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CFD SIMULATION AND ANALYSIS OF PARTICULATE DEPOSITION ON GASTURBINE VANES THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By PRASHANTH S. SHANKARA, B. TECH Graduate Program in Aeronautical and Astronautical Engineering The Ohio State University 2010 Master's Examination Committee: Dr. Jeffery P. Bons, Advisor Dr. Ali Ameri Dr. Jen Ping Chen Copyright by Prashanth S Shankara 2010 ABSTRACT Syngas from alternate fuels is used as a fuel in land based gas turbine engines as a lowgrade fuel. The reduction in cost by use of these fuels comes at the cost of deposition from particulate in the syngas on turbine blades, a ffecting the turbine performance and component life. A computational deposition model was developed based on a model developed at BYU to simulate and study the effects of deposition on gas turbine vanes with film cooling. The deposition model was built using the CFD software, FLUENT with User-Defined Functions (UDF) programmed in C language and hooked to FLUENT. The particle trajectories were calculated by Euler-Lagrange method. The fluid flow and heat transfer were solved first using RANS and deposition simulations were run as postprocessing in 3 steps – moving, sticking and detachment. Improvements to the wall friction velocity from the BYU model were incorporated and simulations on a bare 3D domain showed reasonable agreement with experimental results and followed the trend of capture efficiency decreasing with decreasing temperature. Deposition prediction on 3D coupon with film cooling showed the relationship between hot-side surface temperature and capture efficiency at different blowing ratios. Inaccurate prediction of hot-side surface temperature resulted in higher capture efficiencies. Deposition patterns were obtained from simulations using User-Defined Memory Locations to show number of particles depositing at each location on the surface. Simulation of deposition on a VKI ii blade in 3D domain showed interesting insight into particle behavior at different diameters. Smaller particles tended to follow the flow field and as the diameter increased, the particles showed a tendency to keep their path along the line of injection and not follow the flow field. Deposition predictions showed higher sticking efficiency at lower diameter (~1) and very low sticking at higher diameters. A new Young‟ modulus correlation was developed to account for the dependence of particle Young‟s modulus and deposition on surface temperature. Simulations with new model improved predictions on a very fine mesh with y+ less than 1 at blowing ratios, M=1 & 2 while M=0.5 still showed larger capture efficiency due to inaccurate surface temperature prediction. iii Dedication To my Mom, Dad & Brother for always being there iv ACKNOWLEDGMENTS This work would not have been possible without the support of my advisor, Dr. Jeffrey P. Bons, who offered me the chance to be a p art of his wonderful research group and believed in me just when I was at the crossroads of my graduate studies. Many thanks, Dr. Bons, for your faith in me and the desire to live up to your expectations has constantly pushed me to work harder. I would also like to thank my mentor, Dr. Ali Ameri, for constantly being a source of immense knowledge, advice and most importantly, for also being so understanding and supportive and always encouraging me to see the light at the end of the tunnel. My sincere thanks go out to Dr. Jen Ping Chen for being a part of my thesis committee and providing his valuable insights. I would also like to thank the University Turbine Systems Research (UTSR) group for their financial support. The numerical simulations were made possible through the use of supercomputing resources provided by the Ohio Supercomputer Center (OSC). Special thanks to Brett Barker who helped with the numerical simulations, Ai Weiguo for passing on his knowledge of UDF‟s and also to Trevor Goerig and Curtis Memory for answering my endless questions and making the lab a fun place to work at. A special note of thanks to Dr. Gerald M. Gregorek. Our interactions may have been few but you were a source of inspiration and a major reason behind me choosing to come to Ohio State. This thesis would not have been possible without the unconditional love and support of my family back in India. Thank you, Mom and Dad, for letting me follow my dreams and v vi . Special note of thanks to all my wonderful friends for making everyday life fun at OSU.to follow my own path in life even though it was light years away from the norm. TECH... Aerospace Engineering..VITA March 2003……………………………………….. Chennai..B. Mechanical Engineering. SRM University. India Sep 2007-Present…………….M.. The Ohio State University FIELDS OF STUDY Major Field: Aeronautical & Astronautical Engineering vii . School. India March 2007….S.SDAV Hr... Sec.…………….. Lagrangian Particle Tracking………………………………………………….1.xi Nomenclature……………………………………………………………………………xiii 1.. Turbulence Models……………………………………………………………...27 viii .21 4.. Coupling of discrete & continuous phase……………………………………….v Vita………………………………………………………………………………………vii List of Tables……………………………………………………………………………. Particle Trajectory Calculations……………………………………………….3.17 3.3. Eulerian Particle Tracking……………………………………………………….. Discrete Phase………………………………………………………………….3 2. Lite rature Review……………………………………………………………………3 2.12 3.1... Turbulent Particulate Dispersion………………………………………………. Particle Deposition Model………………………………………………………….. Particle Tracking Methodology……………………………………………………10 3.10 3..1.6 3....x List of Figures…………………………………………………………………………….5. Carrier Phase……………………………………………………………………..TABLE OF CONTENTS Abstract……………………………………………………………………………………ii Acknowledgements……………………………………………………………………….1 2..4 2.2..20 3.4..2.26 4. Introduction………………………………………………………………………….... Particle-Wall Interaction………………………………………………………. Results………………………………………………………………………….30 4.. Boundary Conditions……………………………………………………………65 7..1.82 Appendix: Particle Deposition Model – UDF Source Code ix . Particle Deposition on a Coupon…………………………………………………..74 9. Application to VKI blade………………………………………………………….26…………………………….63 7.53 7.1A.. Boundary Conditions & Simulations…………………………………………..3.47 6.4...41 6.51 6.1.3.A.. Improvements to the Deposition Simulations…………………………………….2A.78 References………………………………………………………………………………. Particle Sticking……………………………………………………………….66 8.3A. Simulations & Results………………………………………………………….27 4. Deposition Model Development in FLUENT 6.2... Carrier Phase Simulations………………………………………………………..4.. Particulate Deposition on Coupon with Film Cooling…………………………. Geometry & Grid Generation…………………………………………………. Particle Detachment…………………………………………………………….3. Boundary Conditions……………………………………………………………41 6.4.2..2..43 6.47 6..32 5.39 6. Particle Phase Simulations………………………………………………………42 6. Conclusions & Recommendations………………………………………………….35 6. Results…………………………………………………………………………. Young‟s Modulus Determination………………………………………………. 41 Table 6.1: Boundary conditions for the VKI blade………………………………………66 x .42 Table 7.1: Forces acting on the particle in the dispersed phase………………………….2: Ash particle properties………………………………………………………..17 Table 6..1: Summary of experiments for the bare coupon case………………………….LIST OF TABLES Table 3. ...1: Forces responsible for particle adhesion on a surface………………………….57 Fig.1.28 Fig 5..5. 6.54 Fig.…………40 Fig 6.5: Capture Efficiency vs Gas Temperature………………………………………... 1.11: Surface temperature contours at different blowing ratios on 1 inch diameter coupon……………………………………………………………………………………55 Fig 6..43 Fig: 6.. 6.7: View of the tetrahedral volume mesh for the 3D case…………………………50 Fig.....…39 Fig.6: Schematic of the 3D computational domain…………………………………. 2 along centerline plane……………………………………………………………………………………..20 Fig 4.13: Comparison of capture efficiency vs b lowing ratio at 1453 K………………. 6. S.44 Fig: 6. 6.41 Fig: 6. 6.10 Velocity magnitude contours (m/s) for M=0.1: Deposition Mode Flowchart…………………………………………………….3: Cut section of the mesh along X-plane…………………………………………. Classification of flow regimes for gas-solid flows.9: Surface mesh on the plate for 3D tetrahedral grid………………………………50 Fig.56 Fig 6.LIST OF FIGURES Fig: 3..60 xi .1: Computational domain for the bare coupon simulation…………………….. 6.12: Comparison of area-averaged surface temperature on coupon at 1453 K……....15: Deposition patterns from the model for M=2…………………………………. Elgobashi.49)…..8: Cut-section view of the volume mesh for the 3D case…………………………50 Fig 6.4: Impact efficiency vs Particle Diameter at 1453 K……………………………..14: Velocity vectors along the centerline plane for M=1…………………………58 Fig 6. 6.37 Fig...48 Fig.2: Geometry and boundary conditions of the model in 2D view………. 02 by OSU………………………………….4: Mach number contours for M=1.71 Fig.65 Fig 7.2………..67 Fig 7.67 Fig 7.. 8.64 Fig 7.02 by El-Batsh………………………………...70 Fig 7.75 Fig..3: Comparison of capture efficiency from new correlation with earlier results…. 7.5………61 Fig 6.Fig 6.9: Particle trajectories through the passage for d p = 10 μm……………………….10: Sticking Efficiency vs Particle Diameter at M=0.77 xii ....5: Mach number contours for M=0.2: Computational domain and Internal Region…………………………………….60 Fig 6. 7.69 Fig..61 Fig 7.6: Mach number contours for M=1.2: View of the tetrahedral mesh for the computational domain…………………. 8.16: Deposition patterns from the model for M=0.3: Mach number contours for M=0.5………………………………. 7.1: Computational grid used for the VKI blade……………………………………..7: Particle trajectories through the passage for d p = 0...17: Deposition patterns from the model for M=1………………………………….18: Comparison of deposition from experimental & simulation for M=0. 8.67 Fig..1μm………………………69 Fig..85………………………….85 by OSU………………………………….19: Comparison of deposition from experiments & simulation for M=0.66 Fig 7.8: Particle trajectories through the passage for d p = 1μm……………………….60 Fig 6.1: Close up view of the boundary layer on the coupon………………………….75 Fig.85 by El-Batsh………………………………. C µ Coefficients for eddy lifetime model.K] C L. [J/kg. [-] Cd Coefficient of drag. Dp Particle diameter. [m] E El-Batsh parameter. [N] Fs Saffman lift force. [Pa] Ei Mean velocity of fluid. [m/s 2 ] Gk Generation of turbulence kinetic energy due to mean velocity gradients Gω Generation of ω xiii . [m2 ] Mean molecular speed. [m/s] Cc. [Pa] FD Drag force on particle. [Pa] Es Surface Young‟s modulus. [N] gx Acceleration term in the particle trajectory equation. D Cooling hole diameter. [N] Fx Additional force term in the particle trajectory equation. [-] d. Cu Cunningham correction factor. [m/s] dp . [N] Fpo Particle sticking force. [-] Cp Specific heat of particle. [m/s] Ep Particle Young‟s modulus. [m] dij Deformation tensor.NOMENCLATURE Symbol Ap Surface Area of particle. [K] Tp Particle temperature. [W/m2 K] I Turbulence intensity. Sω User defined source terms S Ratio of particle density to fluid density. [-] kf Thermal conductivity of the continuous phase.mol] Rep Reynold‟s number of the particle. [-] Kr Local velocity gradient. [-] Nu Nusselt number. [Pa] Pr Prandtl number. [m2 /s2 ] k1. [m/s] Le Eddy length. [kg] M Blowing ratio. [-] P0 Total pressure of fluid. [-] K Constant coefficient of Saffman‟s lift force. [m] mp Mass of the particle. k2 El-Batsh parameter constants. [-] s Distance between cooling holes. [-] Kn Knudsen number. [s] T Gas temperature. [W/m-K] ks Sticking force constant. [Pa] R Universal gas constant. [K] xiv . [%] k Turbulence kinetic energy.hc Convective heat transfer coefficient. [-] t Time. [-] P Static pressure of fluid. [-] M Mach number. [m] Sk . [J/K. [m/s] WA Work of sticking. [-] ε Turbulent dissipation rate. [m2 /s3 ] λ Mean free path of the gas molecules.s] ν Kinematic viscosity. [-] Yω Dissipation of ω due to turbulence. [m/s] up Particle velocity. [m2 /s] νp Poisson‟s ratio of particle material. [m/s] uτc Critical wall shear velocity. [m/s] Uf Freestream velocity. [m/s] uj Instantaneous fluid velocity. [m/s] v‟ Gaussian distributed random velocity fluctuation.T∞ Free-stream temperature. [kg/m. [m/s] u‟ Gaussian distributed random velocity fluctuation. [m/s] Uj Coolant velocity at exit of cooling holes. [m] Yk Dissipation of k due to turbulence. [m/s] vn Normal velocity. [m] y+ Dimensionless wall distance of first cell center from the wall. [m/s] w‟ Gaussian distributed random velocity fluctuation. [-] α2 Volume fraction of dispersed phase. [-] xv . [-] y Distance of first cell center from the wall. [m/s] u* Wall friction velocity. [ µm] µ Dynamic viscosity of fluid. [K] u Fluid velocity. [m/s] vcr Capture velocity. [K] Tavg Average between particle and surface temperature. [Pa] Lifetime of eddy. [s] Wall shear stress. [-] ω Specific dissipation rate. [kg/m3 ] ρp Particle density. ρf Density of fluid. [s-1 ] ρ. [m2 /s] Γω Effective diffusivity of ω.νs Poisson‟s ratio of surface material. [kg/m3 ] Γk Effective diffusivity of k. [s] xvi . [m2 /s] Particle relaxation time. (62). These low-grade fuels are usually gasified to produce syngas which contains a number of impurities.. Various experiments have been conducted to study the effects of deposition on turbine vanes and blades.. Soltani & Ahmadi (57). sticking. particle impact. Bons et al. The phenomenon of deposition from syngas fuels on turbine vanes is of specific interest in this thesis. (44) have been conducting deposition experiments on gas turbine material coupons and turbine vanes with particular interest on the effect of deposition on film cooling. Erosion & Corrosio n) phenomenon in gas turbine engines. Numerical simulations have been performed in concurrence with these experiments at various stages to validate the experimental results and also with a goal to build a numerical model that can effectively simulate deposition conditions inside a gas turbine.. Ai & Fletcher (17).. Hamed et al. This thesis is an extension of the earlier numerical simulations and is aimed at building & delivering a particle deposition 1 . Guha (15) and Wang & Squires (14) have all performed numerical simulations for varying cases to simulate particle trajectories. (44). El-Batsh et al. INTRODUCTION Land-based turbine manufacturers have recently moved towards low. (59).grade fuels in an effort to reduce the high costs associated with high-quality fuels. Greenfield & Quarini (24).1. especially on the film cooling and heat transfer in the turbine. Brach et al. These impurities are the major causes of the DEC (Deposition. deposition and so forth. Numerical simulation of deposition is highly important to corroborate the results obtained from the experiments and also to shed light on various deposition issues that might be hard to decipher in the experiments. 2 .model that can be applied to future simulations of deposition on a turbine vane with film cooling. (1) and Zhao et al. The gas and particle phases are treated as interpenetrating continua and are coupled together by exchange coefficients. Two different approaches for particle deposition have been dealt with in literature – namely Eulerian and Lagrangian. The Eulerian method considers particles as a continuum and develops the particle tracks based on the conservation equation applied on a control volume basis with particles grouped together under various control volumes.1) Eule rian Particle Tracking The Eulerian particle tracking is the most preferred method for indoor environments as shown by Murakami et al. 3 . Initial simulations of particle transport and deposition were aimed at analyzing the effect of parameters like surface temperature.2. particle temperature.. particle diameter. (2 & 3). The gas phase is always modeled by the Eulerian approach where the gas is treated as a continuum and can be solved either by RANS simulations (Reynolds Averaged Navier Stokes) or DNS/LES (Direct Numerical Simulations/Large Eddy Simulations). on deposition. 