficients for intermediate directions. Note: When the symmetry is XZ and YZ the yaw moments must be zero, so OrcaFlex forces zero yaw coefficients in this case. 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, and the curve shows the interpolated coefficients that will be used for intermediate 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. Yaw Rate Drag Factors The yaw rate drag factors only apply to the hydrodynamic load data. They determine the yaw drag moment, and any surge and sway drag forces, that result if the vessel has a non-zero rate of yaw. With wind drag this effect is insignificant. For a slender ship, and if the load origin has been placed at the centre of the vessel, then the surge and sway drag factors can usually be taken to be zero, and then yaw drag factor can be estimated based on the vessel length and draught. See Drag Loads due to Yaw Rate for details. Wave Drift Loads The Wave Drift tab on the vessel type form contains the Quadratic Transfer Functions (QTFs) that OrcaFlex uses to calculate a wave drift load (sometimes called the slow drift load). Note that the wave drift load is only calculated for a vessel that has its primary motion set to Calculated. See Modelling Vessel Slow Drift for details. See Wave Drift Load Theory for details of how OrcaFlex calculates the wave drift loads. QTF Origin The QTF origin is the point on the vessel to which the QTFs apply. The wave drift loads are calculated based on the wave conditions at this point and they are applied at this point. The QTF origin is specified relative to the vessel axes and different draughts can use different origins. There is no need to specify the z-coordinate of the point since the loads are calculated and applied only for the surge, sway and yaw degrees of freedom. Wave Drift QTFs The way QTF data is entered in OrcaFlex has many similarities with RAO data. In particular: • For each draught, QTF tables are specified for each of a number of wave directions. To insert a new table use the Insert Direction button and to delete a table select that table's tab and then click the Delete Direction button. To change the direction associated with a table, select that table's tab and then edit the Selected Direction value. Some of the RAO conventions apply to the QTFs. The relevant conventions are shown on the Wave Drift tab as a reminder, but to edit them you must go to the Conventions tab. If the vessel type has some symmetry (see the conventions tab) then OrcaFlex automatically generates QTF tables for all the reflected directions implied by that symmetry. You must provide QTF tables for enough directions for OrcaFlex to have data (either userspecified or generated based on symmetry) for directions that cover the wave directions the vessel will experience. • • 253 w • Each QTF table consists of data for a range of wave periods or frequencies (depending on the convention specified). 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. Warning: The settings on the conventions tab apply to all draughts and they apply to both the vessel type's RAOs and to its wave drift QTFs. If your RAO and QTF data use different conventions you will therefore need to transform you QTFs into the conventions of the RAOs (or vice versa) before using them in OrcaFlex. QTFs are only entered for surge, sway and yaw, since OrcaFlex does not calculate wave drift loads (or vessel slow drift) for heave, roll and pitch. This is because the heave, roll and pitch wave drift loads are normally not significant when compared to the typically much larger buoyancy restoring forces in those degrees of freedom. The QTF amplitudes are entered in non-dimensional form. No phases are required because only the diagonal terms of the full QTF matrix are entered in OrcaFlex, and these diagonal terms always have zero phase. OrcaFlex uses Newman's approximation to obtain the offdiagonal QTFs from the diagonal QTFs specified. See Wave Drift Load Theory for details. Importing QTFs Wave drift QTF data can be imported into OrcaFlex from text files in one of two different formats. Standard format is the same as the text format used to import RAOs, except of course that no phases or heave, roll or pitch data are required. Here is a simple example: *** OrcaFlex Start Data *** Draught Transit Direction 45 WP surge sway yaw 0.0 0.030 0.090 -0.006 5.0 0.030 0.090 -0.006 10.0 0.001 0.005 -0.002 15.0 0.000 0.001 -0.001 Infinity 0.000 0.000 0.000 *** OrcaFlex End Data *** NMIWAVE format is for use with the NMIWAVE diffraction program. The file should be the text NMIWAVE output file with a new line containing the string 'NMIWAVE Wave Drift' inserted at the start of the file. Here is an example: *** NMIWAVE Wave Drift Data *** Scaled Tanker: Lpp, B, T (m) =310.90 ,48 0.31090E+03, -0.10000E+01, 0.10250E+04 45.00 1 0.50000E+01, 0.30000E-01 0.10000E+02, 0.10000E-02 0.15000E+02, 0.00000E+00 -0.10000E+01, 0.00000E+00 2 0.50000E+01, 0.90000E-01 0.10000E+02, 0.50000E-02 etc. Note that NMIWAVE uses the ITTC conventions, which are surge +ve forward, sway +ve to starboard, heave +ve down, roll +ve starboard down, pitch +ve bow up, yaw +ve bow to 254 w starboard. If your RAOs also use these conventions then they can be set on the Conventions tab. Otherwise you will need to modify the data to allow for convention differences. The wave heading convention used by NMIWAVE is that wave heading is measured +ve clockwise when viewed from above, and zero wave heading means a stern wave. This is the same as OrcaFlex uses, except that OrcaFlex measures +ve anti-clockwise. OrcaFlex automatically handles this by changing the sign of the wave headings when an NMIWAVE file is imported. Inertia and Damping The Inertia and Damping tab (on the vessel type form) contains the following data that is only used if the vessel's primary motion is set to Calculated. The main use of this data is when modelling vessel slow drift. Centre of gravity (CG) The coordinates of the vessel type's centre of mass, relative to vessel axes. Mass and Moments of Inertia The vessel type's mass and its moments of inertia about axes through the CG in the vessel x, y and z directions. This should include the structural and contents mass and inertia, but not the added mass. Added Mass and Damping matrices The damping and added mass matrices are specified with respect to axes through the CG in the vessel x, y and z directions. These matrices are multiplied by the vessel velocity and acceleration, respectively, to obtain the resulting load resisting the motion. For details of the units of this data, and the theory used, see Vessel Theory: Added Mass and Damping. These matrices can generally be obtained from the results of a diffraction program. They are assumed to be frequency independent over the range of frequencies involved in wave drift motion, so you should specify values that are appropriate to the vessel motion frequency you expect. Since the data is used by OrcaFlex in the calculation of the slow drift motion of the vessel, it is normally appropriate to enter low frequency values. The damping matrix given by a diffraction program models wave radiation damping. However there is another, often more important, source of damping, namely wave drift damping. See Damping Effects on Vessel Slow Drift. Wave drift damping can be modelled in OrcaFlex by adjusting the diagonal entries in the damping matrix. Importing RAOs The Import RAOs button on the vessel types forms enables RAO data to be imported into OrcaFlex from text files or from a *.rao file exported by OrcaMotion. Import RAOS from *.rao Files The preferred method of importing RAOs is from text files (see below) but you can also import from an OrcaMotion *.rao file. In this case please note the following: • Each OrcaMotion file contains data for one wave direction, but the direction is not defined in the file. Therefore, to import from a *.rao file, you must select the draught and direction to which the *.rao file applies and then click the Import button. The imported data will overwrite the RAO table for the currently selected draught and direction. 255 w • Because the data in *.rao files always use the Orcina standard conventions, the conventions data in OrcaFlex will be set to these standard conventions. Warning: These conventions apply to all RAO data for this vessel type, so any existing data that does not conform to the standard Orcina conventions, will be invalidated by importing a *.rao file. Import RAOS from Text Files You can use text files to import RAO data from some other source, for example from a ship response calculation program or from model test results. Note: When you import RAOs from a text file, any RAO data previously present in OrcaFlex for the draughts given in the text file will be deleted. (Other data for these draughts, e.g. wind and hydrodynamic drag data, will not be affected.) So for each draught you import, all the RAOs for that draught must be in a single file. You can therefore either put all the RAOs in a single file, or else have separate files for separate draughts. RAO data in a text file can be imported providing that the data appears in tabular form and markers are first inserted into the file to identify the data to OrcaFlex. This saves the laborious and error prone job of typing in a large table of RAO data. The markers, described below, can be inserted using a text editor or word processor; if using a word processor, note that the file must be saved as an ASCII text file and not as a word processor document. A text RAO file must contain the RAO data in the following form. It is usually easy to create a suitable file by adding a few lines to your original response data file. See the examples. • The RAO data must appear in the file in one or more tables, each table being for one draught and direction. To enable OrcaFlex to find the tables, each table must be preceded by a line containing the string OrcaFlex RAO Start Data and must be immediately followed by a line containing the string OrcaFlex RAO End Data. There must not be any blank lines between these two marker lines. Any mixture of upper and lower case is accepted. Immediately following the line containing the OrcaFlex RAO Start Data string there must be two lines (in either order) specifying the draught and direction that applies to that table. The line specifying the draught must be of the form Draught DraughtName, where DraughtName is the name of the draught (a string, without any spaces). The line specifying the direction must be of the form Direction n, where n is a number specifying the direction the wave is progressing, in degrees, measured positive from forward towards the port side. So direction 0 means waves coming from astern and direction 90 means waves coming from the starboard side. Following these two lines, the first line of the table must be a set of headers defining the subsequent columns. This headers line consists of a number of character strings, separated by spaces. The strings indicate the contents of the columns; the following header strings are recognised by OrcaFlex; otherwise the corresponding column is ignored. See Header Strings for Text RAO Tables If you want OrcaFlex to ignore a column, for example because it contains irrelevant or superfluous data, then insert a header string, (e.g. "N/A" or "~") that is not listed in the above table. In particular, if the table contains both wave period and frequency you must indicate that one of these is to be ignored, since OrcaFlex will not accept two columns specifying the same information. The remaining lines in the table must contain numbers, one for each header in the headers line, separated by any string of characters that cannot appear in a number (i.e. anything except 0..9,-,+,. or E). Please note that it is the order of the columns that matters, not their • • • • 256 w actual position across the page. Hence, although it is natural to align the headers above the columns of numbers, this is not in fact necessary. • There is no provision for specifying the associated conventions (other than whether the RAOs are given by period or frequency) in the text file; the conventions data must be set to correspond to the imported data. Since the conventions apply to all RAO data for the vessel type, the period/frequency convention specified by the header (WP or WFH or WFR) must be consistent throughout the file. Similarly, the input origin to which the RAOs apply is not read in, but must be set on the Vessel Type form. Header Strings for Text RAO Tables When importing RAOs from a text file, the following strings can be used in the headers line. Header string WP WFH WFR XA XP YA YP ZA ZP RXA RXP RYA RYP RZA RZP Column contains Wave period in seconds Wave frequency in Hz (cycles per second) Wave frequency in radians/second Surge amplitude Surge phase Sway amplitude Sway phase Heave amplitude Heave phase Roll amplitude Roll phase Pitch amplitude Pitch phase Yaw amplitude Yaw phase. (In these header strings X, Y and Z represent the vessel axes, 'A' denotes amplitude, 'P' denotes phase and 'R' rotation about the given axis.) RAO Data Checklist To derive vessel point motions, you need to obtain data giving both RAOs and phases for the vessel for the relevant wave period. You also need to know what conventions apply to your data; these may be documented with the data, but sometimes you may have to deduce what they are. 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, but you need to be sure. If it is not specified check with your data supplier. Are the responses in dimensional or RAO form? RAO form is the most common; data giving dimensional form would have to also give the corresponding wave amplitudes/heights. OrcaFlex will only accept RAO form. 257 w In what form are the rotational roll, pitch and yaw RAOs? Units such as degrees/metre or radians/metre almost always mean the rotational motions are relative to waves of unit amplitude. Very rarely, rotational RAO amplitudes are given per unit wave height (i.e. double amplitude) check your data source. In this case you will have to divide the RAOs by 2 manually, before entry to OrcaFlex. Units such as degrees/degree, radians/radian, or no units, imply rotational RAOs relative to waves of unit steepness or maximum slope. For long wave periods in deep water, the rotational RAOs in the wave plane (e.g. 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. Are the phases in degrees or radians? Unless you only have a small amount of data, this should be obvious from the range of phase values. What directions are positive for surge, sway, heave, roll, pitch and yaw? Often they are surge positive forward, sway positive to port, heave positive up, but some authors use heave positive downwards. Roll, pitch and yaw are usually positive when clockwise about the positive surge, sway and heave directions. Most data sources use right-handed axes, but not all. OrcaFlex allows complete generality in its data input, but you must find out how your data are defined. To what phase time origin are the phases relative? OrcaFlex allows you to specify that the phases to be relative to the time the wave crest or trough passes the phase origin. The passage of the crest passed the RAO origin is the most common phase time origin, but you need to check and tell OrcaFlex - see note on phase leads/lags below. Are the phases leads or lags? Phase conventions are sometimes documented by giving the formula used to represent the harmonic motion. Commonly used ones are: • • A.cos(w.t - P) or A.cos(P - w.t) imply that phase P is a lag. cos(w.t + P') implies that phase P' is a lead. Using sine rather than cosine in the above formulae has no effect on whether the phases are leads or lags. Checking RAOs The Check RAOs button on the vessel types form allows a visual check on the RAO data. For a given draught and wave direction, it displays graphs (one for each vessel degree of freedom) showing how the RAO and phase vary with wave period. The graphs initially show the RAOs for the currently selected draught and direction. You can switch to other draughts and directions, either by using the navigation buttons at the bottom of the form to step through the data, else or by selecting from the drop-down lists. You can change the scale of the graphs (double click on the graph and change the ranges of the axes). This is useful if the curve does not initially fit on the graph. 258 w R φ 0 0 Figure: RAO Graph for Amplitude (R) and phase (φ) The graphs depicts the RAO data specified by the user for the specified RAO origin. 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. The point at the origin represents the 'short' wave (zero period) response and always has zero amplitude (this is enforced by OrcaFlex since no vessel can respond to infinitely fast waves). Moving along the curve away from the origin corresponds to the wave period increasing from zero. For surge, sway and heave, the other end of the curve is the 'long' wave RAO data specified for period 'Infinity'. For roll, pitch and yaw, the RAO data for period 'Infinity' cannot (for technical reasons) be included in the curve, 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. This is calculated by OrcaFlex and only applies to free-floating vessels. Also the yaw response limit only applies to slender vessels (i.e. to vessels that are long in the x-direction and narrow in the y-direction). See RAO Quality Checks for details of the expected long wave RAOs. Warning: The expected long wave response limits calculated by OrcaFlex only apply to free-floating vessels. Also, the yaw response limit only applies to slender vessels (i.e. to vessels that are long in the x-direction and narrow in the ydirection). 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. See How to Check RAO Data for details. The graph represents RAOs as points in polar coordinates (R,φ), where: • R is the non-dimensional amplitude. For surge, sway and heave R is the vessel motion amplitude divided by the wave amplitude. And for roll, pitch and yaw, R is the rotational response normalised with respect to maximum wave slope - i.e. it is vessel rotation amplitude divided by the maximum wave slope. φ is the phase lag from the time the wave crest passes the RAO origin until the maximum positive motion occurs. Note: Positive here means as in the OrcaFlex conventions (not necessarily the same as the vessel type RAO conventions). So positive surge is forward, positive sway is to port, positive heave is up, positive roll is starboard down, positive pitch is bow down and positive yaw is bow to port. • • 259 w This polar coordinates way of representing RAOs is better than drawing separate graphs of amplitude and phase, since it presents all the information on a single graph and also the resulting curves are smooth, whereas phase graphs frequently show phase jumps. How to Check RAOs For each draught and wave direction, you should check that the curves on the RAO graphs are reasonably smooth and approach the circle, which is the expected long-wave limit for a freefloating vessel. Note that: • The curve may not approach the expected long wave limit if the RAO data does not include values for any long waves. Wave periods over 20 seconds for ships, or 30 seconds for semisubmersibles, are considered to be sufficiently long for this purpose. The curve might also not approach the circle if the vessel is not free-floating. For example the heave RAO amplitude of a tension leg platform will not approach the usual long wave limit of 1. The circle on the yaw graph only applies to slender vessels (i.e. long in the x-direction and narrow in the y-direction). Smooth graphs can only be expected if the data includes RAOs for reasonably closely spaced periods. 1.5 1.5 • • • As examples, consider the following three example graphs: 1.5 1 1 1 0.5 0.5 0.5 0 0 0 -0.5 -0.5 -0.5 -1 -1 -1 -1.5 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1.5 -1 -0.5 0 0.5 1 1.5 The first graph shows a typical, well-behaved set of RAO data - the curve is smooth and the long-wave limit agrees with the expected value marked by the circle. For a freely floating vessel, the second graph is clearly in error, since the curve does not lead to the expected long wave limit. The RAO data for long waves (represented by the end of the curve) has the correct amplitude, but its phase differs by 180º from the expected long-wave value (represented by the circle). 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 else that the convention data for the direction of positive motion has been set wrongly (this would give a phase error of 180º). The curve on the third graph approaches the expected long wave limit, but then suddenly goes to zero. This suggests that the RAO data for period 'Infinity' has not been set correctly and is zero. Common Problems It is not unusual to be given RAO data for a vessel but not be given all the conventions apply to the data. Below are some common problems and their symptoms. But beware that several common problems have very similar symptoms, 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. It is therefore important to get as much information as possible from the original RAO data supplier. 260 w • The quoted wave direction might be measured clockwise (viewed from above) from the xdirection, rather than anticlockwise (which is the OrcaFlex convention). The effect would be a 180 degree shift in the sway, roll and yaw phases. The quoted wave direction may be the direction the wave is coming from, rather than the direction it is progressing towards (which is the OrcaFlex convention). The effect would be to negate all the phase values. The phases may be leads instead of lags (OrcaFlex will accept either - see RAO Phase Conventions). The effect of an error here would be to negate all the phase values. • • 7.5.4 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. The first order terms generate motion at wave frequency and this is modelled in OrcaFlex using RAOs. The second order terms are much smaller but they include loads with a much lower frequency. 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. One common situation where the wave drift loads can matter is with a moored vessel. The vessel's natural frequencies in surge, sway and yaw are typically quite low and so the low frequency wave drift loads can generate quite significant slow drift excursions. If you have already calculated the vessel slow drift motion then that motion can be applied in OrcaFlex using harmonic motion or a time history file. But OrcaFlex can calculate and apply the slow drift motion for you. To do this you need to do the following: • • • • Specify QTF data on the wave drift tab of the vessel type form. The wave drift loads are calculated based on this data. Specify the vessel centre of gravity, mass, moments of inertia, added mass and damping properties. This data is on the Inertia and Damping tab on the vessel type form. Specify appropriate data for the hydrodynamic and wind drag loads, any applied load, etc. Set the vessel's primary motion to Calculated. This tells OrcaFlex to apply the mean wave drift load to the vessel during the static analysis, and then in the simulation to apply the time varying wave drift load and calculate the low frequency vessel surge, sway and yaw motion that results from these and other loads. The 'other loads' referred to here are any specified hydrodynamic or wind drag, loads from added mass or damping, applied loads and loads from any lines or other objects that are connected to the vessel. Set the vessel's superimposed motion according to whether and how you want to model first order wave frequency motion. • In the dynamic simulation OrcaFlex will then calculate all the loads on the vessel and the resulting slow surge, sway and yaw motion. Damping Effects on Vessel Slow Drift Drag and damping loads have an important effect on vessel slow drift motions. The following discussion documents the various damping effects and how they are modelled in OrcaFlex. See CMPT (1998) section 3.12. • Hydrodynamic drag and skin friction on the vessel hull. This is modelled in OrcaFlex using a combination of the OCIMF approach plus a yaw drag moment proportional to (yaw rate)^2. See the Hydrodynamic Drag data on the vessel type data form. For details of the 261 w theory see Vessel Theory: Drag Loads. Note that OrcaFlex does not yet have the dependency of yaw drag on sway velocity proposed by Wichers, 1979. • Wind drag on the vessel hull. This is the aerodynamic drag due to wind and any vessel velocity. It is modelled in OrcaFlex based on the OCIMF approach. See the Wind Drag data on the vessel type data form. For details of the theory see Vessel Theory: Drag Loads. Hydrodynamic drag on the risers/moorings. This is modelled in OrcaFlex by the drag force part of the Morison force on the lines that model the risers/moorings. Wave radiation damping. This is not usually very significant at low frequencies, because the asymptotic limit of the wave frequency damping is zero. It can be modelled in OrcaFlex using the damping matrix on the vessel type form. Wave drift damping. This arises because the wave drift loads vary with vessel velocity. It can be modelled in OrcaFlex by including it in the damping matrix on the vessel type data form. See CMPT (1998) page 3-78 and Faltinsen (1990) page 161. Material damping in the risers/moorings. This is the structural damping in the material of the risers and mooring lines. This can be modelled in OrcaFlex by the line target damping value. However Triantafyllou et al (1994) concluded that its effect is negligible. 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. It is modelled in OrcaFlex by the friction between the seabed and the line used to model the mooring/riser. However Triantafyllou et al (1994) concluded that its effect is negligible. • • • • • 7.5.5 Vessel Results For details on how to select results variables see Selecting Variables. Results Tables The results tables report the position of the vessel, plus the loads acting on it from various sources. The loads are labelled according to their source: • • • Applied load is the sum of the local and global applied loads specified on the vessel data form. Current and Wind loads are those that result from the vessel type's current and wind properties. Connections load is the total load from all attached lines, links, winches, solids, etc. In mooring analysis this is therefore the mooring load if only mooring lines are attached to the vessel. Dynamic Results For vessels the results variables available in dynamics are as follows: Position Results The vessel motion is split into two components called the primary and superimposed motions. To provide both components of the motion, plus the total overall motion, OrcaFlex provides the following 3 sets of positions results. 262 w Primary X, Primary Y, Primary Z, Heel, Trim, Heading The primary position of the vessel, as produced by any primary motion, relative to global axes. So Primary X, Primary Y and Primary Z are the global X,Y,Z coordinates of the primary position of the vessel origin, and Heel, Trim and Heading are the primary orientation of the vessel, again relative to global axes. Trim is in the range -90 to +90. Range jump suppression is applied to Heel and Heading (so values outside the range -360 to +360 degrees might be reported). Surge, Sway, Heave, Roll, Pitch and Yaw The offset of the vessel, due to any superimposed motion, relative to the primary position of the vessel. They are therefore the wave-generated part of the motion, so Surge, Sway and Heave are the offsets from the primary position to the final position and are measured in the primary vessel axes directions. And Roll, Pitch and Yaw are the wave-generated rotations and are relative to the primary vessel axes directions. Pitch is in the range -90 to +90. Range jump suppression is applied to the Roll and Yaw angles (so values outside the range -360 to +360 degrees might be reported). X, Y, Z, Rotation 1, Rotation 2 and Rotation 3 The position of the vessel, relative to global axes, due to the combination of the primary and superimposed motion. So X, Y and Z are the global coordinates of the final vessel origin position and Rotation 1, 2 and 3 define the final orientation relative to global axes. The 3 rotations (called Euler angles) are 3 successive rotations that take the global axes directions to the final axes directions. Rotation 2 is in the range -90 to +90. Range jump suppression is applied to the Rotation 1 and Rotation 3 angles (so values outside the range -360 to +360 degrees might be reported). Force and Moment Results Force, Lx-Force, Ly-Force and Lz-Force Moment, Lx-Moment, Ly-Moment and Lz-Moment The magnitude and components (in vessel axes directions) of the total force and moment exerted on the vessel. The moments are about the vessel origin. These results include applied loads and drag loads and loads from any objects connected to the vessel. If the Primary Motion of the vessel is set to Calculated, then they also include the wave drift loads and the damping loads. They do not include weight and buoyancy loads. Multiple Static Results For multiple statics calculations the results variables available are as follows. The loads reported are the total loads, including those from current, wind, applied loads and attached lines and other objects. Restoring Force The magnitude of the horizontal component of the total force applied to the vessel. Note that this force is not necessarily in the offset direction. Vertical Force The vertically downwards component of the total force applied to the vessel. 263 w GZ-Moment The total moment, about the vertical, applied to the vessel. Worst Tension The largest tension in any segment of any Line connected to the Vessel. 7.6 3D BUOYS 7.6.1 3D Buoys OrcaFlex 3D Buoys are simplified point elements with only 3 degrees of freedom -X,Y and Z. They do not rotate, but remain aligned with the global axes. They therefore do not have rotational properties and moments on the buoy are ignored. They should therefore be used only where these limitations are unimportant. 3D Buoys are able to float part-submerged at the surface, and may also be used independently, with no lines attached. Although they are much less sophisticated than 6D Buoys, 3D Buoys are easier to use and are convenient for modelling buoys at line junctions etc. height/2 z B y x Buoy Axes always aligned with Global Axes height/2 Figure: 3D Buoy 7.6.2 Data Name Used to refer to the 3D Buoy. Included in Static Analysis Determines whether the equilibrium position of the buoy is calculated by the static analysis. See Buoys Included in Static Analysis. 264 w Mass Mass or weight in air. Volume Used to calculate buoyancy and added mass. Bulk Modulus Specifies the compressibility of the buoy. If the buoy is not significantly compressible, then the Bulk Modulus can be set to Infinity, which means "incompressible". See Buoyancy Variation with Depth. Height Used to model floating buoys correctly, where the buoyancy, drag etc. vary according to the depth of immersion. It also determines the height used to draw the buoy. The Height is the vertical distance over which the fluid-related forces change from zero to full force as the buoy pierces the surface. It is taken to be symmetrical about the buoy's origin. Initial Position Specifies the initial position for the buoy origin as coordinates relative to the global axes. If the buoy is not included in the static analysis then this initial position is taken to be the static position of the buoy. If the buoy is included in the static analysis, 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. See Include Buoys in Static Analysis. Drag Drag forces are applied in each of the global axes directions OX, OY and OZ. For each direction you must specify a Drag Coefficient and Drag Area. Added Mass You must specify the added mass coefficient Ca for each global axis direction. The added mass is set to be Ca multiplied by the mass of water currently displaced. The inertia coefficient, Cm, is set automatically to equal 1+Ca. 7.6.3 Results For details on how to select results variables see Selecting Variables. For 3D Buoys the available variables are: X,Y and Z Positions of the buoy origin, relative to global axes. Surface Z Elevation of the sea surface directly above the instantaneous position of the buoy origin. 265 w Dry Length Length of buoy above the water surface, measured along the buoy z axis. For this purpose, the z-extent of a 3D buoy is assumed to be ½ Height either side of its volume centre. 7.7 6D BUOYS 7.7.1 6D Buoys 6D Buoys are objects having all six degrees of freedom - 3 translational (X,Y and Z) and 3 rotational (Rotation 1,2 and 3). The forces acting on a buoy are mass, buoyancy, added mass and damping and drag in the three principal buoy directions. Corresponding moments are applied for the rotational degrees of freedom. Buoys can be surface-piercing, and have a notional height; this allows the hydrostatic and hydrodynamic forces to be proportioned depending on the depth of immersion. 6D Buoys can have wings attached to them. A wing is a rectangular surface, attached to the buoy at a specified position and orientation, which experiences lift and drag forces, and a moment, due to the relative flow of the sea past the wing. Lines attached to a 6D Buoy can thus experience both moment effects and translations as the buoy rotates under the influence of hydrodynamics and applied loads. Lines can be attached to an offset position on a buoy - this allows the direct study of line clashing, including the separation introduced by spaced attachment points. Three types of 6D Buoy are available, the differences being the way in which the geometry of the buoy is defined. Lumped Buoys The first type, Lumped Buoys, are specified without reference to a specific geometry. This necessarily restricts the accuracy with which interactions with the water surface are modelled. 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 (thus buoyancy changes linearly with vertical position without regard to orientation). This model does not provide the rotational stiffness that would be experienced by most surface piercing buoys. Interactions with the seabed and with shapes are also modelled in a fairly simple manner, and friction effects are not included. Arbitrary hydrodynamic and physical properties are modelled by deriving equivalent terms which are applied at the centre of mass. Spar Buoys The second type, called Spar Buoys, are intended for modelling axi-symmetric buoys whose axis is normally vertical, particularly where surface piercing effects are important (such as for a CALM buoy). Spar Buoys are modelled as a series of co-axial cylinders mounted end to end along the local zaxis (see Spar Buoy and Towed Fish Properties). This allows you to provide some information about the buoy geometry, by specifying the number of cylinders and their lengths and diameters. A conical or spherical shape can be approximated as a series of short cylinders of gradually increasing or diminishing diameter. Spar Buoys model surface-piercing effects in a much more sophisticated way than Lumped buoys. 