ANSYS_Fluent_Theory_Guide 15.0.pdf

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FLUENT 15.0 官方用户手册教程,详细讲述了FLUENT中各种模型的建立,是进行FLUENT分析的重要参考书。一套共三本,分别是Users guide、tutorial、theory
Table of contents Using This Manual… The Contents of this manual s.R. XXVII 2. The Contents of the fluent manuals 3. Typographical Conventions 4. Mathematical Conventions 5. Technical Support… 4I.NNRRINI.. XXXI 1. Basic fluid flow 1.1. Overview of Physical Models in aNsyS Fluent...... 12. Continuity and momentum equations....….……,……………2 1.2.1. The Mass Conservation Equation…………………… 中·· 1.2.2. Momentum Conservation Equations............. 1.3.User- Defined scalar(UDS) Transport Equations………,…,…,…,…,…,…,………,………4 1.3.1. Single phase F|oW…..........,.….,.,….….…4 1.3.2 Multiphase F|oW…,,,…,,,…,,…, 看鲁 4. Periodic flows∴ 1.4.1. Overview∴6 1. 42. Limitations 14.3. Physics of Periodic Flows……,…,…,…,…,…,…,…,…,…,…,…,,,…,,…,,,……,,7 1.4.3.1. Definition of the Periodic Velocity 1.4.3.2. Definition of the streamwise-Periodic Pressure ........................,....................................8 .5. Swirling and Rotating Flows….....… 788 1.5.1. Overview of Swirling and rotating Flows 1.5.1.1. Axisymmetric Flows with Swirl or Rotation...................9 1.5.1.1.1. Momentum Conservation Equation for Swirl velocity...……………,10 1.5.1.2. Three-Dimensional Swirling Flows.................10 1.5.1.3. Flows Requiring a moving reference frame 1.52. Physics of Swirling and Rotating Flows………,…,…,…,…,…,…,,, 11 1.6. Compressible flows 1.6.1. When to Use the Compressible Flow Model.…,…,…,…,…,…,…,…,,… 13 1.6.2. Physics of Compressible Flows................ 1.6.2.1. Basic Equations for Compressible Flows ∴…14 1.6.2.2. The Compressible form of the gas Law 14 1.7. viscid flows∴………………….…………15 1.7.1. Euler Equations. 15 1.7.1.1.The Mass Conservation Equation.... 非·······非·非 15 1.7.1.2. Momentum Conservation Equations 1.7.1.3. Energy Conservation Equation 16 2. Flows with Moving Reference Frames ···· 17 2.1. Introduction 。。非·非非 ,17 2. 2. Flow in a Moving Reference Frame 2.2.1. Equations for a Moving Reference frame 2. 2.1.1. Relative velocity Formulation 20 2.2.1.2. Absolute Velocity Formulation.................... ·······.··.···.::··.··:··:· 21 2.,2.1.3. Relative Specification of the Reference Frame Motion……,…,…,…,,…,…,…,,,,21 2.3. Flow in Multiple Reference frames ∴22 2.3.1. the multiple reference frame mode 22 2.3.1.1.0 verview 22 2.3.1.2. Examples……,…,…, :·····.···:····:·····:················.···· 23 2.3.1.3. The MRF Interface Formulation 24 23.1.3.1. Interface Treatment: Relative velocity Formulation……………………….24 Release 15.0-@ SAS /P Inc. All rights reserved -Contains proprietary and con/idential in/ormation of ansys inc and its subsidiaries and affiliates Theory guide 2.3.1.3.2. Interface Treatment: absolute Velocity Formulation......25 2.3.2. The Mixing Plane Model.……,……,…… 25 2.3.2.1.○ verview. ···音普。·。音非音着普·非非着·音音·非普。音非着鲁自非非非普自自非·音。音·。音音非音音着鲁非·音音 26 2.3.2.2. Rotor and stator domains…….26 2.3.23. The mixing Plane Concept.,……,…,…,………………………27 2.3.2.4. Choosing an Averaging method……,……,…,…,…,…,…,……,…,…,………28 2.3.2.4.1. Area averaging..…............................28 2.3.2.4.2. Mass Averaging…………………………,28 2.3.2.4.3. Mixed-Out Averaging 29 2.3.2.5. Mixing Plane algorithm of aNsYS Fluent..... 