2. LITERATURE REVIEW Numerical simulation of particle deposition has been performed by various researchers previously although cases of deposition simulation on gas turbine vanes with film cooling are few and far between. turbulent dispersion etc. Friedlander and Johnstone (18) and Davies (19) developed the first deposition model based on an Eulerian approach. The Eulerian-Eulerian method performs particle tracking by focusing on the control volume while the Eulerian-Lagrangian method focuses on the particle tracks instead.. 2) Lagrangian Particle Tracking The Lagrangian approach treats the particles as a dispersed phase and tracks individual particles.(10) used the Eulerian deposition model to simulate the deposition of fine particles on coal-fired gas turbines. particle density and fluid viscosity. thereby solving the continuity equations under turbulent flow conditions.3 to 1000. The inter-phase exchange rates and the closure laws. The particle volume fraction is usually assumed negligible compared to the carrier phase volume and particle-particle interactions are usually neglected. 2. They solved the equation of motion for particles with relaxation time ranging from 0... The relaxation time is usually the time required by the particle to respond to changes in fluid velocity and depends on particle size. The particle relaxation time is: 4 . Wood(7) & Kladas(8) used the Eulerian method by solving all particles on the basis that they were outside the boundary layer. turbulent diffusion and thermophoresis on the particles. in addition to the strong coupling between the phases have to be accurately defined for a proper Eulerian simulation which often presents quite a challenge. Yau & Young(6). Huang et al. Dehbi (5) noted that the Eulerian approach is very suitable only fo r flows with dense particle suspensions where the particle-particle interaction is too large to ignore. The particle relaxation time is a measure of particle inertia and denotes the time scale with which any slip velocity between the particles and the fluid is equilibrated.(9) and Ahluwalia et al. Kallio & Reeks (11) calculated the deposition of particles in a simulated turbulent flow field using the Lagrangian model in a turbulent duct.Menguturk & Sverdrup (4) developed an Eulerian model based on the assumption that the particles were very small and hence the inertia effect can be ignored. They both considered the effects of Brownian diffusion. (13) used the Lagrangian approach whilst solving the carrier phase flow by DNS method while Wang & Squires (14) used LES to simulate the flow field in their Eulerian-Lagrangian calculations. El. (17) and is intended to extend the applicability of the deposition model to actual turbine vane geometries with film cooling. Guha (15) noted that when particle motion is significantly affected by turbulence and the fluctuating flow field velocities become important..1) Their model showed very good agreement with the experimental data of Liu & Agarwal (20). The OSU model is an extension of the model used by Ai et al. This deposition model was based on three processes: particle transport. (12) and Brooke etal. Moreover.(2.Batsh et al. 5 . Lagrangian calculations are needed. FLUENT by developing a deposition model based on Eulerian-Lagrangian approach and successfully demonstrated the model for various experimental cases. (16) pioneered the Lagrangian DPM (Discrete Phase Method) modelin the CFD software... This method is valid for all particle sizes as particles are treated individually. (17) employed the El-Batsh study the particle-wall interaction in the previous phase of this research study. Ounis et al.. particle sticking and particle detachment and serves as the basis for the development of the OSU model. Ai et al. Lagrangian approach provides a more detailed and realistic model of particle deposition because the instantaneous equation of motion is solved for each particle moving through the field of random fluid eddies.. They developed and validated the deposition model with experimental results of deposition on a bare and TBC coated coupon with film cooling. it provides information about particle collision at the surface which is helpful while incorporating the sticking model. DNS solves the exact Navier-Stokes equations without any empiricism or modeling and hence is very computationally extensive. The relevant turbulent eddies are resolved and the unsteady flow is represented accurately. Greenfield & Quarini (24 & 25) modeled the turbulence as a series of random eddies with a lifetime of their own and associated random fluctuating velocities. FLUENT for particle deposition simulations on turbine vane successfully. This choice was based more on the fact that the CFD software.. 2. Mazur et al (23) used LES with the CFD software.. Shah (21) used LES to study the particle transport in an internal cooling ribbed duct. Abuzeid et al. impinging velocity and particle direction relative to the surface. Lagrangian particle tracking calculations provided information about number of particles impinging on the surface. RANS simulations assume isotropic turbulence which is not the case near-wall and hence the accuracy is affected due to empiricism in the turbulence model. El-Batsh et al. (17) both used the RANS in their simulations.3) Turbulence Models: El-Batsh et al... They found that the Lagrangian simulation was more accurate than Eulerian for various particle sizes. (16) and Ai et al. (22) used LES with one-way coupling for particle deposition onto rough surfaces with good results. FLUENT did not offer the k-ω turbulence 6 . (16) used the Standard k-ε model and the RNG k-ε model in conjunction with the Standard wall function and the two-layer zonal model..The turbulence model used in the Eulerian simulation of the flow field is usually chosen based on the flow physics. LES is mainly used for unsteady flows as it uses small and more universal scales and minimizes empiricism in turbulence modeling. Iacono et al. In addition. (26) modeled the transport of particles in turbulent flow field using both Eulerian & Lagrangian simulations. models at that time. Presence of surface roughness and blockage of film cooling holes due to deposition seriously affect film cooling effectiveness and performance. (27) reported that the k-ω model gave better prediction of the near-wall flow structures compared to the k-ε model. Bogard et al. They also found that deposition decreased cooling effectiveness by as much as 25%. They also compared the same for different mes h groups.. Their simulations showed that the RKE model better predicted the film-cooling effectiveness in the region of 2 ≤ x/D ≤ 6. The turbulence model affects the particle trajectory through the turbulent kinetic energy which is used to calculate the fluctuating velocities. Higher film cooling effectiveness leads to lesser deposition due to the cooler temperatures on the surface. although selection of the right turbulence model based on the flow field characteristics will ensure accurate flow field prediction which affects particle transport. (67) conducted deposition experiments using molten wax materials and found that leading edge film cooling reduced the deposition compared to no film cooling. (28) predicted film-cooling effectiveness using 3 different turbulence models: the Realizable k-ε model (RKE). Ajersch et al. hybrid and tetrahedral grids. Standard k-ω model and the v2 -f model. They noted that tetrahedral grids needed enough near wall resolution to accurately predict the film-cooling effectiveness which has been found to influence the particle deposition greatly in litera ture. Harrison and Bogard (29) found that the standard k-ω (SKW) model 7 .. There is not enough literature on the effect of various turbulence models on particle transport. The deposition on a surface depends on the particle and the surface temperature.. Silieti et al. namely hexahedral. Particle deposition also affects the film cooling effectiveness. Ai et al. So et al (63) proved in their simulations that the k-ε turbulence model over-predicts the turbulent kinetic energy 8 . Jin (64) noted from his simulations that the standard wall functions used with the k-ε model generate unrealistic large steady state velocities within the boundary layer leading to large deposition velocities for particles with relaxation time less than 10. (16) showed that the Std. The k-ε model depends on isotropic turbulence assumption which is not the case near wall and hence leads to over-prediction of deposition velocity for particles with relaxation time less than 10. The general idea from the literature is that accounting for anisotropic effects is important when using the standard turbulence models in FLUENT.best predicted laterally averaged adiabatic effectiveness. The std k-ε model has been used to simulate indoor flow field successfully by Zhang & Chen (30). thereby eliminating the approximation of particle trajectory near the wall and resolving the actual trajectory equations for better prediction. The k-ω model was used to eliminate the use of wall functions. El. k-ε model with standard wall functions over-predicts the deposition velocity for particles with relaxation time less than 10. Theodoridis (32) et al used a std k-ε model with std wall function for simulation of turbine blade film cooling without lateral injection.. and that the realizable k-ε model was best along the centerline. York and Laylek (33) used a realizable k-ε model which over predicted the results in the region between stagnation line and the second row of holes..Batsh et al. k-ω model with RANS to compute flow field and heat transfer for their analysis of particle deposition on a turbine coupon. Turbulence intensity predicted in the stagnation region was not realistic and an anisotropy correction was applied for better prediction. (17) used Std. Jovanovic et al (31) et al used std k-ω model for their two-phase flow modeling of air-coal mixture channels with single blade turbulators. within the viscous sub. The k-ω turbulence model can be applied throughout the boundary layer provided the near wall mesh resolution is sufficient.layer where the turbulence energy damps out much faster. This causes some regions in the viscous sub-layer to acquire abnormally high fluctuating velocities normal to the wall. Particles with low relaxation time change quickly with the flow field changes and the high normal velocities in the flow cause these particles to acquire a high normal velocity. 9 . This model requires no special near-wall treatment and hence will be used in this study. leading to over-prediction of deposition velocity. Particle tracking in FLUENT is divided into two phases: Carrier phase and Discrete phase. FLUENT 6. The particles are considered to be in the discrete phase since the particle loading volume is considerably negligible in all cases compared to the carrier phase volume.3. The RANS equations will be used as the governing equations to transport the flow field quantities. Hence. incompressible and Newtonian. The effect of particles on the flow field is negligible and is not taken into account. he noted that FLUENT is very capable in cases where particle-particle interaction is negligible. Zevenhoven (34) compared 6 different CFD packages with particle tracking capabilities. DNS is expensive for the current problem and not available in FLUENT.26. 3.3. PARTICLE TRACKING METHODOLOGY The particle tracking methodology used in the OSU model is based on the Discrete Phase Model (DPM) of the CFD simulation software. FLUENT was used for particle tracking simulations through the Ohio Supercomputer Center (OSC).3.26 was chosen after a careful consideration of various commercial CFD packages. The conservation equations for mass and 10 .1) Carrier Phase: The flow field is assumed to be single phase. FLUENT 6. Although STAR-CD was found to be the most versatile. The DPM model follows Lagrangian particle tracking and hence the carrier phase flow field is solved initially and allowed to reach a steady state before the discrete phase is injected into the carrier phase. LES is computationally intensive and needs several computers using the same jobs to process different datasets on different CPU‟s simultaneously. 2) and  (  u )      ( )   ( )  G  Y  S     t  x  x  x i k i j j (3. Γk and Γω represent the effective diffusivity of k and ω. 11 . Yk and Yω represent the dissipation of k and ω due to turbulence. The turbulence kinetic energy.3) Where k is the turbulent kinetic energy.. Standard k-ω turbulence model will be used for the closure equations. (17) are incompressible flows and the later cases with turbine vanes are compressible flows and solved accordingly. respectively.momentum are solved for all flows with an additional energy equation solved for cases with heat transfer or compressibility. The governing equations for the carrier phase are from the FLUENT manual (35) as: ( ui t u ui j x j )   p  xi   x j ( ui x j )  x j (  u iu j ) (3. which is based on the Wilcox k-ω model. k. The initial cases of validation of the model with results from Ai et al. and the specific dissipation rate ω are obtained from the following transport equations:   ( ku )  k   k i ( )   (  )  G  Y  S k k k k  t  x  x  x i j j (3. Gω represents the generation of ω. ω is the specific dissipation rate. In these equations.1) where u i u j is the Reynolds stress. Gk represents the generation of turbulence kinetic energy due to mean velocity gradients. Sk and Sω are user-defined source terms. .  For the particle sizes considered in the study.3. which is written in a Lagrangian reference frame..  The particle density is substantially larger than the fluid density. the second term is the effect of gravity on the particle and F x indicates all other additional forces.  Inter-collision forces are neglected due to low volume fraction of the particles. Also. 12 . (37) and Kaftori et al. In all the simulations in this study. in the near-wall region where the particle concentration may be locally large. This force balance equates the particle inertia with the forces acting on the particle.4) Where the first term on the right hand side is the drag force on the particle per unit particle mass.  