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, allowing for the instantaneous position and attitude of the buoy in the wave. However note that 266 w OrcaFlex does not calculate radiation damping (a linear damping term resulting from the creation of surface waves as the buoy oscillates) or impact loads (slamming). Because they are modelled as a stack of concentric cylinders, Spar Buoys are often not suitable for fully submerged objects with more complex geometries. As with Lumped Buoys, the modelling of seabed interaction is simplistic and friction effects are not included. Hydrodynamic loads on Spar Buoys are calculated using Morison’s equation. 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. For partly immersed cylinders, added mass and drag are proportioned according to the fraction of the cylinder which is immersed. 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. Towed Fish The third type, called Towed Fish, are intended for modelling bodies, such as towed fish, whose principal axis is normally horizontal. 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, rather than along the z-axis. 7.7.2 Wings 6D buoys can have a number of wings attached; these are useful for representing lift surfaces, diverters etc. Each wing has its own data and results available. A wing is a rectangular surface, attached to the buoy at a specified position and orientation, which experiences lift and drag forces, and a moment, due to the relative flow of the sea past the wing. Wings do not have any mass, added mass or buoyancy associated with them; any mass, added mass or buoyancy due to wings should be added into the properties specified for the buoy itself. The drag force on a wing is the force applied in the direction of relative flow. The lift force is the force at 90º to that direction. 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. These loads are applied at the wing centre and are specified by giving lift, drag and moment coefficients as a function of the incidence angle α between the relative velocity vector and the wing plane. 267 w +ve lift Relative Velocity Vector V Wy Principal Wing Axis W Wx Wz Chord α Span -ve lift Figure: Wing Model Each wing has its own set of local wing axes, with origin W at the wing centre and axes Wx, Wy and Wz. Wy is normal to the wing surface and points towards the positive side of the wing; the positive side of a wing is the side towards which positive lift forces act. Wx and Wz are in the plane of the wing and Wz is the primary axis of the wing - it is the axis about which the wing can be pitched. The wing is therefore a rectangle in the Wxz plane, centred on W. We refer to its length in the Wz direction as its span and its width in the Wx direction as its chord. If the wing is not completely submerged, then the forces and moments applied by OrcaFlex are scaled down according to the proportion of the wing area that is below the surface. However, note that the true effects of breaking surface, for instance planing and slamming, are much more complex than this and are not modelled. 7.7.3 Common Data All types of 6D Buoy use a local coordinate system with the origin at the centre of gravity. The following data items are common to all types. Name Used to refer to the 6D Buoy. Type Three types of buoy are available: Lumped Buoys, Spar Buoys and Towed Fish. Connection A 6D Buoy can either be Free, Fixed or connected to a Vessel or a Line (provided that line includes torsion). • If the buoy is Free then it is free to move in response to wave loads, attached lines etc. In this case the buoy's Initial Position and Attitude are specified relative to global axes. 268 w • • If the buoy is Fixed then it cannot move. Its Initial Position and Attitude are specified relative to global axes. If the buoy is connected to a Vessel or a Line, then it is rigidly connected to that object and so moves and rotates with it. All resulting forces and moments on the buoy are transmitted to the object. In this case the buoy's Initial Position and Attitude are specified relative to the object to which it is connected. Initial Position and Attitude Specifies the initial position of the buoy origin (which must be the centre of gravity) and its initial orientation. If the buoy is Free or Fixed then its initial position is specified by giving the X, Y and Z coordinates of the buoy origin B, relative to the global axes. And its initial orientation is specified by giving 3 angles Rotation 1, Rotation 2, Rotation 3, which are successive rotations that define the orientation of the buoy axes Bxyz, relative to global axes, as follows. First align the buoy with global axes, so that Bxyz are in the same directions as GXYZ. Then apply Rotation 1 about Bx (=GX), followed by Rotation 2 about the new By direction, and finally Rotation 3 about the new (and final) Bz direction. 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. If the buoy is included in the static analysis, 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. See Degrees of Freedom Included in Static Analysis. If the buoy is connected to a Line, then the Initial Position and Attitude specify where on the line it is connected, and with what orientation, as follows: • • • The Initial Position z-coordinate specifies the arc length at which the buoy should be connected to the line. The buoy will be connected to the nearest node to that arc length. The buoy will be connected to that node, but with an offset relative to that node's axes that is given by (x, y, 0). The buoy orientation relative to the node axes is specified by the Initial Attitude angles. Degrees of Freedom Included in Static Analysis Determines which degrees of freedom are calculated by the static analysis (see Buoy Degrees of Freedom Included in Static Analysis). 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. X,Y,Z: the buoy position is calculated by the static analysis, but its orientation is simply set to the initial orientation set on the buoy data form. All: the buoy position and orientation are calculated by the static analysis. Normally this data item should be set to All so that the static analysis calculates the true equilibrium position and orientation of the buoy. However it is sometimes useful to fix the buoy position or orientation, for example if the static analysis is unable to find the equilibrium position or orientation. Mass Mass or weight in air. 269 w Moments of Inertia The solid moments of inertia of the buoy about its local x, y and z axes. Bulk Modulus Specifies the compressibility of the buoy. If the buoy is not significantly compressible, then the Bulk Modulus can be set to Infinity, which means 'incompressible'. See Buoyancy Variation with Depth for details. 7.7.4 Applied Load You can apply to the buoy an external Global Load that does not rotate if the buoy rotates. This is specified by giving the components of Applied Force and Applied Moment relative to global axes. These components remain constant, so if the buoy rotates then the load does not rotate with it. In addition, you can specify an external Local Load that does rotate with the buoy. This is specified by giving the components of Applied Force and Applied Moment relative to buoy axes. Again these components remain constant, so if the buoy rotates then the load does rotate with it. This is suitable for modelling thrusters, for example. In both cases the Point of Application of the load is specified by giving its x,y,z coordinates relative to buoy axes. 7.7.5 Wing Data 6D buoys can have a number of wings attached, each having its own data and type. Name Used to refer to the wing. Span The length of the wing, in the local Wz direction. Chord The width of the wing, in the local Wx direction. Centre of Wing The position of the centre of area of the wing, relative to buoy axes. Orientation The orientation of the wing is specified by giving 3 angles - azimuth, declination and gamma relative to the buoy axes. The angles can either be fixed or vary with simulation time. If they are variable then linear interpolation is used for times between those specified in the variable data table, and truncation is used for times beyond those specified in the table. The angles define the orientation of the local wing axes relative to the buoy axes as follows: • Start with the wing axes Wxyz aligned with the buoy axes Bxyz and then rotate Wxyz about Bz by the azimuth angle. This leaves Wz aligned with Bz but Wx now points in the direction towards which the declination is to be made. 270 w • Now rotate by the declination angle about the new direction of Wy. This declines Wz down into its final direction, i.e. Wz now points along the direction whose azimuth and declination angles are as specified. Finally rotate by the gamma angle about this final Wz direction. This is a rotation about the principal wing axis, so it allows you to adjust the pitch of the wing. • For each of these rotations, positive angles mean clockwise rotation and negative angles mean anti-clockwise rotation, when looked at along the axis of rotation. When setting these orientation angles, it is easiest to first set the azimuth and declination values to give the desired Wz-direction. This is the direction of the axis about which the wing pitch is set. Then set gamma to give the correct pitch 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 Determines the properties of the wing. You can define a number of wing types - click the "Wing Types" button to access the wing types data form. 7.7.6 Wing Type Data 6D buoys can have a number of wings attached, each having its own data and type. Name Used to refer to the wing type. Wing Type Properties The properties of each wing type are specified by giving a table of lift, drag and moment coefficients as a function of the incidence angle of the flow relative to the wing. A "Graph" button is provided - this displays a graph of the 3 coefficients so that you can visually check your data. Incidence Angle The incidence angle is the angle, α, that the relative flow vector makes to the wing surface. This equals 90º minus the angle between Wy and the relative flow vector. The incidence angle is always in the range -90º to +90º, where positive values mean that the flow is towards the positive side of the wing (i.e. hitting the negative side) and negative values mean that the flow is towards the negative side of the wing (i.e. hitting the positive side). The incidence angles in the table must be given in strictly increasing order and the table must cover the full range of incidence angles, so the first and last angle in the table are set to -90º and +90º and cannot be changed. Linear interpolation is used to obtain coefficients over the continuous range of angles. Note: The wing lift, drag and moment are assumed to only depend on the incidence angle, not on the angle of attack in the wing plane. OrcaFlex will therefore use the same lift, drag and moment coefficients for flow (with the same incidence angle) onto the front, the side or the back of the wing, even though your data may only apply over a limited range of in-plane attack angles. 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. 271 w Lift Coefficient The lift coefficient Cl(α) defines the lift force applied to the wing, as a function of incidence angle α. The lift coefficients can be positive or negative and the lift force is given by: Lift Force = ½.Cl(α).ρ.A.V² where ρ is the water density, A is the area of wing that is under water at the time and V is the relative flow velocity at the wing centre. The lift force is applied at the wing centre, along the line that is at 90º to the relative flow vector and in the plane of that vector and Wy. For α= ±90º this line is ill-defined and the lift coefficient must be zero. Positive lift coefficients means lift pushing the wing towards its positive side. Drag Coefficient The drag force is defined by the drag coefficient Cd(α) using the formula: Drag Force = ½.Cd(α).ρ.A.V² where ρ is the water density, A is the area of wing that is under water at the time and V is the relative flow velocity. The drag coefficient cannot be negative, so the drag force is always in the relative flow direction. Moment Coefficient The moment coefficient Cm(α) defines a moment that is applied to the wing. This moment represents the fact that the position of the centre of pressure may depend on the incidence angle α. The moment coefficients can be positive or negative and the moment is given by: Moment = ½.Cm(α).ρ.A.V².Chord where ρ is the water density, A is the area of wing that is under water at the time and V is the relative flow velocity. This moment is applied about the line that is in the wing plane and is at 90 degrees to the relative flow vector. For α = ±90º this line is ill-defined and the moment coefficient must be zero. Positive moment coefficients mean that the moment is trying to turn the wing to bring Wy to point along the relative flow direction. Negative moment coefficients mean the moment tries to turn the wing the opposite way. 272 w 7.7.7 Lumped Buoy Properties Vertices z (heave) yaw y (sway) pitch B (centre of gravity) roll x (surge) Figure: Lumped Buoy For a Lumped Buoy the forces and moments are calculated as follows (ρ is water density, g is acceleration due to gravity). Each degree of freedom is calculated independently. Geometry Volume is the total volume of the buoy, with its centre at the Centre of Volume, defined relative to the local buoy axes Bxyz. Height is the buoy vertical dimension, assumed equally spaced about the centre of volume. Height is assumed to be independent of buoy rotation. To allow for interaction with the water surface "Proportion Wet", PW, is defined such that: PW = 1.0 when the centre of volume is Height / 2 or more below the water surface, P = 0.0 when the centre of volume is Height / 2 or more above the water surface. Between these two limits, PW varies linearly with immersion. Wetted volume is then given by PW . Volume. Centre of wetted volume is a distance Height . (1-PW) / 2 below Centre of Volume. Hydrostatic and hydrodynamic forces are applied at the centre of wetted volume. Warning: For Lumped Buoys, since OrcaFlex has no information regarding the actual body geometry, there is no contribution to roll and pitch stiffness from free surface effects when the buoy pierces the surface. Static stability of a floating buoy is therefore not correctly represented. Damping Hydrodynamic damping forces and moments may be applied to the buoy. These are loads that are directly proportional to the relative velocity, or angular velocity, of the sea past the buoy. For each of the local buoy axes directions, you specify the magnitude of the Unit Force that is applied when the relative velocity is 1 length unit/second. OrcaFlex then scales these magnitudes according to the actual relative velocity and applies the resulting force or moment. Similarly you can specify a Unit Moment that is applied when the relative angular velocity is 1 radian/second. 273 w Drag Hydrodynamic drag forces and moments may be applied to the buoy. These are loads that are proportional to the square of the relative velocity, or angular velocity, of the sea past the buoy. The drag force properties are specified by giving, for each of the local buoy axes directions, the Drag Area that is subject to drag loading in that direction and the corresponding Drag Coefficient. Drag moment properties are specified in a similar way, except that instead of specifying a drag area you must specify a Moment of Area. Note: Fluid Inertia Fluid inertia properties are those that are proportional to the acceleration of the sea and the buoy. These accelerations have two main effects. Firstly, they result in forces and moments being applied to the buoy - these are referred to as the fluid acceleration loads. Secondly, the buoy experiences an increase in inertia - this is known as the added mass. These properties are specified separately for translational and rotational motions and also separately for each local axis direction. The translational fluid inertia properties of the buoy are specified, for each of the local buoy axis directions, by giving a reference Hydrodynamic Mass together with the two inertia coefficients, Ca and Cm. The translational Hydrodynamic Mass values can be set to '~', meaning equal to the fully submerged displaced mass.(= volume x water density). This is often a convenient reference mass to use. Ca determines the amount of added mass that is added to the buoy in that direction - it equals Ca multiplied by the reference Hydrodynamic Mass for that direction. Cm determines the fluid acceleration force that is applied in that direction. It equals: Cm . Hydrodynamic Mass . Af where Af is the component, in that direction, of the fluid acceleration at the buoy. Just as translational relative acceleration of the sea past the buoy gives rise to added mass and fluid inertia forces, so rotational relative acceleration of the sea past the buoy gives rise to added rotational inertia and fluid inertia moments. The rotational fluid inertia properties of the buoy are specified in the same way as for the translational properties, except that a reference moment of inertia is specified, instead of a reference mass. Drag Area Moment is the 3rd absolute moment of drag area about the axis. Separate Cd values are given for force and moment calculations. 7.7.8 Lumped Buoy Drawing Data Vertices and Edges This defines a "wire frame" representation of the buoy. The data layout and interpretation is the same as for Vessels. The wire frame representation of the buoy is used to draw the buoy and is also used to calculate the interaction of the buoy with shapes and the seabed. The vertices are also used in calculating the interaction of the buoy with shapes and the seabed. See 6D Buoy Theory for details. 274 w 7.7.9 Spar Buoy and Towed Fish Properties Buoy Axis Cylinder 1 Diameter Cylinder 1 Length z (heave) yaw y (sway) pitch x (surge) (centre of gravity) B roll Stack Base Position Figure: Spar Buoy The figure above shows the geometry of a Spar Buoy. The geometry of a Towed Fish is identical except that the buoy axis is aligned with the x-axis of the buoy. If you are modelling a CALM or SPAR buoy then see also Modelling a Surface-Piercing Buoy. The following data items apply to Spar Buoys and Towed Fish. Stack Base Centre Position The centre of base of the stack, relative to buoy axes. Note that the centre of gravity of the buoy must be at the origin of the buoy axes, so this data positions the stack relative to the centre of gravity. Munk Moment Coefficient Slender bodies in near-axial flow experience a destabilising moment called the Munk moment. This effect can be modelled by specifying a non-zero Munk moment coefficient. 275 w Cylinders The cylinders are numbered from the top downwards. 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. Diameter and Length The diameter of the cylinder and its length measured along the axis. These parameters define the buoy geometry from which buoyancy forces and moments are determined. When the buoy pierces the water surface, 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, and includes the appropriate contributions to static stability. The remaining parameters determine the hydrodynamic loads acting on each cylinder. Loads are calculated for each cylinder individually, then summed to obtain the total load on the buoy. Drag Forces and Moments Drag loads are the hydrodynamic loads that are proportional to the square of fluid velocity relative to the cylinder. For details of the drag load formulae see 6D Buoys: Spar Buoy and Towed Fish Theory. For information when modelling a SPAR of CALM buoy see Modelling a Surface-Piercing Buoy. The drag forces are calculated on each cylinder using the "cross flow" assumption. That is, the relative velocity of the sea past the cylinder is split into its normal and axial components and these components are used, together with the specified drag areas and coefficients, to calculate the normal and axial components of the drag force. 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). The Drag Area is a reference area that is multiplied by the Drag Coefficient in the drag force formula. You can therefore use any +ve Drag Area that suits your need, but you then need to give a Drag Coefficient that corresponds to that specified reference area. The Drag moments are specified and calculated in a similar way to the drag forces, except that the reference drag area is replaced by a reference Area Moment. This and the Drag Coefficient are multiplied together in the drag moment formula, so again you can use any +ve Area Moment that suits your need, providing you then specify a Drag Coefficient that corresponds to the specified Area Moment. There are two alternative methods that you can adopt when specifying the drag data. The first method is to set the OrcaFlex data to get best possible match with real measured results for the buoy (e.g. from model tests or full scale measurements). This is the most accurate method, and we recommend it for CALM and discus buoys - see Modelling a Surface-Piercing Buoy for details. Because the Drag Area and Drag Coefficient data are simply multiplied together, you can calibrate the model to the real results by fixing one of these two data items and then adjusting the other. For example, 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. Or, you could set the axial Drag Area to a fixed value (e.g. 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. The second method is to set the drag data using theoretical values or given in the literature. It is less accurate but can be used if you cannot get any real buoy results against which to calibrate. To use this method, set the data as follows. 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 & 276 w Adams, 1991, Hoerner,1965 and DNV, 1991). Note that the drag area specified should be the total projected area exposed to drag when the buoy is fully submerged, since OrcaFlex allows for the proportion wet in the drag force formula. For a simple cylinder of diameter D and length L the total projected drag area is D.L for the normal direction and (π.D^2)/4 for the axial direction, but if the buoy has attachments that will experience drag then their areas must also be included. Set the Drag Area Moments to the 3rd absolute moments of projected area exposed to drag in the direction concerned; see Drag Area Moments for details. And then set the Drag Moment Coefficients based on values given in the literature. Added Mass Translational added mass effects are calculated using the displaced mass as the reference mass for each cylinder. Separate added mass coefficients are given for flow normal (x and y directions) and axial (z direction) to the cylinder. Rotational added inertia is specified directly (so no reference inertia is involved). Separate values can be given for rotation about the cylinder axis and normal to that axis. See Spar Buoy Theory. Damping Forces and Moments Damping forces and moments are the hydrodynamic loads that are proportional to fluid velocity (angular velocity for moments) relative to the cylinder. They are specified by giving the Unit Damping Force and Unit Damping Moment for the normal and axial directions. These specify the force and moment that the cylinder will experience, in that direction, when the relative fluid velocity (angular velocity for moments) in that direction is 1 unit. See Damping Forces and Moments for details. 7.7.10 Results For details on how to select results variables see Selecting Variables. 6D Buoy Results For 6D Buoys the available variables are: X, Y and Z The position of the buoy origin, relative to global axes. Rotation 1, Rotation 2 and Rotation 3 Define the orientation of the buoy relative to global axes. They are 3 successive rotations that take the global axes directions to the buoy axes directions. See Initial Position and Attitude for the definition of these angles. Rotation 2 is in the range -90 to +90. Range jump suppression is applied to Rotation 1 and Rotation 3 (so values outside the range -360 to +360 degrees might be reported). Surface Z Elevation of the sea surface directly above the instantaneous position of the buoy origin. 277 w Dry Length The length of buoy above the water surface, measured along the buoy z axis, calculated as follows: • • For a Lumped Buoy, this is calculated by assuming that the z-extent of a Lumped Buoy is ½ Height either side of its volume centre. For a Spar Buoy it is the sum of the dry lengths of each of its cylinders, where the dry length of an individual cylinder is calculated as (cylinder length) . (submerged volume of cylinder) / (total volume of cylinder). Connection Force, Connection Moment Connection x-Force, Connection y-Force, Connection z-Force Connection x-Moment, Connection y-Moment, Connection z-Moment These connection load results are only available for buoys that are connected to other objects. They report the total force and moment applied to the buoy by the object to which it is connected. Connection Force and Connection Moment report the magnitudes of the connection loads (they are therefore always non-negative). The other results report the components of the connection force and moment in the buoy axes directions. These connection force and moment results include the inertial load on the buoy due to any acceleration of the object to which it is attached. This means that these results can be used for sea fastening calculations, by using a 6D buoy to model the object to be fastened and then attaching it to a vessel. The connection force and moment include the weight of the buoy and the inertial loads due to the vessel acceleration. 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. Wing Results If the 6D buoy has wings attached then for each wing the following results are available. Wing X, Wing Y, Wing Z The position of the wing origin, relative to global axes. Wing Azimuth, Declination and Gamma The orientation angles of the wing, relative to the buoy. Lift The lift force applied to the wing. This is applied at 90º to the relative flow direction and positive values mean a force trying to push the wing towards its positive side, negative values towards its negative side. Drag The drag force applied to the wing. This is applied in the relative flow direction and is always positive. 278 w Moment The moment applied to the wing. This is applied about the line that is in the wing plane and at 90º to the relative flow direction. Positive values are moments trying to turn the wing to bring Wy to point along the relative flow direction; negative values are moments trying to turn the wing the opposite way. Incidence Angle The angle, α, that the relative flow vector makes with the plane of the wing, in degrees in the range -90 to +90. Positive values mean that the flow is towards the positive side of the wing (i.e. hitting the negative side) and negative values mean that the flow is towards the negative side of the wing (i.e. hitting the positive side). Beta Angle The angle of the relative flow direction, measured in the wing plane. More specifically, it is the angle between wing Wx axis and the projection of the relative flow vector onto the wing plane, measured positive towards Wz. Zero beta angle means that this projection is in the Wx direction, 90º means it is along Wz and -90º means it is along the negative Wz direction. Range jump suppression is applied to the Beta Angle (so values outside the range -360 to +360 degrees might be reported). 7.7.11 Buoy Hydrodynamics 3D and Lumped 6D buoys are generalised objects for which no geometry is defined in the data other than a value of 'height': this is used only for proportioning hydrodynamic properties when the object is partially immersed, and for drawing a 3D buoy. Since the geometry of the object is undefined, it is necessary to define properties such as inertias, drag areas, added masses, etc. explicitly as data items. This can be a difficult task, 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. We cannot give a simple step-by-step procedure for this task since different objects can have widely differing geometries. As an example, the hydrodynamic properties in 6 degrees of freedom are derived for a rectangular box. This gives a general indication of the way in which the problem should be approached. If a 3D buoy is used, the rotational properties are not used. 279 w 7.7.12 Hydrodynamic Properties of a Rectangular Box O is the centre of the box Z Y z X O y Figure: Drag areas In X direction: Ax = y . z In Y direction: Ay = x . z In Z direction: Az = x . y Box Geometry x Drag Coefficients for Translational Motions These are obtained from ESDU (1971), Figure 1 which gives data for drag of isolated rectangular blocks with one face normal to the flow. The dimensions of the block are a in the flow direction b and c normal to the flow direction (c>b). The figure plots drag coefficient, Cx against (a/b) for (c/b) from 1 to infinity (2D flow). Cx is in the range 0.9 to 2.75 for blocks with square corners. Note: ESDU (1971) uses Cd for the force in the flow direction; Cx for the force normal to the face. For present purposes the two are identical. Drag Properties for Rotational Motions There is no standard data source. As an approximation, we assume that the drag force contribution from an elementary area dA is given by dF = ½.ρ.V².Cd.dA where Cd is assumed to be the same for all points on the surface. Note: This is not strictly correct. 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. However we do not allow for this here. 280 w Z dz z O X Figure: Integration for rotational drag properties Consider the box rotating about OX. The areas Ay and Az will attract drag forces which will result in moments about OX. For the area Ay, consider an elementary strip as shown: For an angular velocity ω about OX, the drag force on the strip is dF = ½.ρ.(ωz).|ωz|.Cd.x.dz and the moment of this force about OX is dM = ½.ρ.(ωz).|ωz|.Cd.x.dz.z = (½.ρ.ω.|ω|.Cd).x.z³.dz Total moment is obtained by integration. Because of the V.|V| form of the drag force, simple integration from -Z/2 to +Z/2 gives M = 0. We therefore integrate from 0 to Z/2 and multiply the answer by 2. The result is M = (½.ρ.ω.|ω|.Cd).(x.z /32) OrcaFlex calculates the drag moment by M = (½.ρ. ω.|ω| .Cdm).(AM) so we set Cdm = Cd, AM = x.z /32. This is the drag moment contribution about OX from the Ay area. There is a similar contribution from the Az area. Since Cd is generally different for the 2 areas, it is convenient to calculate the sum of (Cd.AM) for both, set AM equal to this value and set Cd equal to 1. Added Mass OrcaFlex requires the added mass and inertia contributions to the mass matrix, plus the hydrodynamic masses and inertias to be used for computation of wave forces. For each degree of freedom (3 translations, 3 rotations), 3 data items are required. These are Hydrodynamic Mass in tonnes (or Inertia in tonne.m²); and coefficients Ca and Cm. Added mass is then defined as Hydrodynamic Mass . Ca; and wave force is defined as (Hydrodynamic mass . Cm) multiplied by the water particle acceleration, aw. On the usual assumptions intrinsic in the use of Morison's equation (that the body is small by comparison with the wavelength), the wave force is given by (∆ + AM) . aw, where ∆ is body displacement and AM is added mass. OrcaFlex calculates the wave force as Cm . HM . aw where HM is the Hydrodynamic Mass given in the data. 281 w For translational motions, set HM = ∆ for all degrees freedom. Then Ca = AM/∆, Cm = 1 + Ca. For rotational motions, set HI = ∆I, the moment of inertia of the displaced mass. Then Ca = AI/∆I, Cm = 1 + Ca where AI is the added inertia (i.e. the rotational analogue of added mass). Translational Motion DNV (1991), Table 6.2, gives added mass data for a square section prism accelerating along its axis. The square section is of side a, prism length is b, and data are given for b/a = 1.0 and over. The reference volume is the volume of the body which is the same definition we have adopted. We can therefore use the calculated Ca without further adjustment. Consider the X direction: Area normal to flow = Ax. For a square of the same area, a = √(Ax). Length in flow direction = x. Hence b/a = x/√(Ax). Hence Ca can be obtained from DNV (1991) by interpolation, and then Cm = 1 + Ca. If b/a < 1.0 this approach fails and we use the data given in DNV (1991) for rectangular flat plates. If y > z, aspect ratio of the plate = y/z. Hence CA from DNV (1991) by interpolation. The reference volume in this case is that of a cylinder of diameter z, length y. Hence: Added mass = CA.ρ.(π/4).y.z² = AMx, say and then Ca = AMx/∆ and Cm = 1 + Ca. Note: If y < z, then aspect ratio = z/y and reference volume = CA . ρ. (π/4) . z . y². Rotational Motion DNV (1991) gives no data for hydrodynamic inertia of rotating bodies. The only data for 3D solids we know of is for spheroids (Newman 1977). Fig 4.8 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. We assume that the same coefficient applies to the moment of inertia of the displaced mass of the rectangular block. Rotation about X ∆I = ∆(Y² + Z²)/12 Added inertia: Using data for spheroids from Newman 1977 : Length in flow direction = 2a = x, so a = x/2. Equivalent radius normal to flow, b, is given by πb² = yz, so b = √(y . z/π). Hence Ca from Newman 1977. For b/a < 1.6 Ca can be read from the upper figure where the value is referred to the moment of inertia of the displaced mass. In this case no further adjustment is required. 