2.3.2.6. Mass Conservation .30 2.3.2.7. Swirl conservation.,……30 2.3.2.8. Total Enthalpy Conservation 31 3. Flows Using Sliding and Dynamic Meshes.…,,…,,…,,,……,,…,…,,……,……,,33 31. Introduction 33 32. Dynamic Mesh Theory…… 34 3.2.1. Conservation Equations 35 3. 2. Six DOF(6DOF) Solver Theory ...·.·:···..:·.·:·.:·.a..··· ∴,36 33. Sliding Mesh Theory………,…,……,…… 37 39 4.1. Underlying Principles of Turbulence Modeling 39 4.1.1. Reynolds(Ensemble)Averaging 39 4.1.2. Filtered Navier-Stokes Equations…,…,…,…,…,…,…,…,…,…,…,…,,…,40 4.1.3. Hybrid RANS-LES Formulations *···· 41 4.1.4. Boussinesq Approach vs. Reynolds Stress Transport Models 42 4.2. Spalart-Allmaras model 42 4.2.1. Overview D。垂 42 4.2. 2 Transport Equation for the Spalart-Allmaras model 43 423. Modeling the turbulent Viscosity……,,,,… 43 4.2. 4 Modeling the turbulent Production .:: 44 4.2.5. Modeling the turbulent Destruction. ............................................................45 4.2.6. Model Constants 45 4.2.7. Wall Boundary Conditions….....,.,…,….,…,,…,…,,…,…,…,,…,….,,45 4.28. Convective Heat and Mass Transfer Modeling…………,…,…,…,… 46 4.3. Standard, RNG, and Realizable k-E Models 46 4.3.1. Standard k-E Model 47 4.3.1.1. Overview 47 4.3.1.2. Transport Equations for the Standard k-e Model.….…..….….……….……………,47 4.3.1.3. Modeling the turbulent Viscosity .............47 4.3.1.4 Model constants a····· 48 4.3.2. RNG k-E Model 48 4.3.2.1. Overview,.……..,,448 4.3.2. 2 Transport Equations for the rngk-E Model....... 48 4.3.2.3. Modeling the effective viscosity 49 4.3.2, 4. RNG Swirl Modification ,50 4.3.2.5. Calculating the Inverse Effective Prandtl Numbers. .................................50 4.3.2.6.TheR- the E Equation 50 4.3.2.7. Model Constants 4.33. Realizable k-s Model………气,… :·····:·········:·*····:··········:····:····:··········:············ 4.3.3.1. Overview∴ 555 ········::·:·:····:·:···:···::················:·····:····::···:······:·:····· 4.3.3. 2 Transport Equations for the realizable k-e Model..... 52 4.3.3.3. Modeling the turbulent Viscosity 53 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates Theory Guide 4.3.3.4. Model constants∴………54 4.34. Modeling turbulent Production in the k-ε Models…… 54 4.3.5. Effects of buoyancy on turbulence in the k-E Models 55 4.3.6. Effects of Compressibility on turbulence in the kε Models……………………….56 4.3.7. Convective Heat and mass transfer modeling in the k-E Models ···.··.··· ∴56 4.4. Standard and sst k-w Models .. 4. 4.1. Standard k-w model 。;非自非自非自。自d。非非。。非 58 4.4.1.1. Overview∴ 非着·音·非· 58 4.4.1.2. Transport Equations for the Standard k-w Model ............58 4.4.1.3. Modeling the Effective diffusivity.......... 59 4.4.1.3.1. LoW-Reynolds-Number Correction :·.·.· 59 4.4.1.4. Modeling the turbulence production 4.4.1.4.1.Production of k 4.4.1.4.2. Production of u,……60 4.4.1.5. Modeling the turbulence Dissipation 垂音·D要垂看.垂垂 60 4.4.1.5.1. Dissipation of k............. 60 4.4.1.5.2. Dissipation of w............. ······ 61 44.1.5.3.C0 mpressibility Correction......,,,……………,61 4.4.1.6. Model constants wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww 62 4.4.2. Shear-Stress Transport(SST)k-w Model..........................62 4.4.2.1. Overview∴ 62 4.4.2.2. Transport Equations for the sst k-w Model 着非非D。音。非自非着D非自番D。非自非。自。。B非自曲自非非非 63 4.4.23. Modeling the Effective Diffusiⅳvity…………………………………………….263 4.4.2.4. Modeling the turbulence Production . 