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ANSYS Fluent Theory Guide
ANSYS, Inc. Release 15.0
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Table of Contents
Using This Manual................................................................................................................................... xxvii
1.The Contents of This Manual........................................................................................................... xxvii
2.The Contents of the Fluent Manuals............................................................................................... xxviii
3.Typographical Conventions............................................................................................................. xxix
4. Mathematical Conventions............................................................................................................... xxx
5.Technical Support ........................................................................................................................... xxxi
1. Basic Fluid Flow....................................................................................................................................... 1
1.1. Overview of Physical Models in ANSYS Fluent.................................................................................... 1
1.2. Continuity and Momentum Equations............................................................................................... 2
1.2.1.The Mass Conservation Equation.............................................................................................. 2
1.2.2. Momentum Conservation Equations........................................................................................ 3
1.3. User-Defined Scalar (UDS) Transport Equations.................................................................................. 4
1.3.1. Single Phase Flow.................................................................................................................... 4
1.3.2. Multiphase Flow....................................................................................................................... 5
1.4. Periodic Flows .................................................................................................................................. 6
1.4.1. Overview................................................................................................................................. 6
1.4.2. Limitations............................................................................................................................... 7
1.4.3. Physics of Periodic Flows.......................................................................................................... 7
1.4.3.1. Definition of the Periodic Velocity.................................................................................... 7
1.4.3.2. Definition of the Streamwise-Periodic Pressure................................................................ 8
1.5. Swirling and Rotating Flows.............................................................................................................. 8
1.5.1. Overview of Swirling and Rotating Flows.................................................................................. 9
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................................................................... 11
1.5.2. Physics of Swirling and Rotating Flows.................................................................................... 11
1.6. Compressible Flows........................................................................................................................ 12
1.6.1.When to Use the Compressible Flow Model............................................................................ 13
1.6.2. Physics of Compressible Flows................................................................................................ 13
1.6.2.1. Basic Equations for Compressible Flows......................................................................... 14
1.6.2.2.The Compressible Form of the Gas Law.......................................................................... 14
1.7. Inviscid Flows ................................................................................................................................. 15
1.7.1. Euler Equations...................................................................................................................... 15
1.7.1.1.The Mass Conservation Equation.................................................................................... 15
1.7.1.2. Momentum Conservation Equations.............................................................................. 16
1.7.1.3. Energy Conservation Equation....................................................................................... 16
2. Flows with Moving Reference Frames................................................................................................... 17
2.1. Introduction ................................................................................................................................... 17
2.2. Flow in a Moving Reference Frame.................................................................................................. 18
2.2.1. Equations for a Moving Reference Frame................................................................................ 19
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 Model...................................................................................... 22
2.3.1.1. Overview....................................................................................................................... 22
2.3.1.2. Examples....................................................................................................................... 23
2.3.1.3.The MRF Interface Formulation...................................................................................... 24
2.3.1.3.1. Interface Treatment: Relative Velocity Formulation................................................. 24
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2.3.1.3.2. Interface Treatment: Absolute Velocity Formulation............................................... 25
2.3.2.The Mixing Plane Model......................................................................................................... 25
2.3.2.1. Overview....................................................................................................................... 26
2.3.2.2. Rotor and Stator Domains.............................................................................................. 26
2.3.2.3.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........................................................................ 29
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
3.1. Introduction ................................................................................................................................... 33
3.2. Dynamic Mesh Theory.................................................................................................................... 34
3.2.1. Conservation Equations ......................................................................................................... 35
3.2.2. Six DOF (6DOF) Solver Theory................................................................................................. 36
3.3. Sliding Mesh Theory....................................................................................................................... 37
4.Turbulence............................................................................................................................................. 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............................................................................................................................... 42
4.2.2.Transport Equation for the Spalart-Allmaras Model................................................................. 43
4.2.3. 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
4.2.8. Convective Heat and Mass Transfer Modeling.......................................................................... 46
4.3. Standard, RNG, and Realizable k-ε Models........................................................................................ 46
4.3.1. Standard k-ε Model................................................................................................................ 47
4.3.1.1. Overview....................................................................................................................... 47
4.3.1.2. Transport Equations for the Standard k-ε Model............................................................. 47
4.3.1.3. Modeling the Turbulent Viscosity................................................................................... 47
4.3.1.4. Model Constants........................................................................................................... 48
4.3.2. RNG k-ε Model....................................................................................................................... 48
4.3.2.1. Overview....................................................................................................................... 48