282 w For b/a > 1.6 The coefficient CA is read from the lower graph in which the reference volume is the sphere of radius b. In this case: Ca = CA . (2 . b³)/(a . (a²+b²)) In either case, Cm = 1 + Ca. 7.7.13 Modelling a Surface-Piercing Buoy Surface-piercing buoys, such as CALM buoys, SPAR buoys or meteorological discus buoys, can be modelled in OrcaFlex using the Spar Buoy version of a 6D Buoy. Despite its name, the OrcaFlex Spar Buoy can be used to model any axi-symmetric body. See the example simulation file CALM Buoy.SIM. Spar Buoys have many data items available. This enables you to model a wide range of effects, but it also makes setting up a Spar Buoy model more complicated. To help in this task we describe, in this section, the approach we adopt for setting up an OrcaFlex model of a surface-piercing buoy. 1. Create a simple model containing just a Spar Buoy Start by modelling the free-floating behaviour of the buoy, without any lines attached. This allows us to get the basic behaviour of the buoy correct, before complications such as moorings etc. are introduced. We therefore set up an OrcaFlex model containing just a Spar Buoy and with no waves or current. Set the buoy's Applied Load to zero. This data allows you to apply extra forces and moments to the buoy, in addition to those from any lines that you attach to it. You can use this later to model the wind force on the upper part of the buoy. To do this you will need to know the projected area (i.e. the area exposed to wind) of the pipe work etc. in the upper part of the buoy. Set the buoy's Munk Moment Coefficient to zero. This data item is only used for slender bodies in near axial fully-submerged flow only. Set the number of wings to zero. Wings are normally only relevant for towed fish. Finally, we start by setting all the buoy's drag and added mass data to zero. We will set up the actual values later. 2. Set up the geometry data The Spar Buoy has its own local coordinate system. This must have its origin at the buoy centre of gravity (CG) and must have the local z-axis pointing upwards along the axis of the buoy. You therefore need to know the position of the centre of gravity. The buoy manufacturer should supply this information. Set the Stack Base Position. This is the position of the centre of the bottom of the buoy, relative to the centre of gravity. The Stack Base Position is therefore (0, 0, -h) where h is the distance from the bottom of the buoy to the centre of gravity. Now set up a number of cylinders, and their lengths and diameters, in order to model the shape of the buoy. To do this you need the dimensions of the various parts of the buoy. The buoy manufacturer should supply this information. Set the cylinder lengths and diameters so that you get the correct length and volume for each section. You can represent tapered sections by a series of short cylinders with diameters changing progressively from one to the next. 283 w We recommend using a number of short cylinders, even where the buoy diameter is constant over a long length. Using more cylinders gives more accurate results, though at the cost of reduced computation speed. You can check your geometry data by zooming in on the buoy in a 3d view window. Turn on the local axes so that you can check that the buoy origin (=centre of gravity) is in the correct place. The Bulk Modulus data item is not relevant to a surface-piercing buoy, so it can be left at the default value of Infinity. 3. Set up the mass and inertia data Now set the Mass and Moments of Inertia of the buoy. The buoy manufacturer should supply this information. The mass equals the weight of the buoy in air. The moments of inertia are those of the buoy (in air) about its centre of gravity, as follows: • • lz = the moment of inertia about the buoy axis lx and ly = the moments of inertia about axes perpendicular to the buoy axis, through the centre of gravity. Usually it is sufficient to assume that Ix = ly. If you cannot obtain data for the moments of inertia, then they can be approximately calculated from a knowledge of the masses of the various parts of the buoy, and approximately how that mass is distributed. 4. Check 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. The initial position is the position of the buoy local origin, and therefore of the CG, and you can calculate this point's expected equilibrium position from the buoy draught, which should be available from the buoy manufacturer. The Initial Attitude defines the initial orientation of the buoy. Set it to (0,0,0), which orients the buoy with its axis vertical and the buoy local x,y axes aligned with the global X,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. If the data has been set up correctly then the buoy should have stayed basically in its initial position and attitude, with perhaps just small oscillations about that position. If the buoy Z has oscillated significantly then the model's equilibrium position does not match the expected equilibrium position. This means that something is wrong in the data and this needs tracing and correcting before you proceed. You can estimate the model's equilibrium position by looking at the mean Z position in the time history. 5. Check that the buoy is stable Now check that the buoy is stable - i.e. that if it is pitched over to one side and released then it rights itself. In the Initial Attitude data, set the Rotation 2 value to say 10 degrees and run the simulation. If the buoy falls over then there is something wrong with the CG position or the volume distribution, and this must be corrected. Note: The buoy on its own may not be intended to be stable, e.g. stability may only be achieved when the moorings are attached. In this case you will need to model the moorings in order to check stability. 284 w 6. Set the Added Mass data The x and y added mass coefficients can be set to 1.0, which is the standard value for a cylinder in flow normal to its axis. Added mass in the z direction should be estimated for the buoy from the published literature (DNV rules, Barltrop & Adams, 1991) and distributed between the immersed cylinders (remember that hydrodynamic loads are only applied to the immersed parts of the model). Ideally, this 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, and adjustments made as necessary. 7. 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, or a surface-following Discus shape such as an oceanographic buoy. CALM buoys are usually closer to the Discus configuration, often with a damping skirt which is submerged at normal draft. Spar Buoys Set the Drag Areas for each cylinder to the areas, of the part of the buoy which that cylinder represents, that are exposed to fluid drag in the direction concerned. Note that you should specify the areas that are exposed to drag when the buoy is fully submerged. 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. So if a cylinder is not submerged, or is partially submerged, then the drag loads will be scaled accordingly for you. For a simple cylinder, of diameter D and length L, the normal drag area is D.L since that is the area of a cylinder when viewed normal to its axis. And the axial drag area is (π.D²)/4 since that is the area of the cylinder when viewed along its axis. However, where a cylinder is representing part of the buoy that is not in reality a simple cylinder (for example, 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, then the drag areas should be set accordingly. For example, 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.d²)/4 to model that shielding. Set the Drag Force Coefficient based on values given in the literature. For short simple cylinders fully immersed there are standard values given in the literature (see Barltrop & Adams, 1991, Hoerner,1965 and DNV, 1991). However, the standard book values do not include energy absorption by wave-making at the free surface. Strictly, this is a linear term (forces directly proportional to velocity), but in OrcaFlex this must be done by adjusting the drag coefficients of one or more cylinders. The Unit Damping Force data can be set to zero. 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. Set the Drag Area Moments, Drag Moment Coefficients and Unit Damping Moment data. For the normal direction these data items can usually all be left as zero, providing you have subdivided the buoy into short enough cylinders (since these terms involve a high power of L, the cylinder length). For the axial direction these data items model the yaw drag and damping effects, so if this is important to you then set them to model the two main sources, namely skin friction on the cylinder surface and form drag on any protuberances on the buoy. 285 w Having set up this drag and damping data, 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. Discus and CALM Buoys These types of buoy require different treatment since they have little axial extension. Instead it is their radial extension that most affects the buoy's pitch properties. As a result the axial discretisation of the buoy into cylinders does not capture the important effects. For example the pitch damping is often mostly due to radiation damping, i.e. surface wave generation; this is especially important for a CALM buoy with a skirt. To deal with this OrcaFlex offers the rotational drag and damping data, but there is little information in the literature to help in setting up this data. We therefore strongly recommend that you set the data up by calibration against real test results from model or full scale tests. The easiest information to work with are time history graphs of the buoy heave and pitch in still water, starting from a displaced position. 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. Here is the approach we use: • • For the normal direction, set the Drag Area, Drag Force Coefficient and Unit Damping Force as described for Spar buoys above. 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, i.e. with the same initial Z displacement. Then adjust the axial Drag Area and Drag Force Coefficients until the OrcaFlex buoy's Z time history matches the real time history. These two data items are simply multiplied together when they are used to calculate the drag force, so you can give one of the two data items a fixed +ve value (e.g. 1) and then adjust the other. The match will probably be poor in the later parts of the time history, where the heave amplitude has decayed to small values. 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 where the amplitude is small. You may find that this disturbs the match in the large amplitude part, in which case you might need to readjust the drag data. For the axial direction, set the Drag Area Moment, Drag Moment Coefficient and Unit Damping Moment as described for Spar buoys above. Then set the normal Drag Area Moment, Drag Moment Coefficient and Unit Damping Moment to best match the real pitch time history, in a similar way to that used above to match the heave time history. • • • • 7.8 LINES 7.8.1 Lines Lines are flexible linear elements used to model cables, hoses, chains or other similar items. Lines are represented in OrcaFlex using a lumped mass model. That is, the line is modelled as a series of lumps of mass joined together by massless springs, rather like beads on a necklace. The lumps of mass are called nodes and the springs joining them are called segments. Each segment represents a short piece of the line, whose properties (mass, buoyancy, drag etc.) 286 w have been lumped, for modelling purposes, at the nodes at its ends. See the figure below, which shows an example line spanning from a Vessel to a Buoy. End positions and no-moment directions are defined relative to the objects to which the ends are connected and move with those objects. z End A z V B y x End B y x section 1 (3 segments) Clump section 3 (9 segments) 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. 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. A Line Type is simply a set of properties (for example the diameter, mass per unit length and bend stiffness) given a name so that they can be called by that name. The Line Types are defined separately, on the Line Types data form. This allows the same set of line properties to be used for a number of different sections of the line, or for different lines. There is also a Line Type Wizard tool that helps you set up Line Types representing common structures like chains, ropes, etc. In addition, a number of attachments may be specified, to represent items that are connected to the Line. For example, attachments may be used to model clump weights, drag chains or buoyancy bags attached to the line. Two types of attachment are available - clumps (buoyancy or heavy) and drag chains. 287 w Each attachment attached to the Line is specified by giving the Attachment Type and the arc length, measured from end A, at which it should be attached. The attachment is then attached to the nearest node to that arc length. Attachment Types are similar to Line Types - they are simply named sets of attachment properties. The properties themselves are then given separately, on the Attachment Types data form. This allows the same set of attachment properties to be used for a number of different attachments. The two ends of a Line are referred to as end A to end B and each end can be Free, Fixed, Anchored or else connected to a Vessel or Buoy. The two ends of a line are treated basically the same, but some aspects of the line are dependent on which end is which. In particular the numbering of parts of a Line is always done starting at end A. 7.8.2 Line Data Line Data For every line in the system there is a data form defining its structure and interconnection. It is on these data forms that the system is built up by connecting lines between the objects that have been defined. Name Used to refer to the Line. Include Torsion Torsional effects can be included or ignored, for each line in the model. If torsion is included then the line type torsional properties must be specified. See Torsional Stiffness. To see the line orientation visually on the 3D views, select Draw Local Axes on the View menu. OrcaFlex then draws the node axes Nxyz at each node, and these axes allow you to see how the line is behaving torsionally. Notes: The node axes are drawn using the node pen, specified on the line data form. If torsion is included for a line, you must specify the torsional orientation at each end of the line. This is done by setting the Gamma angle of the end connections on the line data form. The Gamma angle determines the torsional position of the line end - for details see Line End Orientation. To check visually that you have the orientation you expect, select Draw Local Axes on the View menu. If torsion is included for a line, the static analysis should also include the effect of torsion - otherwise the simulation will start from a position that is not in torsional equilibrium and an unstable simulation may result. Torsion is only included in the "Full" statics, so Full Statics (on the line data form) is always set to Yes when torsion is included. Connections The line end connection data specifies whether the line ends are connected to other objects, the position, angle and stiffness of the connection, and whether the end is released during the simulation. You can view and edit an individual line's connection data on the line's data form. Or you can view and edit the connection data for all the lines together on the Line Ends data form. 288 w Connect to Object The line spans from end A to end B and each end may be connected to another object in the model, such as a buoy or vessel, or else Fixed, Anchored or left Free. Object Relative Position • • • • If the end is connected to another object this defines the coordinates of the connection point relative to that other object's local axes. If the end is Fixed this defines the coordinates of that point relative to global axes. If the end is Anchored this defines the X and Y coordinates of the anchor relative to global axes, plus the Z-coordinate relative to the seabed level at that (X,Y) position. If the end is Free then this defines the coordinates of the estimated equilibrium position of the line end, relative to global axes. End Orientation When a line is connected to an object, 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, Declination and Gamma angles. These angles define the end fitting orientation relative to the object, so for objects that rotate (e.g. vessels and 6D buoys) the fitting rotates with the object. For Fixed or Anchored ends the end orientation is defined relative to global axes. For Free ends the end orientation is not used. Azimuth, Declination and Gamma define the end fitting orientation by specifying the directions of the axes (Ex, Ey, Ez) of its frame of reference, where E is the end fitting origin - the point to which the line end is connected. See Line End Orientation. The direction of Ez is defined by specifying its Azimuth and Declination angles. Ez is the end fitting axial direction; when the end segment is aligned with Ez then no bending moment is applied by the joint, so Ez is sometimes called the no-moment direction. Note that Ez must be specified using the "A to B" convention, i.e. Ez is into the line at end A, but out of the line at end B. Ex and Ey are perpendicular to Ez and they are defined by specifying the Gamma angle, which is a rotation about Ez. The Ex and Ey directions are used for reporting results (e.g. the 2 components of shear force). And if the line has torsion included and the joint twisting stiffness is non-zero, then Ex and Ey also define the line end orientation at which no torsional moment is applied by the joint. The connection at a line end is modelled as a "ball-joint" with this orientation being the preferred "no-moment" orientation, i.e. the orientation of the line end that gives rise to no moment from any rotational stiffness of the connection. If all of the end connection stiffness values are zero, e.g. to model a ball joint that is completely free to rotate, then the end orientation angles have no effect on the line behaviour. The angles then only serve to define the local x, y and z-directions that are used to define results (e.g. shear and bend moment components, stress components, etc.) that depend on the local axes directions. Bending and Twisting Stiffness The connection at a line end is modelled as a joint with the specified rotational stiffness. The restoring moments applied by the joint depend on the deflection angle, which is the difference between the end fitting orientation and the orientation of the line. The end orientation is therefore the orientation of the line that corresponds to zero moment being applied by the joint. 289 w The connection stiffness is the slope of the curve of restoring moment against deflection angle. The x bending and y bending values specify the connection bending behaviour for rotation about the end Ex and Ey directions, respectively. For an isotropic ball joint the two values must be equal; this can conveniently be specified by setting the y-bending value to '~', meaning 'same as x-value'. A non-isotropic ball joint can be modelled by giving different x and y bending values; in this case the line must include torsion. The x bending and y bending behaviour can either be linear or non-linear, as follows: • • For a simple linear behaviour, specify the bending stiffness to be the constant slope of the curve of restoring moment against deflection angle. For a non-linear behaviour, use variable data to specify a table of restoring moment against deflection angle. OrcaFlex uses linear interpolation for angles between those specified in the table, and linear extrapolation for angles beyond those specified in the table. The restoring bend moment must be zero at zero angle. The Twisting Stiffness value is only relevant if torsion is included for the line. It specifies the rotational stiffness about the end Ez direction. For the twisting stiffness this variation is always modelled as linear so the twisting stiffness you specify should be the slope of the linear anglemoment curve. The bending and twisting stiffness can be set to zero (free to rotate with no resistance), nonzero (can rotate but with resistance) Infinity (a rigid connection) or variable (non-linear, for bending only). Note that Infinity can be abbreviated to ‘Inf’. A flex joint can be modelled by setting the stiffness values non-zero (and less than infinity). Warning: Avoid specifying large connection stiffness values (except the special value Infinity) since they require very short simulation time steps. Release at Start of Stage If desired each line end can be disconnected at the start of a given stage of the simulation. If no release is wanted then set this item to "~", meaning "not applicable". Line Ends Form The Line Ends form allows you to view or edit the end positions and connections for all the lines, on a single form. It can be opened using the model browser or using the pop-up menu on the individual line data forms. Similarly, the pop-up menu on the Line Ends form provides a link to the individual line data forms. The Sort By box allows you choose whether the form displays the line ends in Line order (i.e. both ends of first line, then both ends of second line, etc.) or End order (i.e. end A of all lines, then end B of all lines). Positions and Connections Tabs The Positions and Connections tabs allow you to view or edit all the connection data for the line ends. This is exactly the same data as on the individual line data forms - the only difference is that you can view or edit the data for all the line ends on a single form. The positions are Cartesian coordinates relative to the frame of reference of the object to which the line end is connected. 290 w Polar Coordinates Tab The Polar Coordinates tab provides a way of viewing or setting the positions of the line ends using polar coordinates, relative to a choice of frames of reference. This facility is useful for cases, for example mooring arrays, where a series of line ends need to be laid out around a circle. The polar coordinates (R, Theta, Z) are those of the line end position relative to the polar coordinates frame of reference chosen on the form for that line end. (The Cartesian coordinates of the line end, relative to the same reference frame, are (R.cos(Theta), R.sin(Theta), Z) ). On the other hand, the Object Relative Position data (on the Positions tab and on the individual line data form) are the Cartesian coordinates of the line end relative to the frame of reference of the object to which it is connected. OrcaFlex keeps the two sets of coordinates synchronised, so if you change one then the other is automatically updated to match. If you change any other data then the Cartesian Object Relative Position coordinates are taken to be the master data and so left unchanged, and the polar coordinates are updated to match. You have a quite a lot of flexibility to choose what reference frame you want for the polar coordinates. The reference frame has its origin at your chosen Reference Origin and has its axes are parallel to those of your chosen Reference Axes. For the reference origin you can choose between: • • • • • • the global origin if one end is anchored, then the origin for anchored ends. This is the point on the seabed that is directly below the global origin. the origin of the frame of reference of any object to which that line's ends are connected. the position of the other end of that line. And for the reference axes directions you can choose between: the global axes directions the axes directions of the frame of reference of any object to which that line's ends are connected. Example of Using Polar Coordinates The choices of reference frame for the polar coordinates may seem complex at first sight, but they allow various useful coordinate transformations to be done easily and accurately. Here is an example. Consider mooring a spar with an array of 4 lines, each of which has end A connected to the spar and end B anchored. Suppose you want to place the A ends of the lines so that they are evenly spaced circumferentially around the spar, all at radius 5m from the spar axis and all 3m below the spar origin. To do this easily, first sort into End order so that all the A ends are grouped together. Then, for the first line, set the reference frame origin and axes to be the spar origin and spar axes and set its polar coordinates to be R=5, and Z=-3. You can now use copy+paste or fill down to set all the other A ends to the same reference origin, axes and R and Z coordinates. Finally you can set the Theta coordinates for the A ends to 0, 90, 180 and 270 degrees Similarly, suppose you want the B ends to be anchored to the seabed, with the anchors again evenly spaced circumferentially, and with each line spanning 200m horizontally. The easiest 291 w reference frame for this is with the reference origin being End A and the reference axes being the spar axes. The Theta coordinates should again be set to 0, 90, 180 and 270 degrees and the R coordinates set to 200m. But this time, to set the vertical positions of the B ends, it is easier (especially if the seabed is sloping) to go to the Connections Tab and set Connect To Object to be Anchored and then go to the Positions tab and set the Object Relative Position z coordinate to zero. Contents Contents Density If any section of the line is of a line type that is hollow, i.e. has non-zero inner diameter, then its mass is increased by: Density . Inner Cross Sectional Area . Section Length. Mass Flow Rate The rate of flow of mass through the line. If it is non-zero then it is used to calculate the centrifugal and Coriolis forces due to flow of fluid in the line. Positive values mean flow from End A to End B; negative values mean flow from end B towards end A. To convert between mass flow rate, volume flow rate and flow velocity use the following simple formulae: Volume flow rate = Mass flow rate / ρ Flow velocity = Mass flow rate / (ρ π d² / 4) where ρ is the contents density and d is the internal diameter of the line. Contents Pressure The internal pressure in the line at End A. This value is only used for reporting the wall tension and stress results - it does not affect any other results. The internal pressure at end A is assumed to remain constant at this value throughout the simulation. Internal pressure elsewhere in the line is calculated. See Line Pressure Effects for details of contents pressure modelling. Structure & Hydrodynamics Each line can be made up of up a number of sections with different properties, the sections being defined in sequence from end A to end B. Line Type This determines the properties of the section. Section Length The length of the section. Number of Segments The number of segments in the section. Clash Check Clash modelling is included when this data item set to Yes. If it is set No then the section will be ignored for clashing purposes. 292 w Note: Clash checking is quite time-consuming, so you should only set this item to Yes for those sections for which you need clash modelling to be included. See Line Clashing. Drag Formulation A number of authors have proposed formulae to model how the drag force on a line varies with the incidence angle. OrcaFlex offers the choice of the Standard, Pode or Eames formulations. All of these use drag coefficients, which are specified in OrcaFlex on the line type data form. For details of the formulations see the Line Theory section. Attachments A number of attachments may be added to each line. Each attachment can either be of a specified Attachment Type or else be a clone of a specified 6D buoy. Attachment Type Can be a Clump Type, a Drag Chain Type or an existing 6D Buoy. 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. The 6D buoy from which the attachment is cloned cannot be deleted, without first deleting all the attachments that are clones of it. 6D buoy attachments are useful when you want a number of identical 6D buoys attached to a line. To attach 20 identical buoys to a line, for example, first create the first buoy separately from the line and then connect it to the line by setting its connection data item on the buoy data form. This first buoy acts as the master from which all the other attachment buoys are cloned. Then, on the line data form, specify 19 attachments and set their attachment type to be the first 6D buoy. Note: Position The x, y and z coordinates specify the position of the attachment relative to the line. • For Clumps and Drag Chains the x and y coordinates must be zero and the z coordinate is the arclength. Clumps and Drag Chains are connected at the node nearest to this arclength. 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. 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). 6D Buoy attachments can only be used when the Line includes torsion. • For 6D Buoy attachments the z coordinate specifies the arc length at which the buoy should be connected to the line. The buoy will be connected to the nearest node to that arc length. The buoy will be connected with an offset relative to that node's axes that is given by (x, y, 0). See 6D Buoy Initial Position for more details. Orientation For 6D Buoy attachments only. Rotation 1, Rotation 2 and Rotation 3 determine the Initial Attitude of the attached buoy. 293 w Name For 6D Buoy and Drag Chain attachments only. This is the name of the attached object and is used to select results for that object. Drawing You can define the colour, line style and thickness of the pens used for drawing the nodes and sections of the line. See How Objects Are Drawn. For the sections there is a choice for which pen is used, the choice being made by clicking on the "Sections" box. You may either specify the pen explicitly on the Line Data form, in which case it will be used for all sections of that line. This allows you to use different pens to distinguish between different lines. Alternatively, you can choose to have the sections drawn using the appropriate Line Type Pen defined on the Line Types table. This allows you to use different pens to distinguish sections of different line types. For Lines with Prescribed Statics Method you can control how the track is drawn. You can switch between the options of drawing the track in the chosen pen and not drawing it at all. Similarly 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. Statics Statics Method For lines, there is a choice of calculation methods available for the static analysis. The method may be set to Catenary, Spline, Prescribed or Quick. The normal setting is Catenary, in which case the static analysis finds the equilibrium catenary position of the line, allowing for weight, buoyancy, drag, but not allowing for bend stiffness or interaction with shapes. See Catenary Calculation. The Catenary solution has some limitations and some systems, such as those with slack or neutrally buoyant lines, can be troublesome. For such lines you can instead specify Spline, in which case the line is instead set to a 3D spline curve based on spline control points specified by the user. See Spline Data. For pull-in analysis the Prescribed option has been provided. Here the user specifies the starting position of the line as a sequence of straight line or curved sections on the seabed. See Prescribed Starting Shapes. Finally, you may specify Quick, in which the line is left in the rough catenary shape used in the Reset state. Full Statics This calculation finds a full equilibrium position for the model. Unlike the Catenary method, bend stiffness and interaction with shapes are included. Full statics needs a starting shape for the line, and it uses the specified Statics Method to obtain this; it then finds the equilibrium position from there. You must therefore also set the Statics Method to give a reasonable starting shape, choosing from one of the above statics methods. See Full Statics. For more details of the Statics Calculation see Statics Analysis. Warning: If you do not use the Catenary method or Full Statics, then the starting position will not (in general) be an equilibrium position. 294 w Note: It is only possible to include buoys in the static analysis (see Include Buoys in Static Analysis ) if either the Catenary method or Full Statics is used for all lines in the model. Include Friction Friction can be included in the static analysis only if the Statics Method is Catenary or if Full Statics is used. With seabed friction present there is not, in general, a unique static position for the line, since the position it adopts depends on how it was originally laid and its history since then. In order to define a unique solution, we therefore need to make some assumptions about how the line was originally laid and friction is then assumed to act towards this position. If the Statics Method is Prescribed, then this ‘originally laid’ position is assumed to be the position defined by the Prescribed track. Otherwise, the ‘originally laid’ position is defined by specifying the Lay Azimuth and Pre-Tension values. Lay Azimuth This data is only used when seabed friction is included in the static analysis and the Statics Method is not Prescribed. It then defines the position in which the line is assumed to have been originally laid, and friction is then assumed to act towards this position. When Statics Method is not Prescribed, it is assumed that: • The line was originally laid, with the specified Pre-Tension, starting with end B at its specified position (or at the point on the seabed directly below, if end B is not on the seabed) and then leading away from there in the Lay Azimuth direction and allowing for the seabed slope at end B. End A was then moved slowly from that original position to its specified position. • To help set this data item, there is a button on the form marked Set. This button sets the Lay Azimuth value to be the direction from End B towards End A, based on their current positions. Notes: If a profile seabed is used then for the purposes of calculating this assumed original lay position, the seabed is treated as a simple plane with slope equal to the local seabed slope at end B. In other words the assumed original laid position does not track down into any hollows or over any hills, and the effect is that it bridges any hollows and is stretched by any hills along its path. Whilst the program will accept any Lay Azimuth, 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. For example, if we have a line top at X=0, Y=0, and anchor at X=100, Y=0, we would expect trouble for a Lay Direction of 90 degrees. Pre-Tension If the Spline or Prescribed statics methods are used, then the line is laid out along the specified curve with a strain determined by the axial stiffness and this Pre-Tension value. This data item is also used if friction is included in the static analysis. It determines the strain with which the line is assumed to have been originally laid, and this original position is used as the target position towards which friction acts. Otherwise, this data item is not used. 295 w Catenary Convergence If the Catenary statics method is chosen, then an iterative catenary calculation is used to determine the static position of the line. This calculation is controlled by a number of convergence parameters which can normally be left at their default values. However sometimes the calculation can fail to converge. If this happens, 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. The catenary calculation cannot handle lines with slack segments - try increasing the number of segments in the relevant section of the line. For lines that touch down on the seabed, 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 degrees. Is the line buoyant, either deliberately or by mistake. The catenary calculation has problems with floating lines - you may need to use the Spline statics method instead. Does the line have a surface-piercing buoyant clump attached? If the clump is short then the catenary calculation is more difficult. • • • If the calculation still fails to converge, then it is sometimes possible to obtain convergence by changing one or more of the convergence parameters, as follows: Max Iterations The maximum number of iterations that OrcaFlex will make before treating the calculation as having failed to converge. Increasing this value can sometimes help. Tolerance The non-dimensional accuracy to which the calculation is done, before the calculation is treated as having converged. Increasing the tolerance increases the chances of convergence but reduces the accuracy. Min Damping The minimum damping factor to be used in the calculation. Convergence can sometimes be achieved by increasing this parameter to a value greater than 1 - try values in the range 1.1 to 2.0. The minimum damping should not be set to less than 1. Mag. of Std. Error, Mag. of Std. Change These parameters control the maximum size of the change, in the estimated solution, this is allowed in a single step. Reducing these values can sometimes help, but the calculation will then usually require more iterations. The remaining parameters should not normally be changed. For further information contact Orcina. 