4.4.2.4.1. Production of k∴.….64 4.4.2.4.2. Production of w .64 4.4.2.5. Modeling the turbulence Dissipation......... 65 4.4.2.5.1. Dissipation of k 65 4.4.2.5.2. Dissipation of w........................... ·····.·.:.·:::·:·:····: 65 4.4.2.6. Cross- Diffusion modifⅰcatⅰon… 4.4.2.7. Model Consta 65 4.4.3. Turbulence Damping .. 看,鲁D帮 4.44.Wal! Boundary Conditions…… 67 4,5. k-kl-w Transition model .··.:··:······::··············.·:·.:·:.·:··:::····:······ 67 4.5.1. verviev,………………… ∴67 4.5. 2 Transport Equations for the k-kI-w Model 。着着 67 4.5.2.1. Model constants 71 4.6. Transition sst model.wNNN..71 4.6.1. Overview 71 4.6. 2 Transport Equations for the transition SST Model 71 4.6.2.1. Separation-Induced Transition Correction ...... 74 4.6.2.2. Coupling the transition model and Sst transport equations ................... 74 4.6.2.3. Transition SST and Rough Walls ∴.75 463. Mesh requirements...............…..…..…,75 4.6.4. Specifying Inlet Turbulence Levels 78 4.7. Intermittency Transition Model ·················· 4.7..Overview 9 47.2 Transport Equations for the Intermittency Transition Model.……………….80 4.,7.3. Coupling with the other Models……………,…,…,…,,,………………82 474. intermittency Transition Model and rough Wa|ls…,,,…,…,…… 82 4. 8 the v2F Model 82 4.9. Reynolds Stress Model (rsm)......... 83 Release 15.0-@ SAS /P Inc. All rights reserved -Contains proprietary and con/idential in/ormation of ansys inc and its subsidiaries and affiliates Theory guide 4.9.1. Overview 83 4.9.2. Reynolds Stress Transport Equations∴…,…,…,…,… 83 4.93. Modeling turbulent Diffusive transport∴.…….84 4.94. Modeling the Pressure-Strain Term……………………………,85 4.9.4.1. Linear Pressure-Strain Model . .........................................................................................85 4.9.4.2. Low-Re modifications to the linear pressure- Strain model 86 4.9.4.3. Quadratic Pressure-Strain Model 着曲着自自自自自自省音自着自非音音·自音音d普自由4 86 49.4.4.Low- Re stress-Omega Model…….….….…..….…….,……,…,…,…,…, ··中:.::· 87 4.9.5. Effects of Buoyancy on Turbulence ·+· 89 4.96. Modeling the turbulence Kinetic Energy……………,…, 89 4.9.7. Modeling the dissipation Rate ·..·.“···· ···..=.. 90 4.9.8. Modeling the turbulent viscosity .................................................................................90 4.9.9.Wa! Boundary Conditions……… 0 49.10.C。 invective heat and mass Transfer modeling…..,,.,… 91 4.10. Scale- Adaptive Simulation(SAS) Model….….…… 量着鲁 92 4.10.1. Overview∴……………92 4.10.2. Transport Equations for the SST-SAS Model 93 4.103 SAS With Other w-Based Turbulence models 94 4.1-. Detached Eddy Simulation(DES)…………… 音·着音D音 ∴95 4.11.1. Overview,………,,,, 95 4.1.2. DES With the Spalart-Allmaras model,…… 95 4113. DES with the realizable k-e model 96 4.11.4 DES with the sst k-w model 97 4.11.5 DES With the Transition Sst Model 97 4.11.6. I mproved Delayed Detached Eddy Simulation(DDES)…………………………………98 4.11.6.1.Overview of idDeS .98 4.11.6.2. IDDES Model Formulation ∴98 4.12. Large Eddy Simulation(LES) Model..... 4.12.1. Overview..… ····;·················::···:·· ∴99 4.12.2. Subgrid-Scale models 100 4.12.2.1. Smagorinsky-Lilly Model.... 4101 4.12.2,2. Dynamic Smagorinsky- Lilly Model………… 101 4.12.23.Wa‖ Adapting Local Eddy-Viscosity( WALE)Model.…..… 102 4.12.24. Algebraic Wal| Modeled les model( (WMLES)……………,……………103 4.12.2.4.1. Algebraic WMLES Model Formulation 104 4.12.2.4.1.1. Reynolds Number Scaling ... ··非鲁非 104 4.12.2.4.2. Algebraic WMLES S-Omega Model Formulation......... 