Particles do not affect fluid turbulence. sub-grid scales have a negligible effect on particle trajectories. (38) have shown that for low volume fractions the turbulence modifications are negligible.2) Discrete Phase FLUENT predicts the trajectory of a discrete phase particle (or droplet or bubble) by integrating the force balance on the particle. and can be written (for the direction in Cartesian coordinates) as: (3. the following assumptions were made regarding the dispersed phase based on the experimental conditions and the particle characteristics used in the experiments:  The particles are rigid spheres and they are considered as points located at the center of the sphere. the turbulence intensities are modified by a very small amount and can be neglected. Experiments by Kulick et al. The acceleration of the fluid near the particle causes the flow around the particle to differ from that in the steady motion. The drag force is the most dominant force for particle motion.. especially when the particle Reynolds number is less than 100. The particles in the flow field are assumed to be spherical particles throughout this study and are subjected to various forces as explained by Rudinger (36) as follows: ΣFp = drag force + added mass effect + history effect + gravitational force + Buoyancy force + Lift force + Intercollision force + Brownian force + Thermophoresis force + Magnus force + Basset Force These forces have been discussed extensively by El-Batsh et al. The drag force is based on the Stokes‟ law when Re p <1. The second term describes the acceleration of the fluid near the particle surface from fluid velocity to the particle velocity. modified Stokes‟ law when 1<Rep <500 and the Newton‟s law when 500<Re p <2x105 . (17) and many others in previous literature and hence only a brief description of these forces is provided here. Drag force is the Stokes drag that acts on the particle due to the relative velocity between the fluid and the particle and acts in the direction of the flow. The force required to maintain the flow pattern was approximated by Basset and 13 . Mass of fluid that undergoes this acceleration is called “carried mass” which is equal to one half of the displaced mass of the fluid. Various deposition models in literature have used either one or a combination of the forces mentioned above based on the characteristics of the particle flow expected. The effect of material roughness is not considered when bouncing the particles from the wall. Identification of the forces that affect the particle regime for a particular case is extremely important for accurate tracking of the particle trajectory. Saffman‟s lift force is caused by the shear of the surrounding fluid which results in a non-uniform pressure distribution around the particle. Conversely. This force depends on the history of the particle trajectory and hence is called the “history effect”. Kallio & Reeks (11) noted that it is an order of magnitude lesser than the Saffman force in most regions of flow field and hence neglected. Sommerfeld (41) and Elgobashi and Truesdell (39) showed that the Basset forces are only important for particles with (ρp /ρf << 1). Basset Force. The added mass effect was also found to be true in the same regime. The lift is caused by the pressure dfference between both sides of the particle resulting from the velocity dfference due to rotation. This force assumes non-trivial magnitudes only in the viscous sublayer. This force usually enhances deposition velocity and Wang et al (40) have shown that neglecting this force results in a small decrease in the deposition rate. The particles used in this study are in the region of 1-15 µm and hence this force is neglected. The effect of the added mass and Basset forces is negligible for particles with density substantially larger than the fluid density. It is usually important when the volume fraction of the dispersed phase is high. If a particle leads the fluid motion. if the particle lags the fluid. Intercollision force is the force exerted due to inter-particle collisions.is represented by the third term. then the lift force is positive and it moves up the velocity gradient away from the wall. Brownian and Thermophoretic forces are 14 . The gravitational force is the body force acting on the particle and is only important for large particles in a Stokes regime. Magnus force is the lift developed due to rota tion of the particle. then the lift force is negative and the particle moves down the velocity gradient towards the wall. Buoyancy Force and added mass effect are usually negligible for particle deposition studies and hence neglected. 7) where R is the gas constant. This force is caused by the unequal momentum exchange between the particle and the fluid.important for sub. 15 . (3. Brownian force is caused by the random impact of particles with agitated gas molecules. El-Batsh et al (16) noted that based on the results of Talbot et al. The higher molecular velocities on one side of the particle due to the higher temperature give rise to more momentum exchange and a resulting force in the direction of decreasing temperature.micron particles. (42) showed that the thermophoretic force is caused by the unequal momentum exchange between the particle and the fluid.. (42). the particle motion is induced by collisions of gas molecules with the particle surface. rarefaction effects are important when the particles are in the submicron region as there is a reduction in the drag coefficient.6) and the mean molecular speed are given by: (3. Both these forces are neglected as the particles considered in this study are larger than 0. Instead. The Knudsen number is defined as the ratio of the mean free path of the gas molecules to the particle size.. Talbot et al.03 μm. the gas flow around the particle cannot be regarded as a continuum. In such a situation. The rarefaction is important in the non-continuum regime which is decided by the Knudsen number (Kn).5) And (3. (17) used the drag force at steady state and Saffman Lift Force in their simulation of particle deposition on high pressure turbine vane.. Ai et al. (22) used drag force. Table 3. (42) have shown in their experiments that there is considerable reduction of drag coefficient due to rarefaction effect for Kn>0.All experimental cases in this study have 0. The reduction in the drag coefficient is accounted for by the Cunningham correctio n factor described by Talbot et al.8) Shah et al. 16 . Talbot et al. Hamed et al (43) also considered only the drag and gravitational force in addition to their model for rotating machinery and the force due to rotation can be ignored... gravitational force and Saffman Lift Force as the effect of Saffman Lift on particle deposition is high in the viscous sublayer. Iacono et al.1 summarizes the various forces considered and identifies those that are incorporated in the current model. Dehbi (5) considered only the drag force in his Eddy Interaction Model..02 and hence this effect is included. (21) used the drag force and the gravitational force only and considered other forces to be negligible based on previous literature..1<Kn<10. (42) as: (3. Table 3. Continuum: Kn < 0.1<Kn<10 though sub-micron Free-molecule: Kn > 10. 7 Gravity NO ρ p / ρ f >> 1 decrease in deposition rate if neglected.1: Forces acting on the particle in the dispersed phase FORCE 1 Drag Domain of Importance Dominant force for particle motion.1. 6 NO ρ p / ρ f >> 1 density.03 µm NO dp > 0. Important for Kn>0. Transition: 0.3) Particle Trajectory Calculations Based on the particle characteristics and previous literature.02 particles are less Virtual Mass Important for small values of particle material density to gas Effect density.03 µm 10 Intercollision Important for high-volume fraction of particles NO Low volume fraction of particles 3. Modified Stokes' Included YES 1<Rep < 500 Law: 1<Rep < 500.1 < Kn < 10 0. Stokes' law: Rep < 1. ρ p / ρ f << 1 5 YES Important in Stokes Regime for large particles YES More accurate deposition rate NO No particle rotation in the flow NO Very small particles 8 Thermophoretic Important for sub-micron particles and Kn < 2 NO Kn > 10 9 Brownian Important for dp < 0. spherical particles assumed. the forces that are considered to be acting on the particle throughout this study are as follows: 17 . atleast an order of magnitude lower than Saffman force in most regions. Rep<100. ρ p / ρ f << 1 Basset Important for small values of particle material density to gas Saffman Lift Magnus Non-trivial magnitudes only in the viscous sub-layer. slight Lift force due to particle rotation. Newton's Law: 500< Rep< 2 x 105 2 3 4 Rarefaction Important for sub-micron particles (<1µm) for non-continuum Effect regime. The drag force is given by: (3.11) where λ is the molecular mean free path.10) where the Cunningham correction factor is (3. FLUENT provides controls to include the Cunningham correction factor and the Saffman force in the particle trajectory calculations.4 can be re-written as follows to calculate the particle trajectory by integrating the following equation of motion (in the x direction): (3. Drag Force with Cunningham correction factor for rarefaction effect  Saffman Lift Force Accordingly.12) where K r is the local velocity gradient. A user-defined subroutine can also be used to include these forces. A more accurate representation of this force is given by Li and Ahmadi (48) who used the following generalized expression of the force for three-dimensional shear fields: 18 . this expression was originally derived for an unbounded shear flow and does not include the effects due to proximity of the wall and finite Reynolds numbers. 3. The Saffman Lift force was initially given by Saffman (47) as: (3.9) where Cd is the drag coefficient. The first term on the right hand side represents the drag force per unit particle mass and the second term contains only the Saffman Lift Force. However. eq. ν is kinematic viscosity. and hc is the convective heat transfer coefficient.13) where. K = 2. is the velocity of the particle. The particle energy equation in terms of particle temperature is given by: ) where mp (3. where Ej is the mean velocity of the fluid. C p is the particle specific heat.594 is the constant coefficient of Saffman's lift force and is the instantaneous fluid velocity with uj = Ej + u:.15) is the particle mass. Ap is the surface area of the particle. the particle Reynolds number based on the particle-fluid velocity difference must be also smaller than the square root of the particle Reynolds number based on the shear field. Tp is the particle temperature. The assumption is made that the particle has no effect on the fluid flow due to the dilute particle flow.(3. The convective heat transfer coefficient is evaluated using the correlation given by FLUENT (35) and Crowe et al (45): (3. and u is its fluctuating component. S is the ratio of particle density to fluid density. In addition.14) The expression for the Saffman lift force is restricted to small particle Reynolds number.16) 19 . The calculation of heat transfer to or from the particles in this study considered only heating or cooling of the particles and neglected any phase changes or particle radiation. is the deformation tensor and is given by: (3. d is the particle diameter. The present problem can be modeled with one-way coupling as the particle volume is very low compared to the flow volume and hence the effect of particles on turbulence and on each other is very negligible. Fig: 3. (46) showed in their studies that there can be three types of coupling for solid particles in turbulent flows as follows:  One-way coupling: Effect of turbulence on particle trajectories and dispersion  Two-way coupling: Effect of particles on turbulence  Four-way coupling: Effect of particles on each other Usually.4) Coupling of discrete and continuous phase: Goesbet et al. (49) 20 . Hence. the body or particle has uniform temperature throughout and t he lumped mass system approximation can be used to solve the Heat Transfer 3. Elgobashi. Classification of flow regimes for gas-solid flows.1. for example. The body has high internal conductivity at these values and the temperature change remains the same.where Nu is the Nusselt number and Pr is the Prandtl number. The Biot number in these experiments in less than 0. was 0.043. S. The Biot number for 5μm. the particulate flow in compressor or turbine regimes is very dilute flow.1 and there is negligible internal resistance to heat transfer at these Biot number values. α2 is the volume fraction of the dispersed phase.1 shows the various flow regimes and the type of coupling suitable between carrier and dispersed phase. FLUENT s imulates particle streams rather than individual particles. τt 1 is the Lagrangian Integral time scale in seconds and τx 12 is the particle relaxation time in seconds. Stochastic models are similar to the deterministic models but they also take into account the effect of turbulent fluctuations on particle motion and interface transport. Turbulent dispersion is best studied from a Lagrangian viewpoint by following the motion of fluid elements. The particle dispersion in the turbulent flow field can be accounted for by two methods in FLUENT (35): (1) Stochastic tracking/Discrete Random Walk (DRW) model (2) Particle cloud approach For a case of steady state particle tracking. 3. Turbulence is able to mix and transport species. Information about the discrete phase concentration can only be obtained by two-way coupling. momentum and energy much faster than is done by molecular diffusion. 21 .Fig 3. Kuo (50) noted that turbulent dispersion can be accounted for by either a deterministic or Stochastic model. τk is the Kolmogorov time scale in seconds.5) Turbulent Particulate Dispersion One of the prominent characteristics of turbulent flows is their diffusivity. Deterministic models take into account the slip velocity and calculate the interface mass/heat transport rates using the slip velocity by taking into account the Reynolds number and the Sherwood/Nusselt number. The one-way coupling method is generally used to simulate the particle tracks. FLUENT uses a probability distribution function (PDF) for calculation of the perturbation in flow field velocities. only one particle trajectory is calculated for each injection point and the effects of turbule nce are ignored which is not a valid assumption. Mass flow rates and exchange source terms for each injection are divided equally among the multiple stochastic tracks. in turbulent flow field. turbulence diffusion by instantaneous flow fluctuations is the main mechanism for particle dispersion and depositions. This accounts for the dispersion effect and ensures the deposition calculation is performed for 22 . This is in addition to the other mechanisms such as molecular diffusion. For practical applications. For „n‟ number of stochastic tries. In the DRW model. Therefore. turbulence fluctuation is mainly estimated using a variety of stochastic approaches. The most faithful simulation of fluctuation velocity should be able to capture the details of the turbulence eddy structures.As explained by Tian & Ahmadi (66). Without Stochastic Tracking. Currently. this is only possible by DNS that is only practical for low Reynolds number duct flows. „n‟ values of perturbation are calculated for „n‟ different regions in the PDF and „n‟ different particle tracks are generated from the same injection point. But the mass flow rate for the injection at that point will be divided equally among the „n‟ particles. The „number of tries‟ option in the „Injections‟ panel in FLUENT is used to set the number of times every injection needs to be tracked. convective transport and gravitational sedimentation. it is critical to incorporate appropriate model for simulating turbulence fluctuations for accurate analysis of particle transport and deposition processes. thus matching the total mass flow rate through the inlet while accounting for the particle dispersion. however. each injection is tracked repeatedly to obtain a statistically meaningful sampling. One drawback of the EIM/DRW model is that it does not account for the strong anisotropic nature of turbulence inside the boundary layer as it is based on an assumption of isotropic turbulence. the EIM aims at reconstructing the instantaneous field from the local mean values of velocity and turbulent intensity.17) 23 . The DRW model moves each particle through the medium using the velocity field obtained from the solution of the flow equation to simulate advection and adds a random displacement to simulate dispersion. where u is the mean velocity and u’(t) the fluctuating velocity. a particle with velocity up is captured by an eddy which moves with a velocity composed of the mean fluid velocity. Hence. another interaction is generated with a different eddy. the eddy has the following length and lifetime: (3. and so forth. augmented by a random “instantaneous” component which is piecewise constant in time. The EIM models the turbulent dispersion of particles as a succession of interactions between a particle and eddies which have finite lengths and lifetimes. thus being more representative of deposition. It is assumed that at time to . the transport equations are not solved directly and the approach is free of numerical dispersion and artificial oscillations. By computing the paths of a large enough number of particles. The EIM is a stochastic random walk treatment in which particles are made to interact with the instantaneous velocity field u+u’(t). the effects of the fluctuating flow field can be taken into account. Based on the model of Gosman and Ioannides (51).