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. This process is controlled by a number of convergence parameters, found on the Line data form. These can normally be left set to the Default values, but in some cases where the calculation fails to converge to a solution it may be necessary to use Specified values that suit the problem being handled. If Specified 296 w parameters are used, the following parameters can be edited, and a command is available to reset them to the default values. 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. 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*LineDryWeight (including contents). Reducing the Tolerance value will give a more accurate static equilibrium position, but will take more iterations. The program may not be able to achieve the Tolerance specified if it is too small, since the computer has limited numerical precision. Delta This is a perturbation size, used to calculate the Jacobian matrix for the problem. Delta should always be less than the tolerance specified. Min / 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, or to try to speed up slow cases, the default values can be altered. For difficult cases that appear to make the convergence unstable (e.g. giving very bad line positions on the screen) the maximum damping factor should be increased. To speed up convergence for simple cases where damping is not necessary, the maximum damping factor can be set low, e.g. equal to 1. If this causes the convergence process to become unstable, the maximum damping factor should be increased again. The minimum damping factor should always be left equal to 1. The remaining parameters should not normally be changed. For further information contact Orcina. Splines The following data is only used if the Spline statics method is specified. Order This sets the smoothness of the spline shape; generally order 3 is reasonable. If a higher order is chosen, a smoother curve results. The order cannot exceed the number of spline points. Control Points The line shape is specified by a number of Control Points. 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. These intermediate control points may be adjusted to 'pull' the curve into the desired shape. 297 w The first and last control points correspond to line ends A and B respectively. The line is stretched to the specified pre-tension and laid out following the spline curve starting at End A and working towards End B. For a line with a Free end the line is laid out along the curve until End B is reached. 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). For a line with a Fixed end, Anchor or attached to some object the curve is automatically expanded or contracted to allow the end to lie at the specified end position. A warning is generated if this process fails. Track Data The Track Data is only used if the Prescribed statics method is specified. It can be found in the Starting Shape group 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. OrcaFlex then creates an arc of the specified Length and Turn, and the X and Y coordinates of the end of this section, and all subsequent sections, are automatically adjusted to match. By editing the X and Y coordinates of the ends of a track section on the line data form. 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,Y) point. The Length and Turn values for this section, and the X and Y coordinates for subsequent sections, are then automatically adjusted to match. By dragging the end points of the track sections on a 3D view using the mouse. The track and the track section end points are drawn on the 3D views. Dragging a track section end point is equivalent to editing its X and Y values, as described above. • • The individual data items (see Figure: Plan View of Example Track) are as follows: End A Azimuth The initial direction of the track. Track Sections The number of sections used to define the track. Section Length The length of the circular arc (or straight line if Section Turn = 0). Section Turn The amount by which the track azimuth increases over this section. A positive value denotes a turn to the left, when viewed from above, and a negative value denotes a turn to the right. A value of zero can be entered to specify a straight track section. Section Radius The radius of curvature of the circular arc. The radius equals (180L)/(πT), where L is the section length and T is the absolute value of section turn, in degrees. For straight sections (i.e. if Section Turn = 0) the radius is reported as Infinity. 298 w Notes: This is a reported value, not an editable data item, and is hence always shown in grey. With a sloping seabed the actual track on the seabed will have a slightly different radius of curvature - see Laying Out the Line. Section X and Y The global X and Y coordinates of the end of this track section. You can either edit these X and Y coordinates explicitly, on the line data form, or else by dragging the end point on a 3D view. 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. Section Z The global Z coordinate of the section end point on the seabed. This is a reported value, not an editable data item, and is hence always shown in grey. Section Arc Length The total arc length to the end of the section. This is a reported value, not an editable data item, and is hence always shown in grey. Section Azimuth The azimuth direction at the end of the section. This is a reported value, not an editable data item, and is hence always shown in grey. Track Pen This controls how the track is drawn. You can switch between the options of drawing the track in the chosen pen and not drawing it at all. Laying Out the Line The track data defines a sequence of straight lines and circular arcs in the horizontal plane, which are then projected vertically onto the seabed to define the track itself. The program then lays the line out along the track, allowing for any pre-tension specified by the user on the line data form. Because the line is modelled as a series of straight segments, 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. The size of this discrepancy reduces as more segments are used. If End A is above the seabed then the line descends linearly to the seabed, reaching the seabed at the end of the first track section. If the end of the last track section is reached before all the line has been laid out, then the rest of the line is laid out in a straight line in the direction of the end of the track. Sloping Seabeds The track on the seabed is obtained by projecting the specified circular arcs or straight sections vertically down onto the seabed. With a horizontal seabed this vertical projection has no effect on the shape of the track. But with a sloping seabed the vertical projection does not preserve distances and this causes some effects that users should note: 299 w • The section lengths and arc lengths that appear in the prescribed starting shape data table are lengths in the horizontal plane, i.e. before projection down onto the seabed. With a sloping seabed the true section and arc lengths on the seabed will differ, the difference depending on the slope of the seabed. The actual arc lengths can be obtained by running the static analysis and looking at the Full Results table for the line. The section radius reported in the prescribed starting shape data table is that of the circular arc in the horizontal plane, i.e. before projection down onto the seabed. When the circular arc is projected down onto a sloping seabed the resulting track section is slightly elliptical rather than circular, so again the actual radius of curvature will differ. The actual radii of curvature can be obtained by running the static analysis and looking at the Full Results table for the line. • 7.8.3 Attachments Attachment Types The Attachment Types form defines the properties of a number of named attachment types. Attachments with these properties can then be connected to lines. Attachment Types can be either Clump Types or Drag Chain Types. The attachment types form must include all the attachment types referred to on all of the Lines data forms, but it can also include other attachment types that are not currently in use in the model. This allows you to build up a library of standard attachment types that can then be easily used when building Lines. Clumps A clump is a concentrated attachment that is connected to a node on a Line. It can be buoyant or heavy and is a small body that experiences forces (weight, buoyancy, drag etc.) exactly as for a 3D Buoy. 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. A clump therefore adds to the mass, buoyancy and hydrodynamic force of the node to which it is attached. Clumps only have 3 degrees of freedom - X,Y and Z - which are determined by the position of the node to which they are attached. Clumps do not rotate - their local axes always remain aligned with the global axes directions. Each clump is assigned a height and an offset from the node, both measured vertically. These 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. Where the clump pierces the water surface, buoyancy and hydrodynamic forces are applied in proportion to the immersed length of the clump. Each clump is of a named clump type, from which it inherits all its properties. The clump types are specified on the Attachment Types form and have the following data. Clump Type Name Used to refer to the Clump Type. Mass Mass or weight in air. 300 w Volume Used to calculate buoyancy and added mass for each clump of this type on a line. Clumps may be either net buoyant or heavy as desired. Note: If a clump is net heavy in water, then it is treated as a Drag Chain. This means that its length is truncated at the point where it touches the seabed, and the weight force acting on the line is reduced proportionately. The program also calculates a friction force due to the part of the drag chain supported by the seabed. This friction force acts on the node to which the clump is attached, and uses the coefficient of friction supplied for that line. Height Used for drawing the clump and also to determine how much of the clump is below the water surface. A heavy clump (modelling a Drag Chain) is assumed to start at the Offset distance below the node, and extend downwards for its Height, or until it meets the seabed. A buoyant clump is assumed to be centred at the Offset position above the node, and extend for half its Height above and below this point. Offset A clump may be offset vertically from the line, for example to represent a line supported below the surface by floats. 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. Note: Drag Drag forces are calculated in global horizontal and vertical directions for each clump on a line. drag force = ½ . Water Density . (velocity)² . Cd . Drag Area where Cd is Drag Coefficient as specified here, Drag Area is specified here, velocity is the velocity of the fluid relative to the clump in the appropriate direction. Added Mass Coefficients Added mass in global horizontal and vertical directions are given by added mass = Ca . Water Density . Volume where Ca is Added Mass Coefficient as specified here. Pen Defines the colour, line style and thickness of the pen used for drawing this clump type. See How Objects Are Drawn. The way in which Offset is used depends on whether the clump is heavy or buoyant - see the note above. 301 w Drag Chains Drag chains are attachments to a line that model straight chains that hang down from the line. They apply weight, buoyancy and drag forces to the node to which they are attached, but not any added mass effects. For details see Drag Chain Theory. Drag chains include two facilities that can be important in modelling towed systems. Firstly, the chain's drag coefficients can vary with the incidence angle of the relative flow; 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, which is applied to the line. Secondly, drag chains interact with the seabed (in a simple manner); if the node comes closer to the seabed than the chain length, then the seabed provides a supporting reaction force and a friction force, both of which are applied to the node. Each drag chain is of a named drag chain type, from which it inherits all its properties. The drag chain types are specified on the Attachment Types form and have the following data. Name Used to refer to the Drag Chain Type. Length Length of the drag chain. Effective Diameter Effective diameter of the drag chain. This is the diameter of the cylinder that has the same displaced mass per unit length. Mass Mass per unit length. Mass is assumed to be uniformly distributed along the length of the drag chain. Friction Coefficient Coefficient of friction for contact with the seabed. This coefficient is used for all directions of friction. The value can be set to '~', in which case the drag chain will instead use the axial friction coefficient of the node to which the drag chain is attached. Drawing Defines the colour, line style and thickness of the pen used for drawing drag chains of this type. See How Objects Are Drawn. Drag Coefficients A table specifying normal and axial drag coefficients, as a function of the incidence angle of the relative velocity vector. The incidence angle is the angle between the relative velocity vector and the drag chain. So 0 means flow axially along the drag chain and 90 means flow normal to the drag chain. Coefficients are specified for a range of incidence angles between 0 and 90 degrees and linear interpolation is used to obtain coefficients for intermediate angles. The Graph button shows the resulting coefficient variation. Symmetry is used to obtain coefficients for angles outside the range 0-90. 302 w See Drag Chain Theory for further details. 7.8.4 Line Types Line Type Data The Line Types form defines the properties of a number of named line types, which can then be used to specify the structure of the Lines used in the model. The line types form must include all the line types referred to on all of the Lines forms, but it can also include other line types that are not currently in use in the model. This allows you to build up a library of standard line types which can then be easily used when building Lines. There isn't room on the screen to show all the properties of all the line types, so OrcaFlex offers two view modes. Individual mode shows one line type at a time, but shows you all its properties. All mode shows all the line types, but different types of properties are shown in different tables. There is also a Line Type Wizard that helps set up line type data to represent commonly used structures such as chains, ropes etc. Line Type Name Used to refer to the Line Type. Outer and Inner Diameter Used to define buoyancy, drag area and mass of contents per unit length respectively. CG Offset The x and y coordinates of the centre of gravity (CG) relative to the centreline. These data items are only used when torsion is being modelled. 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. Bulk Modulus Specifies the compressibility of the line type. If the line type is not significantly compressible, then the Bulk Modulus can be set to Infinity, which means "incompressible". See Buoyancy Variation with Depth. Mass per Unit Length The mass of the line or pipe structure, excluding contents, per unit length. Commonly quoted as "weight in air, empty". Axial Stiffness The axial stiffness is the slope of the tension-strain curve. You can either specify linear or nonlinear behaviour, as follows: • For a simple linear behaviour, specify the axial stiffness to be the constant slope of the tension-strain line. This slope is the equivalent EA value for the line, where E is Young's modulus and A is the cross section area. It equals the force required to double the length of any given piece of line, assuming perfectly linear elastic behaviour. (In practice, of course, most lines would yield before such a tension was reached.) 303 w • For a non-linear behaviour, use variable data to specify a table of tension against strain. OrcaFlex uses linear interpolation for strains between those specified in the table, and linear extrapolation for strains beyond those specified in the table. The tension must be zero at zero strain. Warning: Non-linear behaviour breaks the assumptions of the stress results and fatigue analysis. See Calculating Tension Forces for details of the tension model used. Warning: The axial stiffness specified here has a major effect on how long the dynamic simulation will take, since very large axial stiffness values lead to very small natural periods for the nodes and this in turn requires very small simulation time steps. See Inner and Outer Time Steps. Fortunately, the value of axial stiffness used is often not very important, providing it is large enough that the axial strains produced are small. The exception to this is where snatch loads occur, since the axial stiffness directly affects the peak tension that results. It is therefore normally quite acceptable to specify a much smaller axial stiffness value than applies to the real line, so enabling much faster simulations. We recommend that artificially low axial stiffness values are specified, particularly for early investigative simulations. The effect of this can easily be investigated later by re-running a selection of important simulations with the actual axial stiffness value. Bend Stiffness The bend stiffness is the slope of the bend moment-curvature curve. You can specify linear or non-linear behaviour, as follows: • For a simple linear behaviour, specify the bend stiffness to be the constant slope of the bend moment-curvature line. This slope is the equivalent EI value for the line, where E is Young's modulus and I is the section moment of area. It equals the bend moment required to bend the line to a radius of curvature of 1 radian per length unit. For a non-linear behaviour, use variable data to specify a table of bend moment against curvature. OrcaFlex uses linear interpolation for curvatures between those specified in the table, and linear extrapolation for curvatures beyond those specified in the table. The bend moment must be zero at zero curvature. Warning: Non-linear behaviour breaks the assumptions of the stress results and fatigue analysis. You can specify separate values for bending about the x and y-directions, but often the bend stiffness for the x and y-directions are equal. This can be specified by setting the y-bend stiffness to '~' which means 'same as x-bend stiffness'. The bend stiffness specified may be zero, for example for chains. It can also be very large values, for example for steel pipes, but this will often result in short natural periods in the model and hence require short simulation time steps. See Inner and Outer Time Steps. See Calculating Bend Moments for details of the bending model used. Torsional Stiffness Each line type can have a linear torsional stiffness; it is used only if torsion is included on the line data form. The torsional stiffness is the torsional moment that results if the line is given a twist of 1 radian per unit length. • 304 w Torque per Unit Tension This data item defines the effect of tension on torsion; it is used only if torsion is included on the line data form. Many pipes or cables with a spiral-wound construction have the property that when tension is applied a torsional moment is produced. The Torque Per Unit Tension data item allows you to model this effect - set it to the torque that results when 1 unit of tension is applied to the line. If your line has no tension-torque interaction then set the data item to zero. Contact Stiffness and Damping The stiffness and damping values used by the clashing algorithm. See Line Clashing. Drag Coefficients The drag coefficients for the normal (x and y) directions and axial (z) direction are specified on the line type data form. For the x and y directions you can either specify a fixed constant value, or else a value that varies with Reynolds number. Often the coefficients for the x and ydirections are equal and this can be specified by setting the y-coefficient to "~", which means "same as x-coefficient". 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 further details see the Line Theory section. Added Mass Coefficients The added mass coefficients Ca for normal (x and y-directions) and axial (z-direction) flow. Often the coefficients for the x and y-directions are equal and this can be specified by setting the y-coefficient to "~" which means "same as x-coefficient". For each flow direction, the inertia coefficient, Cm, is automatically set to equal 1+Ca. See Added Mass for details. Friction Coefficients and Bias Power OrcaFlex applies Coulomb friction between the line and the seabed. The friction force applied is ≤ µR where R is the seabed reaction force and µ is the friction coefficient. See Seabed Friction Data for published friction data. Lines lying on the seabed often move axially more readily than the move laterally. To enable this effect to be modelled, you can specify different friction coefficients µ for motion normal (i.e. lateral) and axial to the line. For intermediate directions of motion OrcaFlex interpolates between these two values to obtain the friction coefficient µ to use. If the axial friction coefficient is be set to '~' then the normal friction coefficient is used for µ for all directions of motion. This provides a convenient way of using the same friction coefficient for all directions of motion. If different friction coefficients are specified for motion normal and axial to the line, then as well as varying the magnitude of the friction force according to the direction of motion, OrcaFlex can also bias the direction of the friction force towards the direction of the larger friction coefficient. This reflects the tendency of a line, when pulled diagonally, to slide not exactly in the direction of pull but instead to slide more in the axial direction (assuming the axial direction has the lower friction coefficient). You can control the strength of this direction bias by setting the Bias Power. This non-dimensional constant only affects the direction of the friction force, not its magnitude, and only applies when the motion is diagonal (i.e. when the line is moving both laterally and axially). 305 w If the bias power is zero, or if the normal and axial friction coefficients are equal, then no bias is applied - the friction force is applied directly opposing the direction of motion. If the bias power is positive, and the normal friction coefficient is greater then the axial coefficient (as is common for a line), then the friction force direction is changed so as to make the line move more in the axial direction. The larger the bias power, the larger is this change in direction and so the more the line tends to move axially. Note: The friction direction bias is not yet available with profile seabeds. See Seabed Touchdown and Friction for further details of the friction model used. Stress Outer and Inner Diameter The stress diameters are the inside and outside diameters of the load-bearing cylinder. They are used in the wall tension and stress results calculations, which are based on the assumption that the loads in the line are taken by a simple homogeneous cylinder. For simple cases, the stress diameters can be set to '~', in which case they will be taken to be the same as the pipe diameters. For more complex cases, for example where the pipe outside diameter allows for added buoyancy modules that are not load bearing, the stress diameters can be set separately. See Line Results - Forces. Allowable Stress The maximum allowable stress for this type of line. This value is only used to draw a limit curve on Stress Range Graphs; it does not limit the stress achieved in the line. If no limit curve is wanted then you may input the tilde character "~" (meaning not applicable) instead of a number. Stress Loading Factors These are used to specify what proportion of the loads (tension, bend moment, shear and torque) are to be used when calculating wall tension and stress results. The effective tension, bend moment, shear force and torque are multiplied by the appropriate stress loading factor when they are used to calculate the wall tension and stress results. For many cases, e.g. when modelling a simple homogeneous pipe that carries all the loads, these load factors should be set to 1, the default value. In some cases, values less than 1 may be suitable. For example, consider a case where the line models a composite structure that consists of a main carrier pipe and an external piggyback pipe. You might estimate that the main pipe takes all of the tensile and torsional loads, but only carries 70% of the bending loads, the other 30% being taken by the piggyback pipe. 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 0.7. Note: These data items have no affect on the simulation. They only affect the wall tension results, stress results and fatigue analyses. Maximum Tension The maximum permitted tension for this type of line. This value is only used to draw a limit curve on Tension Range Graphs; it does not limit the tension achieved in the line. If no limit curve is wanted then you may input the tilde character "~" (meaning not applicable) instead of a number. Minimum Bend Radii You can specify the minimum permitted radii of curvature for bending about the x and ydirections. These values are optional - they are only used to draw "allowable" curves on range 306 w graphs - they do not limit the bend radius of 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 xvalue"). Often the radii for the x and y-directions are equal and this can be specified by setting the yradius to "~" which means "same as x-radius". The specified values are used to draw "allowable curvature" curves on the x- and y-Curvature range graphs, and also (if the x and y-minimum radii are equal) on the Curvature range graph. In addition, 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 also (if the x and y-values are equal) on the Bend Moment range graph. Note: The "allowable" curve may not be visible on the range graph, since it may be outside the range covered by the graph. To see the "allowable" curve in this case you will need to modify the graph to increase the range of values covered. Limit Compression The program has two modes for handling slack segments, i.e. 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. This is the preferred model except where bend stiffness is insignificant. Yes: means that the segment is treated as an elastic Euler strut - the compression is limited to the segment Euler load. This is a better model for cases where the bend stiffness is insignificant, such as for chains and soft ropes. The segment Euler load is given by π².EI/L0² where EI is the bending stiffness of the pipe and L0 is the unstretched length of the segment. In all cases, whenever a segment has been compressed to or beyond the segment Euler load, then a warning of this is given on the results form and in the statistics table. For items such as mooring chain, the bending stiffness is zero, and the segment Euler load is also zero. In this case "Limit Compression" should be set to "Yes" - this correctly models a chain or very flexible rope, which cannot support any compression. The segment Euler load warning is then simply a warning that the line has gone slack. 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. Effectively, bending is occurring at a scale that is less than the segment length, so shorter segments are needed to model it accurately. Using shorter segments in that area will give a larger segment Euler load, and to obtain an accurate solution you should, ideally, use sufficiently short segments that the resulting segment Euler load is not reached. See Line Compression and Modelling Compression in Flexibles for details. Pen Defines the colour, line style and thickness of the pen used for drawing this line type. See How Objects Are Drawn. For each line there is a choice, on the Line Data form, of whether to draw the sections of the line using these Line Types pens, or whether to define a specific pen to use for all the sections of the line. 307 w Line Type Properties On the line types form, you can display various properties of the currently-selected line type by right clicking and then selecting Properties. The properties displayed include weight in air, displacement, weight in water, and diameter to weight (in water) ratio. For Line Types that have a non-zero bore you must specify the contents density to be used in the calculation of properties, since this will affect the properties that involve weight. The properties form also displays the names and contents densities of each line that uses that line type. 7.8.5 Line Results Line Results This section describes the line results that are available for the static and dynamic analyses. These results are available using the Results Selection form. Results from the modal analysis and fatigue analysis are described elsewhere - see the Modal Analysis and Fatigue Analysis sections. Selecting which Categories of Line Results are Shown For Lines there are a large number of results variables available on the Results form. So OrcaFlex groups the results variables into the following categories. Positions Motions X, Y, Z, Surface Z, Depth, Seabed Clearance, Arc Length Velocity, GX-Velocity, GY-Velocity, GZ-Velocity Acceleration, GX-Acceleration, GY-Acceleration, GZ-Acceleration Relative Velocity, Normal Relative Velocity, Axial Relative Velocity Azimuth, Declination, Gamma, Twist Ez-Angle, Exy-Angle, Ezx-Angle, Ezy-Angle No-Moment Azimuth, No-Moment Declination End Force Azimuth, End Force Declination, End Force Ez-Angle End Force Exy-Angle, End Force Ezx-Angle, End Force Ezy-Angle Effective Tension, Wall Tension Shear Force, x-Shear Force, y-Shear Force Vortex Force, GX-Vortex Force, GY-Vortex Force, GZ-Vortex Force Curvature, x-Curvature, y-Curvature Bend Moment, x-Bend Moment, y-Bend Moment Torque Line Clearance, Line Clash Force, Line Clash Impulse, Solid Contact Force Internal Pressure, External Pressure Direct Tensile Stress, Max Bending Stress, Worst Hoop Stress Max xy Shear Stress, Max von Mises Stress, von Mises Stress RR Stress, CC Stress, ZZ Stress, RC Stress, RZ Stress, CZ Stress Angles Forces Moments Clashing Pipe Stresses 308 w End Loads End Force, End Moment End GX-Force, End GY-Force and End GZ-Force End GX-Moment, End GY-Moment, End GZ-Moment 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 Bend Restrictor Load 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. To get the full list of available variables simply select all the categories. But normally there are several categories of variable that you do not currently need, in which case de-selecting them reduces the displayed list of variables to a more manageable set. Specifying the Position on the Line For line results you need to specify the position on the line at which you want results. This is done by setting the entries in a row in the Position table on the results form. You are then offered the Variables that are available for the point specified by the currently-selected row. Each row in the table specifies one point on the line. There are multiple rows in the table, 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. In a row that you don't want to use you can set the Node or Arclength column to '~', meaning 'unspecified'. 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. The next to last row in the table is dedicated to the Touchdown point. This is defined to be immediately before the first node on the seabed (starting from End A). If the results variable selected is a segment variable (i.e. 