105 4.12.2.5. Dynamic Kinetic Energy Subgrid- Scale model.………….…..….…….,106 4.12.3. Inlet Boundary Conditions for the LES Model 106 4.1231. Vortex method ...w..m.m..m.m.w...106 4.12.3.2. Spectral Synthesizer 108 4.13. Embedded Large eddy simulation(eles) 。··非··鲁· 109 4.13.1. Overview .109 4.13.2. Selecting a model..........….,109 4.13 3 Interfaces treatment 109 4.13.3.1. RANS-LES Interface ...................................................................................................110 4.13.3.2. LES-RANS Interface ∴110 4.13.3.3. Internal Interface without les zone 。·。自音·看··自。·音自·。自非非看自··.非非·非自··非音非·鲁鲁非·音。 111 4.13.3.4. Grid generatⅰ on guidelines..,,,…,,,,,…11 4. 14. Near-Wall Treatments for Wall-Bounded Turbulent flows 112 4.14.1. Overview 112 4.14.1.1. Wall Functions vs Near-Wall model 113 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates Theory Guide 4.14.1.2.Wal‖! Functions.……415 4.142 Standard Wall Functions 115 4.14.2.1. Momentum 115 4.14.22. Energy…………………116 4.14.23.5 pecies….......,…,… ∴118 4.14.2, 4. Turbulence ,...............................................................................................................118 4.143ScalableWallFunctions,w.awww....w.,119 4.14.4.Non- Equilibrium Wa‖! Functions……………, 4120 4.14.4.1. Standard Wall Functions vs Non-Equilibrium Wall Functions 121 4.14.4,2. Limitations of the wa‖! Function Approach…………………………,121 4.14.5. Enhanced Wall Treatment E-Equation(EWT-E · .。。4 ..122 4.14.5.1. Two-Layer Model for Enhanced Wall Treatment. ..........................................................122 4.14.5.2. Enhanced Wall Treatment for Momentum and Energy equations 124 41456 Enhanced wall treatment w- Equation( EWt-w)..,,,…,…,……………,127 4.147. User-Defined wall functions 127 4.14.8. LES Near- Wall Treatment……………127 4.15. Curvature Correction for the Spalart-Allmaras and Two-Equation Models 128 4.16. Production Limiters for Two-Equation Models ∴130 5. Heat Transfer 133 5.1. Introduction∴……………133 5.2. Modeling Conductⅳ ve and Convective heat Transfer………… 133 5.2.1. Heat Transfer Theory................................... 自自非自非·自非自。音自 133 5.2.1.1. The Energy equation……………,…,…,…………,…,……,133 52.1.2. The energy equation in Moving Reference Frames……….…......…...134 5.2.1.3. The Energy Equation for the Non-Premixed Combustion Model 134 5.2.1.4. Inclusion of Pressure Work and Kinetic Energy terms .........135 5.2.1.5. Inclusion of the viscous Dissipation Terms 135 5.2.1.6. Inclusion of the Species diffusion Term 135 5.2.1.7. Energy sources due to reaction....….,.,…,…,…,………,136 5.2.1.8. Energy Sources due To radiation 136 5.2.1.9. Interphase Energy Sources 5.2.1.10. Energy equation in Solid regions 136 5.2.1.11. Anisotropic Conductivity in Solids.................. 音垂。 137 5.2.1.12. Diffusion at inlets∴……4137 52.2. Natural Convection and Buoyancy-Driven Flows Theory………….……,137 5.3. Modeling radiation 138 5.3. 1 Overview and limitations 138 5.3.1.1. Advantages and Limitations of the dtrm…….……………,…,……,…………………139 5.3.1.2. Advantages and limitations of the p-1 Model 139 5.3.1.3. Advantages and Limitations of the rosseland model ............. 5.3.1.4. Advantages and limitations of the do model 5.3.1.5. Advantages and Limitations of the S2S Model 5.3. 