4.3.2.2. Transport Equations for the RNG k-ε 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. The R-ε Term in the ε Equation........................................................................................ 50
4.3.2.7. Model Constants........................................................................................................... 51
4.3.3. Realizable k-ε Model............................................................................................................... 51
4.3.3.1. Overview....................................................................................................................... 51
4.3.3.2. Transport Equations for the Realizable k-ε Model............................................................ 52
4.3.3.3. Modeling the Turbulent Viscosity................................................................................... 53
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4.3.3.4. Model Constants........................................................................................................... 54
4.3.4. Modeling Turbulent Production in the k-ε Models................................................................... 54
4.3.5. Effects of Buoyancy on Turbulence in the k-ε Models............................................................... 55
4.3.6. Effects of Compressibility on Turbulence in the k-ε Models...................................................... 56
4.3.7. Convective Heat and Mass Transfer Modeling in the k-ε Models............................................... 56
4.4. Standard and SST k-ω Models.......................................................................................................... 57
4.4.1. Standard k-ω Model............................................................................................................... 58
4.4.1.1. Overview....................................................................................................................... 58
4.4.1.2. Transport Equations for the Standard k-ω 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............................................................................. 60
4.4.1.4.1. Production of k..................................................................................................... 60
4.4.1.4.2. Production of ω..................................................................................................... 60
4.4.1.5. Modeling the Turbulence Dissipation............................................................................. 60
4.4.1.5.1. Dissipation of k..................................................................................................... 60
4.4.1.5.2. Dissipation of ω..................................................................................................... 61
4.4.1.5.3. Compressibility Correction.................................................................................... 61
4.4.1.6. Model Constants........................................................................................................... 62
4.4.2. Shear-Stress Transport (SST) k-ω Model................................................................................... 62
4.4.2.1. Overview....................................................................................................................... 62
4.4.2.2. Transport Equations for the SST k-ω Model..................................................................... 63
4.4.2.3. Modeling the Effective Diffusivity................................................................................... 63
4.4.2.4. Modeling the Turbulence Production............................................................................. 64
4.4.2.4.1. Production of k..................................................................................................... 64
4.4.2.4.2. Production of ω..................................................................................................... 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 ω..................................................................................................... 65
4.4.2.6. Cross-Diffusion Modification.......................................................................................... 65
4.4.2.7. Model Constants........................................................................................................... 65
4.4.3.Turbulence Damping.............................................................................................................. 66
4.4.4.Wall Boundary Conditions...................................................................................................... 67
4.5. k-kl-ω Transition Model................................................................................................................... 67
4.5.1. Overview............................................................................................................................... 67
4.5.2. Transport Equations for the k-kl-ω Model................................................................................ 67
4.5.2.1. Model Constants........................................................................................................... 71
4.6.Transition SST Model....................................................................................................................... 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
4.6.3. Mesh Requirements............................................................................................................... 75
4.6.4. Specifying Inlet Turbulence Levels.......................................................................................... 78
4.7. Intermittency Transition Model....................................................................................................... 79
4.7.1. Overview............................................................................................................................... 79
4.7.2.Transport Equations for the Intermittency Transition Model..................................................... 80
4.7.3. Coupling with the Other Models............................................................................................. 82
4.7.4. Intermittency Transition Model and Rough Walls..................................................................... 82
4.8.The V2F Model................................................................................................................................ 82
4.9. Reynolds Stress Model (RSM)........................................................................................................... 83
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4.9.1. Overview............................................................................................................................... 83
4.9.2. Reynolds Stress Transport Equations....................................................................................... 83
4.9.3. Modeling Turbulent Diffusive Transport.................................................................................. 84
4.9.4. 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.................................................................................... 86
4.9.4.4. Low-Re Stress-Omega Model......................................................................................... 87
4.9.5. Effects of Buoyancy on Turbulence......................................................................................... 89
4.9.6. 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.Wall Boundary Conditions...................................................................................................... 90
4.9.10. Convective Heat and Mass Transfer Modeling........................................................................ 91
4.10. Scale-Adaptive Simulation (SAS) Model......................................................................................... 92
4.10.1. Overview ............................................................................................................................. 92
4.10.2.Transport Equations for the SST-SAS Model........................................................................... 93
4.10.3. SAS with Other ω-Based Turbulence Models.......................................................................... 94
4.11. Detached Eddy Simulation (DES)................................................................................................... 95
4.11.1. Overview ............................................................................................................................. 95
4.11.2. DES with the Spalart-Allmaras Model.................................................................................... 95
4.11.3. DES with the Realizable k-ε Model......................................................................................... 96
4.11.4. DES with the SST k-ω Model.................................................................................................. 97
4.11.5. DES with the Transition SST Model........................................................................................ 97