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. When there are no nodes on the seabed then the results variable is reported to be zero. Arclength and Node Columns The Arclength column specifies how far along the line the point is, measured from zero at end A. For information, if you set the Arclength column then the adjacent Node cell is set to the number of the nearest node to that arclength. The Node column can also be used as an alternative way of setting the arclength. You can set the Node column to the number of a node on the line. The adjacent Arclength cell will then be set to the arclength to that node. The node number must be in the range 1 (the node at end A) to N+1 (the node at end B), where N is the total number of segments in the line. Note The actual arc length for which line results are reported may not be exactly the specified arclength. OrcaFlex reports results for the 'nearest appropriate' result point. See Result Points below. R and Theta Columns For some variables (e.g. stress components) you must also specify the position of the point within the cross section through the specified arclength. Whenever one of these variables is selected in the Variables list, two extra columns become visible in the Position table. These 309 w extra columns specify the polar coordinates (R,Theta) of the point within the cross section; see the diagram in the Pipe Stress Calculation section. The R column can only be set to either Inner or Outer, meaning the radii corresponding to the Stress ID or Stress OD respectively. Results are not available for points between these two radii. Result Points OrcaFlex uses a discretised model and so results are only available at nodes, mid-segment points and line ends; we call these points 'result points'. The available result points depend on which variable you request, they are documented in the description of the variable. When you ask for a variable at a specified arclength OrcaFlex gives the value for the 'nearest appropriate' result point. The phrase 'nearest appropriate' here means that OrcaFlex considers the available result points that are in the same section as the arclength you specified and then chooses the one that is nearest to the arclength you specified. If you specify an arclength that is exactly at the boundary of two sections then OrcaFlex uses the section that starts at that arclength. OrcaFlex always labels results with the actual arclength 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. Positions X, Y and Z Available at nodes only. The global coordinates of the selected node. Proportion Wet Available at nodes only. 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. Surface Z Available at nodes only. The global Z coordinate of the sea surface directly above the instantaneous position of the selected node. Depth Available at nodes only. The depth of the node beneath the sea surface (= Surface Z - Node Z). Seabed Clearance Available at nodes only. The clearance is the shortest distance between the centre of the node and any point on the seabed. The value reported is for the node that is nearest the specified arclength. A negative value indicates that the node is in contact with the seabed. For a horizontal flat seabed the clearance is simply the height of the node above the seabed. For a sloping flat seabed it is the distance in the direction normal to the seabed. For a curved seabed it is the shortest distance, allowing for the curvature of the seabed. Arc Length Available at nodes only. The arc length from end A to the selected point. This is normally only useful for the touchdown point, since for other points it is constant. For the touchdown point it gives the arc length from end A to the first node on the seabed, or zero if there is no touchdown. 310 w Motions Velocity, GX-Velocity, GY-Velocity, GZ-Velocity Acceleration, GX-Acceleration, GY-Acceleration, GZ-Acceleration Available at nodes only. The magnitude and components (with respect to global axes) of the velocity and acceleration of the node. Warning: The velocity results are derived by numerically differentiating the logged positions of the node with respect to time, using the central difference scheme. The acceleration results are derived by a further such numerical differentiation. Because of this the accuracy of the results (especially the accelerations) will depend on the log sample interval. If the log sample interval is large then the results will not show higher frequency components of velocity and acceleration. Relative Velocity, Normal Relative Velocity, Axial Relative Velocity Available at nodes only. 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. Note: For a node that is above the water surface OrcaFlex reports a relative velocity based on the fluid velocity at the surface. Warning: The relative velocity results are derived using the node velocity results, so see the accuracy warning given above. Reynolds Number Available at nodes only. The Reynolds number is a measure of the flow regime. It is given by the equation: Re = V.D / ν where V = magnitude of the normal component of the relative velocity vector at the node D = line outer diameter ν = kinematic viscosity at the node. x-Drag Coefficient, y-Drag Coefficient, z-Drag Coefficient Available at nodes only. These are the line drag coefficients used in the calculation. If the line's drag coefficients are constant then these results report the values given in the user's data, except for a node at the junction between two sections with different drag coefficients, where an effective average value is used. If the line's drag coefficients vary with Reynolds number then these results report the computed value that was used. 311 w Angles Azimuth, Declination and Gamma Available at mid-segment points only. The azimuth, declination and gamma angles at the midsegment point. These angles report the local orientation of the line relative to global axes. The gamma angle is defined as for line ends (see Line End Orientation) and is only available if the line twist orientation is defined. Declination is in the range 0 to 180 degrees. Range jump suppression is applied to Azimuth and Gamma (so values outside the range -360 to +360 degrees might be reported). Twist Available at mid-segment points only. The twist per unit length experienced by the segment. Fluid Incidence Angle Available at nodes only. The angle between the relative velocity direction and the line axial direction. A value in the range 0 to 90 degrees. Ez-Angle, Exy-Angle, Ezx-Angle, Ezy-Angle Available at mid-segment points only. The direction angles of the mid-segment point with respect to the end axes of the nearest line end. See End Direction Results. These results are only available if the end orientation angles are defined. Ez-Angle is in the range 0 to 180 degrees. Range jump suppression is applied to Exy-Angle, Ezx-Angle and Ezy-Angle (so values outside the range -360 to +360 degrees might be reported). No-Moment Azimuth, No-Moment Declination Available at line ends only. The azimuth and declination angles, relative to global axes, of the no-moment direction at the end, allowing for any motion of the object to which the line is attached. These results are only available if the end orientation angles are defined. No-Moment Declination is in the range 0 to 180 degrees. Range jump suppression is applied to No-Moment Azimuth (so values outside the range -360 to +360 degrees might be reported). End Force Azimuth, End Force Declination Available at line ends only. The azimuth and declination of end force vector, relative to global axes. End Force Declination is in the range 0 to 180 degrees. Range jump suppression is applied to End Force Azimuth (so values outside the range -360 to +360 degrees might be reported). End Force Ez-Angle, End Force Exy-Angle, End Force Ezx-Angle, End Force Ezy-Angle Available at line ends only. The direction angles of end force vector, with respect to the frame of reference of the line end. See End Direction Results. These results are only available if the end orientation angles are defined. End Force Ez-Angle is in the range 0 to 180 degrees. Range jump suppression is applied to the other 3 end force angles (so values outside the range -360 to +360 degrees might be reported). 312 w Forces Effective Tension and Wall Tension Available at mid-segment points and line ends only. The structural force along the line axis. Positive values denote tension and negative values denote compression. For details of the difference between the effective tension and the wall tension see the Line Pressure Effects section. Shear Force, x-Shear Force, y-Shear Force Available at mid-segment points and line ends only. The structural force normal to the line axis, and its components in the local x and y-directions. Vortex Force, GX-Vortex Force, GY-Vortex Force, GZ-Vortex Force The magnitude of the lift and drag force on the node, and its components in the global axes directions. Available at nodes only and only when line uses one of the time domain VIV models from the VIV Toolbox. For details, see the documentation of the relevant time domain VIV model. Moments Torque Available at mid-segment points and line ends only, and available only for lines with torsion included. The component of structural moment along the line axis. Note that Torque includes any torque generated by tension-torque interaction. Curvature, x-Curvature, y-Curvature Available at mid-segment points and line ends only. The curvature and the magnitude of its components in the local x and y-directions. Warning: Curvature results are accurate only if the segment length is short. Bend Moment, x-Bend Moment, y-Bend Moment, Available at mid-segment points and line ends only. The bend moment and the magnitude of its components in the local x and y-directions. Clashing Line Clearance Available at mid-segment points only. The centreline clearance from this line to any other line. More precisely, the clearance reported for a segment is the shortest distance from the centreline of the segment to the centreline of any segment on any other line. Note that the clearance reported therefore does not allow for the radii of the lines involved. Note also that line clearance is only available if there are at least 2 lines in the model. The line clearance variable is useful for checking for clashing between lines. It is available in both range graph and time history form. The range graph, for a given period of the simulation, enables you to see where on the line clashing may be a problem. You can then examine the time history of line clearance for that point on the line, to see when closest approach occurs. You can then use the replay to examine which other line is coming closest. 313 w It is sometimes worth choosing carefully which line to check for clearance. An example is checking for clashing between a single mooring line and one or more of a number of closely spaced flowlines. The clearance graphs for the flowlines will include clearance to the other flowlines, between which clashing may not be a concern. The mooring line clearance is probably more useful, since it only includes clearance to the flowlines. Line clearance only checks against other lines, not against edges of vessels, buoys, etc. However you can check clearance against part of a vessel, for example, by attaching a dummy single-segment line to the vessel, spanning across the area of interest. The line clearance graphs for that dummy line will then show how close other lines come to that area of the vessel. Notes: The segment used is the one containing the selected arclength. The clearance reported does not allow for the outer diameters of the lines involved. Warning: For complex models, building and updating clearance graphs can be slow. Having "live" clearance graphs open whilst a simulation is running can significantly slow down the simulation. Line Clash Force, Line Clash Impulse Available at mid-segment points only. The Line Clash Force is 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. See Line Clashing for details. Line Clash Force is given for the segment containing the selected arclength and results are available in the form of time histories and range graphs. 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. The Line Clash Impulse is the integral of the Line Clash Force with respect to time. It is therefore a cumulative measure of the line clash force. Solid Contact Force Available at nodes only. The magnitude of the force per unit length due to contact with elastic solids. Pipe Stresses Stress results are available at mid-segment points and at line ends. Note: The loads (tension, bend moment, shear and torque) which are used in stress calculations are scaled by the stress loading factors before being used. Warning: The stress calculation makes various assumptions - see below. In particular it is assumed that the pipe is made of a uniform, homogeneous, linear material and that the tension and shear are uniformly distributed across the pipe wall. It is therefore only valid for pipes such as steel or titanium risers, not for composite flexible risers, ropes chains, etc. Also, it also does not allow for the stress concentrations that occur at joints etc. Warning: OrcaFlex 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. The stress calculations included are only valid under the assumptions given below; detailed stress analysis is still necessary. The stress calculation makes the following assumptions: 314 w • • • • 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. Internal pressure in the line generates wall tension in the line as it would do in a sealed cylinder. 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. • For terminology see Pipe Stress Calculation. Internal and External Pressure Available at mid-segment points and line ends only. The internal and external static pressures, Pi and Po. See Line Pressure Effects for details. Direct Tensile Stress Available at mid-segment points and line ends only. This is the axial stress due to wall tension (which includes the effects of internal and external pressure). It is constant across the crosssection and equals Tw/A. A positive value indicates tension; a negative value indicates compression. Max Bending Stress Available at mid-segment points and line ends only. This is the maximum value that the Bending Stress takes anywhere in the section. It is given by Max Bending Stress = (C2.M.StressOD/2) / Ixy and this maximum occurs at the extreme fibre on the outside of the bend. Worst Hoop Stress Available at mid-segment points and line ends only. 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 only. The value √(RZStress² + CZStress²) is called the xy-Shear Stress. This varies across the cross-section, and OrcaFlex reports the maximum value that takes anywhere in the cross-section. This is the Max xy-Shear Stress and it is given by Max xy-Shear Stress = (C4.τ.StressOD/2) / Iz + C3.S / A 315 w von Mises Stress, Max von Mises Stress Available at mid-segment points and line ends only. The von Mises stress 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: von Mises Stress = Sqrt( ( (s1-s2)^2 + (s2-s3)^2 + (s3-s1)^2 )/2 ) where s1,s2,s3 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, Theta) 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 commonlyused 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 = ±StressID/2 and ±StressOD/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 consists 36 Theta-values (i.e. every 10 degrees around the pipe circumference) at each of 5 R-values across the pipe wall. Warning: If torsion is included then the reported maximum von Mises stress is therefore approximate, since the actual maximum may not occur at a grid point. RR Stress, CC Stress, ZZ Stress, RC Stress, RZ Stress, CZ Stress Available at mid-segment points and line ends only. These are the individual stress components at a point in the cross-section. The point is specified by its polar coordinates (R, Theta) within the cross section. See Pipe Stress Calculation and Pipe Stress Matrix for details. • End Loads Most results variables that are available for mid-segment points are also available at the line end points. For example to obtain the end tension at end A you can ask for the Effective Tension (or Wall Tension) at end A. The enables you to obtain the following results at a line end: • • • • Effective Tension, Wall Tension and Torque Shear, Bend Moment and Curvature, and their components in the local x and y-directions. Seabed Clearance Stress results. For the forces, moments and stresses, the difference between the end value the mid-segment value for the end segment is that the end value includes allowance for the loads on the last half segment adjacent to the end. In addition the following extra load results are only available at line ends. 316 w End Force, End Moment End GX-Force, End GY-Force and End GZ-Force, End GX-Moment, End GY-Moment, End GZ-Moment End Lx-Force, End Ly-Force and End Lz-Force, End Lx-Moment, End Ly-Moment, End LzMoment End Ex-Force, End Ey-Force and End Ez-Force, End Ex-Moment, End Ey-Moment, End Ez-Moment 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. • If the line end is not free, then the end force and end moment are the total load acting between the end node and the object to which it is connected. If the line end is free, then the end force and moment are the total load acting between the line end and any links or winches attached to the end node. 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 no-moment direction. 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". Modal Analysis The modal analysis form enables you to calculate and view the undamped natural modes of a line in the model. To open this form, see the Modal Analysis command on the Results menu. Note that the analysis is only available when the static position of the model has been calculated. Doing a Modal Analysis To perform a modal analysis you need to specify the following: • • • Which line you want to analyse. Note that the analysis is not yet available for lines that have torsion included. Which modes you want to calculate. You can ask for All modes or a specified range of modes. See Modal Analysis Theory for details. Whether you want to calculate the mode shapes or just the natural periods. If you exclude the mode shapes then the analysis only calculates the natural periods of the line, not the shapes of the natural modes. If you include the model shapes then the analysis takes longer. 317 w When you have made your selections click the Calculate button. The modal analysis will then calculate the undamped natural periods and, if requested, the mode shapes. Each mode is normalised to have largest offset magnitude equal to 1, i.e. the offsets vectors are scaled so that largest offset vector is a unit vector. Mode Table The Table tab then displays a spreadsheet giving the results in numerical form. If you do not calculate the mode shape then the table reports only the periods of the requested natural modes. If you calculate the mode shapes then the table also gives the shape in the form of the displacements of each free node. Mode View If you requested the mode shapes then the View tab displays a 3D view of the line showing one selected mode shape superimposed on the static position of the line. The current direction is also shown on the view, and you can control the view angle, zoom etc., as on any 3D view. Note that if you may need to zoom out in order to see the line, and you may need to adjust the view angle to suit the mode that you are viewing. For example an out of plane mode is best viewed by looking along the plane of the line. You can use the Mode drop-down list to control which mode is shown on the view. 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. The Drawing Exaggeration value allows you to control the amplitude of the mode. (A mode shape does not define the overall amplitude of the oscillation - it only defines how the amplitude varies along the line.) Export SHEAR7 Mds File This button exports a SHEAR7 .Mds file. It is only available if the VIV Toolbox is enabled. Modal Analysis Theory The model analysis calculates the undamped natural modes of a single line. Each free node in the line (i.e. nodes that are mid-nodes or free end nodes) has 3 degrees of freedom (for a line with torsion not included). A line with N free nodes therefore has 3N degrees of freedom, and as a result the discretised model of the line has 3N natural modes. These modes are given in decreasing order of period and are numbered starting from 1. Note that the analysis calculates the natural modes of the discretised model, not those of the real continuous line. However the discretised modes are close to the continuous ones and for any given mode number the accuracy improves as more and more elements are used to model the line. 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. The highest numbered modes are unlikely to be realistic since they are oscillations whose wavelengths are of the same order as the segment length. Typically there are 3 types of natural mode - lateral in plane, lateral out of plane, and axial. The first two modes are often the simple out-of-plane and in-plane 'fundamentals' - i.e. the modes where the whole line swings to and fro together and the graph of displacement against arc length consists of just 1 half cycle. Then follow the higher harmonics, both in-plane and out-ofplane, with progressively more and more half cycles of displacement along the line length. The axial modes usually have much higher frequencies and so they are usually found among the high number modes. 318 w If the line hangs in one of the global axis planes then you can often distinguish whether a mode is in-plane or out-of-plane by looking at the pattern of zeros in the table of displacements. For example if the line hangs in the XZ plane then the out-of-plane modes have non-zero Ydisplacements but zero (or very small) X- and Z-displacements, and the in-plane modes have the opposite pattern of zeros. Non-Symmetric Effects Seabed friction is a non-conservative force that introduces non-symmetric terms into the line stiffness matrix. The OrcaFlex modal analysis can only handle a symmetric stiffness matrix. To deal with this problem OrcaFlex does the modal analysis using the symmetric part of the matrix (which is given by (K+Ktranspose)/2). This is an approximation that neglects the non-symmetric effects of friction, so OrcaFlex warns you if this approximation is being done. Outline Theory Modal analysis is a standard technique that is well-documented in the literature, but here is a brief outline. First consider a single degree of freedom system consisting of a mass attached to a linear spring. The equation of motion is: Mx''(t) = -Kx(t) where x(t) is the offset (at time t) from mean position, x''(t) is the acceleration, M is its mass and K is the stiffness of the spring. Note that this analysis neglects damping and so the results are referred to as the undamped modes. The effect of damping is usually small. The solution of the equation is known to be simple harmonic, i.e. of the form x(t) = a.sin(ωt), where a and ω are unknowns to be found by solving the equation. Differentiating x(t) gives: x''(t) = -ω^2.a.sin(ωt) so when we substitute into the equation of motion we obtain: -M.ω^2.a.sin(ωt) = -K.a.sin(ωt) which can be rearranged to give: ω = sqrt (K/M). This is the angular frequency of the oscillation and so the natural period T is given by: T = 2.π.sqrt (M/K) For this simple harmonic oscillator there is just a single undamped natural mode, corresponding to the single degree of freedom. For a continuous riser there are an infinite number of degrees of freedom, and hence an infinite number of undamped natural modes, but computer models inevitably have to use discretised models with a finite number of degrees of freedom. In OrcaFlex a line has 3N degrees of freedom, where N is the number of nodes that are free to move, so the discretised model has 3N undamped natural modes. In this situation the above equations still apply, but they now have to be interpreted as matrix/vector equations. ω and T remains scalars, but a, x and x'' become vectors with 3N elements, and M and K become matrices with 3N rows and 3N columns. Equation (1) then turns out to have 3N solutions, the i'th solution being ωi and ai, say, where ωi is a scalar and ai is a vector with 3N components. This i'th solution is called the i'th natural mode. It is an oscillation of the line in which all the degrees of freedom oscillate at the same angular frequency ωi. But different degrees of freedom have different amplitudes, given by the components of ai, and this amplitude variation is called the mode's shape. (1) 319 w 7.8.6 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 +ve value indicates an upwards force. See Drag Chain Theory for details on how the drag force is calculated. 7.8.7 Line Type Wizard 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: • • • • • • Chains: see Data for Chains and Modelling Mooring Chains Ropes: see Data for Ropes and Modelling Ropes Lines with Floats: see Data for Lines with Floats and Modelling Lines with Floats Homogeneous Pipes: see Data for Homogeneous Pipes and Modelling Homogeneous Pipes. Hoses: see Data for Hoses and Modelling Hoses and Cables. Cables: see Data for Cables and Modelling Hoses and Cables. 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 for representing 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. 320 w 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 that 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. 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 it was 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. The properties include minimum breaking load for chains and ropes. 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 is data that has been derived for you by the Wizard, based on the special line type data you specified. Non-bold text is data that has not been set by the Wizard - this data will be as you last set it. 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. 321 w 7.8.8 Modelling Mooring Chains Modelling Mooring Chains 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: Mooring Chain Geometry. The properties of an equivalent line type are given below. For the derivations of these values, click the property concerned: Studless OD ID Mass/Length Axial stiffness Bend stiffness Limit Compression Normal drag coefficient Axial drag coefficient Normal added mass coefficient Axial added mass coefficient Stress diameters Allowable stress Friction coefficient Reference Puech A, 1984. 1.80 D 0 19.9 D² 0.854x10 D² 0 yes 1.17 0.042 1.0 0.08 '~' Studlink 1.89D 0 21.9D te/m for D in m 1.01x10 D² kN for D in m 0 yes 1.20 0.040 1.0 0.07 '~' '~' '~' typically 0.4 - 0.8 depending on the seabed Geometry D = Nominal Diameter AFACE AEDGE 3.35D (3.6D) 3.35D (3.6D) Figure: Mooring Chain Geometry 6D 322 w Data Chains are widely used in a variety of offshore applications, most obviously in mooring. The Line Type Wizard helps derive a line type to represent a chain based on the following input data. Bar Diameter The diameter of the metal bar that forms the links. Link Type Can be either studlink or studless. The Line Type data that are derived, and the associated underlying expressions, are detailed in Modelling Mooring Chains. Mechanical Properties Catalogue Data When modelling mooring chains the Line Type Wizard aims to derive data for a line type whose characteristics are equivalent to that of a chain. Warning: The values generated by the Wizard are approximate only and are intended as first estimates for preliminary use. They 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. In deriving these some of the available catalogue data will prove useful and we outline here the relevant aspects. The Mooring Chain figure shows the geometry of a pair of chain links. The values are given in terms of the nominal bar diameter of the chain (D), assumed to be in metres, and are given for both a studless chain and, where different, for a studlink chain (in italics). The geometry given in the figure is based on catalogue data available from the chain manufacturer Scana Ramnas (1990 & 1995), as is the following expression for mass per metre: Studless Mass per metre (M) 19.9D² te/m (Studlink) (or 21.9D² te/m). The catalogue also gives the following value for the Young’s Modulus of the chain that has been deduced from stress-strain relationships in which the cross-sectional area of two bars is taken to be the load bearing area: E = 5.44 x 10^7 kN/m² (or 6.40 x 10^7 kN/m²). Minimum Breaking Loads For information, the properties window displays minimum breaking loads that depend on the nominal diameter and chain grade. They are derived using the following relationship, which was obtained from the manufacturer's catalogue: Min Breaking Load = c.D^2.(44 - 80D) kN Here the grade-dependent constant, c, is catalogued as follows: Grade 2 -1.37e4; Grade 3 1.96e4; ORQ - 2.11e4; R4 - 2.74e4. Studless and Studlink chains with the same nominal diameters are stated to withstand the same break- and proof-loads. 323 w Derived Data It will be useful to know the centreline length of bar needed to make a single link. We can obtain this by noting that, for a long chain, there is one chain link every 4D length of chain. Hence, the number of links per metre of chain is N = 1/(4D), and thus for a single link: Mass per link = M / N = 79.6D³ te (or 87 6D³ te) Assuming that the chain is made from steel, and using ρs as density of steel (= 7.8 te/m³), this then leads to: Volume per link = (M / N) / ρs = 10.2D³ m³ (or 11.2D³ m³). But, by considering the geometry of a link, we also have Volume = L . πD²/4, where L is centreline length of bar needed to make a single link (including the stud in the case of the studlink chain). Hence: L = Volume / (πD²/4) = 13.0D m (or 14.3D m). Outer and Inner Diameter The Line Type Wizard sets up Outer and Inner Diameter for a chain as follows: 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. Firstly, note that the volume per metre can be expressed as both: Volume per metre = M / ρs and also as Volume per metre = π OD² / 4 where OD is the equivalent diameter for a line with constant volume along its length. Equating these expressions leads to: Outer Diameter = √ [4M / (π ρs)] = 1.80D m (or 1.89D m) Chains do not have any contents, so the Inner Diameter is set to zero. Axial and Bending Stiffness The Line Type Wizard sets up Axial and Bending Stiffness and Limit Compression 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. Taking A to be the combined cross-sectional area of two bars, that is: A = 2(πD² / 4) m² leads to: EA = 0.85 x 10^8 D² kN (or 1 x 10^8 D² kN). 324 w 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. Limit Compression In conjunction with a zero value for bend stiffness, Limit Compression is set to 'yes'. Axial Added Mass Coefficient The Line Type Wizard sets up Axial Added Mass Coefficient for a chain as follows. As for axial drag the parts attracting added mass in axial flow are the projecting lobes only - see the figure. Each pair of lobes are simply a link with the middle sector removed and can be viewed roughly as an ellipsoid split down the centre with the following dimensions: length 6D, width D and height 2.35D (or 2.60D). J N Newman, 1977, (page 147, Fig 4.8) gives added mass coefficients for spheroids. We approximate the ellipsoid as a spheroid with mean width of 1.675D (or 1.80D), which has an aspect ratio (width/length) of about 0.3 in both cases. Newman gives Ca = 0.1 for this case, in axial flow. Therefore, we have that: Axial Added Mass = 0.1ρ [N . Vollobes]. However, the reference displaced volume in the expression for added mass includes whole links, not just the lobes as considered above. A suitable scaling of the above coefficient is needed to reflect this. If we consider that for each link, the lobes represent approximately 11.0D (or 10.7D) effective length of a total bar length 13D (or 14.3D) we see that the lobe volume is about 84.6% (or 74.8%) of the link volume. Hence, in reference to the total link volume: Caa = 0.08 (or 0.07). Axial Drag Coefficient The Line Type Wizard sets up Axial and Drag Coefficient for a chain as follows: Generally, axial drag is very low for smooth pipes, being due to skin friction only. However, for a chain there is some projected area present even in axial flow and we consider the drag force due to this effect. We ignore the effect of skin friction in the derivation outlined below. As in the calculation for normal flow we consider two adjacent links and calculate their projected area. The projected area, normal to the flow, for axial flow consists of the four "lobes" only, since the central part is effectively shielded from the flow - see the figure. There is effectively no difference between studlink and studless links in this case. The projection of each lobe is 1.30D, square at one end, rounded at the other. So the total projected area per metre (normal to the flow) is given by the following expression: Anormal = 4 (0.8D² + πD²/8) (1/(8D)) = 0.60D. Hence, the drag force per metre length of chain as: Drag force = ½ ρv² Cda-chain (0.60D). Hoerner (1965), page 5-8, Fig 14c, gives Cda = 0.32 for a hemispherical rivet head projecting from a plane. The lobes here are similar - more elongated in the flow direction (implying a lower Cda) but on a less smooth body (implying a higher Cda). Hence, we assume Cda-chain = 0.40. As detailed above, we also have an expression for the drag force when considering the chain in terms of the equivalent line type parameters. In this case, we are only interested in the drag due to friction on the wetted area of the equivalent line type (i.e. the circumference): 325 w Drag force = ½ ρv² Cda (π OD) and equating the two expressions leads to: Cda = Cda-chain 0.6 D / (π OD) = 0.042 (or 0.040). Normal Drag Coefficient The Line Type Wizard sets up Normal Drag Coefficient for a chain as follows: We first calculate the drag force on a chain in normal flow, for which we require a value for its projected area (normal to the flow). To calculate this we must consider the chain as a collection of pairs of adjacent links, one face on to the flow, with projected area AFACE, and one edge on, with projected area AEDGE - see Figure. The overall projected area per metre will be a multiple of the sum of these two areas. AFACE = L D - 2D² = 11.0 D² m² (or 12.3D² m²) and AEDGE = 5D D + 2(πD²/4)/2 = 5.79 D² m². There are 1/(4D) links per metre and hence 1/(8D) such pairs of links per metre. Hence, the total projected area per metre (normal to the flow) is given by the following expression: ANORMAL = (AFACE + AEDGE) (1/(8D)) = 2.10D m (or 2.26D m). So, we are now able to calculate the drag force per metre length of chain as: Drag force = ½ ρv² Cdn-chain ANORMAL for a given drag coefficient Cdn-chain, where ρ is the density of seawater and v is the flow velocity. For irregular shaped bluff bodies such as chain links, of either type, a suitable value for Cdn-chain is 1.00. However, we are actually interested in the drag coefficient for the equivalent line, Cdn, associated with the reference area of (1xOD) of a cylindrical line: Drag force = ½ ρv² Cdn OD. Equating these two expressions for the drag force leads to: Cdn = ANORMAL / OD = 1.17 (or 1.20). Normal Added Mass Coefficient The Line Type Wizard sets up Normal Add 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. This is due to the extra force required to displace the water in the vicinity of the submerged part of the line. 