2 Radiative Transfer Equation 141 5.3.3. P-1 Radiation Model Theory ....................................................................................142 5.3.3.1. The P-1 Model Equations ∴143 53.3.2. Anisotropic Scattering……,,,,,,,,…,…,…,…,,,,,…,……,144 53.33 Particulate effects in the p-1 model 144 5.3.3.4. Boundary Condition Treatment for the p-1 Model at Walls........ 145 5.3.3.5. Boundary Condition Treatment for the p-1 Model at Flow Inlets and Exits. .....................146 5.3.4. Rosseland radiation Model Theory 5.34.1. The rosseland model Equations………,…,…,…,…,…,……,…,…,…,……,…,………,146 5.3.4.2. Anisotropic Scattering 147 Release 15.0-@ SAS /P Inc. All rights reserved -Contains proprietary and con/idential in/ormation of ansys inc and its subsidiaries and affiliates Theory guide 5.3.4.3. Boundary Condition Treatment at Walls.,…,,,……,…,…,…,…………,…,147 5.3.44. Boundary Condition Treatment at Flow Inlets and Exits……… 147 5.3.5. Discrete Transfer Radiation Model(DTRM)Theory 音。·省非。自看。着。音非非。4自非。非非自非非非鲁非·非。。非省鲁D非非非 148 5.3.5.1. The dTRM Equations…………………,…….…,………………………,148 5.3.52. Ray Tracing…......,.….…,148 5.3.53. Clustering∴………… 149 5.3.5.4. Boundary Condition Treatment for the dtrm at Walls. ..................................................150 53.55. Boundary Condition Treatment for the DTRM at Flow Inlets and Exits……………,150 536 Discrete ordinates(DO) Radiation Model Theory…....…..….….…….150 5.3.6.1. the do model equations.......................,.... 51 5.3.6.2. Energy Coupling and the do model .152 5.356.2.1. Limitations of do/ Energy Coupling……,…,……,153 5.3.6.3. Angular Discretization and Pixelation 153 53.64. Anisotropic Scattering…….……………,………………………….,156 5.3.6.5. Particulate effects in the do model 157 5.3.6.6. Boundary and Cell Zone Condition Treatment at Opaque Walls 157 5.3.6.6.1. Gray diffuse Walls……… 159 5.3.6.6.2. Non-Gray Diffuse Walls......….………………159 53.67.Ce! Zone and Boundary Condition Treatment at Semi- Transparent Walls…………,160 5.3.6.7.1.5emi- Transparent Interior Wa|ls........,.,,,…,…………,160 5.3.6.7. 2 Specular Semi-Transparent Walls 5.3.6.7.3. Diffuse Semi-Transparent Walls..... 自。非。曲。自。音非非·d。。。自非自非指鲁虚非 163 5.3.6.74. Partially Diffuse Semi- Transparent Walls.…………,,…,………………,164 5.3.6.7.5. Semi-Transparent Exterior Walls 164 5.3.6.7.6. Limitation5…166 5.3.6.7.7. Solid Semi-Transparent media 167 5.3.6. 8 Boundary Condition Treatment at specular Walls and Symmetry boundaries ...... 167 5.3.6.9. Boundary Condition Treatment at Periodic Boundaries ∴167 53.6.10. Boundary Condition Treatment at Flow Inlets and Exits…………………,167 37. Surface-to-Surface(S2S) Radiation Model Theory……… ∴167 5.3.7.1. Gray-Diffuse Radiation............................. 167 5.3.7.2. The S2S Model Equations 168 5.37.3. Clustering… D。垂非 169 5.3.7.3.1. Clustering and View Factors………..….…….…,….…,…………………,169 5.3.7.3.2. Clustering and Radiosity 53.8 Radiation in Combusting Flows∴… 170 5.3.8.1. The Weighted-Sum-of-Gray-Gases Model..............................170 5.3.8.1.1. When the total( Static) Gas Pressure is Not Equal to1atm………… 171 5.382. The effect of soot on the absorption Coefficient…....…………172 53.83. The Effect of Particles on the absorption Coefficient…………,……,…………,….,172 5.3.9. Choosing a Radiation Model........................172 5,3.9.1. External radiation 173 6. Heat Exchangers 175 6.1. The Macro Heat Exchanger Models 6.1.1. Overview of the macro heat Exchanger models 带,看·垂看非看看看4 175 6.12. Restrictions of the macro heat Exchanger Models.