„n‟ different trajectories instead of just one particle track. The DRW model is also popularly known as the „Eddy Interaction Model‟ and was developed by Gosman & Ioannides (51). When the lifetime of the eddy is over or the particle crosses the eddy. In essence. 20) Each eddy is characterized by a Gaussian distributed random velocity fluctuation and a time scale in this model. The particle cloud model considers the statistical evolution of a particle cloud about a mean trajectory. A particle cloud is required for each particle type in this model. The cloud expands due to turbulent dispersion as it is transported through the domain until it exits. The cloud enters the domain either as a point source or with an initial diameter. Although this would be a much more accurate representation of particle dispersion in turbulent flows. while C‟s are constants. The concentration of particles about the mean trajectory is represented by a Gaussian probability density function (PDF) whose variance is based on the degree of particle dispersion due to turbulent fluctuations. The 24 . As mentioned before. In FLUENT.19) Where (3. the distribution of particles in the cloud is defined by a probability density function (PDF) based on the position in the cloud relative to the cloud center. Dehbi (5) successfully included a boundary layer model which models the turbulence differently inside and outside the boundary layer. the fluid velocity fluctuations are assumed isotropic and the rms values of the velocity are obtained from the following relationship: (3. The mean trajectory is obtained by solving the ensemble-averaged equations of motion for all particles represented by the cloud.18) where k and ε are respectively the turbulent kinetic energy and dissipation rate. previous deposition studies have used the default isotropic FLUENT model with success for particle deposition studies.(3. This model is computationally less expensive but is less accurate since the gas phase properties like temperature are averaged within a cloud.value of the PDF represents the probability of finding particles represented by that cloud with residence time t at location x i in the flow field. the Stochastic DRW model was chosen to model the turbulent dispersion of particles. 25 . Hence. spread & flash based on impact energy & wall temperature  Interior – particle passes through an internal boundary zone Since none of these boundary conditions accurately represent the particle-wall interaction in the compressor and turbine regimes. (17)..in conditions and offers the following boundary conditions when a particle strikes a boundary face:  Reflect – elastic or inelastic collision  Trap – particle is trapped at the wall  Escape – particle escapes through the boundary  Wall-jet – particle spray acts as a jet with high Weber number & no liquid film  Wall. A UDF is a routine (programmed by the user) written in C using standard C functions and pre-defined FLUENT macros that can be dynamically linked with the solver.. rebound. 26 . (16) and the BYU model by Ai et al. The source files containing UDFs can either be interpreted or compiled by the user in FLUENT. while extending the applicability to simulate deposition on a 3D turbine vane with film cooling. PARTICLE DEPOSITION MODEL The OSU deposition model based on the previous deposition models of El-Batsh et al. The main goal of the deposition model was to accurately model the particle-wall interaction and to improve upon the BYU model.4.film – stick. FLUENT has built. a deposition model was built.in FLUENT using User Defined Functions (UDF) which would serve as the boundary condition for modeling particle-wall interaction. Visser (54). involving a purely mechanical interaction and a fluid dynamic interaction.1) Particle-Wall Inte raction: Interaction of a particle with a surface usually results in sticking and buildup (deposition).2 and they are:  Van der Waals force – Arises due to molecular interaction between solid surfaces  Electrostatic force – Caused by charging the particles electrically in the gas stream 27 . Once the particle sticks. This study is primarily concerned with modeling the deposition under the assumption of smooth surfaces.2) Particle Sticking: Extensive reviews of particle adhesion/sticking have been provided in literature by Corn (52). The particle-wall interaction leading to deposition is a two-step process. impact removal of the surface (erosion) and chemical buildup (corrosion). Tabor (55) and Bowling (56). The modeling process will deal with the build-up of deposition and the subsequent effect on film cooling effectiveness due to this buildup in the next stage. The sticking model is based on the previous adhesion models in literature which consider the elastic properties of the particle and the surface only under dry conditions. the next process is to determine whether the particle remains stuck to the surface or is removed from the surface based on the critical moment theory.4. 4. The mechanical interaction called the „sticking process‟ is the determination of whether the particle sticks to the surface when it comes into contact with a wall. This step is called the „detachment process‟ and is the fluid dynamic interaction. There are three main forces that contribute to particle adhesion as shown in fig 3. Krupp (53). a finite contact area exists. According to this model. This model was nicknamed the JKR theory. Soltani & Ahmadi (57) concluded that the Van der Waals force is the major contributor to surface adhesion under dry conditions. while the macroscopic approach dealt directly with the bulk properties of the interacting bodies.1: Forces responsible for particle adhesion on a surface From the literature mentioned above. Kendall. The Van der Waals force was calculated by either a microscopic or a macroscopic approach. the contact area does not disappear entirely. One shortcoming of these early theories was that the effect of contact deformation on the adhesion force was neglected. the alkali vapors condense and form the liquid bridge. If the temperature in the thermal boundary layer is lower than the dew point of the alkali vapors. instead. Johnson. The microscopic approach was based on the interactions of the individual molecules. the use of low-grade fuels containing alkali components gives rise to alkali vapor in addition to ash. Soltani & Ahmadi (57) used the JKR theory as a basis to form the evaluation of the minimum critical shear velocity to be used in the critical moment theory for particle 28 . at the mome nt of separation. and Roberts (58) used the surface energy and surface deformation effects to develop an improved contact model. Liquid Bridge force – Caused by the formation of a liquid bridge between particles and surface. Fig 4. In gas turbines. the co-efficient of restitution is defined as the ratio of the particle rebound velocity to the particle normal velocity. El.2) where E is the composite Young‟s modulus which is determined based on the Young‟s modulus of the particle and the surface. it rebounds. As the particle normal velocity decreases. The particle normal velocity (vn ) is then compared to the capture velocity. Brach and Dunn (59) formulated an expression to calculate the capture velocity of a particle using a semi-empirical model.1) where ks is a constant equal to 3π/4.. vn < vcr . For any particle. This velocity at which capture of a particle occurs is known as the capture/critical velocity. WA is a constant which depends upon the material properties of the particle and of the surface and has the units of J/m2 . vn > vcr .particle sticks. else. the particle rebound velocity decreases and eventually reaches a point where no rebound occurs and the particle is captured. The JKR model gives the sticking force based on the particle size a nd material properties with constants being derived from experiments. This sticking force is given by the JKR model as: (4. In this model. the particle sticks to the surface.Batsh et al. This constant is obtained experimentally for some materials. If the particle normal velocity is less than the capture velocity.detachment. The Work of Sticking. the capture velocity of the particle was calculated based on the experimental data and is given as follows: (4. Based on all the previous literature on deposition.particle rebounds 29 . (16) put together a complete deposition model to model the sticking and detachment process. 6) where uτc is the critical wall shear velocity.4) and (4. The El. d p is the particle diameter [m] and ρp is the particle density [kg/m3]. These detachment mechanisms have been discussed by Wang [60]. slide over it or roll on the surface. νs is the Poisson's ratio of surface material.5) where vcr is the particle capture velocity [m/s]. among others. The critical moment theory of Soltani & Ahmadi (57) is used to determine the detachment of particle from the surface. Ep is the Young's modulus of particle material [Pa]. Here.Batsh parameter is based on the Young‟s modulus of the particle and the surface and is given as: E (4. it continues on its trajectory until it leaves the domain or impacts the surface again. dp is the diameter of particle and Kc is the El. particles may lift-off from the surface. Cu is the Cunningham correction factor. the critical wall shear velocity is defined as: (4. The particle will be removed from the surface if the turbulent flow has a wall friction velocity ( 30 ) where τ w .Batsh parameter. νp is the Poisson's ratio of particle material. Es is the Young's modulus of surface material [Pa].3) and (4.3) Particle Detachment A particle may be detached from a surface when the applied forces overcome t he adhesion forces. Therefore. 4.Once the particle rebounds. Detachment occurs when the fluid dynamic moment in the viscous sublayer exceeds the moment exerted o n the particle by the sticking force. The BYU model used the particle velocity at the center of the first cell near the wall and the corresponding distance of the cell center from the wall to calculate the velocity gradient resulting in the following formulation: (4. The BYU model calculated the wall friction velocity of the particle based on the particle velocity instead of the gas velocity. The OSU model has 31 . This was based on the assumption that the particle and the gas phase are in equilibrium. The wall shear stress is usually given by: (4. A user-defined function (UDF) was created in the C programming language using the various UDF macros available to create a deposition model which would determine the capture velocity and critical wall shear velocity of every particle that hits the surface and create a dataset for all particles that deposit on the surface.8) The particles are considered to be spherical particles and hence the distance of the cell center from the wall was considered to be the distance of the center of the particle from the wall. The development of the UDF and its incorporation into FLUENT will be dealt with in the next section.7) Where u is the time-averaged velocity at the wall and the shear stress is the shear stress calculated at the wall.is the wall shear stress) which is larger than uτc. assuming that the particle is in contact with the surface. The effects of viscosity were not accounted for in these simulations as using the same flow conditions as the BYU model would help identify the areas of concern in the model. The wall friction velocity in the model was calculated as follows: (4. the 32 . 4. (16) used a deposition model to calculate the deposition for the impact of an Ammonium Fluorescein sphere against a Molybdenum surface. Also. y is the distance of the first grid point from the wall and is the local kinematic viscosity in m2 /s. to study the effect of surface temperature on particle sticking. One of the problems encountered when calculating the capture velocity in the BYU model is the information on the material properties of the particle and the surface. The deposition model differed from the BYU model in the calculation of the wall friction velocity and was validated against the previous simulation results from BYU.4) Young’s Modulus Determination El-Batsh et al. The Young's modulus of the Ammonium Fluorescein sphere and the Molybdenum surface were known from experimental results previously. These properties were not available in literature for the fly-ash material. viscosity will be used as a function of temperature and this can be specified in the FLUENT MATERIALS panel.9) where is the dimensionless wall distance.done away with this assumption and calculates the wall friction velocity from the y+ formulation. Still.. in the next phase. This is expected to be a more robust method of calculating the wall friction velocity as the y+ is calculated inherently in the FLUENT code based on the wall shear stress as is the universal method rather than being dependent on the particle velocity. Young's modulus and the temperature in El-Batsh model. Though the gas temperature was used to achieve the correlation. Using the E values obtained for each gas temperature. the capture velocity and subsequently.27 for the Poisson ratio of both particle and the surface based on experimental results. a correlation was developed by Ai & Fletcher (17) as follows: (4. The assumption was made that the particle sticking properties represent the target surface properties as well Richards et al. the capture efficiency decreases. the value of E was changed in the eq. (68) performed deposition experiments for a timeperiod that would build a monolayer on the surface. This 33 . The El-Batsh parameter is needed to calculate the capture velocity and this information is obtained from a correlation by fitting the experimental data.10) Soltani & Ahmadi (57) showed that as the Young‟s modulus increases. the majority of the particles interacting with the surface would be interacting with the monolayer and hence the assumption of same properties for the particle and the surface is valid. using the average temperature of the particle and the surface instead resulted in better agreement with the experimental results.4.2 until the capture efficiency matched that from the experiments. The El.. For every gas temperature. They found that the surface properties were not changing as the monolayer developed. This led to a correlation between the material property.Batsh parameter was calculated by assuming a constant value of 0. The experiments at BYU were run for a period of time long enough to let a monolayer to build on the surface and hence.dependence of material properties like Young's modulus and Poisson's ratio on temperature was required. correlation was used in the current deposition modeling initially before obtaining our own correlation to account for the change in the calculation of the wall friction velocity. „Capture efficiency‟ is defined as the ratio of the mass of the particles deposited on the surface to the total mass of particles entering the domain. It can also be defined as the product of the impact efficiency and the sticking efficiency. „Impact efficiency‟ is the ratio of the mass of the particles impacting the surface to the total mass of the particles entering the domain. „Sticking efficiency‟ is the ratio of the mass of the particles deposited on the surface to the mass of the particles impacting the surface. These 3 efficiencies are the most important parameters in the deposition calculations. 