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 . ρ . Vol where ρ is density of water, Vol is the displaced volume. The parts of a line displacing the fluid are said to be attracting added mass. For asymmetrical bodies the parts attracting added mass will differ in different directions. Hence, we consider the effect due to fluid flow exerting a force in, first, the normal and then the axial directions. For a circular cylinder in flow normal to its axis: 326 w Can = 1.0. The situation for a chain is more complicated as, for flow normal to a link, parts of the link are shielded from the flow but there is also some entrapped water within each edge-on link. An accurate calculation is very problematic and is unlikely to give a value for the normal added mass coefficient far distant from 1.0. Hence we assume: Can = 1.0. Stress Diameters and Allowable Stress These are not relevant for chains which have no contents and so are set to '~', the default values. Any available stress or wall tension results should be ignored. 7.8.9 Modelling Lines with Floats Modelling Lines with Floats You can model floats or buoyancy modules attached to a line by using buoyant Clumps attached at the relevant points. 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, i.e. spread out evenly, along that part of the line. This allows the length and segmentation of the buoyed section to be varied easily without having to add and remove individual floats. To use this 'smeared properties' approach you need to do the following. • • Create a new line type. Set the new line type's properties to be equivalent to those of the original pipe+floats. This is done by spreading each float's buoyancy, drag, etc. uniformly over the length of pipe from Sf/2 before the float centre to Sf/2 after the float centre, where Sf is the float pitch, ie. the spacing between float centres (see 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. The line type wizard will automatically set up this 'equivalent' line type for you. Set up a line section to model the length of line supported by the floats. The section's line type should be set to the equivalent line type and its length should be N x Sf, where N is the number of floats and Sf is the float pitch. 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, since each float is effectively being smeared equally both ways from its centre; see the diagram below, which show the situation when N=3. • We describe below how the Line Type Wizard derives the properties of the equivalent line type. Note that this approach is also suitable for modelling a regularly weighted section of line. Warning: The values generated by the Wizard are based on current best practice, but more specific project data should be used where this is available. 327 w Floats Dp Df Sf Sf Sf Figure: Geometry of Line and Floats We first define the notation to represent the underlying line onto which the floats are to be attached, which we refer to as the Base Line Type - see Base Line Type Notation. We then specify the quantities required to represent the floats - see Float Notation. Data Adding floats to a line to produce extra buoyancy is a common requirement. The Line Type Wizard helps you to quickly derive such a line type by specifying both the existing underlying base line type, onto which the floats will be added, and various properties of the floats: Base Line Type The line type on which the floats are mounted. Float Diameter The outside diameter of each float. underlying base line type. Float Length The axial length of each float. Float Pitch The average distance between the centres of successive floats. Float Material Density The density of the material forming the floats, excluding additional items such as fixing material. 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. Float Normal Drag Coefficient The drag coefficient associated with the float for flow normal to the line. 328 It must be greater than the outside diameter of the w Float Axial Skin Drag Coefficient The drag coefficient associated with the floats, due to the floats' skin friction, for flow along the axis of the line. Float Axial Form Drag Coefficient The drag coefficient associated with the float, due to the projected annulus area of the end of the float, for flow along the axis of the line. Float Normal Added Mass Coefficient The added mass coefficient for flow normal to the line. Float Axial Added Mass Coefficient The added mass coefficient for flow along the axis of the line. The Line Type data that are derived, and the associated underlying expressions, are detailed in Modelling Lines with Floats. 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. The line without floats is assumed to be of circular cross-section and have the following characteristics: • • • • • • • ODp - outer diameter IDp - inner diameter Mp - mass per unit length Cdnp - drag coefficient in normal flow Cdap - drag coefficient in axial flow Canp - Added mass coefficient in Normal flow (commonly taken as 1.0 for circular section) Caap - Added Mass coefficient in Axial flow (commonly taken as zero). Properties of the Floats For modelling lines with floats the following notation is used for the floats. assumed to be short cylinders fitted co-axially on the line at constant spacing: Lf Df ρf Sf mfh Cdnf Cdaf1 Cdaf2 Canf Caaf length diameter float density float pitch float hardware mass (e.g. fixing clamps, bolts, etc.) drag coefficient, normal flow drag coefficient, axial flow due to form drag coefficient, axial flow due to skin friction added mass coefficients in normal flow added mass coefficient in axial flow The floats are With the above information we can calculate the volume occupied by an individual float as: 329 w Vf = π/4 (Df² - ODp²) Lf which leads to the mass of the float being calculated as follows: Mf = Vf.ρf + mfh. Outer and Inner Diameter The Line Type Wizard sets up Outer and Inner Diameter 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.OD² (equivalent line) Vol per unit length (V) = π/4.ODp² + Vf /Sf (line with floats) This leads to: Outer Diameter (OD) = √(4 V /π) 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. 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 Sf length of the section and hence (1/Sf) floats per unit length, giving: Mass per unit length = Mp + Mf / Sf Axial Drag Coefficient The Line Type Wizard sets up Axial Drag Coefficient for a Line with Floats as follows. To derive the drag coefficient when flow is axial to the line we adopt a similar approach to that used above for normal flow. When considering the equivalent line, with the additional buoyancy smeared along it’s outer surface, the drag force per unit length, when flow is axial to the line, is due solely to skin friction and can be expressed as: Drag Forcea = ½ ρv² Cda (π OD) in which the reference area is the circumference of the equivalent line and where r is the density of seawater and v is the flow velocity. As in the case for flow normal to the line, 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. However, 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. Drag Forcea = Drag Forcea-FLOATS + Drag Forcea-EXP LINE = ½ ρv² [Cdaf1.Drag Area1a-FLOATS + Cdaf2.Drag Area2a-FLOATS + Cdap.Drag AreaaEXP LINE] 330 w in which the reference drag area, due to the annulus, for the floats in axial flow is given by: Drag Area1a-FLOATS = π/4 (Df² - ODp²).1/ Sf the reference drag area, due to the skin, for the floats in axial flow is given by: Drag Area2a-FLOATS = πDfLf / Sf and the reference drag area, due to the skin, for the exposed line in axial flow is given by: Drag Areaa-EXP LINE = πODp (1-Lf/Sf). Equating these two expressions leads to: Cda = [Cdaf1.Drag Area1a-FLOATS + Cdaf2.Drag Area2a-FLOATS + Cdap.Drag AreaaEXP LINE]/(πOD). Normal Drag Coefficient The Line Type Wizard sets up 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 OD in which the reference drag area per unit length, normal to the flow, is given by OD and where ρ is the density of seawater and v is the flow velocity. 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.Drag Arean-FLOATS + Cdnp.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 = ODp (1-Lf/Sf). Equating these two expressions leads to: Cdn = [Cdnf.Drag Arean-FLOATS + Cdnp.Drag Arean-EXP LINE] / OD. 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. 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. 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: 331 w 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 (1-Lf/Sf) Equating these two expressions 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. 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. Hence, 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). Stress Diameters and Allowable Stress The stress diameter and allowable stress are set to be the values used by the base line, since it is the base line which is load bearing. 7.8.10 Modelling Ropes Modelling Ropes D = Nominal rope diameter D Fibre rope Figure: Wire with Fibre core Wire with Wire core Rope Geometry Ropes have many applications in the offshore industry including towing, mooring and winching. The Line Type Wizard can be used to derive Line Type data to represent five different types of rope: 8-strand Multiplait Nylon; 8-strand Multiplait Polyester; 8-strand Multiplait Polyethylene; 6x19 Wire rope with Fibre core; and 6x19 Wire rope with Wire core. For documentation of the formulae used by the Line Type Wizard to derive the Line Type properties, see the topics that follow this one. You can access these topics either via the Related Topics link above or via the Previous Topic (<<) and Next Topic (>>) buttons. 332 w Most of the calculations of the derived line properties are based on data from a catalogue published by Marlow Ropes Ltd (1995). All quantities are expressed as a function of the rope's nominal diameter D. Note that this documentation uses the SI units system, so D is in metres in this documentation, but the program automatically adjusts the formulae to match the units specified by the user. Warning: The values generated by the Wizard are approximate only and are intended as first estimates for preliminary use. They 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. Data The Line Type Wizard can be used to create line types representing a variety of ropes. The input data required consists of the following: Rope Nominal Diameter The overall diameter of the rope. The majority of the derived line type data are functions of this Rope Nominal Diameter. Warning: The line type outer diameter derived by the wizard is less than this nominal diameter, in order to give the correct buoyancy. You need to allow for this when setting the line type drag and added mass coefficients, since the coefficients correspond to the derived line type outer diameter, not the nominal diameter. Construction Can be one of nylon, polyester, polyethylene, 6x19 wire with fibre core and 6x19 wire with wire core. The construction affects both the mass per unit length of the line type and the strength of the line type. The Line Type data that are derived, and the associated underlying expressions, are detailed in Modelling Ropes. Mass per unit length The Line Type Wizard sets up Mass for a Rope as follows: The quantity Mass per unit length is available from catalogue data for ropes. The nominal rope diameter and nominal mass are available for a variety of rope constructions. A simple statistical analysis of the available data leads to the following expressions: Mass Per Metre = 0.6476 D² te/m (for Nylon ropes); Mass Per Metre = 0.7978 D² te/m (for Polyester ropes); Mass Per Metre = 0.4526 D² te/m (for Polypropylene ropes); Mass Per Metre = 3.6109 D² te/m (for Wire ropes with fibre core); Mass Per Metre = 3.9897 D² te/m (for Wire ropes with wire core). Outer and Inner Diameters The Line Type Wizard sets up outer and inner diameters for a Rope as follows. The inner diameter is set to zero for all rope construction types. The line type outer diameter, OD, is set as follows: 333 w OD = 0.85 D (for Nylon ropes) OD = 0.86 D (for Polyester ropes) OD = 0.80 D (for Polypropylene ropes) OD = 0.82 D (for Wire ropes with fibre core) OD = 0.80 D (for Wire ropes with wire core) where D is the specified rope diameter. 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. The line type then has the appropriate buoyancy. Note that this effective diameter is less than the specified rope diameter, because there are gaps between the fibres and so not all of the specified rope diameter contributes to buoyancy. The above formulae for the line type OD were derived by equating the line type displaced volume per unit length, πOD²/4, to the rope displaced volume per metre, M/ρ, where M is the rope mass per unit length and ρ is the average density of the rope material. The following average rope material densities ρ (in te/m³) were assumed: Nylon 1.14; Polyester 1.38; Polypropylene 0.91; Wire with fibre core 6.87; Wire with Wire core 7.85. 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, with the fibre taken to have the same density as (fresh) water. Axial and Bending Stiffness The Line Type Wizard sets up Axial and Bending Stiffness and Limit Compression for a Rope as follows Axial Stiffness The expressions for axial stiffness are calculated in different ways for the two groups of fibre ropes and wire ropes. For Fibre Ropes we use the catalogue data. Load/extension characteristics depend on previous load history, whether the rope is wet or dry, and the rate of application of the load. 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, 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%). • • • Incorporating all of the factors indicated above we can produce values of axial stiffness for a range of rope diameters. Once again using simple statistical techniques we obtain the following expression for axial stiffness of fibre ropes: Axial Stiffness = 1.18 x 10^5 D² kN (for Nylon ropes) Axial Stiffness = 1.09 x 10^6 D² kN (for Polyester ropes) 334 w Axial Stiffness = 1.06 x 10^6 D² kN (for Polypropylene ropes). Axial stiffness for Wire Ropes is calculated directly, rather than estimated from empirical relationships. We assume a value for Young’s Modulus, for the 6x19 strand group, of: E = 1.03 x 10^8 kN/m² (for Wire ropes with fibre core); E = 1.13 x 10^8 kN/m² (for Wire ropes with wire core); and work on an assumed metallic area of: A = 0.455 (πD²/4) m² (for both wire ropes). Both of these quantities have been obtained from the HER Group Marine Equipment & Wire Rope Handbook. Note that for wire ropes with a wire core the additional axial stiffness is accounted for in the enhanced Young's modulus. This leads to: Axial Stiffness = 3.67 x 10^7 D² kN (for Wire ropes with fibre core); Axial Stiffness = 4.04 x 10^7 D² kN (for Wire ropes with wire core). Bending Stiffness For all rope construction types the bending stiffness offered by the Wizard is zero. For systems where bend stiffness is a significant factor you should override this value with the true value obtained from the rope supplier. Limit Compression In conjunction with a zero value for bend stiffness Limit Compression is set to yes. Stress Diameters and Allowable Stress The Line Type Wizard sets the stress diameters and allowable stress for a Rope to '~' since the OrcaFlex stress analysis is not applicable to complex structures such as ropes. Any available stress or wall tension results should be ignored. Minimum Breaking Loads The properties window in the line type wizard displays approximate minimum breaking load (MBL) values for ropes. These may be useful for setting the Maximum Tension data item for the line type. The MBL values displayed are calculated using the following functional formulae, where D is rope nominal diameter in metres: Nylon ropes (dry) Nylon ropes (wet) Polyester ropes Polypropylene ropes Wire ropes with fibre core Wire ropes with wire core 163950.D² kN 139357.D² kN 170466.D² kN 105990.D² kN 584175.D² kN 633358.D² kN These formulae were derived from manufacturer's catalogue data, which consist of minimum (dry) strength against nominal diameter for each of the five rope constructions. The formulae were derived using least squares fitting, and they were found to give a good fit to the manufacturer's data, except that they tend to underestimate MBL for small diameter non-wire ropes. 335 w Note: Nylon ropes lose some strength when wet; 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. 7.8.11 Modelling Homogeneous Pipes Modelling Homogeneous Pipes O N N’ O’ Figure: Homogeneous Pipe Given certain of the geometrical and material properties of a homogeneous pipe many of the necessary Line Type data items can be derived. We outline here the calculations used by the Line Type Wizard performed to derive line type data based on: • • • • • ρ - the density of the material E - the Young’s Modulus of the material ν - the Poisson’s Ratio of the material OD - the Outer Diameter of the pipe ID - the Inner Diameter of the pipe Warning: The data derived by the Line Type Wizard are based on average material properties. Project specific data should be used where available. The properties of the derived equivalent line type are given below. Mass per Unit Length Mass per unit length = ρ (π/4) (OD² - ID²) where ρ is the material density specified. Outer and Inner Diameters The line type outer and inner diameters are set to the pipe diameters specified by the user. Axial Stiffness The line type axial stiffness is given by: 336 w Axial Stiffness = EA where E is the Young’s Modulus and A is the cross sectional area, hence: Axial Stiffness = E.(π/4) (OD² - ID²). Bending Stiffness The line type bending stiffness is given by: Bending Stiffness = E.I where I is the second moment of area, about an axis in the plane of the cross-section through the centroid (e.g. NN’), and leads to: Bending Stiffness = E.(π/64) (OD^4 - ID^4). Limit Compression As the bending stiffness is significant this is set to 'no'. Torsional Stiffness The line type torsional stiffness is set as follows. The torque experienced by a pipe of length l when twisted through an angle θ is given by: Torque = [(G.θ)/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). For homogeneous pipes J = 2*I. The quantity G is related to the Young’s Modulus (E) and Poisson’s Ratio (ν) of the material through the following relationship: G = E / [2(1+ν)]. The Torsional Stiffness, representing the Torque resisting a twist of 1 radian, per unit length, is therefore given by: Torsional Stiffness = G.J = [E/{2(1+ν)}] (π/32) . (OD^4 - ID^4). Torque per Unit Tension The line type torque per unit tension is set to zero, since tension applied to a homogeneous pipe does not generate any torque. Stress Outer and Inner Diameters The line type stress diameters are set to ‘~’, since they are the same as the pipe diameters. Stress Loading Factors These are set to one, the default value, as a simple homogeneous pipe carries all the loads. Data The Line Type Wizard helps build a line type to represent a homogeneous pipe, based on the following data: 337 w Material The Wizard provides 3 standard materials for a homogeneous pipe: Steel; Titanium and High Density Polyethylene. For these standard materials OrcaFlex automatically sets Material Density, Young's Modulus and Poisson's Ratio. There is also an option to enter User Defined as the Material. In this case you must set Material Density, Young's Modulus and Poisson's Ratio. Material Density This is the density of the material used in the construction of the pipe. Outer Diameter The Outer Diameter of the pipe and should be greater than the Inner Diameter. Inner Diameter The Inner Diameter of the pipe and should be less than the Outer Diameter. Young's Modulus The ratio of the tensile stress to the tensile strain. Poisson's Ratio The amount of lateral strain experienced by a material subjected to tensile strain as a negative proportion of the tensile strain. The Line Type data that are derived, and the associated underlying expressions, are detailed in Modelling Homogeneous Pipes. 7.8.12 Modelling Hoses and Cables Modelling Hoses and Cables The Line Type Wizard estimates typical properties for hoses and cables based on project data. Warning: The values generated by the Wizard are approximate only and are intended as first estimates for preliminary use. They 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. There are three categories of hoses available: • • • High pressure - which cover high pressure flexible risers and flowlines of unbonded construction with inside diameters in the range 2 to 15 inches (50 to 380mm). Low pressure - which cover low pressure floating hoses of bonded rubber construction with inside diameter from 2 to 20 inches (50 to 500 mm). Fold-flat - which cover low pressure, fold-flat hoses with steel reinforcement; inside diameter around 6 inches (150 mm). There is currently only one category of cable available: • Umbilical - constructed with steel wire armour and thermoplastic hoses and outside diameter up to 250mm. 338 w The properties derived by the Wizard are obtained from empirically estimated relationships with the diameter of the hose/cable. They have been estimated from a limited amount of data covering only the range of diameters indicated above. For simplicity, only those relationships of the form: Y = a X^b, where b is an integer, were considered. In the details below the diameter is assumed to be in metres and the SI units system is applied throughout. The amount of data available for low pressure hoses and fold-flat hoses is very small. There is quite a bit more data for high pressure hoses and umbilicals but it is found to have quite a large spread. To demonstrate this spread, the ratio of the observed value to the fitted value, expressed as a percentage, is calculated and the largest and smallest of these is given. The OrcaFlex stress analysis is not applicable to complex structures such as hoses and cables. Any available stress or wall tension results should therefore be ignored. Data for Cables The Line Type Wizard can help build a line type to represent one type of cable - an umbilical. Umbilical cables have many applications including the carrying of electrical communication wires and hydraulic connectors to submersibles. The Line Type data quantities that the wizard derives have been estimated from a limited amount of project data. Input data for cables consists of: Cable Diameter The outer diameter of the cable. Each derived line type property is a function of the Cable Diameter. Cable Type The only Cable Type currently offered is Umbilical. The Line Type data that are derived, and the associated underlying expressions, are detailed in Modelling Hoses and Cables. Data for Hoses The Line Type Wizard helps you build a line type to represent a hose, based on the following data. 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. The input data consists of: Hose Inner Diameter Each derived line type property is a function of the hose inner diameter. Hose Type The Hose Type can be one of high pressure, low pressure or fold-flat. These categories roughly cover the available project data. The Line Type data that are derived, and the associated underlying expressions, are detailed in Modelling Hoses and Cables. 339 w Outer and Inner Diameters The Line Type Wizard sets up Outer and Inner Diameters for hoses and cables 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 = 1.40 ID m (for High Pressure) [90% 150%] OD = 1.28 ID m (for Low Pressure) OD = 1.34 ID m (for Fold-Flat) Cables The inner diameter (ID) is set to zero and the outer diameter (OD) is specified by the user. Mass per unit length The Line Type Wizard sets up mass for hoses and cables 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 = 0.7523 ID te/m (for High Pressure) [55% 145%] Mass per metre = 0.3642 ID te/m (for Low Pressure) Mass per metre = 0.1844 ID te/m (for Fold-Flat) Cables For the cables the mass per metre has been estimated as a function of outer diameter giving: Mass per metre = 1.8 OD² te/m (for Umbilical) [35% 170%] Axial and Bending Stiffness The Line Type Wizard sets up Axial and Bending Stiffness and Limit Compression for hoses and cables as follows: Axial Stiffness For each type of hose the axial stiffness has been estimated as a function of inner diameter giving: Axial Stiffness = 2.80 x 10^6 ID kN (for High Pressure) [40% 160%] Axial Stiffness = 3.40 x 10^4 ID kN (for Low Pressure) Axial Stiffness = 6.56 x 10^3 ID kN (for Fold-Flat) For the cables the axial stiffness has been estimated as a function of outer diameter giving: Axial Stiffness = 1.44 x 10^6 OD kN (for Umbilical) [15% 415%] 340 w Bending Stiffness For each type of hose the bending stiffness has been estimated as a function of inner diameter giving: Bending Stiffness = 3 x 10^4 ID^4 kN.m² (for High Pressure) [45% 300%] Bending Stiffness = 6 x 10^2 ID^3 kN.m² (for Low Pressure) Bending Stiffness = 1 x 10^3 ID^3 kN.m² (for Fold-Flat) For the cables the bending stiffness has been estimated as a function of outer diameter giving: Bending Stiffness = 3 x 10^3 OD^3 kN.m² (for Umbilical) [55% 240%] Limit Compression As the bending stiffness is significant this is set to ‘no’. 7.8.13 Modelling Line Ends Modelling Line Ends Lines in OrcaFlex run from End A to End B. Travelling from A to B, the orientation of any segment in the line is defined in terms of Azimuth and Declination angles, relative to global axes. Azimuth is measured in the X-Y plane, Declination is measured downwards from the Z axis. See No-Moment Direction. No-Moment Direction Associated with each end is a stiffness, and a no-moment direction which is described in terms of azimuth and declination. This too uses the 'A to B' convention, so if we hang up a catenary of line, and then freeze the ends, the no-moment directions are as shown below: No moment direction ( Az = 0, Dec = 160 ) No moment direction ( Az = 0, Dec = 45 ) End B End A z Declination Angle y Azimuth Angle x Figure: Directions 341 w If the line end is attached to a body which can move (a Vessel or Buoy), then the no-moment direction is defined relative to the body axes and therefore moves with the body. Otherwise, it is defined in global axes. End Stiffness The stiffness associated with the end can be used to represent an item such as a flexjoint, whose stiffness is in units of moment per unit angle, e.g. kN.m/degree. More commonly, the line end is either free to rotate or fully restrained. In the first case, the end stiffness is set to zero; in the second case, the end stiffness is set to Infinity. 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. Free-to-rotate or Fully-restrained Ends In many practical cases, the line ends are neither completely free nor fully restrained. Nevertheless, we recommend that you should usually choose one of these conditions. When should you use one rather than the other? The following notes offer a brief guide: 1. 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. In such systems, line ends may safely be modelled as free-to-rotate. 2. An exception to this rule is systems which include one or more 6D buoys. The rotational motions of the buoy may then be influenced by moment transfer from the ends of lines attached to it, particularly where buoy rotational inertias are small. In such cases, the end connections to the buoy should be fully restrained. 3. A further exception is systems where the flexible lines are relatively short and stiff, e.g. a large diameter under-buoy hose in shallow water. Bend stiffness, including end moments, may have a significant influence on overall system behaviour in such cases, and the end connections should be fully restrained. 4. Where fully restrained ends are used, it is necessary to pay more attention to the modelling of the line close to the end. In particular make allowance for the additional stiffness of a bend stiffener, if one is fitted and use shorter segments near the line ends so as to represent the moments with sufficient accuracy. 5. Roll-on/roll-off contact (e.g. stern rollers, pipelay stingers, mid-water arches for riser systems). A pinned connection at the average contact point is often sufficient. For a more exact representation, use one or more solids to represent the supporting surface, but remember that there must be sufficient nodes at the line end to interact with the solid. End Force and End Force Ez-Angle The figure below shows the end connection of a flexible line fitted with a bend stiffener. The line applies a load (tension) T as shown. If the local loads (weight, drag, etc.) on the end part of the line, including the bend stiffener, are small by comparison with T, then the reaction force F is equal and opposite to T, and the bend moment at the end fitting is M = T.h. OrcaFlex reports the End Force, F, and the End Force Ez-Angle, θ, as shown. The "No moment direction" is defined in the input data. When the reaction force F acts in the no moment direction, then the reaction moment M is zero. It is clear from this that 1. End Force and End Force Ez-Angle are the same whether the end condition is defined as free-to-rotate, fully restrained, or some intermediate condition; 342 w 2. The bend moment at the end fitting, M, is a function of the lever arm, h, which depends not only on the end condition but also on the bend stiffness distribution in the line/bend stiffener. No moment direction M F θ h T Figure: End connection of a flexible line fitted with a Bend Stiffener Design Loads for End Fittings For design of end fittings, including bend restrictors, the principal parameters provided by OrcaFlex are End Force and End Force Ez-Angle. 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. This approach is usually sufficient, except where End Force is very small. This occurs when the line tension T comes close to zero. The direction of the end force is then no longer dominated by the line tension, and other loads (shear, local drag and inertia loads etc.) which are usually negligible become important. In these conditions, the reported End Force Ez-Angle is misleading and a more appropriate estimate should be made from the system geometry. This can be done using the Ez-Angle results variable. Ez-Angle for any segment gives the angle of that segment relative to the No Moment Direction at the adjacent line end, including allowance for the motion of line end where the line is attached to a vessel or buoy. Ez-Angle for a point near the end of the bend restrictor is a reasonable alternative where End Force Ez-Angle is not suitable. Results for Line Ends When examining results at line ends note that if a stiff pipe goes into compression, line tension becomes negative but End Force remains positive, and End Force Ez-Angle may approach 180º. 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. At the end, OrcaFlex takes the angle change between the end segment of the line and the no-moment direction, and reports the corresponding curvature and bend moment based on the half length of the end segment. Where bend stiffness at the line end is zero (pinned end or a zero stiffness line), curvature and bend moment are reported as zero. Design Data for Bend Restrictors We classify bend restrictors into 3 types: 343 w • • • Bellmouths: curved surfaces which support the flexible and maintain acceptable curvature. Bend Limiters: articulated devices which rotate freely to a specified curvature, then stop. Bend Stiffeners: elastomeric devices which provide a tapered additional bend stiffness. 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. For cases where the bellmouth is not radially symmetrical, OrcaFlex reports components of End Force Angle in the local XZ and YZ planes. End Force Ezx-Angle is the component in the local xz plane; End Force Ezy-Angle is the component in the local yz plane. Bend Limiter There are two design requirements: 1. The limiter length must be not less than a*R where a is End Force Ez-Angle and R is the limiter locking radius. 2. The limiter must be capable of withstanding the maximum bend moment M given by M = R*F*(1-cos(a)) where F, a are simultaneous values of End Force and End Force Ez-Angle. OrcaFlex reports Bend Restrictor Load P = F*(1-cos(a)) as an aid to bend limiter design. P is sometimes called "pseudo-curvature". Bend Stiffener The design process is more complex and the critical design load cases are not always selfevident. 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, with each (F,a) pair defining a load case. The bend stiffener should be designed to prevent infringement of the permitted curvature for any (F,a) pair. In practice, it is often sufficient to consider just the three (F,a) pairs corresponding to maximum values of End Force F, End Force Ez-Angle a and Bend Restrictor Load P. 7.8.14 Modelling Compression in Flexibles Modelling Compression in Flexibles When a flexible line experiences compression, it responds by deflecting transversely: the magnitude of the deflection is controlled by bend stiffness. Under static conditions, the behaviour of an initially straight section of line under pure axial loading is described by classic Euler buckling theory. This defines the maximum compressive load - the "Euler load" - which a particular length of line can withstand before transverse deflection occurs. The Euler load is a function of the length of the straight section, the bend stiffness and the end conditions. For a simple stick of length L, bend stiffness EI, with pin joints at each end, the Euler load is π²EI/L². 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. Under dynamic loading conditions, the transverse deflection is resisted by a combination of inertia and bending. OrcaFlex is fully capable of modelling this behaviour provided the discretisation of the model is sufficient, i.e. provided the segments are short enough to model the deflected shape properly. 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. 344 w Notes: 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. Under compression, the line deflects: the sticks remain straight and the joints rotate. 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. If the compressive load reaches the Euler load for an individual stick, then the real line which the stick represents will start to deform at a shorter wavelength, and deflections within the stick length become significant. Clearly, this stick model is no longer adequate. By replacing each long stick by several short ones, we can make the Euler load for each stick greater than the applied compressive load. Each stick will then remain straight, but we now have more sticks with which to model the deflected shape. 