………………,176 6.13. Macro Heat EXchanger Model Theory………,…,…,…… 177 6.1.3.1. Streamwise Pressure Drop…....……,….,…,….……………,178 6.1.3.2 Heat Transfer Effectiveness ·,·非着·非。着·。非 179 6.1.3.3. Heat rejection,…,…,… D· 180 6.1.3.4. Macro Heat Exchanger Group Connectivity…………… 182 6.2. The dual cell model 183 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates Theory Guide 6.2.1.Overviewofthedualcellmodelwwwwwwww.183 6.2.2. Restrictions of the dual cell model 183 6.2.3. Dual Cell Model Theory.. 鲁着非非非音来音普。音音 183 6.23,1. NTU Relations :····.·:················;···· ∴184 6.2.3.2. Heat Rejection.……....,.…..,...,.,.…..,…..,,184 7 Species Transport and Finite-Rate Chemistry 。自非·非非·非··非非·非·非自是非。自普非非·非·非··非自非非自非音,非 187 7. 1. Volumetric Reactions ,B音。着鲁非自非自 187 7.1.1. Species Transport Equations.…,…,…,…,……, 中:··········中:········ ∴187 7.1.1.1. Mass Diffusion in laminar flows. 7. 1.1.2. Mass Diffusion in Turbulent flows 188 7. 1.1.3. Treatment of Species Transport in the energy equation ..... 7.1.1.4. Diffusion at inlets………189 7.1. 2 The Generalized Finite-Rate Formulation for Reaction Modeling 189 7. 1.2.1.The laminar finite- Rate model wwwwwwwwwwwwwwwwww 189 7.1.2.2. Pressure- Dependent reactions,…,…,… 192 7. 1.2.3. The Eddy-Dissipation Model 193 7. 1.2.4. The eddy-Dissipation Model for leS 194 7.125. The Eddy-Dissipation-Concept( EDCModel....……,…………,195 7.1.2.6. The thickened flame model 7.1.27 The relaxation to Chemical Equilibrium Mo;………………………19 198 7.2. Wall Surface Reactions and Chemical Vapor Deposition……,…,…,…,…,… 199 7. 2.1. Surface Coverage reaction Rate modification 201 7.2,2. Reaction- Diffusion Balance for Surface Chemistry……,…,……,…,……,…………,201 7.2.3. Slip boundary formulation for Low-Pressure Gas Systems .202 7.3. Particle surface reactions,……204 7.3.1. General description 204 7. 3.2. ANSYS Fluent Model formulation 205 7.3.3. Extension for Stoichiometries with Multiple Gas Phase Reactants 206 7.3.4.Solid-solidreactionswwww..ww.wwwww.wwww...207 7.3.5. Solid Decomposition Reactions…,…,,,,… 207 7.3.6. Solid Deposition Reactions. 7.3.7. Gaseous Solid Catalyzed Reactions on the Particle Surface ,208 74. Reacting Channel Model........,,,,…,… 208 7.4.1. Overview and limitations . 74.2 Reacting Channel Model Theory…………………………,28 7.4.2.1.F| ow Inside the reacting channel.....,.…,…,,…,…………,209 7.4.2. 2 Surface Reactions in the reacting Channel 210 74.23. Porous Medium Inside reacting( hannel,….….….……,……,…,…,…,………,………,211 7.4.24. Outer flow in the shell .. 7. 5. Reactor Network model 212 7.5.1. Reactor Network Model Theory ....... 212 7.5.1.1. Reactor network temperature solution . 8. Non-Premixed combustion 215 8.1. Introduction… 21 来·非··非非·。非。非着D·非非非非非·非非非着非 5 8.2. Non-Premixed Combustion and Mixture Fraction Theory 215 821. Mixture Fraction Theory………….……………………,…………………,216 8.2.1.1. Definition of the mixture fraction 216 8.2.1.2. Transport Equations for the mixture fraction. ...............................................................218 8.2.1.3. The Non-Premixed model for les. 8214. Mixture fraction vs. Equivalence ratio….......….…219 8.2.1.5. Relationship of Mixture Fraction to Species Mass Fraction, Density, and Temperature .....220 8.2. 