34 5. DEPOSITION MODEL DEVELOPMENT IN FLUENT 6.3.26 The previous section provided a detailed description of the Lagrangian particle tracking methodology and the particle deposition model to be used in this study. This section will deal with the programming and development of the deposition model and the integration of the model using User Defined Functions (UDF) in the commercial CFD software, FLUENT 6.3.26. The deposition model was programmed using the C language and is shown in appendix.1. User Defined Memory Locations (UDML) were used to store the deposition results in order to enable post-processing of the results and simulate images of deposition. The process of running the FLUENT DPM model with the deposition model is shown below: 1. Create the geometry and mesh in a pre-processor (GAMBIT for tetrahedral grids and GRIDPRO for hexahedral grids) 2. Load the mesh in FLUENT and solve the flow- field and heat transfer 3. Save the case and data file 4. Open the case file 5. Set the number of User Defined Memory Locations (UDML) using Define – User Defined – Memory 6. Initialize the flow field 7. Use Display – Contours to display the UDML on the wall surface where the deposition model is used as a boundary condition to initialize the UDML values to zero 35 8. Compile and load the UDF through Define – User Defined – Function – Compile option. The UDF should be in the same folder as the case and data files 9. Open the data file 10. Set User-defined memory locations through the Execute-on-demand function using Define – User Defined – Execute on Demand 11. Set up the DPM model using Define – Models – Discrete Phase. This panel enables setting up the parameters for steady particle tracking and also the injection parameters 12. Choose Stokes-Cunningham as the drag force parameter and set the value of the Cunningham Correction Factor to 1.2 13. Use the Physical Models tab and enable the „Saffman Lift Force‟ option 14. Use the „Injections‟ option in this panel to setup the particle injections. 15. Choose „inert‟ as the particle type for all simulations. Injection type can be either „group‟ or „surface‟ depending on the simulation 16. Set injection parameters like location, velocity, temperature, diameter, etc. Also, set the number of iterations for the stochastic particle tracking. 17. Use Define – Boundary conditions to select the wall on which the deposition model has to be applied. In the DPM tab in the Boundary Condition panel, choose user-defined as the boundary condition and select the UDF file (*.c) 18. Click Display – Particle tracks to display the particle tracks and run the deposition model A flow-chart detailing the process is shown in fig. 5.1 36 5.Fig.1: Deposition model flow chart 37 . The UDF was programmed using built.in macros in FLUENT for the DPM model. One major point to be noted in the current simulations is that the c hange in the geometry due to the deposition and its effect on the fluid flow and cooling effectiveness is not considered. The DEFINE_DPM_BC macro enables the user to specify a boundary condition that is different from the default boundary conditions for the particle-wall interaction. The EXECUTE_ON_DEMAND macro is used to execute any process at any time during the simulation. In this UDF. Still. 38 . this macro is used to set the user-defined memory locations in the data file. various methods to incorporate the changes in geometry and the subsequent changes in the flow field have been analyzed and a framework on this has been created for the next user. . The bare coupon has a thermal conductivity of 9 W/m. The initial experiments were conducted with a coupon made of Inconel. They obtained their Young‟s modulus correlation from simulations on a bare coupon without film cooling in a 2D domain. The backside of the coupon was insulated with ceramic material.K. resulting in nearly adiabatic conditions. The coupon was set at an angle of 45º to the flow field. The initial computational model was an extension of the BYU 2D simulations in a 3D domain.6) PARTICLE DEPOSITION ON A COUPON Ai et al. (17) used their deposition model on two different cases for a bare coupon. The computational domain in 3D space and the schematic and boundary conditions for the simulations are shown below: Fig. The results from these simulations and comparisons with the BYU model are detailed in this section. without and with film cooling. 6. The OSU model was validated against results from the experiments on the bare coupon without film cooling initially.1: Computational domain for the bare coupon simulation 39 . 2: Geometry and boundary conditions of the model in 2D view The high temperature circular gas jet has a diameter of 25. The coupon holder from the experiments is neglected since it does not affect the deposition and flow field to a large extent and also due to the ease of modeling and meshing the domain by neglecting the holder. The accuracy of the computational model and deposition model are strongly influenced by the quantity.260. 6. The geometry a nd mesh were generated using GAMBIT's unstructured tetrahedral topology grids consisting of tetrahedral cells. The y+ value of the mesh was between 15 & 40. The coupon is 25. Detailed sections of the mesh are shown below: 40 .Fig. in conjunction with the y+ of 12-300 used in the BYU model. cylindrical and has a thickness of 3.4 mm in diameter. The whole domain is a cylindrical section of 508 mm in diameter and height. the same as the equilibrium duct diameter in the experiments. quality and location of grids resolving the flow physics.184.4 mm. The coupon is placed at an angle of 45º to the mainstream gas flow as in the experiments. The total number of computational cells was 1.556 mm. 932 1352 1232 0. along with the coupon surface temperature.87 1425 1281 4.47 173. The fluid/carrier phase was solved using the Reynolds-Averaged Navier-Stokes (RANS) simulations governing the transport of the 41 . The table below gives the experimental conditions and the capture efficiency obtained from the experiments.517 1293 1191 0.1: Summary of experiments for the bare coupon case Inlet Velocity (m/s) Mass mean diameter (μm) Gas Temperature (K) Surface Temperature (K) Capture Efficiency (%) 1453 1311 7. Table 6.2) Carrier Phase Simulations The continuous phase flow field was solved first and then the discrete phase model was used to track the trajectory of the particles.4 1408 1374 1270 1234 2. All walls of the mainstream duct are considered as pressure outlets with a temperature of 300 K.0001 6. The walls of the inlet equilibrium duct were considered to be adiabatic. with gas density a function of the fluid temperature. The gas was modeled as incompressible air using the ideal gas law.938 0.Fig 6.3: Cut section of the mesh along X-plane 6. All other sides of the coupon were considered to be adiabatic.1) Boundary Conditions: The fluid enters through the velocity inlet at 173 m/s and at a gas temperature varying from 1293 K to 1453 K.0 13. simulating atmospheric conditions. The discretization of the energy equation is performed using the secondorder upwind scheme and the discretization of the k and ω equations in the k.K) k(W/m.averaged flow quantities. velocity (<10-6 ). The properties of the ash particle are given below: Table 6. The SIMPLE algorithm couples the pressure and velocity. In group injections.3) Particle Phase Simulations The simulations were performed with group injection in FLUENT. and turbulence quantities (<10-5 ).5 42 .ω turbulence model uses the first-order upwind scheme. (17) d(um) ρ(kg/m^3) Cp(J/kg. Convergence was determined by reduction of normalized residuals for each parameter as follows: continuity (< 10 -4 ). all previous modeling results by Ai & Fletcher were performed using group injection and hence it was carried out to validate the deposition model.4 990 984 0. 5000 ash particles were released at the center of the inlet surface and impinged on the target surface. energy (<10-7 ). Convergence monitors were set up at various points inside the domain to monitor the flow variables and full convergence was deemed to achieved only after the monitors of the flow variab les became steady. 6. The particles are in equilibrium with the gas phase at the inlet of the domain and hence had the same temperature and velocity as the carrier phase.K) 13.2: Ash particle properties from Ai et al.. Although this is not a fair representation of the particle distribution at the inlet. Pressure and Momentum equations are discretized by the PRESTO and QUICK scheme respectively. in μm 8 Fig: 6. 6.friction velocity and the results will shed light on whether the new model improves upon the capture efficiency prediction. The Runge Kutta method was used to integrate the particle equations. All simulations with group injections were run with a minimum of 10-20 tries in the stochastic model to obtain a better representation of each particle's behavior.5 and 6.4) Results Fig 6. This initial comparison was necessary to identify the shortcomings of the OSU model and to validate the model against well-established results before making improvements to the model. Impact Efficiency vs Particle Diameter at 1453K Impact Efficiency (%) 120 100 80 Impact % by OSU 60 Impact % by Ai et al 40 20 0 0 2 4 6 Particle diameter. The OSU model contained the new formulation of wall.6 show the comparison of the impact and capture efficiency from the OSU model with previous results from the BYU model and the experiments.4: Impact efficiency vs Particle Diameter at 1453 K 43 .Particle trajectories and temperatures were modeled on a particle-by-particle basis using the stochastic random-walk model as explained before. 6. Fig. One thing of note in the OSU model is that the capture efficiency does not agree well with the experiments at lower temperatures. On further analysis of the model.Capture Efficiency vs Gas Temperature 9 8 Capture Efficiency (%) 7 6 5 Experimental 4 OSU model 3 Ai et al 2 1 0 1250 1300 1350 1400 Gas Temperature (K) 1450 1500 Fig: 6.5: Capture Efficiency vs Gas Temperature The capture efficiency is based mainly on the impact & sticking efficiency. Fig. 6.4 um. This shows that the particle tracking methodology and parameters used in the OSU model work well since the trajectory of all particles have been calculated for calculating the impact efficiency and this value agreed well with the BYU results. it was decided that the different methodology for calculating the wall friction velocity is the cause for this. and this improved model was expected to give better results when we move on to cases with film cooling and vanes.4 shows that the OSU model shows extremely good agreement with the BYU model for impact efficiency at 1453 K. The newer wall friction velocity was supposed 44 . The OSU model agrees reasonably well with Ai et al.5 shows the comparison of capture efficiency with different gas temperatures for a mass mean diameter of 13. thereby reducing the capture efficiency. Wang et al.to provide improved predictions but is based solely on the y+ at the wall which in turn is dependent on the shear stress of the wall surface. The wall friction velocity in the OSU model is directly proportional to the dimensionless wall distance (y+) and inversely proportional to the distance of the center of the first cell away from the wall to the wall (y). possibly correcting for errors in the y+. The impact efficiency graph shows that 45 . proper modeling of the boundary layer is extremely important for accurate capture efficiency prediction. The 3D simulations throw light on the shortcomings of the previous model and on ways to improve the capture efficiency prediction. The k-ω turbulence model usually needs the mesh to be refined as close to the wall as possible with a y+ of around 1 giving better results than a higher y+ value (35). Dehbi (5) used a separate model to account for the dispersion of particles inside the boundary layer. A lower y+ would also mean a change in the value of y. This correlation will be revisited after the initial simulations to validate the model. Another area of concern is the Young‟s modulus correlation in the BYU model that was developed based on a 2D simulation of a 3D domain. Hence. Resolution of the mesh all the way to the wall will enable more accurate representation of the wall shear stress. The y+ value in these simulations was kept at 15-40 to be in conjunction with the y+ of 12-300 used in the simulations at BYU. A high value of y+ as used in the BYU model will not resolve the boundary layer sufficiently to track particle behavior inside this layer.. The higher capture efficiency shown by both the computational models can be attributed to not resolving the boundary layer completely to the wall. The 2D simulation cannot capture the exact flow field over the coupon as in a 3D simulation due to the circular nature of the coupon. (61) showed that the boundary layer usually acts as a barrier for particles to reach the wall. thus corroborating the results of Ai & Fletcher (17). thereby ensuring the changes to the model hold well for future cases with film cooling in a vane. The OSU model captures the trend expected from the experiments and further improvements will be made in the next simulations with film cooling holes. 46 . the lesser the impact efficiency. Similar calculations for capture efficiency of the model showed a trend similar to the one observed by Ai & Fletcher where the capture efficiency decreased with decreasing gas temperatures.the smaller the particle. 5 and the blowing ratios ranging from M=0. 3.0. 6. The results as mentioned above capture the various trends in deposition effectively and hence the model is validated as fit to be applied to the 3D case with conjugate heat transfer and film cooling. The computational 47 . Our modeling pertains to the single case of s/d=3. The computational domain is the same as the one used by Ai & Fletcher (17) and the simulation has been carried out with the exact same conditions as in their modeling. This has been done in the view that any areas of concern in the deposition model can be easily identified and rectified if the simulation is carried out in the same way as in (17).375 where d=1 mm with blowing ratios of M=0.6-A) CONJUGATE HEAT TRANSFER AND PARTICULATE DEPOSITION ON A COUPON WITH FILM COOLING The deposition model has been tested with previous test results from Ai & Fletcher (17) on a 2D geometry with no film cooling and no conjugate heat transfer. The blowing ratio (M) is defined as the ratio of the coolant velocity at the exit of the cooling holes (Uj) to the free-stream velocity (Uf). The experiments were carried out for various geometries with s/d being 3.375 and 4.6. The distance between the cooling holes is denoted by „s/d‟ with „s‟ being the actual distance between the holes given with reference to the hole diameter (d).5 to M=2.5.1A) Geometry & Grid Generation A schematic of the computational domain is given in figure 6. 