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, then we can have confidence that the behaviour of the line in compression is adequately modelled. OrcaFlex makes this comparison automatically for all segments and reports any infringements in the Statistics tables. The segment Euler load is also plotted in tension range graphs (as a negative value - compression is negative) so that infringements are clearly visible. If the segment Euler load is infringed during a simulation, then we have to decide what to do about it. If infringement occurs only during the build-up period, perhaps as a result of a starting transient, then we can safely ignore it. If it occurs during the main part of the simulation, then we should examine the time histories of tension in the affected areas. Where infringements are severe and repeated or of long duration the analysis should be repeated with shorter segments in the affected area. 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. the segment Euler load used in OrcaFlex as a basis for comparison is the lowest of the various alternatives, and assumes pinned joints with no bend stiffness at each end of the segment. This is a conservative assumption. 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. • Limit Compression Switch For each line type, the data includes a Limit Compression switch. The usual setting is "No". 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. For some special cases, such as chains and soft ropes with little bend stiffness, this is not the most useful model and OrcaFlex offers an alternative. Lines of this sort cannot take compression at all, so the "Limit Compression" switch can be set to "Yes". OrcaFlex then does not allow compressive loading greater than the segment Euler load (which is zero if the bend stiffness is zero). Note: In either case, if the segment Euler load is reached then a Warning is given on the result form and in the statistics table. 345 w 7.9 LINKS 7.9.1 Links Links are simple spring or spring/damper connections linking two points in the model, for example a node on a line to a vessel, or a buoy to an anchor. They pull the two points together, or hold them apart, with a force that depends on their relative positions and velocities. Links have no mass or hydrodynamic loading and simply apply an equal and opposite force to the two points. They are useful for modelling items such as wires where the mass and hydrodynamic effects are small and can be neglected; for example buoy ties can sometimes be modelled using links. 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. The tether remains slack and does not apply a force if the distance between the ends is less than the unstretched length. Spring/Dampers combined spring and independent damper units. The spring can take both compression and tension and can have either a linear or a piecewise-linear length-force relationship. The damper velocity-force relationship can also be either linear or piecewise-linear. Tether: Spring-Damper: Figure: Types of Link 7.9.2 General Data Name Used to refer to the Link. Type may be either: • • Tether: a simple elastic tie having linear stiffness and no damping. Spring/Damper: a combined spring and independent damper, each of which can have linear or piecewise-linear tension relationship. 346 w 7.9.3 Connections Connect to Object and Object Relative Position Specifies the objects to be linked. A point on a Line is specified by arc length measured from end A; the link is attached to the nearest node. For a point on a Buoy or Vessel, the specified coordinates are relative to the object's origin. For a Fixed end they are relative to the global origin. For an Anchored end, the X and Y coordinates are relative to the global origin, but the Z coordinate is relative to the seabed at that X,Y position. Release at Start of Stage The link can be released at the start of a given stage of the simulation, by setting this number to the stage number required. Once released a link no longer applies any forces to the objects it connects. If no release is required, then set this item to '~'. 7.9.4 Properties Unstretched Length Is the unstretched length of the Tether or Spring. Linear Both the spring and damper in a Spring/Damper can have either simple linear force characteristics or else a user-specified piecewise-linear force table. Stiffness For a tether the tension t depends on its strain and stiffness as follows: t = k.(L-L0)/L0 where k is the specified Stiffness, L is the current stretched length between the two ends, L0 is the specified Unstretched Length. Tethers remain slack and exert no force if L is less than L0. For a linear spring in a Spring/Damper the tension (positive) or compression (negative) is given by: t = k.(L-L0) where k is the specified Stiffness, L is the current stretched length between the two ends, L0 is the specified Unstretched Length. The linear spring does not go slack if L is less than L0, but instead goes into compression. Warning: Please note that this is not the same formula as for tethers. 347 w Damping A linear damper in a Spring/Damper exerts an extra tension of t = c.(rate of increase of L) where c is the specified Damping, L is the current stretched length between the two ends. Piecewise-Linear Force Tables For a piecewise-linear spring (or damper) the force characteristic is specified as a table of tension against length (or velocity). The table must be arranged in increasing order of length (velocity) and a negative tension indicates compression. For a passive damper the tensions specified should therefore normally have the same sign as the velocities, since otherwise the damper will apply negative damping. For lengths (velocities) between, or outside, those specified in the table the program will use linear interpolation, or extrapolation, to calculate the tension. 7.9.5 Results For details on how to select results variables see Selecting Variables. For links the following variables are available: Tension The total tension in the link. Length The current stretched length of the link. Velocity The rate of increase of the stretched length. Azimuth and Declination The azimuth and declination angles, relative to global axes, of the 'downstream' direction of the link. 7.10 WINCHES 7.10.1 Winches Winches provide a way of modelling constant tension or constant speed winches. They connect two (or more) points in the model by a winch wire, 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). As well as connecting its two end points, the winch wire may, optionally, pass via intermediate points, in which case it does so as if passing over a small frictionless pulley at that point. The 348 w wire tension either side of the intermediate point is then applied to that point; if the point is offset on the object involved then this also gives rise to an applied moment. Winch may pull via intermediate objects Drive Force f Winch Drive Winch Inertia t t 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. It is assumed that the winch inertia is negligible and the winch drive is perfect, so that it always exactly achieves the requested constant tension or constant speed. Because of these assumptions, no data needs to be given for the winch inertia or winch drive. Detailed Winches Detailed Winches include modelling of the performance of the winch drive system - its deadband, stiffness, inertia, damping and drag - but therefore require more data and are harder to set up. 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. In particular, Simple winches are appropriate: • • • at the early design stage, when the type of winch to be used has not yet been decided if the duty is such that the winch drive will give near to perfect constant tension or constant speed performance if the winch drive data are not available Winch Control OrcaFlex winches allow quite complex offshore operations to be modelled. The winch drive can be operated in either of two modes: Length Control Mode For modelling constant speed winches. The winch wire is paid out or hauled in at a velocity specified in the data. 349 w Force Control Mode For modelling 'Constant tension' winches. Since such winches are usually hydraulic devices whose performance deviates quite seriously from the constant tension ideal, OrcaFlex Winches provides facilities for modelling winch deadband, damping and drag forces (force decrements proportional to velocity and velocity² respectively) and winch stiffness effects such as those caused by hydraulic accumulators. 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. 7.10.2 Winch Data Name Used to refer to the Winch. Type May be either Simple or Detailed. See Winches. Connect to Object and Object Relative Position The (mass-less) winch wire connects at least two objects, one at each end of the winch wire. 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 intermediate connections are specified, the winch wire slides freely through these intermediate points as if passing via small friction-less pulleys mounted there. The winch wire tension on either side then pulls on the intermediate points, so applying forces and moments (if the points are offset) to the objects concerned. Each connection is defined by specifying the object connected and the object-relative position of the connection point. For connecting to a Line, the object-relative z coordinate specifies the arc length to the connection point, measured from end A. The winch wire is then connected to the nearest node. The x,y coordinates are ignored. For Fixed connections the object-relative coordinates given are the global coordinates of the point. For connecting to an Anchor, the object-relative x,y coordinates given are the global X,Y coordinates of the anchor point, and the z-coordinate is the distance of the anchor above (positive) or below (negative) the seabed at that X,Y position. For connecting to other objects, the coordinates of the connection point are given relative to the object local frame of reference. Release at Start of Stage The winch wire can be released at the start of a given stage of the simulation, by setting this number to the stage number required. Once released the winch no longer applies any forces to the objects it connects. If no release is required, then set this item to '~'. 350 w 7.10.3 Wire Properties Wire Stiffness Elastic stiffness of the winch wire. Wire Damping Material damping value for the winch wire. Note: The mass of the winch wire is not modelled. Winch Inertia (Detailed Winches only) The inertia of the winch drive, which resists changes in the rate of pay out of haul in of the winch wire if the winch is in Force Control Mode. The Winch Inertia has no effect if the winch is in Length Control Mode. This is a linear, rather than rotational, inertia. To represent the rotational inertia of a winch drum, set the winch inertia to l / r² where I = drum rotational inertia, r = radius at which the wire is fed. 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. (Such accelerations are resisted indirectly, of course, through the changes they cause to the winch wire path length and hence to the winch wire tension.) To include the true translational inertia of the winch drive, drum and wire it is necessary to suitably increase the masses of the objects to which it is attached. 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. These then require very short time steps for the simulation, slowing the simulation. To avoid this, the winch inertia can be set to zero, rather than to a small value; the winch system inertia is then not modelled at all, but the short natural periods are then avoided. See Winch Theory for full details of the algorithm used when the winch inertia is zero. 7.10.4 Control Winch Control For the static analysis, the Mode of the winch drive can be set to one of Specified Length or Specified Tension. Specified Length The winch drive is locked with the unstretched length of winch wire out, L0, being set to the Value specified. The winch wire tension t then depends on the stretched length L of the winch wire path. 351 w Specified Tension The winch drive operates in perfect constant tension mode, the tension t being the Value specified. The unstretched length out L0 is then set to correspond to this tension. During the simulation the winches are controlled on a stage by stage basis. For each stage the winch control mode can be set to one of Specified Payout or Specified Tension. 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 that stage. That is, the Value specifies the total change in unstretched length during the stage, so to keep a constant length set the Value to zero. Specified Tension The Value specifies the nominal constant tension for this stage. In Simple winches the winch drive is assumed to always achieve this nominal tension, so the Value is used as the actual winch wire tension. In Detailed winches this nominal tension is used as the target tension for the winch drive, which then applies drive force to the winch inertia to try to achieve this target tension. The algorithm for the winch drive force is designed to model the characteristics of realworld winches that are nominally "constant tension". See Winch Theory. Note: Changes of nominal tension are applied instantly at the start of each stage, and this can therefore apply a shock load which, if large enough, may affect the stability of the simulation. 7.10.5 Drive Unit Note: Winch Drive The winch drive controls the winch wire in one of two winch control modes - Length Control Mode ("Specified Length" for statics, "Specified Payout" for dynamics) or Force Control Mode ("Specified Tension"). • Length Control Mode is for modelling a constant speed winch. The winch tension then depends simply on the unstretched length of winch wire out, and the wire properties (Stiffness and Damping). Force Control Mode is for modelling a (nominally) constant tension winch. Because such winches often deviate quite seriously from the constant tension ideal, facilities are provided for modelling winch Deadband, Damping, Drag and Stiffness. The drive unit data applies to Detailed Winches only • Deadband A deadband of +/- this value is applied to the winch drive force between hauling in and paying out the winch. See Winch Theory. for full details. Stiffness This can be used to model, for example, winch hydraulic accumulators. 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. See Winch Theory. 352 w Damping Terms A and B These terms can be used to model damping in a winch's hydraulic drive system. The winch drive force is taken to vary with haul-in/payout velocity at rates A and B, respectively. See Winch Theory. Drag Terms C and D These terms can be used to model drag in a winch's hydraulic drive system. The winch drive force is taken to vary with haul-in/payout velocity² at rates C and D, respectively. See Winch Theory. 7.10.6 Results For details on how to select results variables see Selecting Variables. For winches the available variables are: X, Y and Z The coordinates of the winch mount point, relative to global axes. Tension The tension in the winch wire. Azimuth and Declination The azimuth and declination angles of the 'downstream' direction of the winch wire, relative to the global axes. Declination is in the range 0 to 180 degrees. Range jump suppression is applied to Azimuth (so values outside the range -360 to +360 degrees might be reported). Length The unstretched length of winch wire paid out. Velocity The rate of pay out of winch wire. Positive value means paying out, negative value means hauling in. Surface Z The elevation of the sea surface directly above the instantaneous position of the winch mount. 353 w 8 8.1 VIV TOOLBOX VIV TOOLBOX The OrcaFlex VIV Toolbox provides analysis of vortex induced vibration (VIV) of lines. It offers a choice of various alternative ways of modelling VIV, including both frequency and time domain approaches, and is the product of extensive and ongoing research in co-operation with academics in the UK and USA. VIV analysis is a specialised area that is not required by all OrcaFlex users. Because of this the VIV Toolbox is an optional facility and to use it you will need a VIV licence, which you can purchase or lease from Orcina. When OrcaFlex starts up it looks for a VIV licence on your dongle. If one is available, and the dongle is not shared with other users over a network, then OrcaFlex claims the VIV licence and the VIV Toolbox is enabled. This is indicated by 'VIV' being included in the list of available modules, displayed at the top of the OrcaFlex main window. If the dongle is shared over a network, then any VIV licences on it are shared with other users and so may not always be available. If one is available OrcaFlex gives you the choice of whether to claim it, so you can choose to leave it free for other users if you do not need it. For further information see Running OrcaFlex. Different VIV Models The VIV Toolbox provides facilities for using the following different VIV models: • VIVA Interface. The VIV Toolbox provides a fully integrated link to VIVA. OrcaFlex automatically prepares the VIVA data from the OrcaFlex data, calls VIVA and presents the results. To use this you will need a copy of VIVA, release 2.0.3 or later. SHEAR7 Export. The VIV Toolbox provides facilities for exporting a SHEAR7 .mds file for the current OrcaFlex model. This file is one of two data files needed by SHEAR7 (and is the more difficult of the two to generate manually). Milan wake oscillator model Iwan and Blevins wake oscillator model Vortex Tracking model. • • • • Of all these models, VIVA and SHEAR7 are the two main programs in current use in the industry. They are both independent non-Orcina programs written and distributed by other companies, so to use them you need to purchase and install them on your machine. They are both frequency domain models, so they only analyse steady state conditions. The other models are included in the VIV Toolbox within OrcaFlex, so no further software is needed. They are all time-domain models, so they can analyse non-steady-state conditions. They do not yet have a track record in the industry. For details, see Using VIV Models and the links above to the individual models, in the OrcaFlex help file. Testing, Verification and Warranties VIVA and SHEAR7 are interfaces to third party analysis packages. Orcina’s warranty is limited to providing the data required by each package in the required format to allow the package to 354 w commence its analysis. We cannot accept any responsibility for the results of the analysis, or for any failure by the third party package to complete the analysis, save insofar as the failure to complete results from incorrect preparation of the input data. The other models are software implementations by Orcina of published theory. We have tested our implementations and give guidance to users on the assumptions implicit in using these methods for analysis of practical risers, but give no warranties that such use is valid. Any commercial use of these VIV models is at the user’s own risk and on the understanding that users are aware of the assumptions involved and have taken steps to satisfy themselves that they are justified. For further details contact Orcina. 355 w 9 9.1 • • • TECHNICAL NOTES MODELLING BEND RESTRICTORS First some terminology that we use: A bend restrictor is any device that controls bending at a line end. A bend limiter is something that has no effect until a certain curvature is reached, and then curvature is prevented from going above that value. See Modelling Bend Limiters below. A bend stiffener is something that provides increased bend stiffness near the line end, to more evenly distribute the bending near the end. See Modelling Bend Stiffeners below. Modelling Bend Limiters Non-linear bend stiffness can be used to model a bend limiter. See example G10. A reasonable number of segments will be needed to model the limiter and this require a shorter time step and hence longer run times. To avoid this problem you could use a global model, with the bend limiter omitted, and then a separate local model to examine how the line behaves around the limiter. This is valid providing the limiter only has local effects. Modelling Bend Stiffeners To model a bend stiffener in OrcaFlex, use a series of short sections near the end of the line, to represent the bend stiffener. Each of these sections can then be of a different line type, and these line types can be given different bend stiffness values, according to where it is in the stiffener - the nearer the root then the higher the bend stiffness. The bend stiffness values should include both the bend stiffener stiffness at that point and the pipe bend stiffness. The approach just described applies where a bend stiffener has already been designed, and one of the objectives of the analysis is to confirm that the stiffener provides the required protection. However, in many cases the stiffener design does not yet exist and the analysis is needed in order to define design loads. If this is the case, then run a preliminary analysis using a pinned end (i.e. zero bending stiffness at the line end connection). The load information required for bend stiffener design then consists of paired values of tension and angle at the pinned end. These can be extracted in the form of an X-Y plot showing Effective Tension against Ez Angle for the first segment. In practice, it is often sufficient to consider just three points on this graph, corresponding to maximum tension, maximum angle and maximum bend restrictor load: these can be extracted as linked statistics. As an example, look at Example A01 Catenary Riser. The top end of the riser (End A) is pinned to the ship near the bow. Turn on the Draw Local Axes option and note the direction of the line z axis at End A. The Ez Angle for the first segment is the angle between this direction and the segment direction. A graph of Effective Tension at End A vs Ez Angle at End A gives the information required. Recall that Ez Angle is an absolute magnitude and is therefore always takes a positive value. If a signed value is required (e.g. to define out-to-out load cycles for fatigue analysis), then use the Ezx or Ezy angle as appropriate. It is usually necessary to combine results from several analysis runs in order to fully define the bend stiffener design loading. This is most conveniently done by exporting the Effective Tension vs Ez Angle results as a table of values for each analysis case, combining into a single Excel spreadsheet and using the plotting facilities in Excel to generate a single plot with all results superimposed. A simplified set of load cases representing the overall loading envelope 356 w can then be selected for use in stiffener design. The export to Excel can be done manually or automated through the Results spreadsheet. Bend Stiffener Design - OrcaBend The task of bend stiffener design is usually left to the manufacturer, since the actual stiffener shape selected is governed in part by the manufacturing process, availability of tooling, etc., as well as by the load cases. The Orcina program OrcaBend has been developed to assist this process. There is a demonstration version of OrcaBend on the OrcaFlex CD - see CD:\Demo_CD\ReadMe for details. For further information contact Orcina. 9.2 MODELLING DESIGN WAVES Design wave heights and periods are commonly provided as a design input, but this is not always so, and the data are sometimes incomplete or in a different form from that required for OrcaFlex. For a comprehensive discussion, see Tucker (1991) on which the following notes are based. Maximum Storm In the absence of measured wave data, the maximum storm can be estimated from wind statistics on the assumption that the waves are generated by the local winds. The governing parameters are fetch (i.e. the length of open water over which the wind blows), wind speed and duration. Significant waveheight, Hs, and average zero up-crossing period, Tz, can then be estimated from equations given by Carter (1982): Fetch-limited Hs = 0.0163 × √X × U Tz = 0.439 × X^0.3 × U^0.4 Duration-limited Hs = 0.0146 × D^5/7 × U^9/7 Tz = 0.419 × D^3/7 × U^4/7 where X is fetch in km, U is wind speed in m/s at 10m above mean sea level, and D is duration in hours. Maximum Individual Wave Height Expected maximum waveheight Hmax, occurring in time T in a storm of significant wave height Hs, average zero crossing period Tz is Hmax = k.Hs.√(½ Loge(N)), 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. 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. The maximum crest-to-trough waveheight is generally less than the sum of the maximum crest elevation plus maximum trough depth. Tucker recommends k = 0.9 for the maximum wave; k = 1.0 for more frequent waves (fatigue waves). 357 w Period of the Maximum Wave The period associated with the maximum wave Tass, can take a range of values. Tucker recommends 1.05 . Tz < Tass < 1.40 . Tz The spectral peak period Tp is sometimes specified rather than Tz. For the ISSC spectrum Tp = 1.41 . Tz For the JONSWAP spectrum, the factor varies with the peak enhancement factor γ. The OrcaFlex random wave data form reports the spectral peak frequency fm for the selected spectrum where Tp = 1/fm. For the mean JONSWAP spectrum, γ = 3.3 and Tp = 1.29 . Tz Wave Conditions for Short Term Operations For operations lasting from a few hours to a few days, different criteria apply. A typical requirement is to determine the maximum seastate in which a given operation can safely take place. Whilst the complete operation may take many hours or even days, critical parts such as landing an item of equipment on the seabed may only take a few minutes. It would be too conservative to apply 3 hour maximum conditions in such a case. The question comes down to a balance of cost against risk. The overall risk of failure must be small enough to be acceptable (how small - 1%, 0.01%?), but the cost rises disproportionately as the level of acceptable risk is reduced. The risk of encountering a large wave is only one of many elements to be considered in assessing overall risk. This is a big subject which is rarely addressed rigorously. There is a need here for some feedback from practical experience to determine what is in practice acceptable and what is not. Hindcasting of operations which took place successfully in what were judged to be marginal conditions, and of operations which were not successful because of weather conditions could provide a calibrated basis for analysis of future operations. I don't know anyone who has done this. Until they do, we are left with subjective judgement i.e. we guess. A common guess is to combine the significant wave (a regular wave of height Hs, period Tz or Tp according to preference) for the assumed seastate with a maximum tidal current, applying both waves and current from the worst direction. This has no objective basis, but is plausible. Recommendations 1. Use regular waves for preliminary work. Regular waves are easier to set up, quicker to run, and easier to understand. For regular wave analysis we recommend that you use the Dean stream function theory. 2. If random sea analysis is required, determine the heights and period ranges for the maximum design waves as above, then generate suitable wave trains incorporating these waves following the procedures detailed in Setting up a Random Sea. 3. For analysis of permanent systems (e.g. 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. If field specific data are not available, use the period range recommended by Tucker. 358 w 9.3 MODELLING GUIDE TUBES Assume we wish to model a pipe running through a vertical guide tube in the moonpool of a drilling rig. The guide tube prevents the pipe from moving more than a small distance in the ship X and Y directions but allows free motion in the Z direction (we neglect friction between the riser and the guide). Example data file GUIDE.DAT shows two ways of modelling a guide. The first option is to use two Links to eliminate motion in the X and Y directions. The links should be specified as Spring/Dampers, not Tethers, so that the spring can take compression. Note that the ends of the links are attached to and move with the ship: you can, of course, fix them globally if this is appropriate. Note also that each link is made very long so that vertical movement of the node to which it is attached makes very little difference to the force in the link, and the link remains near-normal to the pipe. The second option is to use a cylinder shape as a guide tube. Again, this can be attached to the ship or fixed globally. The guide must be long enough to ensure that there is always at least one node of the pipe within it, preferably 2 or more. When using the Solid Cylinder option, OrcaFlex may find a static solution with the pipe outside the guide. If this happens, then add a temporary link to force the pipe inside. This is done in the example with the link "Temp_Tie". Its length and end position are chosen so as to pull the riser close to the centre of the cylinder, but to be slack when static convergence is achieved (this is quite easy to arrange by trial and error). Note also that this temporary tie is arranged to release at the start of the dynamic simulation. What stiffness values should we use for the links or the cylinder, and can we model the small amount of clearance between the pipe and the guide? It is not generally necessary to model the true contact stiffness between a steel pipe and a steel guide tube. The important criterion is that the pipe should not penetrate the guide so much as to invalidate the model: in practice this usually means that a few millimetres penetration is quite acceptable. If you have some idea what contact force you are expecting, this will enable you to set an acceptable stiffness. If not, then a preliminary trial run will give you some idea of what you need. In general, it is not a good idea to set the stiffness too high as this may lead to noise in the results and possibly to integration instability and the need to re-run with a shorter timestep. Clearance is easy to represent with the Solid Cylinder: remember that solid contact occurs at the centreline of the pipe, and set the internal radius equal to the required annular clearance. Representing clearance using Links is more difficult and is not recommended. 9.4 MODELLING MID-WATER ARCHES Steep and Lazy S riser systems use mid-water arches to support groups of risers. The risers are typically clamped to the top of the arch and lie on the curved surface to either side. The arch radius is chosen to be not less than the minimum bend radius for the risers. There are two types of arch. Type A provides a separate flared trough for each riser; Type B uses a single curved apron plate for all the risers with dividers at the top to prevent the separate risers slipping sideways. Type B appears to be the preferred design for most present day projects and is the type principally discussed here. A typical Type B arch is shown below. The structure consists of 2 or 4 buoyancy tanks with an arched apron plate over. There is additional structure to connect the elements together, and details at the crown of the arch to separate the several risers: these details are omitted from the sketch. 359 w Z Z Lz X Y Y Apron Plate Buoyancy Tank X Ly Lx Figure: Mid-water Arch OrcaFlex Modelling The arch itself, including its mass, buoyancy and hydrodynamic properties, is best represented as a 6D Buoy in OrcaFlex, using the Lumped Buoy option. Derivation of the data items for the 6D buoy is not easy and requires close attention. The starting point is to decide what to include in the buoy model: in particular, are there any enclosed or nearly enclosed volumes within the buoy which will trap water and force it to move with the buoy? For the arch shown in Fig 1, the apron plate effectively prevents flow in the X and Z directions, and the structure required to hold the buoy together will severely restrict flow in the Y direction. We may therefore approximate the arch as a closed box of dimensions Lx, Ly, Lz, partly full of water, and derive mass, volume and hydrodynamic properties accordingly. Treating the arch as an "equivalent rectangular box", the volume of displacement is V = Lx . Ly . Lz m³ If the net buoyancy of the buoy is B te, then the total mass of the buoy including trapped water is M = ρV - B Moments of inertia about X, Y and Z axes through the centre of gravity can be calculated in detail, but it is usually sufficient to estimate the radii of gyration by eye. The positions of the CG and centre of buoyancy must also be estimated. Note that OrcaFlex defines the CG as the origin of the local coordinate system for the arch. Estimating the hydrodynamic properties of the equivalent box is described in Hydrodynamic Properties of a Rectangular Box . Note, however, that we at present recommend setting all rotational hydrodynamic properties to zero for the reasons set out at the end of this note. 360 w Connecting Risers to the Arch The simplest approach is to omit the length of riser in contact with the arch (the mass of which should be added to the arch mass), and connect the risers to either side of the arch using pin joints. See Lazy S Riser - simple. Alternatively, riser contact with the apron plate can be represented by attaching two cylindrical solids to the arch Lazy S Riser - detailed. In this case, it is necessary to use sufficient nodes in way of the arch to ensure good representation of riser/arch contact. Advantages of the Pin Joint approach are: • • It is simpler to set up. It is generally quicker to run because it does not demand such short segments in the risers near the arch (short segments mean short time steps and longer runs). Note however, that for some systems it is necessary to use short segments at touchdown in the lower catenaries and this may determine the time step. Riser exit angles in 3 planes are easily defined as a basis for determining the size of the apron plate. • Disadvantages are: • The risers are connected at the wrong points so the moments acting on the arch are not correct. Advantages of the Solid Cylinders approach are: • • • • It is a better representation of the real system. Riser exit angles in the horizontal plane at the top of the arch are readily extracted. Disadvantages are: "Full" static analysis is necessary to take account of riser/cylinder interaction, probably starting from a spline. This can be time-consuming to set up. Longer run time (ARCH_SB takes about 10 times as long to run as ARCH_PB). 