2 Modeling of Turbulence-Chemistry Interaction 221 Release 15.0-@ SAS /P Inc. Al/rights reserved. -Contains proprietary and confidential in/ormation of ansys inc and its Theory guide 822.1. Description of the probability density Function.....,…………221 8.2.2.2. Derivation of mean scalar values from the instantaneous mixture fraction . wwww 222 8.2.2.3. The assumed- Shape pde………...…………………222 8.2.2.3.1.TheDoubleDeltaFunctionPDF,223 8.2.3. Non-Adia batic Extensions of the Non-Premixed Mode"..... 822.32.Theβ- Function pde… 223 224 8.2.4. Chemistry Tabulation 227 82.4.1.Look- Up Tables for Adiabatic Systems………,…,…,…,,…,,…,,…,,…,……… 227 8.2.4.2. 3D Look-Up Tables for Non-Adiabatic Systems 228 824.3. Generating Lookup Tables Through automated Grid refinement……,………,230 8.3. Restrictions and Special Cases for Using the Non-Premixed Model .232 8.3.1. Restrictions on the mixture fraction Approach ··非··非·音·音。非非着 232 8.3.2. Using the Non-Premixed Model for Liquid Fuel or Coal Combustion 235 8.3.3. Using the non-premixed model with flue Gas recycle 236 8.3.4. Using the non -premixed model with the Inert model 237 834.1. Mixture Composition.….,…,…,…,…,,…,…,…,………………,237 83.4.1.1. Property Evaluation………,…,…,…,…,…,…,,……,…… ,238 8.4. The diffusion Flamelet Models Theory 8.4.1. Restrictions and Assumptions ····:·.··:········ 238 84.2. The flamelet Concept.....................239 8. 4.2.1. Overview .....................................................................................................................239 8.4.2.2. Strain rate and scalar dissipation ................ ........................ 240 84.23. Embedding Diffusion Flamelets in Turbulent Flames……,…,…,…,…,…,,…,.241 8.4.3. Flamelet generation .242 8.4.4. Flamelet Import 242 8.5. The Steady Diffusion Flamelet Model Theory . 8.5.1. Overview ∴244 8.5.2. Multiple Steady flamelet Librar 245 8.5.3. Steady Diffusion Flamelet Automated grid Refinement 245 8.5.4. Non-Adiabatic Steady diffusion Flamelets 246 86 The Unsteady Diffusion Flamelet Model Theory………,…,…,…,,….,…,……,………,,246 8.6.. The eulerian Unsteady laminar flamelet model 247 8.6.1.1. Liquid reactions 249 862. The diesel Unsteady Laminar flamelet Model…....….....…..….249 863. Multiple diesel Unsteady Flamelets.…...,………………………250 86.4. Multiple Diesel Unsteady Flamelets with Flamelet Reset……,…,…,…,…,………,…,,251 8.6.4.1. Resetting the Flamelets 。着音。自·看 251 9. Premixed combustion 253 9.1Overview and limitations 253 9.1.1. Overview∴253 9.1.2. Limitations ·*·.·+·.+·+.·:+·:·,..a+:+..++.+4++.·+.中·+··4.+=4..··= 254 92.C- Equation Model Theory…….….……….…………………………………………,254 9.2.1. Propagation of the Flame Front ··..··················· 254 941. Zimont Turbulent F| ame Speed Closure moc.………25 9.3. G-Equation Model Theory...... 9.3.1. Numerical Solution of the g-equation 257 9.4. Turbulent Flame Speed Models....... 257 257 9.4.1.1.Zimont Turbulent Flame Speed Closure for les .................... 259 9.4.1.2. Flame Stretch Effect. ......................................................,.............................................259 9. 4.1.3. Gradient Diffusion ∴…………………………………………260 9.4.1.4.Wa! Damping…………,…,…,…,…,…,……,…,…………,…,260 9.4.2. Peters Flame Speed model. ...............................................................................................260 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates

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