2. 1.0 with each of these cases being modeled by Ai & Fletcher (17).0. the solid coupon is inclined at an angle of 45° to the mainstream flow and the cooling holes are at an angle of 30° to the solid coupon surface and this has been replicated in the domain geometry.domain includes a mainstream duct. 48 . The mainstream section is 81 mm in length. The row of 3 film cooling holes are located inclined at an angle of 30° to the plate surface and their centers are located 36 mm from the flat plate leading edge and 45 mm upstream of the mixture outlet. Fig: 6.6: Schematic of the 3D computational domain The cooling holes are 3 in number and are cylindrical in shape. The coolant plenum is 81 mm in length. The mainstream duct has a mixture outlet through which the mixture of gas and coolant flows. The flat plate has a thickness of 3 mm. 39 mm in width and 40. 39 mm in width and 36 mm in height.5 mm in height. In the actual experiments. the coolant plenum and the solid plate with film cooling holes completely occupying the area between the two ducts. The accuracy of the computational model and the deposition model depends on the quality and location on grids fine enough to resolve the flow physics in the areas of interest.5 mm while the coolant enters the plenum through an inlet of diameter 13. Keeping this in mind. 6.5 mm. The total number of computational cells was 746.9. a tetrahedral mesh using GAMBIT and a hexahedral mesh using GRIDPRO. The hexahedral mesh generated using GRIDPRO is shown in fig. 49 . the grid was created with fine cells near the coupon surface and the film cooling holes where there are reasonably large gradients of the flow variables.375 mm.7 and a close-up of the mesh on the plate is shown in fig.75 in FLUENT using polyhedral cells. The y+ was still maintained at 12-300 (tetrahedral mesh) as in the BYU model to gain more insight on how the y+ is affecting the deposition with the new wall friction calculation. Two different grids were generated for this geometry. The deposition model was run on both grids for better insight into whether any one type of mesh has an advantage over another for future cases. Skewness in the grid was kept to a maximum of 0.554 for the tetrahedral case.8. 6. The mainstream gas enters the duct through an inlet of diameter 25.The cooling holes diameter is 1 mm and the hole spacing is 3. The mesh generated was an unstructured tetrahedral mesh as shown in fig 6.86 while meshing and is later brought down to 0. 9: Surface mesh on the plate for 3D tetrahedral grid 50 .7: View of the tetrahedral volume mesh for the 3D case Fig. 6. 6.Fig.8: Cut-section view of the volume mesh for the 3D case for hex mesh Fig 6. The turbulence intensity is: (6. The initial simulations were made based on 51 . The mainstream gas enters the inlet at a temperature of 1453K and a velocity of 173 m/s. The hot and cold sides of the coupon were designated as a coupled boundary in FLUENT. The coolant inlet had a te mperature of 293K and a velocity of 0.6. The side walls of the coupon plate were set to be adiabatic.5 and M=2 were arrived at from the blowing ratio formulation using the free-stream velocity. The turbulence intensity at the mainstream inlet was specified as a value of 4.1) Since prior knowledge of the flow velocity at both inlets was available. A density ratio was chosen such that the entry conditions into the film cooling holes were satisfied. The coolant velocity for the other cases of M=0. The walls of the coolant plenum were set to be adiabatic.79e-05 kg/m-s. This eliminates the need to specify the heat flux or any other boundary conditions and this facilitates conjugate heat transfer between the solid and fluid domains.25% based on the flow conditions. A no-slip condition was applied to all the walls.592 m/s for the M=1 case which would give the desired conditions at the cooling holes entry. The temperatures on the top and side walls of the mainstream duct were specified as 900K while the temperature of the wall close to the inlet was 300K. The viscosity of the fluid was kept as a constant at 1. thereby making the heat flux to flow in only one direction inside the solid plate. The coolant inlet conditio ns were derived at from the blowing ratio and the velocity and the temperature expected at the entry to the film cooling holes. the turbulence intensity was easily calculated.2A) Boundary Conditions & Simulations The boundary conditions for the case were obtained from experimental values from Ai & Fletcher (17). These values were obtained from the experiments. the mesh was found to be too coarse to capture the flow physics effectively and the y+ values were adapted on the hot and cold side to around 1. The thermal conductivity of the solid plate was set to 9 W/m-K. Compressible flow simulations for gases with Mach numbers in the incompressible range are extremely difficult to converge and though the results of temperature and velocity field on the plate were in the vicinity of the previous experimental and modeling results. The surface temperature is the area-weighted average temperature on the plate's hot side over a circle of diameter one inch which is the diameter of the actual coupon used in the experiments. One factor contributing to this is the use of mass flow inlet in FLUENT which significantly takes longer to converge compared to velocity and pressure inlets. Low surface temperatures were observed near the cooling hole exits.000 iterations will be required for the case to converge fully. The residuals for continuity were less than 10e-4. The inlets were mentioned as Velocity Inlets and the outlet was a Pressure Outlet for the incompressible case. The density does not depend on the local relative pressure field. Also. The chosen case was initially run as a compressible flow using the ideal gas law for density as per Ai and Fletcher(17). This was found to bring the temperature down considerably. The incompressible ideal gas law calculates the density based only on the temperature. The Mach number at the gas inlet was 0. The deposition model will also take into account only those particles that are deposited within this circular area. the residuals for velocity was 10e-6.'Incompressible ideal gas law' in FLUENT for the density of air as stated in Ai & Fletcher (17). it was observed that more than 20. the residuals for energy were 10e-7 and the turbulence quantities had 52 .00172 at the coolant inlet. which is the standard y+ value region for the k-ω model.2263 and 0. 3A) Results The flow. Initial deposition simulations were performed on this mesh to determine the effect of the new wall friction velocity calculation on the efficiency.002 for a compressible solver is not suitable. the monitors of pressure.2) The velocity contours below show that at higher blowing ratios. Initially.000 iterations. The hexahedral mesh will be used with a new Young‟s modulus correlation obtained from the OSU model.10. The final deposition simulation has been performed on the flow-field solution from the incompressible solver.a residual of 10e-5. 6. Although the residuals indicated convergence. These are the results from the tetrahedral mesh with y+ of 1540. (6. temperature and velocity at various points inside the domain did not converge. the flow still did not achieve complete convergence and correspondence with the FLUENT support center also reiterated the theory that mass flow inlets for this case will take longer to converge. The formulae for calculating the wall friction velocity depending on the non-dimensionless distance away from the wall is: . A compressible solver may be used if combined with a pre-conditioner for low Mach number flows. the velocity of the coolant coming out of the cooling holes is higher. we were not able to achieve agreement with experimental data for the average surface temperature on the two sides of the plate using compressible flow solver.field results and the surface temperature profiles for all 3 blowing ratios are shown below in fig. Even after 20. This led to the conclusion that incompressible analysis is needed because the cold side flow has a Mach number of 0. thereby pushing more part icles away 53 . 6. These findings have already been reporter by Ai & Fletcher (17). resulting in lesser capture velocity. giving low capture efficiency. more particles have normal velocity greater than the capture velocity and hence do not stick to the surface. This is shown in fig 6. 4.3 where the capture efficiency is lower as the blowing ratio increases. As a result.from the wall resulting in lesser deposition.5 M=1 M=2 Fig.5. M=0.10. 6. 2 along centerline plane 54 .10 Velocity magnitude contours (m/s) for M=0. 1. the presence of more coolant reduces the surface temperature which in turn increases the particle Young‟s modulus (Ep ) as per eq. Also. 11 shows the surface temperature contours for all three blowing ratios.Fig 6. rather a circular area of diameter one inch similar to the coupon in the experiments. The area of interest is not the entire rectangular plate. Flow Direction is from left to right 55 .5 case. The images show the higher surface temperature for the M=0.11: Surface temperature contours at different blowing ratios on 1 inch diameter coupon.5 M=1 M=2 Fig. 6. M=0. thereby resulting in higher capture efficiency. A much more representative injection type is the „surface injection‟ option. All simulations shown in this section have been carried out with the same Young‟s modulus correlation as obtained at BYU. Fig 6. M Fig 6.5 2 2.5 1 1. where a particle is injected from the center of every face in the surface mesh at the inlet.13 show the comparison of the front-side surface averaged temperature and the capture efficiency obtained with the experimental results and the results of Ai & Fletcher (17).12 and 6.12: Comparison of area-averaged surface temperature on coupon at 1453 K 56 . Front side surface Temperature vs Blowing Ratio at 1453K Front-side surface Temperature (K) 1360 1340 1320 1300 1280 Experimental 1260 OSU model 1240 Ai et al 1220 1200 1180 0 0. This has been done so as to compare the deposition results with the new wall friction velocity calculation with those of Ai & Fletcher (17) who used a similar injection. the non-dimensionless wall distance (y+) on the capture efficiency prediction. These results will give an indication of any potential changes that need to be incorporated in the model.5 Blowing Ratio.The initial deposition simulations have been carried out with „group injection‟ where 5000 particles are injected from the center of the hot gas inlet. most particularly revisiting the Young‟s modulus correlation and the effect of wall shear stress and in turn. resulting in a higher capture efficiency. the OSU model exhibits a higher hot-side surface temperature.5 Blowing Ratio (M) Fig 6. At M=1. These results show that modeling the conjugate heat transfer properly plays an important role in the prediction of 57 . At M=2. Particle capture velocity and capture efficiency are directly proportional to the hot-side surface temperature of the coupon. This has a direct correlation to the higher capture efficiency obtained at this blowing ratio in the next figure. the OSU model had a closer agreement with the experimental hot-side surface temperature than the BYU model which is reflected in the better agreement with the capture efficiency.12 shows that the front-side surface temperature from both simulations shows a reasonable agreement with the experimental surface temperature. A higher hot-side surface temperature at M=0.5 2 2. The change in calculation of the wall friction velocity also played a part in the improvement prediction of the capture efficiency at M=1.13: Comparison of capture efficiency vs blowing ratio at 1453 K Fig 6.5 1 1.5 is seen in both OSU and BYU models.Capture % vs Blowing Ratio at 1453 K 7 Capture Efficiency (%) 6 5 4 Experimental 3 OSU model Ai et al 2 1 0 0 0. prominent boundary layers are absent near the wall which is a potential cause of more particles reaching and sticking to the surface. 6. As observed. thereby reducing the chances of particles sticking to the surface. It has been shown in literature that boundary layers act as a deterrent to the particles reaching the wall surface.15 shows the near wall velocity vectors with a y+ value of 12-300 in the OSU model. This directly affects the surface temperature on the plate and also the particle transport near the wall. These images were obtained from the OSU deposition model using the same group injection conditions as 58 . The increased value of surface temperature predicted could be a result of not enough mesh resolution near the wall resulting in fluid flow field not being resolved properly.capture efficiency. The figure 6. Fig.14: Velocity vectors along the centerline plane for M=1 The images of the deposition patterns on the plate at different blowing ratios provide interesting insight into the effects of film cooling on deposition. 5 results in lower velocities coming out of the cooling holes. This results in more particles having lesser normal velocities than capture velocity leading to more sticking.used by Ai et al. Although the images give rise to this conclusion. the following images can be used as a validation of the model as they show almost no deposition in the flowpath right ahead of the cooling holes. The particle normal velocity near the walls is closer to the fluid velocity and the lower values of fluid velocity reduce the particle normal velocity. The images show that deposition is concentrated around the cooling hole in the middle and there is no deposition near or in the flow path of coolant from the cooling holes at the end. Still.5 compared to M=2 as seen in the experiments. it should be noted that the injection type was group injection with all particles released from the center of the inlet. Deposition patterns from surface injection will be obtained for these cases too which will provide better comparison with the actual experimental deposition patterns obtained at BYU due to surface injection being more representative of experimental conditions. 59 . The experiments had uniform distribution of particles throughout the entire inlet area rather than injection from the center and hence the patterns obtained would show deposition all over the one inch diameter coupon. The images also sho w the higher capture efficiency at M=0. This is also seen in the experimental images where deposition is extremely low in the flowpath right ahead of the cooling holes. The deposition is mainly concentrated near the outer edges of the coupon. This is a fair assumption for obtaining capture efficiency but cannot be used to compare the deposition patterns with images from experiments. The low blowing ratio at M=0. Total Impact Sticking Not Sticking Fig 6.15: Deposition patterns from the model for M=2 Total Impact Sticking Not Sticking Fig 6.5 Total Impact Sticking Fig 6.0 60 Not Sticking .16: Deposition patterns for the model for M=0.17: Deposition patterns for the model for M=1. 