9.5 TYPICAL LINE TYPE PROPERTIES The physical properties of the lines are set out in the Line Types form. Where possible, specific data provided for the project should be used, but this is not always possible. Data may be unavailable, incomplete or even incorrect. Where good quality data specific to the project are not available, you could use typical values. Some typical values are given below. Another useful resource is the Line Type Wizard. Typical Line Hydrodynamic Data The hydrodynamic properties suggested here apply to smooth cylindrical lines only. Normal drag coefficients Cdx, Cdy The drag coefficient Cd depends on the Reynolds number Re. As a first approximation, the drag coefficient can be taken as follows: If Re < 3.8E5 then Cd = 1.2. If Re > 4.6E5 then Cd = 0.7. 361 w with linear interpolation linearly between these values. The minimum Cd value of 0.7 follows DNV recommendations. You can estimate the value of Re at the surface by taking the velocity V to be the current velocity plus 15% of maximum horizontal wave particle velocity. Wave particle velocities can be obtained from a preliminary OrcaFlex run for the wave alone without current. At the sea surface in deep water, V = Vc + 0.15 . πH / T where Vc is current velocity, H is wave height and T is wave period. If Re > 3.8E5 at the surface, then it is probably appropriate to specify variable data for the normal drag coefficients. The above values apply where vortex-induced vibration (VIV) is expected to be negligible. If significant VIV is anticipated, then drag coefficients may be increased significantly. If this is the case, a more detailed VIV analysis should be carried out. Axial drag coefficient, Ct Axial drag results from skin friction only. In subcritical flow (Re < 3.8E5), Ct = 0.008 for a smooth cylinder, 0.011 for a rough cylinder, based on ESDU data. At higher Re, ESDU suggest that skin friction may be neglected, i.e. Ct = 0. In practice, axial drag is often negligible and Ct = 0 is often acceptable. Normal added mass coefficient Can = 1. Axial added mass coefficient Caa = 0. Typical Seabed Friction Data Below is information on the influence in calculations of seabed friction. Published data are sparse. Some information is given in Puech (1984) and Taylor and Valent (1984). Both references distinguish between sliding friction and starting friction: starting friction is greater to represent the "breakout" force. OrcaFlex does not draw this distinction. In most cases, the sliding friction coefficient should be used; this will usually be conservative. Both references are written in the context of the contribution of chains and cables to anchor holding power, so we assume the friction values given are axial. Transverse values will be greater, perhaps by 50% to 100%. The values given below are recommendations from Taylor and Valent. Line type Chain Seabed Type Sand Mud with sand Mud/clay Wire rope Sand Mud with sand Mud/clay Starting Friction Sliding Friction Coefficient Coefficient 0.98 0.92 0.90 0.98 0.69 0.45 0.74 0.69 0.56 0.25 0.23 0.18 362 w INDEX —/— /Disable<Module>, 13 /DisableDynamics, 13 /DisableInteractiveStartup, 13 /LocalDongle, 12 /NetworkDongle, 12 address, 16 air density, 193, 221 air gun, 63 Airy wave, 155, 223 single, 155 allowable stress, 306 Alpha, 156, 225 amplitude, 243, 244, 250 analysis, 210 anchor, 30, 59 anchored, 96, 144, 147, 184, 236, 237, 238, 288, 289, 298, 347, 350 angle, 142, 170, 184, 217, 220, 222, 237, 246, 270, 271, 277, 288, 294, 296, 312, 348, 353 azimuth, 142, 170, 218, 237, 246, 270, 289, 295, 296, 312, 348, 353 beta, 279 declination, 142, 170, 237, 270, 289, 312, 348, 353 Exy-angle, 171, 312 Ez-angle, 171, 312 Ezx-angle, 171, 312 Ezy-angle, 171, 312 gamma, 170, 270, 289, 312 incidence, 271, 279, 312 lay azimuth, 295, 296 twist, 312 angular velocity, 202, 273 animation, 96, 97 API, 20, 222 applied, 241, 246, 266, 270 force, 246 load, 266, 270 buoys, 270 vessels, 246 moment, 246 apron plate, 359 arc length, 106, 107, 110, 288, 292, 310, 347, 350 arch, 35, 36, 38, 39, 40 arch radius, 359 area, 162, 186, 198, 199, 200, 205, 234, 235, 252, 273, 275, 303 moment, 252 moment of, 201, 274, 276, 304 of contact, 162, 186, 199, 200, 205, 235 arranging windows, 72 attachment, 210, 287, 293, 300, 302 attachment type, 288, 300 auto arrange, 72, 90 auto backup, 118 AVI file, 97, 112 363 —3— 3D buoy, 38, 49, 51, 63, 78, 94, 143, 198, 210, 264, 265 added mass, 265 added mass coefficient, 265 drag, 265 drag area, 265 drag coefficients, 265 inertia coefficient, 265 statics, 264 3D view, 72, 79, 82, 90, 91, 92, 93, 95, 96, 97, 98, 121 new, 90 —6— 6D buoy, 35, 39, 40, 41, 42, 47, 49, 51, 53, 61, 63, 64, 70, 78, 94, 143, 199, 200, 201, 210, 266, 267, 268, 270, 271, 273, 274, 275, 277, 283, 360 added mass, 203 added mass coefficient, 277 drag moment, 276 fluid acceleration force, 203 —A— acceleration, 152, 181, 198, 199, 233, 243, 311, 351 accuracy, 215, 296 added inertia, 198, 199, 201 added mass, 165, 172, 179, 183, 195, 198, 201, 264, 266, 267, 274, 277, 301, 305, 322, 325, 326, 329, 331, 361 3D buoys, 265 6D buoys, 203 axial, 322, 325, 331 clump, 301 coefficient, 171, 181, 198, 201, 203, 264, 277, 305, 329, 362 3D buoys, 265 6Dbuoys, 277 spar buoys, 277 floating line, 184 line, 180 normal, 322, 326, 331 spar buoys, 203 vessels, 195 w axes, 80, 94, 117, 141, 142, 143, 216, 239, 316 global, 94, 117, 141, 142, 143 local, 82, 94, 117, 142, 317 vessel, 240 axial, 147, 166, 175, 294, 303, 311, 322, 324, 334, 336, 340 relative velocity, 311 stiffness, 147, 167, 175, 295, 303, 322, 324, 334, 336 azimuth, 142, 170, 218, 237, 238, 246, 270, 278, 289, 295, 296, 312, 320, 348, 353 end force, 312 no moment, 312 265, 266, 267, 268, 270, 271, 273, 274, 275, 277, 279, 283, 346, 359 3D, 38, 49, 51, 63, 78, 94, 143, 198, 264, 265 6D, 35, 39, 40, 41, 42, 47, 49, 51, 53, 61, 63, 64, 70, 78, 94, 143, 199, 200, 201, 266, 267, 268, 270, 271, 273, 274, 275, 277, 283, 360 applied load, 270 axis, 274 axi-symmetric, 266 CALM, 266, 283 free floating, 213, 283 hydrodynamics, 279, 283 in static analysis, 214 lumped, 35, 40, 51, 200, 266, 273, 274, 360 spar, 29, 39, 41, 42, 43, 46, 47, 49, 51, 54, 61, 201, 266, 275, 283 statics, 212, 264 ties, 346 towed fish, 64 buoyancy, 34, 44, 147, 154, 165, 198, 200, 217, 265, 266, 267, 276, 286, 300, 303, 327, 328, 329, 330, 331, 332, 359 distributed, 34, 44 module, 327 tank, 359 variation with depth, 154, 217 buoyant line, 296 —B— background colour, 117 ball joint, 183, 289 barge, 239 Barltrop, 20 barriers, 211 batch, 66, 68 batch processing, 66, 68, 87, 120, 121, 122, 124 batch script files, 65, 121 bellmouth, 344 bend, 59, 110, 146, 147, 148, 163, 166, 173, 178, 183, 216, 288, 294, 303, 312, 313, 316, 324, 334, 336, 340, 343, 356, 359 damping, 167, 216 limiter, 59, 344, 356 moment, 148, 178, 304, 313 radius, 110, 306, 359 restrictor, 183, 343, 356 restrictor load, 317, 344 stiffener, 344, 356 stiffness, 147, 148, 165, 168, 173, 289, 294, 304, 324, 334, 337, 341, 356 target damping, 167, 216 beta angle, 279 bias power, 305 black and white, 118 Blevins, 21 block, 35, 37, 236 booms, 184 breaking load, 323, 334, 335 breakout force, 362 breakwater, 234 bridle, 38, 54, 359 buckling, 173, 176, 344 build up, 41, 48, 53, 64, 69, 151, 153, 215 bulk modulus, 154, 217, 265, 270, 303 buoy, 29, 35, 38, 40, 41, 42, 43, 46, 47, 48, 49, 50, 51, 53, 60, 63, 64, 69, 78, 93, 143, 198, 199, 200, 201, 212, 214, 234, 264, 364 —C— Ca, 180, 198, 201, 265, 274, 301, 305 cable, 56, 62, 210, 265, 286, 320, 338, 339, 340 calculation method, 147, 151, 152, 154, 296 CALM buoy, 30, 49, 50, 283 cantilever, 39 caption, 72 Carter, 20, 357 Casarella, 20 cascade, 72, 90 catenary, 29, 33, 34, 35, 36, 40, 43, 52, 62, 66, 67, 147, 184, 210, 294 riser, 29, 32, 67 statics, 147, 184, 210, 294 catenary statics, 37, 147, 162, 296 Cd, 179, 201, 274, 301 centre, 199, 267, 268, 270, 271, 273, 275, 303, 359 of base, 275 of gravity, 267, 268, 270, 271, 303, 359 of pressure, 267 of volume, 199, 273 centrifugal force, 173, 181, 292 w chain, 173, 205, 286, 301, 304, 320, 322, 323, 324, 325, 326, 327 mooring, 322 studless, 323 studlink, 323 Chapman, 20 check box, 102 chinese lantern, 30, 50 chord, 268, 270 clamped end, 183 clash force, 187, 314 clash impulse, 314 clashing, 32, 40, 41, 42, 47, 57, 60, 62, 69, 113, 187, 247, 266, 313 clearance, 32, 42, 45, 69, 113, 187, 310, 313 clipboard, 114, 115 closest approach, 113, 313 clump types, 151, 215, 286, 292, 300 clumps, 51, 54, 61, 94, 292, 300 added mass, 301 drag, 301 Cm, 201, 265, 274, 305 cnoidal wave, 155, 158, 223 colour, 93, 102 command line parameters, 12, 116 comments, 212 compare data, 116 components, 228 Fourier, 228 compressibility, 154, 265, 270, 303 compression, 107, 173, 207, 307, 344, 347 compressive force, 147 connecting objects, 94, 95 connections, 143, 183, 235, 277, 288, 347, 350 loads, 278 shapes, 235 constant, 207, 243, 348, 351, 352 speed, 207, 348, 352 tension, 207, 348, 352 velocity, 243, 348 consultancy, 15 contact, 30, 34, 36, 44, 46, 47, 50, 54, 57, 61, 62, 69, 70, 162, 186, 187, 198, 199, 205, 234, 235, 239, 303 area, 162, 186, 199, 200, 205, 235 damping, 305 energy, 62, 69, 188 force, 31, 46, 61, 62, 69, 239 stiffness, 35, 37, 46, 57, 62, 69, 70, 187, 305 contents, 173, 175, 292, 303 continuous, 98 control, 11, 47, 351 buoy, 47 365 control mode, 207, 348, 351, 352 force, 208, 350, 351, 352 length, 207, 349, 351, 352 controlling views, 92 conventions, 249, 257, 289 convergence, 213, 214, 296 parameters, 214 coordinate systems, 141 copy, 81, 85, 95, 96, 114, 115 Coriolis, 173 Coriolis force, 181, 292 Coulomb friction, 147, 185, 305 crane, 30, 53 creating objects, 95 crest, 357 critical damping, 163, 205, 216, 217, 235 seabed, 219 shapes, 205, 235 cross flow, 179, 202, 276 crosshair cursor, 24 current, 29, 50, 155, 192, 216, 220, 233, 252 direction, 220 exponent, 221 meter, 30, 50 speed, 220 speed at seabed, 221 speed at surface, 221 curvature, 167, 313 customisation, 116 cut, 81, 85 cylinder, 36, 40, 41, 55, 201, 237, 266, 276 —D— damage, 132 damper, 165, 346, 347 damping, 45, 151, 156, 163, 166, 187, 195, 199, 200, 205, 207, 212, 216, 217, 235, 261, 266, 273, 286, 296, 303, 348, 351, 352 bend, 167, 216 clashing, 187, 305 critical, 163, 205, 216, 219, 235 minimum, 296 moment, 200, 273 properties, 199, 213 seabed, 163, 205, 219 structural, 169, 216 target, 151, 216, 286 vessels, 195, 261 data, 11, 72, 78, 82, 83, 95, 100, 101, 102, 212, 217, 235, 275, 300, 303 environment, 217 form, 72, 95, 100, 101, 102 line type, 303 open, 78, 83 w save, 78, 84 shapes, 235 spar buoys, 275 deadband, 207, 348, 352 Dean, 20, 155, 158, 159, 160, 222 wave, 155, 158, 159, 160, 223 declination, 142, 170, 237, 270, 278, 289, 312, 320, 348, 353 end force, 312 no moment, 312 default value, 102 degrees of freedom, 244, 250, 264, 266, 269 Deksnis, 21 delete, 85, 95 density, 154, 217, 221, 292 air, 221 seawater, 154, 217 deployment, 30, 58, 64 depth, 162, 186, 198, 199, 201, 205, 217, 234, 235, 264, 266, 310 of immersion, 201, 264, 266 of penetration, 162, 186, 199, 201, 205, 235, 264 seabed, 218 water, 218 design wave, 230, 231, 357 destroying objects, 95 diameter, 43, 276, 302, 340 effective, 44 differences, 116 direction, 142, 170, 183, 185, 218, 220, 223, 238, 288, 295, 296, 341, 348, 353 conventions, 142 no moment, 183, 289, 341 disk space, 215 displaced mass, 180, 277 distributed buoyancy, 34, 44 diverter, 267 DNV, 20 dongle, 10, 12 drag, 93, 116, 164, 171, 179, 183, 192, 198, 201, 202, 208, 210, 212, 252, 264, 266, 267, 271, 274, 275, 278, 283, 286, 300, 302, 303, 311, 320, 322, 325, 326, 329, 330, 331, 352, 361 3D buoys, 265 area, 179, 198, 201, 202, 274, 276, 301 3D buoys, 265 area moment, 203, 276, 285 axial, 322, 325, 330 chain, 94, 210, 301, 302 clump, 301 coefficient, 172, 179, 198, 201, 202, 276, 301, 302, 305, 311, 329, 361 3D buoys, 265 366 floating line, 184 minimum distance, 117 moment, 201, 202, 274, 276 6D buoys, 276 spar buoys, 276 normal, 322, 326, 331 spar buoys, 276 starting velocity, 214 vessels, 192, 252 drag & drop, 83 dragging, 72, 91, 95, 117 drawing, 31, 45, 53, 62, 93, 226, 238, 240, 247, 248, 274, 292, 294 as seen in example files, 45, 54, 62 data, 226, 294 shapes, 238 vessels, 247 drilling rig, 359 dry length, 266, 278 dynamic analysis, 29, 151, 152, 207 dynamics data, 214 —E— Eames, 180, 293 edges, 93, 240, 247, 274 edit, 100, 101, 102 effective diameter, 44 effective tension, 167, 175, 313 eigenvalues, 316 elevation, 81, 88, 91, 92, 117, 233 e-mail, 16 empirical cumulative distribution, 110 Encastre, 31, 36, 39, 40, 61 end bend moment, 316 end curvature, 316 end directions, 289 end Ez-angle, 183 end faces, 237 end fittings, 183, 342, 343 end force, 312, 317, 342, 343 azimuth, 312 declination, 312 Exy-angle, 312 Ez-angle, 312, 342, 344 Ezx-angle, 312, 344 Ezy-angle, 312, 344 end loads, 143, 183, 316, 342 Exyz, 143, 183, 316, 342 GXYZ, 316 Lxyz, 316 end moment, 317 end orientation, 141, 289, 317 end shear, 316 end stiffness, 342 end tension, 316 end torque, 316 w energy, 187 contact, 188 environment, 210, 216, 217, 233 equilibrium, 147, 212, 264, 267, 268, 270, 271, 289, 294 error message, 79 ESDU, 20 Euler, 110, 173, 175, 303, 344, 345 buckling, 173, 175, 344 load, 110, 173, 307, 344, 345 strut, 173, 307 example, 29, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69 exit, 84 export, 74, 75, 84, 96, 97 extend simulation, 87 Exy-angle, 171, 312 Ez-angle, 171, 312 Ezx-angle, 171, 312 Ezy-angle, 171, 312 floats, 320, 327 flow velocity, 173, 292 flowline, 53 fluid, 163, 179, 198, 200, 201, 273, 292 acceleration force, 198, 201, 274 6D buoys, 203 spar buoys, 203 acceleration load, 274 flow, 181, 292 inertia, 201, 274 fluid incidence angle, 312 fm, 227 fonts, 119 force, 111, 116, 147, 163, 179, 187, 198, 207, 239, 241, 246, 263, 270, 273, 292, 313, 316, 348, 351, 352, 361 applied, 246 breakout, 362 centrifugal, 181, 292 clash, 187, 314 compressive, 147 contact, 239 control mode, 208, 350, 351, 352 Coriolis, 181, 292 end, 317 fluid acceleration, 198, 274 line clash, 314 Lx-Ly-Lz-force, 263 out of balance, 118 restoring, 111, 263 shear, 313 solid contact, 314 vertical, 111, 263 Fossati, 20 Fourier, 105, 227 components, 228 transform, 228 FPSO, 41, 42, 67 frames, 96, 97 free, 96, 143, 183, 288, 289, 298 frequently asked questions, 13 friction, 33, 42, 46, 54, 69, 147, 185, 266, 295, 301, 302, 305, 319, 362 Froude Krylov force, 172, 181 Froude scaling, 248 full statics, 50, 61, 146, 148, 149, 288, 294, 296 —F— Falco, 20 Faltinsen, 20 FAQs, 13 fastening, 278 faster simulations, 304 fatigue, 29, 67, 115, 125, 126, 127, 130, 131, 132, 357 analysis, 30, 67, 125, 126, 127, 130, 131, 132 damage, 132 load case, 126, 128 points, 131 rainflow, 125, 133 regular, 125, 133 S-N curve, 130 spreadsheet, 115 waves, 357 fax, 16 Fenton, 20, 21, 158 fetch, 357 FFT, 228 fields, 101 Fill, 81, 103 finite element model, 9, 163 fixed, 96, 144, 236, 237, 238, 288, 289, 298, 347, 350 flex joint, 44, 290 flexible, 177 pipe, 177 floating hose, 61, 184 floating line, 30, 61 floating platform, 239 367 —G— g, 142 gamma, 156, 170, 270, 278, 288, 289, 312 general preferences, 118 global, 93, 116, 141, 142, 143 axes, 94, 117, 141, 142, 143 coordinates, 141 origin, 141 w relative, 141 graph, 72, 109, 111, 112, 113, 114, 115, 120 Gregory, 21 guide tube, 359 GUIDE.DAT, 359 GX-velocity, 311 GY-velocity, 311 GZ-moment, 264 GZ-velocity, 311 inner time step, 152, 214 inside diameter, 292, 303, 336 instability, 46, 214, 215, 359 installation, 9 integration, 152, 214 interaction, 32, 36, 41, 42, 54, 58, 60, 64 interaction with seabed and shapes, 186 intercept, 114 interference, 40, 240 internal pressure, 175 interpolation, 104, 144, 219, 251 introduction, 9 Isherwood, 21, 225 isometric, 91 ISSC, 156, 223, 230, 231 iterations, 147, 296 maximum, 296 Iwan, 21 —H— hanging length, 320 harmonic motion, 244, 338 Hartnup, 21 hauling in, 207, 352, 353 hawser, 49 heading, 142, 241, 243, 263 heave, 141, 190, 240, 244, 263 heel, 241, 263 height, 155, 199, 200, 224, 229, 265, 266, 273, 300 help, 15, 79, 90 hide, 46, 93 Hoerner, 21 hollow, 292 hose, 60, 61, 286, 320, 338, 339, 340 fold flat, 338 high pressure, 338 low pressure, 338 thermoplastic, 338 hot, 80, 95, 98 keys, 80, 98 zone, 95 Hs, 156, 227, 357 hydraulic accumulators, 350, 352 hydrodynamic, 199, 200, 273 mass, 201, 274 properties, 199 hydrodynamics, 171, 279 hydrophone, 63 —J— joint, 94, 95, 143 JONSWAP, 156, 223, 230, 231, 357 jumper, 29, 38, 40 —K— keep open, 106 keyboard actions, 80 keys, 80, 98 hot, 80, 98 kinematic stretching, 223 —L— lambda, 227 Larsen, 21 Lathier, 21 lay azimuth, 31, 33, 295, 296 lazy, 29, 34, 35, 37, 38, 40, 42, 43, 65, 359 S riser system, 29, 35, 38, 43, 359 wave, 29, 34, 65 lazy S riser system, 359 legend, 114 length, 173, 201, 207, 241, 248, 265, 276, 277, 310, 347, 348, 351, 352, 353 arc, 310 control mode, 207, 349, 351, 352 cylinder, 204 dry, 266, 278 unstretched, 173, 207, 347, 351, 353 vessel, 241 library, 74, 76, 84, 300, 303 licence, 12 lift, 267, 271, 278 surface, 267 limit compression, 31, 36, 49, 173, 307, 325, 335, 337, 341, 345 —I— impact, 188 import, 74, 76, 255 incidence angle, 179, 271, 279 include in statics, 212, 241, 264 inertia, 198, 199, 201, 207, 264, 267, 268, 270, 271, 274, 305, 348, 351, 352, 359 coefficient 3D buoys, 265 moment of, 270, 359 information box, 79 initial, 264, 268 attitude, 269 position, 265, 269 368 w line, 29, 34, 35, 37, 43, 44, 50, 61, 66, 78, 94, 96, 141, 143, 147, 163, 170, 171, 173, 175, 179, 183, 184, 186, 187, 210, 216, 264, 266, 286, 288, 290, 292, 293, 294, 296, 297, 300, 303, 308, 310, 311, 312, 313, 314, 316, 320, 322, 327, 332, 338, 341, 361 added mass, 180 attached, 264, 266 attachments, 293 buoyancy module, 327 clash force, 314 clashing, 187 clearance, 313 connections, 170, 288 contents, 292 data, 288, 361 direct tensile stress, 315 effective tension, 175 end coordinates, 141, 170 end directions, 170 end joints, 143 end orientation, 141, 170, 171 ends, 183, 288, 290, 341 floating, 30, 61, 183, 296 floats, 327 flow in, 181, 292 lay azimuth, 185 max bending stress, 315 max xy-shear stress, 315 pressure forces, 175 results, 308, 310, 311, 312, 313, 314, 316 statics, 147, 294 structure, 292 style, 93 theory, 163 type data, 303 type wizard, 34, 36, 37, 44, 45, 51, 66, 320, 327, 332, 338 types, 287, 292, 303, 308, 320 von Mises stress, 316 wall tension, 175 width, 93 worst hoop stress, 315 linear, 152, 155, 346, 347 link, 31, 37, 38, 41, 42, 45, 46, 47, 48, 52, 54, 59, 64, 70, 79, 94, 143, 211, 346, 347, 348, 359 linked statistics, 108, 138 load, 78, 126 case, 126 local, 32, 35, 50, 80, 93, 116, 141, 142, 316 axes, 36, 94, 117, 141, 142, 317 coordinates, 141 Locate, 73 locking objects, 73, 89, 95 369 log, 107, 215 file, 106, 215 precision, 215 samples, 215 logging tension, 107 lumped, 9, 35, 40, 51, 155, 163, 200, 214, 266, 273, 274, 286, 359 buoy, 35, 40, 51, 200, 266, 273, 274, 360 mass model, 9, 164, 215, 286 Lxyz moment, 263 Lxyz-force, 263 —M— magnitude, 296 of standard change, 296 of standard error, 296 main window, 72 maintenance, 15 margins, 118 mass, 152, 164, 173, 179, 198, 200, 265, 266, 267, 269, 273, 277, 286, 292, 300, 302, 303, 330, 333, 336, 340, 346, 350, 351 flow rate, 173, 181, 292 per unit length, 303, 330, 333, 336, 340 master, 94, 95, 143 master relative, 143 maximum, 108, 110, 138, 296, 303, 313 iterations, 296, 297 tension, 110, 306 MBL, 335 mean, 108, 110, 138 measuring tape, 91 menus, 72, 82, 83, 84, 85, 86, 87, 89, 90 message box, 79 Miche, 161 mid-water arches, 35, 359 minimum, 108, 110, 116, 138, 296, 303 damping, 296 drag distance, 117 radius, 306 modal analysis, 317 model, 73, 76, 78, 82, 85, 92, 210 browser, 73, 78, 85 centre, 92 modelling, 173, 210 compression, 173 modules, 12 moment, 111, 148, 163, 178, 200, 201, 241, 246, 263, 268, 270, 273, 275, 279, 303, 313, 316, 359 applied, 246 bend, 148, 178, 304, 313 damping, 200, 273 drag, 201, 202, 274, 276 end, 317 w end bend, 316 GZ, 264 Lx-Ly-Lz-moment, 263 munk, 205, 275 of area, 201, 274, 276, 304 of inertia, 270, 359 yaw, 111 monochrome output, 118 moonpool, 45, 46, 53, 54, 234, 359 mooring, 41, 47, 48, 49, 50, 51, 58, 151, 291, 322 chain, 322 line, 41, 47, 48, 49, 50, 51 Morison, 21, 171, 199, 267 Morison's equation, 153 most recent files, 116 mouse, 80, 95, 101, 102, 117 selection zone, 117 moving objects, 74 Mueller, 21 multiple statics, 86, 109, 111, 151, 246, 263 munk moment, 205, 275 connections, 143 creating, 95 destroying, 95 locking, 89, 95 new, 78, 95 relative, 141, 289, 347, 350 obstacles, 234 Ochi Hubble, 21, 157, 227, 230, 231 OCIMF, 192 offset, 109, 111, 151, 199, 246, 266, 292, 300, 348, 350 graph, 111 table, 109 open, 78, 83 data, 83 OrcaFlex, 9 OrcaFlex offers a choice of 3 methods of k, 156 OrcaMotion, 255 OrcaRiser, 15 OrcFxAPI, 120 Orcina, 9, 15 orientation, 171, 236, 241, 243, 269, 270 vessel, 241 origin, 141, 155, 199, 200, 216, 220, 236, 264, 265, 268, 277 oscillations, 215 out of balance force, 118 outer time step, 153, 214 output preferences, 118 outside diameter, 179, 186, 303, 336 —N— name, 102, 235, 241, 264, 268, 270, 271, 288, 303, 346, 350 natural modes, 317 natural period, 108, 214, 219, 351 neutrally buoyant, 294 new, 24, 78, 82, 85, 90, 95 3D view, 90 line icon, 24 object, 78, 86, 95 Newman, 21, 197 Newton's law, 153, 208 NMIWAVE, 254 no moment, 170, 183, 288, 312, 341 azimuth, 312 declination, 312 direction, 183, 289, 341 node, 108, 143, 162, 164, 184, 186, 286, 288, 304 noise, 33, 38, 46, 69 non linear, 31, 32, 104, 290, 303, 304 non-linear wave theory, 155, 158 normal relative velocity, 311 North Sea, 231 NPD spectrum, 222 numbers, 102 numeric, 102 —P— Paidoussis, 21 Parsons, 20 paste, 81, 85, 95, 113, 115 pause, 78, 79, 80, 87 payout, 207, 352 peak enhancement factor, 225, 231, 358 pen, 31, 37 penetration, 162, 186, 199, 205, 219, 235 depth of, 162, 186, 199, 205, 235 period, 109, 111, 155, 224, 229, 244 phase, 155, 189, 244, 250, 258 Pierson-Moskowitz, 155, 223, 231 pin end, 39 pin joints, 39, 361 pinned end, 183 pinned-ended line, 356 pipe, 29, 52, 56, 173, 175, 177, 237, 303, 320, 336, 337 flexible, 177 lift, 30, 52, 56 steel, 177 titanium, 177 pipelay, 30, 52 370 —O— object, 78, 82, 89, 93, 95, 100, 106, 141, 143, 210, 288, 347, 350 browser, 100, 106 connecting, 94, 95 w PIPELAY.SIM, 52 pitch, 34, 37, 39, 49, 50, 51, 190, 244, 249, 264, 267, 268, 271 plan view, 81, 88, 92 plane, 238 planing, 205, 268 pliant S, 29, 38 pliant wave, 29, 37, 41, 42 Pode, 21, 180, 293 point of application, 246, 270 point on plane, 238 polar coordinates, 291 position, 108, 241 post-processing, 115, 120 post-processing results, 134 PowerPoint, 112 preferences, 89, 95, 116, 119 prescribed, 146, 147, 294, 298, 299 statics, 147 prescribed motion, 243 presentation, 97, 112 pressure, 175, 178, 233, 315 forces, 175 static, 234 pre-tension, 185, 295, 299 primary motion, 196, 242, 245, 263 print, 80, 91, 100, 113, 115, 119 print setup, 119 printed output, 28 profile, 32, 42, 46, 54, 105, 155, 229 programming interface, 120 proportion wet, 198, 200, 201, 273, 310 Puech, 22, 362 pull up, 30, 54, 55, 56 pulley, 348, 350 pull-in, 30, 53, 55, 56, 57, 147 report, 243 rotational, 190 spreadsheet, 243 text files, 251, 256 vessels, 251 rate of turn, 243 Rawson & Tupper, 22 reaction, 162, 184, 186, 198, 200, 205, 237, 274, 305 Reber, 180 recent files, 119 rectified, 32, 34 reference axes, 291 reference current, 220 reference origin, 291 references, 20 refresh rate, 117, 121 regular fatigue analysis, 125, 133 regular wave, 155, 224, 251 relative velocity, 311 releasing, 30, 41, 48, 58, 61, 64, 69, 70, 151, 290, 347, 350 replay, 79, 82, 91, 96, 97, 98, 112 reset, 77, 78, 79, 80, 87, 92, 110, 111, 113, 294 response amplitude operators, 239, 243 Resta, 20 restoring force, 111, 263 results, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 79, 89, 106, 107, 108, 109, 113, 115, 119, 134, 136, 137, 139, 215, 233, 239, 277, 348, 353 in example files, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 63, 64, 66, 67, 68, 69, 70 shapes, 239 spreadsheet, 134, 136, 137, 139 Reynolds number, 179, 217, 305, 311, 361 Richtmyer, 180 roll, 190, 244, 249, 264, 267, 268, 270, 271 rope, 173, 307, 320, 332, 333, 334 fibre, 332, 333, 334 nylon, 332, 333, 334 rotate view, 81, 88, 117 rotation, 39, 40, 47, 50, 53, 262, 266, 277 1, 263, 266, 277 2, 50, 263, 266, 277 3, 263, 266, 277 rotational, 183, 189, 266 RAOs, 190 stiffness, 183, 266 run simulation, 79, 80, 87, 152 run time, 153 371 —Q— QA, 14, 74 QTF, 196, 253, 261 quick statics, 37, 147, 294 —R— rainflow fatigue analysis, 125, 127, 133 ramping, 151, 173, 220 random waves, 156, 224, 251 range graph, 106, 109, 110, 138, 173, 306, 313 RAOs, 43, 46, 47, 62, 64, 189, 190, 210, 239, 243, 244, 249, 250, 255, 257, 258 checking, 190, 258 conventions, 189, 249, 257 graphs, 258 importing, 255 origin, 250, 257 phase origin, 250 w —S— salinity, 217 Sarpkaya, 22 save, 78, 83, 139 data, 84, 140 scale bar, 117 SCR, 29, 43, 44 script files, 121 scroll bars, 72, 97, 101 sea, 24, 93, 154, 155, 183, 215, 216, 217, 222, 229, 233, 310, 353 density, 154, 217 results, 233 surface, 24, 183 surface and seabed, 94, 217, 233, 310, 353 seabed, 29, 32, 42, 44, 53, 94, 143, 147, 155, 162, 184, 199, 200, 205, 215, 216, 218, 235, 266, 274, 295, 310 clearance, 310 critical damping, 219 damping, 163, 205, 219, 235 depth, 218 direction, 218 friction, 31, 147, 185 origin, 218 profile, 31, 42, 54, 218 slope, 31, 32, 44, 218 slope direction, 218 stiffness, 219 theory, 162 touchdown, 147, 184 type, 218 seastate, 227, 357 section, 287, 292 seed, 225 segment, 156, 165, 286 segmentation, 32, 33, 36, 43, 52, 56, 57, 67, 68 seismic, 63 select, 95, 107 object, 95 variable, 107 session log, 116, 121 set lay azimuth, 295 shape, 79, 94, 143, 148, 205, 211, 234, 235, 238, 239, 266, 274 connection, 235 critical damping, 205, 235 data, 235 drawing, 238 results, 239 shape, 235 stiffness, 234, 235 theory, 205 type, 235 shear, 178, 313, 314 force, 313 stress, 315 shielding, 234 ship, 239 short term operations, 358 shortest natural period, 108, 214 SI Units, 212 Sigma, 156 simulation, 72, 77, 79, 80, 82, 83, 86, 96, 120, 151, 214, 303, 352 extend, 87 open, 78 run, 79, 80, 87 save, 78, 83 speed of, 304 unstable, 215 single Airy wave, 155 single statics, 146 skin friction, 362 Skjelbreia & Hendrickson, 22 slack, 147, 294, 296, 307, 347 slamming, 54, 205, 267, 268 slave, 94, 95, 143 sliding friction, 362 slip joint, 45 slope, 155, 218, 220, 238, 294 slow drift, 253, 261 smear, 31, 34, 44, 45 S-N curve, 129, 130 snag catcher, 57 snatch loads, 216, 304 solid, 32, 34, 35, 36, 38, 39, 40, 41, 46, 51, 52, 54, 57, 60, 62, 64, 70, 79, 94, 143, 148, 205, 234, 235, 238, 239, 266, 274, 313, 359 block, 35, 37 contact force, 61, 314 cylinder, 36, 40, 41, 55, 359, 361 data, 235 stiffness, 205 theory, 205 span, 268, 270 spar buoy, 29, 39, 41, 42, 43, 46, 47, 49, 51, 54, 61, 201, 234, 275, 283 added mass, 203 added mass coefficient, 277 data, 275 drag, 276 drag moment, 276 fluid acceleration force, 203 Sparks, 22 spectral, 113, 215, 222, 234, 357 density, 113, 215 energy parameter, 225 372 w peak, 358 peak frequency, 225 spectrum, 156, 157, 224 speed, 97, 98, 207, 243, 303, 348, 351, 352, 357 constant, 207, 348, 352 of simulation, 304 wind, 357 spike, 43 spin buttons, 102 spline, 37, 42, 50, 60, 146, 147, 294, 297 control points, 297 order, 297 statics, 50, 61, 147 spreadsheet, 115, 134, 139 results, 134, 139 stress, 139 spring, 346, 347 spring/damper, 41, 45, 46, 211, 346, 347, 359 stages, 31, 41, 48, 53, 54, 55, 56, 57, 61, 64, 151, 215, 290, 347, 350, 352 standard deviation, 108, 138 start, 98 starting friction, 362 starting shape, 297, 298 starting velocity, 214 start-up, 11 state, 72, 76, 78, 79, 95 statically indeterminate, 213 statics, 26, 36, 50, 60, 77, 78, 79, 86, 108, 109, 111, 115, 120, 146, 147, 148, 151, 162, 184, 207, 210, 212, 214, 234, 241, 242, 246, 262, 264, 268, 288, 294, 296, 297, 351, 359 analysis, 26, 148, 151, 207, 212, 269, 294, 296, 351 buoy, 212, 264 catenary, 37, 147, 162, 184, 210, 294, 296 covergence, 214, 359 data, 212, 214 full, 50, 61, 146, 148, 149, 288, 294, 296 line, 147, 294 method, 147, 294, 296, 297 catenary, 37, 147 full statics, 148 prescribed, 147 quick, 37, 147 spline, 147 multiple, 86, 109, 111, 151, 246, 263 quick, 37, 294 single, 146 vessels, 242 statics only OrcaFlex, 12 statistics, 106, 107, 108, 115, 232, 357 373 linked, 108 wave, 232, 357 wind, 357 status bar, 72, 77, 79, 95, 96 steady state, 146 steel, 177 pipe, 177 steep riser system, 359 steep S, 36 steep wave, 29, 34, 44 step replay, 89 stiffness, 36, 46, 147, 162, 165, 166, 173, 175, 183, 186, 199, 200, 207, 219, 234, 235, 266, 288, 294, 303, 322, 324, 334, 340, 346, 347, 351, 352, 359 axial, 147, 175, 295, 322, 324, 334, 340 bend, 147, 165, 168, 289, 324, 334, 341 contact, 37, 305 rotational, 183, 266 shapes, 234, 235 torsional, 304 twisting, 289, 304 value, 359 stinger, 52 Stokes' wave, 155, 158, 223 stop, 78, 98 storm, 357 stowed line, 30, 60 stream function, 158, 224 streamer, 30, 63 stress, 29, 44, 66, 67, 127, 132, 134, 139, 175, 178, 303, 314, 337 allowable, 306 analysis, 30, 66 axial, 140 components, 139, 140, 316 concentration factor, 129, 133 diameter, 31, 44 hoop, 140, 178 loading factor, 175, 306, 337 longitudinal, 140 matrix, 133, 178 radial, 140 shear, 315 spreadsheet, 134, 139 von Mises, 316 studless, 323 chain, 323 studlink, 323 chain, 323 style, 93 superimpose, 98 superimposed motion, 243, 245 supported length, 320 surface piercing, 183, 266, 283, 300 surface Z, 265, 277, 310, 353 w surge, 141, 190, 240, 244, 263, 310 sway, 141, 190, 240, 244, 263, 310 swell, 157, 227 symmetry, 249, 252 —T— target damping, 151, 167, 168, 169, 216, 286 technical notes, 13 telephone, 16 temperature, 212, 217 tension, 107, 110, 167, 175, 178, 207, 303, 347, 348, 351, 352, 353 constant, 207, 348, 352 maximum, 110, 306 tension leg platform, 47 tensioned riser, 45 tensioners, 45 termination, 183 tether, 37, 38, 41, 42, 47, 50, 52, 211, 346, 347, 359 text, 72, 101, 106, 109, 115 tie-down, 42 ties, 346 tile, 72, 80, 90, 91, 113 time, 78, 105, 106, 107, 108, 109, 137, 151, 152, 155, 214, 222, 233, 245, 257, 303, 313, 351 history, 105, 106, 107, 109, 137, 223, 233, 245, 313 vessels, 245 history file format, 105 history multiple, 107 origin, 151, 156, 223, 258 step, 78, 108, 151, 152, 214, 304, 351 titanium pipe, 177 TLP, 29, 47 tolerance, 296, 297 toolbar, 72, 78 torque, 179, 303, 313, 336 per unit tension, 305, 337 torsion, 288 torsional stiffness, 304, 337 touchdown, 184, 309 towed fish, 53, 64, 267 towed systems, 146, 214 tower, 29, 39, 40, 53 track, 147, 294, 298, 299 trails, 98 transient, 38, 41, 48, 64, 151, 153, 214, 244 trapped water, 32, 46, 55, 172, 205, 234, 235 data, 235 theory, 206 trim, 241, 263 trough, 35, 38, 39 374 truncation, 104 Tucker, 22, 357 turn, 298 turret, 29, 41 tutorial, 24, 25, 26, 27, 28 twist, 312 twisting stiffness, 289, 304 Tz, 156, 227, 357 —U— umbilical, 40, 47 unattended, 120 undo, 84 unit mass, 303, 330, 333, 336, 340 units, 128 unstable simulation, 215 unstretched length, 173, 207, 347, 351, 353 Ursell number, 160 US customary units, 212 use static line end orientations, 213 use static positions, 213 user defined spectrum, 223, 226 user defined units, 212 —V— values, 106, 107 variable data, 31, 59, 104, 179, 217, 220, 270, 290, 304, 305 variables, 107, 108, 109, 111, 233, 239, 262, 265, 277, 308, 320, 348, 353 velocity, 233, 243, 311, 348, 353 axial relative, 311 constant, 243, 348 GY-velocity, 311 GZ-velocity, 311 normal relative, 311 relative, 311 version, 72, 224 vertical force, 111, 263 vertices, 93, 200, 236, 240, 247, 274 vessel, 24, 78, 94, 143, 151, 189, 190, 192, 195, 196, 201, 207, 210, 229, 239, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 255, 257, 258, 260, 261, 262, 275, 348, 351, 353 added mass, 195 applied load, 246 axes, 240 checking RAOs, 258 constant velocity, 243 current load, 192, 252 damping, 195 drag, 192 draught, 241, 248 drawing, 247, 248 driving, 243 w harmonic motion, 244 heading, 243 length, 229, 241, 252 motion, 189, 190 orientation, 241 origin, 240 phases, 189 prescribed motion, 243 RAO conventions, 257 RAO origin, 257 RAOs, 250, 251, 255 response, 245 results, 262 slow drift, 192, 196, 253, 261 static analysis, 242 statics, 242 time history, 245 type, 240, 248, 249, 250, 255, 257, 258, 260 wind load, 192, 252 video, 97, 112, 118 view, 80, 82, 87, 91, 92, 93, 116, 217 angle, 92 area, 92 centre, 92 control, 92 default view, 88, 92 parameters, 87, 91, 92 plan, 88 profile, 219 rotate, 81, 88, 117 rotation increment, 117 size, 92, 93 viscosity, 217, 311 VIV, 354 volume, 198, 200, 264, 273, 276, 292, 301 flow rate, 292 vortex force, 313 vortex induced vibration, 354 vortex-induced vibration, 362 components, 156, 225 crest, 250 crest-to-trough height, 357 Dean, 155, 158, 159, 160, 223 design, 357 direction, 190, 222, 251 drift load, 196, 253, 261 fatigue, 357 height, 224, 227 irregular, 114, 115, 155, 229, 244 maximum, 357 maximum height, 357 period, 214, 224 phase, 225 random, 156, 215, 224, 229, 230, 233, 244, 251 regular, 155, 215, 223, 224 significant height, 357 single Airy, 155 slope, 249 statistics, 232, 357 steepness, 229, 249 Stokes', 155, 158, 223 theory, 158 time history, 227 train, 222, 223 trough, 250, 357 type, 223 web site, 16 weight, 198, 200 weight in air, 300, 303 wetted volume, 273 Wichers, 22, 194 Wichers (1979), 192 width, 93 Wilson, 180 winch, 31, 47, 53, 54, 55, 56, 57, 61, 78, 94, 143, 151, 207, 211, 348, 350, 351, 352, 353 constant speed, 207, 348, 352 constant tension, 207, 348, 352 constant velocity, 348 control mode, 349, 351 detailed, 349 drive, 207, 348, 351, 352 drum, 348, 351 hydraulics, 348 mount, 353 simple, 349 theory, 207 type, 349, 350 wire, 350, 351, 353 wind, 192, 221, 252, 357 direction, 221 load, 192, 252 speed, 221, 357 375 —W— wake oscillator, 354 wall tension, 175, 313 water, 205, 216, 217, 233, 234 depth, 218 level, 217 particle, 233 trapped, 206, 234 wave, 100, 113, 115, 155, 158, 159, 160, 161, 189, 190, 196, 214, 216, 222, 227, 229, 230, 232, 233, 244, 249, 250, 253, 261, 357 Airy, 155, 223 breaking, 161 cnoidal, 155, 158, 223 w statistics, 357 window size, 92 wing type, 271 wings, 266, 267, 270 wire, 110, 235, 237, 238, 239, 247, 248, 274, 332, 346, 348 frame, 237, 238, 240, 247, 248, 274 rope, 332 wizard, 31, 36, 37, 44, 45, 51, 66, 320 wizard data, 321 word processor, 115 worst tension, 111, 264 XY graph, 109 —Y— Y, 263, 264, 265, 266, 277, 278, 310, 353 yaw, 111, 190, 244, 249, 262 moment, 111 Young's modulus, 303 —Z— Z, 263, 264, 265, 266, 277, 278, 310, 353 zero crossing period, 227, 357 zero up-crossing period, 357 zoom, 81, 88, 91, 93, 114 —X— X, 263, 264, 265, 266, 277, 278, 310, 353 376