19: Comparison of deposition from experiments & simulation for M=2 The above images show the comparison of the simulation pattern developed from the OSU model with the actual deposition images from the experiments. the deposits in the film cooling hole downstream is almost negligible compared to the total amount deposited which is the main observation from the experimental images.18: Comparison of deposition from experimental & simulation for M=0. Still.5 Fig 6. The 61 .Fig 6. The deposition simulation for M=2. These images do not show the deposition but a representation of the number of particles deposited at each location.0 predicted a higher capture efficiency than in the experiments and hence there are more deposits around the edges. 62 . In the next phase of the research.accumulated number of particles at each face location on the surface is shown as the value of the cell to which the face belongs to. generation of images with realistic deposition heights will be handled. This vane was chosen as there are well documented experimental results obtained at the Von Karman Institute (VKI) for flow field measurements.5 Throat. The velocity values used in these experiments satisfied the requirements of modern day gas turbines.02. (mm) : 14. The surface velocity and the downstream total pressure distribution are known from the experiments. The model will be applied for 2 Mach numbers. Experimental results were not available but since the deposition model was already validated for various cases and agreed well with experimental data.7. APPLICATION TO VKI BLADE El-Batsh et al. All previous validation of the OSU model ha s been against experimental data from coupons made of turbine material and it is essential to test the model‟s performance on an actual turbine vane.65 Pitch. Validation on this 2D vane is essential before moving onto a 3D vane with film cooling. a simulation on this vane with similar boundary conditions as expected in actual vanes would provide insight into how deposition works on vanes.93 63 .85 and M=1. (mm): 67. The vane geometry and the mesh are given below: Chord Length. namely M=0. (mm) : 57. (16) used their deposition model on a VKI transonic turbine inlet guide vane. The mesh at OSU was generated with time constraints in mind and hence is much coarser than the mesh used by El-Batsh. the mesh generated was deemed to be suitable enough to accurately represent the trend of the sticking efficiency with particle diameter as noticed 64 . Also. pbns .fitted mesh was generated to better resolve the boundary layer properties along the surface of the vane. The passage behind the vane is crucial due to larger pressure distribution variations and so is the leading edge of the vane. There are not enough cells in the region near the leading edge of the blade and also in the aft region of the trailing edge where the flow leaves the vane. 2009 FLUENT 6.Fig 7.1: Computational grid used for the VKI blade Grid Oct 19. A body. enough mesh cells are not available in the blade suction surface to account for the difference in length between the pressure and suction surfaces. El-Batsh (17) used a structured body.fitted 2D hexahedral grid to accurately resolve the pressure distribution behind the vane.3 (2d. rngke) A hexahedral mesh was created in a 2D domain with 5168 cells. The mesh at OSU was generated using GRIDPRO by breaking up the domain into multiple regions of interest. thereby preserving the fineness of the mesh in the important areas of the flow field. Even with these considerations in mind. 7. The k-ε turbulence model was used with enhanced wall treatment.by El-Batsh et al (17). The turbulence length scale was set using l=0.07L where L is the characteristic length and was set to be the blade pitch. it would be futile to spend time on matching his exact flow field conditions and wiser to concentrate simply on validating whether the deposition model follows the trend for deposition on a turbine vane. Fig 3.1) Boundary Conditions The inlet and exit boundary conditions were specified using a Pressure Inlet and Exit boundary condition in FLUENT.02 and the flow was solved using the compressible solver in FLUENT. The inlet Mach number was set to 0.1 lists the boundary conditions used.2: Computational domain and Internal Region The total pressure was used at the inlet and the static pressure was used at the exit.85 and then to 1. Fig 7.2 shows the schematic of the computational domain and table 3. Since the exact injection properties used by El-Batsh are not known. The total pressure was calculated from the following relation using the standard air properties: 65 . 1: Boundary Conditions for the VKI Blade Mach Number Total Inlet Pressure.85 1.1) Table 7. [Pa] 89600 82300 Wall Temperature. [K] 1273 1273 Incidence Angle. Fig 7.02 147500 159600 Total Inlet Temperature. [deg] 0.2) Simulations and Results The pressure-velocity coupling was performed using the SIMPLE discretization scheme.3: Mach number contours for M=0. [Pa] 0. [mm] 4 4 Static Outlet Pressure.0 7.85 by OSU 66 . [K] 420 420 Freestream Turbulence [%] 1 1 Turbulence Characteristic Length.0 0. The flow-field results for the two Mach number cases are shown below.(7. The Quadratic Upwind Interpolation (QUICK) scheme was used as the discretization scheme to provide higher order accuracy. 4: Mach number contours for M=1.02 by El-Batsh 67 .6: Mach number contours for M=1.02 by OSU Fig 7.5: Mach number contours for M=0.85 by El-Batsh Fig 7.Fig 7. 1 & 10 μm with surface injectio n at M=0. The pressure side distributions are very smooth with smooth transition in the Mach numbers too. The figures below show the particle trajectories for 3 different particle diameters of 0. specially the stator vane. The Mach number distribution from OSU simulations on the suction side.The Mach number contours show the pressure distribution expected in a vane passage. Hamed et al. the OSU simulations not showing accurate Mach number as in the simulations by El-Batsh. Still.85 68 . These simulations also give valuable information on particle tracking and modeling the particlewall interaction in the flow-field of a turbine. especially from the region between the mid-chord and the trailing edge differ from the results from El-Batsh in that the shock observed is less prominent in the OSU simulations. (62) performed erosion simulations on a GE E3 first stage LP turbine with similar conditions for particle sticking. Their simulations provide insight into the particle trajectory behavior in a turbine. These differences can be attributed to not enough mesh resolution in these passages in the mesh generated at OSU. Also to be noted is the flow leaving the trailing edge. the variations are not considerable enough to affect the particle trajectories to a great extent.1. Fig. 7. 7.1μm Fig.8: Particle trajectories through the passage for d p = 1μm 69 .7: Particle trajectories through the passage for d p = 0. 8 shows similar pathline results for the 1μm diameter particles. The smaller particles tend to follow the carrier phase flow since the effects of inertia are less prominent. Particles that stick to the wall and are sheared away by the friction forces are still influenced greatly by the flow field and are „carried away‟ by the fluid flow in its path. 7.Fig. This explains the lower impact efficiency but higher sticking efficiency at low particle diameters. The impact on the pressure side is similar 70 . 7. This gives a greater chance of their normal velocity being lesser than the capture velocity and hence sticking to the wall.7 shows the particle pathlines at a particle diameter of 0. The particles that do tend to impact the surface have very low normal velocities. The image shows that the particles move very close to the wall and hence a lesser chance of impacting the wall as they are almost parallel to the wall. This affirms the notion that smaller particles tend to impact the wall less than the larger particles and also tend to have greater capture efficiency. 7.9: Particle trajectories through the passage for d p = 10 μm Fig.1 μm. Fig. 85 71 .to the earlier case but the number of impacts on the suction surface is considerably lesser. In this case. leading to more chance of the normal velocity being greater than the capture velocity resulting in greater number of particles not sticking to the surface. Most of the impacts on the suction surface are caused by the particles reflected from the pressure surface of the neighboring blade in the passage. Sticking Efficiency vs Particle Diameter at Wall Temperature of 1273K 1 Sticking Efficiency (%) -2 0 2 4 6 8 10 12 0.1 OSU model El-Batsh model 0.10: Sticking Efficiency vs Particle Diameter at M=0. resulting in trajectories completely different from the fluid flow path.01 0. Fig. This in turn causes greater normal velocities. 7.9 shows an even more prominent behavior of the particle trajectory based on the particle size.001 Particle Diameter (μm) Fig 7. Larger particles tend to almost centrifuge after impacts and also are prone to more impacts due to a change of angle from the fluid flow and reach the wall surface almost perpendicular to it. the particles deviate away from the suction surface very early and hence are moving away from the suction side of the next blade. The 10μm particles are inertia-dominated and hence are not greatly influenced by the flow field. leading to more impacts. All this leads to the lesser sticking efficiency usually noted at large diameters. Batsh simulations show a much more prominent shock than the OSU simulations.. the sticking efficiency is so low in both the models that the number of particles sticking might be anywhere 72 . Three particle diameters were considered for this case – d=0. There is no experimental data for these cases to compare with and the wall friction velocity calculation used by El.The above graph shows the comparison of the particle sticking efficiency predicted from the OSU model in comparison with El. Hence. The Young‟s modulus was assumed as per the following correlation: Ep = 120 (1589 – Tp )3 (7.Batsh are accurate values for these cases considering the lack of experimental data to support these predictions. 1 and 10 µm. The Young‟s modulus correlation was changed according to the material used by El-Batsh but the correlation was still dependent on the gas temperature. at 10μm.Batsh is not known. Also. (10). The thermal conductivity of the ash particle used by El-Batsh was unknown and was considered to be the same as the one used in the previous simulations. The sticking efficiencies calculated by the OSU model are not the same as El-Batsh at higher diameters.Batsh et al.2) The trend of the sticking efficiency decreasing with increasing diameter as seen by ElBatsh is reflected by the OSU model. The mach number contours show that El. The particle velocity and temperature at injection were considered to be the same as the gas properties at the inlet. The particle density was considered to be 1700 kg/m3 based on the experimental results of Ahluwalia et al. the values obtained from the OSU model cannot be dismissed altogether. The specific heat of ash from the corresponding experiments was found to be 710 J/KgK.1. There is no proof that the sticking efficiencies calculated by El. Samples of 4100 particles were injected with a uniform distribution over the blade pitch. Also. the deposition model matches the trend and this is a desirable result and a validation checkpoint before moving onto the OSU turbine vane simulations with film cooling.7-1. Still.8 for 1μm for wall temperature of 1476K which is in the range predicted by BYU model. these results for the VKI vane are considered enough for validation. the deposition model will be similarly validated for the GE-E3 vane in a 3D domain and with the time constraints in mind. 73 .between one and five particles out of a total of 4100. The DPM results from FLUENT cannot be expected to accurately predict the exact number of particles sticking due to the various assumptions that go into the deposition model and the calculation of model parameters by different methods in different models. the simulations from the BYU model predict a sticking efficiency of between 0. The OSU model shows a sticking efficiency of 0.0 for temperatures in the range of 1400 K for a particle diameter of 1μm for simulations on a bare coupon. Incidentally. All BYU simulations were performed on computational grids with y+ of 12-300 and the k-ω turbulence model.field is achieved.258 cells in the 2-D domain. The mesh was generated with 165. IMPROVEMENTS TO THE DEPOSITION SIMULATIONS In this section.. in turn. requires the y+ value to be less than 1 to achieve a fine mesh near the wall surface of interest. the k-ω turbulence model usually requires the mesh to be resolved all the way up to the wall. Ai & Fletcher (17) developed their Young‟s modulus correlation based on the older method of calculating the wall friction velocity and also on a mesh with a y+ of 12-300. This. A hexahedral boundary layer was fitted to the 74 . A 2-D mesh for the same geometry as in the 3-D simulations on the bare coupon in Section. Also.field results for obtaining the new correlation are obtained from a finely resolved near-wall mesh. as shown by Wang et al. One of the major changes from the BYU model is the change in the ca lculation of wall friction velocity from being based on the particle velocity to being based on the non-dimensionless distance to the wall (y+) and in turn. A better resolution of the flow.8. ensuring the flow. Further. especially of the viscous boundary layer near the wall with a finer mesh. the shear stress at the wall. a description of changes and improvements to the deposition simulations is given. (61) boundary layers ensure lesser number of particles reach the surface which is an actual phenomena occurring in the experimental cases.6 was generated with enough near-wall resolution to give a y+<5 which is the acceptable region for the k-ω turbulence model used in these simulations. Although this y+ lies outside the viscous sub-layer zone. It was deemed fit to arrive at a newer correlation using the OSU model. Instead. the OSU deposition model was applied to all 6 temperatures as in the earlier case. the value of the Young‟s modulus was iterated with the OSU model until 75 .field simulation conditions were the same as in the bare coupon case. 8. Fig.2: View of the tetrahedral mesh for the computational domain Once the flow-field solution was obtained. The BYU Young‟s modulus correlation was not used here. All boundary conditions and flow.1: Close up view of the boundary layer on the coupon Fig.coupon wall and the remaining areas of the domain were meshed with tetrahedral cells. 8. the model gave the exact capture efficiency as in the experiments. The OSU model was tested with the new Young‟s modulus correlation on the flow.3. this new correlation is expected to give better deposition prediction for the case of turbine vane with film cooling.1) where Tavg is the average of the temperature between the gas and the surface. except the turbulence model. 9. Thus. Hence. All simulations on the vane with film cooling in the next stage will be performed on a hexahedral mesh created in GRIDPRO with enough mesh resolution to give a y+ < 5. The hexahedral mesh shown in Section 3 for the coupon with film cooling holes was generated in GRIDPRO and has a y+ of less than 1. 76 . 6 different Young‟s modulus values were obtained for every gas temperature and these results were used to come up with a new correlation based on the improved wall friction velocity prediction and a better resolution of the flow field. The results are shown below in fig. This newer correlation was obtained from a very finely resolved mesh with clear boundary layers and hence is better applicable to solutions with y+ < 5. the OSU model with Ai & Fletcher‟s correlation and the experimental results. The new Young‟s modulus correlation is given below: (8. The SST k-ω turbulence model was used instead of the Standard model due to convergence issues. The capture efficiency predictions from the new correlation are compared against the results from the BYU model.field results from the hexahedral mesh. All simulation conditions are the same as in the earlier case. 3: Comparison of capture efficiency from new correlation with earlier results The deposition prediction has improved at blowing ratios M=1 and 2 with the new correlation and the hexahedral mesh.5 is still not agreeable with the experimental results.5 1 1.5 2 2. 9. 77 .Capture % vs Blowing Ratio at 1453 K 7 6 Capture Efficiency (%) 5 4 Experimental OSU model 3 Ai et al OSU with new correlation 2 1 0 0 0. the new correlation is expected to be an improvement and is considered a better fit for future simulations with very fine near-wall mesh resolution. Still. This is due to the fact that the surface temperature on the hot side (1340 K) is still not the same as the one from the experiments (1270 K).5 Blowing Ratio (M) Fig. The capture efficiency at M=0. A tetrahedral and a hexahedral mesh were created for the 3D simulations of the bare coupon with film cooling. The model was developed in FLUENT using User-Defined Functions (UDF) and was programmed using the C language.26.3.9) CONCLUSION & RECOMMENDATIONS A deposition model was developed and validated to be used for deposition simulations on a turbine vane with film cooling using the commercial CFD software. Simulations on the tetrahedral mesh predicted higher capture 78 . The capture efficiency compared well at high temperatures but did not agree well at lower temperatures similar to the BYU model. particle sticking and particle detachment. The deposition model consisted of particle tracking.. Initial simulations were run on the 2D computational domain with just the bare coupon and results showed good agreement for impact efficiency and particle tracking with experimental results and the BYU model. The OSU model included a different method of calculating the wall friction velocity that is used in the detachment model. Special User-Defined Memory (UDM) locations were used to facilitate post-processing of the deposition results and also to obtain deposition patterns on the vane in future. FLUENT 6. (16) and also the BYU model (17). The model was based on the deposition model developed by El Batsh et al. The y+ and in turn the wall shear stress were utilized to calculate the wall friction velocity which should give more accurate representation of detachment than the BYU model that was based on the particle velocity. The model utilized the UDF macros in FLUENT to built a tailor-made boundary condition for the wall surface where the particles impact. Another cause for the over-prediction was the use of k-ω turbulence model as used in the BYU model with y+ ranging from 15-40. Despite the many changes from the El-batsh model. These results were later re visited with the hexahedral mesh with a y+ of less than 1. No previous deposition results are available for this vane and hence this case was used to validate the results from the VKI blade for a vane in 3D domain. 1 & 10µm) were used in this case and the simulations showed that the smaller particles tend to follow the flow. Validation of the model was performed by simulating deposition on the VKI blade as done by El-batsh et al.. Particle trajectory images showed similar results as in the VKI blade for different diameters and impact efficiency increased as the particle diameter increased as shown by Ai & Fletcher (17). The surface temperature prediction at M=0. The final case was the simulation of deposition on GE E3 vane.field and the larger particles tend to maintain their injection trajectory due to greater Stokes number & greater drag force that reduces lift-off with the flow.5 & 2 was higher in the model which was a cause of the over-prediction. The k-ω model needs the mesh to be refined all the way to the wall.5 & M=2 than experimental results but agreed well at M=1. (16).efficiencies at M=0.1. the OSU model still showed considerable agreement with the sticking efficiencies predicted by El-batsh et al. Three different particle diameters (0. 79 . The areas of concern in the model were identified in this phase and refinement of the grid all the way to the wall was established as a criterion for better prediction in future.. The post-processing capability in the UDF delivered good images of the deposition pattern on the coupon and also will be useful for build-up of deposition in the simulations in future. (16). 5 was still higher which indicated that other factors like surface temperature.field of particle size could also be a major factor for deposition. Tafti (63) used a model based on critical viscosity to predict the particle deposition.field and particle tracking. Further investigation needs to be done to identify ways to implement this and also to incorporate the effect of deposition build-up on the flow. 3. The gas viscosity in the current model is set to a constant value but future simulations should look into modeling the viscosity accurately as a function of temperature. The tools and data collection mechanisms are in place to develop patterns of fouling on the blade due to deposition. The newer correlation and the changes in the model led to better prediction of capture efficiency at M=1 & M=2 compared to the BYU model. flow.A new correlation for the Young‟s modulus was developed since the OSU model differed from the BYU model in some aspects and this correlation was used for simulations on the hexahedral mesh with y+ less than 1 for the coupon with film cooling. Although the model improved prediction of capture efficiency & captured the trends expected in particle depositions effectively for different cases. Capture efficiency at M=0. The OSU model is validated and ready to be applied to simulations of deposition on turbine vane with film cooling which will be done in the next phase of the research. Analysis of this model and identifying the changes in prediction brought about by using the critical viscosity will provide good insight into the characteristics of the OSU model. 80 . 2. there is scope for improvement in the model and some of the recommendations are given below: 1. 81 . 7. Conjugate Heat Transfer plays an important role in the capture efficiency prediction and enough care should be taken to accurately solve the flow. 5. Mesh should be refined all the way to the wall to better capture the boundary layer as this plays an important role in the transport of particles to the wall surface. Particle tracking in a hexahedral domain with lower number of cells used more computational time than a similar tetrahedral domain with more cells and this should be investigated to determine whether this was an isolated incident. The deposition patterns developed currently in the simulations shows the exact locations of the deposition but not the accurate height of deposition and the changes in the flow field due to deposition build up.field and heat transfer before applying the deposition model as this could save valuable time.4. 6. Using the particle path file with software like MATLAB to simulate this height should be studied. Journal of Engineering for Power. pp... (1982). and Tanaka. 2005.” ASHRAE Transactions. E. Zhang... 104. Li. part 1. and Huang. Vol. X.” Building and Environment. “Comparison of diffusion characteristics of aerosol particles in different ventilated rooms by numerical method. pp. 5) Dehbi. Transaction of ASME. Kato. 2004. 4) Menguturk. 429-435. M. pp.109. B. 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Thole. f.h" #include "sg.15 #define NUM_UDM 6 /* No. of user-defined memory locations8/ real ParticleTotalMass.dim) 90 . real P_Stick_Mass[6].27 /*Poisson ratio of the particle*/ #define VISC 1.APPENDIX /*DEPOSITION MODEL UDF AUTHOR: PRASHANTH S. SHANKARA */ #include "udf. real P_Impact_Mass[6].27 /*Poisson ratio of the surface*/ #define nu_p 0. Domain *domain.h" #define nu_s 0.f_normal.7894e-05 /*Viscosity*/ /*#define RGAS (UNIVERSAL_GAS_CONSTANT/MW)*/ #define Tdatum 288. real P_Mass[6].t.h" #include "mem.h" #include "dpm.p. *Get domain pointer and assign later to domain*/ /* Boundary condition macro for the deposition model*/ DEFINE_DPM_BC(udfdeposition8. ufr. 91 .Ep. real Cu.4.utc..lamda.ds.*/ cell_t c=P_CELL(p). */ /*Thread *tcell=RP_THREAD(&p->cCell).wvel..calc. FILE *fp.Tavg. real normal[3]. real tan_coeff=0.8..A_by_es. int i.wallfricv4=0.es[ND_ND]..dr0[ND_ND]..du=0.wallfricv3=0.. real tem_Mass=0. real tem_Particle_Dia=0.ucws.val.dudz. utc1. real yplus.tauwall3=0.{ #if !RP_HOST /* Used only for 3D cases*/ real crit_vel...del.wallfricv1=0.kn.area.vcr=0. real utau2.kc.. real A[ND_ND].h. /* Exact thread location of particle*/ /*cell_t c=RP_CELL(&p->cCell).dumag=0.wall_shear_stress.MassImpact. real tauwall1=0...ff.E...cbar. real vn=0...wallfricv2=0.alpha. real nor_coeff=0.utaunew.ivu=0...tauwall2=0.uvel.wallfricv5=0.Es.* Thread *tcell=P_CELL_THREAD(p).utau1.wall_shear_force.vvel.k2.k1..jvv=0. /* Exact cell location of particle*/ Domain *d.idim=dim.kvw=0. real R=287.utau.vpabs=0.. real Wa = 0. C_UDMI(c. for (i=0. real x[ND_ND].V[i]*normal[i]. i<idim. d=Get_Domain(1).039. i++) normal[i] = f_normal[i].Tavg). /*computing critical velocity*/ Tavg = (F_T(f. } vpabs = pow(vpabs.tcell))/2..5). if(p->type==DPM_TYPE_INERT) /* Checks if inert particle is used*/ { /*computing normal velocity*/ for(i=0.*/ 92 .i<idim.V[i].t)+C_T(c..2.*/ /*Message("particle temp is %g\n". /*Message("Avg temp is %g\n".).0.P_T(p))...tcell.i++) { vn += p->state.0) += 1. vpabs += pow(p->state. *3.*lamda)/P_DIAM(p).*/ MassImpact=P_FLOW_RATE(p)*pow(10.2+(0.+kn*(1.vcr).tcell)*C_T(c.-(nu_s*nu_s))/(3.41*exp(-0.tcell))/(C_R(c. k2 = (1.*E)/P_DIAM(p)).. /*Message("particle density is %g\n".)))*exp(-0. kn = (2.51*(pow(calc. /*Cunningham Correction Factor*/ Tavg = (F_T(f. cbar = sqrt(((8..*/ /*Message("normal face temp is %g\n". /* Knudsen number*/ Cu = 1.*/ /*Message("Ai particle density is %g\n".F_T(f. /*Message("capture velocity is %g\n".(10.02365*Tavg).tcell)*cbar).p->init_state.rho).*(pow(P_RHO(p).1.88/kn)))./5. /*Message("Young's mod is %g\n". /*Avg of particle & surface temperature*/ 93 .5))).*/ /*NEW CORRELATION*/ Ep=(3. E = 0. C_UDMI(c. Es=Ep.14)).*/ k1 = (1.14*Ep).))).9).tcell))/3.)).20.14*Es).Ep). lamda = (2.*C_RGAS(c.t)).*C_MU_EFF(c.tcell))/2.tcell)).t)+C_T(c.1)+=MassImpact.F_T(f.*(pow(10.tcell.-(nu_p*nu_p))/(3.14*(k1+k2))/(4.Batsh parameter*/ vcr = pow(((2./7.P_RHO(p)).(2./*Message("face temp from tcell is %g\n".14*3. /* El.*/ calc = (5. utc). kc = (4. jvv=C_V(c.tcell)*P_DIAM(p)))*(pow((Wa/(P_DIAM(p)*kc)). kvw=C_W(c. utc = sqrt(ucws).*/ yplus=F_STORAGE_R(f.*/ utc1=pow(ucws. 94 .t.2.2.tcell)*normal[2].SV_WALL_YPLUS_UTAU). /*Calculating critical wall shear velocity*/ ucws = ((Cu*Wa)/(C_R(c.tcell)*normal[0].)))/Ep)./3. /* Message("wall shear vel is %g\n".tcell).0.)/val.))).tcell)*normal[1]./*Calculating El-Batsh parameter*/ val = ((1. /*Alternate Method 2*/ ivu=C_U(c.-(pow(nu_s.*/ /*utau1 = sqrt((VISC*dudz)/C_R(c.tcell)).utau1).*/ /*Message("Friction vel by regular formula is %g\n".(1. /*Calculating wall friction velocity*/ /* Alternate Method 1*/ /*dudz = C_DUDZ(c./3.5).-(pow(nu_p.)))/Es)+((1. t. wallfricv1=sqrt(tauwall1/C_R(c.*/ if (yplus<11. wallfricv2=sqrt(tauwall2/C_R(c. /* Message("wall distance is %g\n".*/ tauwall1=C_MU_EFF(c.41)*log(yplus*9.tcell))+C_DUDZ(c.ds).du =ivu+jvv.wallfricv2). } /* Message("wallfrictionvelocity 2 is %g\n".tcell)+C_DUDX(c. Thread *t0=THREAD_T0(t).tcell)*(du/ds).dr0). /* Message("wallfrictionvelocity 1 is %g\n".tcell)*C_STRAIN_RATE_MAG(c.tcell).es. BOUNDARY_FACE_GEOMETRY(f.tcell)*(C_DUDX(c.A.tc ell))+C_DUDY(c. cell_t c0=F_C0(f.tcell))./0.t).ds.tcell)).tcell)*(C_DUDY(c.wallfricv1).).tcell)+C_DVDX(c.25) { tauwall2=C_MU_EFF(c.A_by_es.*/ /* Alternate Method 3*/ tauwall3=C_MU_EFF(c.tcell)*sqrt(C_DUDX(c.tcell)*(C_D 95 . } else { wallfricv2 = (1. /* Message("wallfrictionvelocity 5 is %g\n".tcell)*ds)).tcell)+C_DUDY(c.tcell)*dumag)/(C_R(c. vvel=C_V(c0.tcell)+C_DWDZ(c.tcell)*ds)).*/ ds=C_WALL_DIST(c.tcell))+C_DVDZ(c.tcell)*(C_DVDX(c.tcell).tcell)+C_DVDY(c.t0).tcell)).tcell)*(C_DV DZ(c.tcell)+C_DVDZ(c.tcell)+C_DWDY(c.tcell)+C_DWDX(c.tcell)).tcell)+C_DUDZ(c.tcell))+C_DWDX(c. /*ACTUAL WALL FRICTION VELOCITY CALCULATION*/ /* Message("wall yplus is %g\n".tcell)*(C_DVDY(c. wallfricv4=(VISC*yplus)/(ds*C_R(c.t0). if(yplus>10) wallfricv5=sqrt((C_MU_EFF(c. wallfricv3=sqrt(tauwall3/C_R(c.UDZ(c.tcel l))+C_DWDY(c.tcell)*(C_DWDY(c.tcell)*(C_D WDZ(c.tcell))).t0).*/ 96 . dumag=sqrt((uvel*uvel)+(vvel*vvel)). wvel=C_W(c0.tcell))+C_DVDX(c.wallfricv5).tcell)*(C_DWDX(c.yplus). else wallfricv5=sqrt((VISC*dumag)/(C_R(c. /* Alternate Method 5*/ uvel=C_U(c0.tcell))+C_DWDZ(c.tce ll))+C_DVDY(c. Ep.utaunew). . tem_Particle_Dia=P_DIAM(p)*pow(10. else if(tem_Particle_Dia>5 && tem_Particle_Dia<7) P_Impact_Mass[3]+=P_FLOW_RATE(p)*pow(10.ucws.MassImpact.9)."a"). 97 %f\n".6). fprintf(fp. else if(tem_Particle_Dia>1 && tem_Particle_Dia<3) P_Impact_Mass[1]+=P_FLOW_RATE(p)*pow(10.9).tcell. if(tem_Particle_Dia<1) P_Impact_Mass[0]+=P_FLOW_RATE(p)*pow(10.9).vcr.3) += P_FLOW_RATE(p)*pow(10. else P_Impact_Mass[5]+=P_FLOW_RATE(p)*pow(10.vn.2f %f %f %f P_DIAM(p).2) += 1.3f %6. else if(tem_Particle_Dia>3 && tem_Particle_Dia<5) P_Impact_Mass[2]+=P_FLOW_RATE(p)*pow(10.9)."%6.txt".9). else if(tem_Particle_Dia>7 && tem_Particle_Dia<10) P_Impact_Mass[4]+=P_FLOW_RATE(p)*pow(10.fp=fopen("Impact2.0.9).2f %6. C_UDMI(c.9).tcell. /* PARTICLE DOES NOT STICK*/ if(abs(vn)>vcr) { C_UDMI(c. i++) p->state0. /*Add reflected normal velocity. i++) p->state. i<idim.i++) p->state. i<idim.V[i].for(i=0.V[i]-=nor_coeff*vn*normal[i]. i<idim. /* Store new velocity in state0 of particle*/ for (i=0. */ for (i=0.V[i]=p->state. i++) p->state.i<idim. } /* PARTICLE DEPOSITS*/ else if(wallfricv4 < utc) { /*num of particles deposited or num of hits*/ 98 . /*Apply tangential coefficient of restitution.V[i]-=vn*normal[i]. */ for (i=0. return PATH_ACTIVE.V[i]*=tan_coeff. 9). else P_Stick_Mass[5]+=P_FLOW_RATE(p)*pow(10.tcell.tem_Mass. else if(tem_Particle_Dia>5 && tem_Particle_Dia<7) P_Stick_Mass[3]+=P_FLOW_RATE(p)*pow(10.) P_Stick_Mass[0]+=P_FLOW_RATE(p)*pow(10.utaunew).2f %f\n".9).9)."a").2f %f tem_Particle_Dia.4) += 1."%f %f %6. /* mass of particles deposited*/ C_UDMI(c.Ep. else if(tem_Particle_Dia>1 && tem_Particle_Dia<3) P_Stick_Mass[1]+=P_FLOW_RATE(p)*pow(10.5) += P_FLOW_RATE(p)*pow(10.9).vn. } } 99 %6.2f %6.txt".9).ucws. fprintf(fp. if(tem_Particle_Dia<1.vcr.9). fp=fopen("Stick2.C_UDMI(c.9). else if(tem_Particle_Dia>7 && tem_Particle_Dia<10) P_Stick_Mass[4]+=P_FLOW_RATE(p)*pow(10. . fclose(fp). tem_Mass=P_FLOW_RATE(p)*pow(10.tcell.9).0. else if(tem_Particle_Dia>3 && tem_Particle_Dia<5) P_Stick_Mass[2]+=P_FLOW_RATE(p)*pow(10. d) { begin_c_loop(c.t) { for(i=0.i++) C_UDMI(c. face_t f. Message("Setting UDMs \n").t) 100 .i)=0.i<6. d=Get_Domain(1). #endif /* Only for 3D cases*/ } /*Setting UDM locations and initializing them to 0*/ DEFINE_ON_DEMAND(reset_UDMsnew) { int i=0.t.return PATH_ABORT. Thread *t. Domain *d. } end_c_loop(c. thread_loop_c(t. cell_t c.0. } } 101 .