4.11.6. Improved Delayed Detached Eddy Simulation (IDDES).......................................................... 98
4.11.6.1. Overview of IDDES....................................................................................................... 98
4.11.6.2. IDDES Model Formulation............................................................................................ 98
4.12. Large Eddy Simulation (LES) Model................................................................................................ 99
4.12.1. Overview ............................................................................................................................. 99
4.12.2. Subgrid-Scale Models......................................................................................................... 100
4.12.2.1. Smagorinsky-Lilly Model............................................................................................ 101
4.12.2.2. Dynamic Smagorinsky-Lilly Model.............................................................................. 101
4.12.2.3.Wall-Adapting Local Eddy-Viscosity (WALE) Model...................................................... 102
4.12.2.4. Algebraic Wall-Modeled LES Model (WMLES).............................................................. 103
4.12.2.4.1. Algebraic WMLES Model Formulation................................................................ 104
4.12.2.4.1.1. Reynolds Number Scaling......................................................................... 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
4.12.3.1.Vortex Method........................................................................................................... 106
4.12.3.2. Spectral Synthesizer................................................................................................... 108
4.13. Embedded Large Eddy Simulation (ELES)..................................................................................... 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........................................................................... 111
4.13.3.4. Grid Generation Guidelines........................................................................................ 111
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
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4.14.1.2.Wall Functions........................................................................................................... 115
4.14.2. Standard Wall Functions..................................................................................................... 115
4.14.2.1. Momentum............................................................................................................... 115
4.14.2.2. Energy....................................................................................................................... 116
4.14.2.3. Species...................................................................................................................... 118
4.14.2.4.Turbulence ................................................................................................................ 118
4.14.3. Scalable Wall Functions....................................................................................................... 119
4.14.4. Non-Equilibrium Wall Functions.......................................................................................... 120
4.14.4.1. Standard Wall Functions vs. Non-Equilibrium Wall Functions....................................... 121
4.14.4.2. Limitations of the Wall Function Approach................................................................. 121
4.14.5. Enhanced Wall Treatment ε-Equation (EWT-ε)...................................................................... 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
4.14.6. Enhanced Wall Treatment ω-Equation (EWT-ω).................................................................... 127
4.14.7. 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 Conductive and Convective Heat Transfer...................................................................... 133
5.2.1. Heat Transfer Theory............................................................................................................. 133
5.2.1.1.The Energy Equation.................................................................................................... 133
5.2.1.2.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........................................................................................... 136
5.2.1.10. Energy Equation in Solid Regions............................................................................... 136
5.2.1.11. Anisotropic Conductivity in Solids.............................................................................. 137
5.2.1.12. Diffusion at Inlets....................................................................................................... 137
5.2.2. 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.................................................... 140
5.3.1.4. Advantages and Limitations of the DO Model............................................................... 140
5.3.1.5. Advantages and Limitations of the S2S Model.............................................................. 140
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
5.3.3.2. Anisotropic Scattering................................................................................................. 144
5.3.3.3. 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....................................................................................... 146
5.3.4.1.The Rosseland Model Equations................................................................................... 146
5.3.4.2. Anisotropic Scattering................................................................................................. 147
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5.3.4.3. Boundary Condition Treatment at Walls........................................................................ 147
5.3.4.4. Boundary Condition Treatment at Flow Inlets and Exits................................................. 147
5.3.5. Discrete Transfer Radiation Model (DTRM) Theory................................................................. 148
5.3.5.1.The DTRM Equations.................................................................................................... 148
5.3.5.2. Ray Tracing.................................................................................................................. 148
5.3.5.3. Clustering.................................................................................................................... 149
5.3.5.4. Boundary Condition Treatment for the DTRM at Walls................................................... 150
5.3.5.5. Boundary Condition Treatment for the DTRM at Flow Inlets and Exits............................ 150
5.3.6. Discrete Ordinates (DO) Radiation Model Theory................................................................... 150
5.3.6.1.The DO Model Equations............................................................................................. 151
5.3.6.2. Energy Coupling and the DO Model............................................................................. 152
5.3.6.2.1. Limitations of DO/Energy Coupling..................................................................... 153
5.3.6.3. Angular Discretization and Pixelation........................................................................... 153
5.3.6.4. 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
5.3.6.7. Cell Zone and Boundary Condition Treatment at Semi-Transparent Walls...................... 160
5.3.6.7.1. Semi-Transparent Interior Walls........................................................................... 160
5.3.6.7.2. Specular Semi-Transparent Walls......................................................................... 161
5.3.6.7.3. Diffuse Semi-Transparent Walls............................................................................ 163
5.3.6.7.4. Partially Diffuse Semi-Transparent Walls............................................................... 164
5.3.6.7.5. Semi-Transparent Exterior Walls........................................................................... 164
5.3.6.7.6. Limitations.......................................................................................................... 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
5.3.6.10. Boundary Condition Treatment at Flow Inlets and Exits............................................... 167
5.3.7. 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
5.3.7.3. Clustering.................................................................................................................... 169
5.3.7.3.1. Clustering and View Factors................................................................................ 169
5.3.7.3.2. Clustering and Radiosity...................................................................................... 169
5.3.8. 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 to 1 atm.................................... 171
5.3.8.2.The Effect of Soot on the Absorption Coefficient........................................................... 172
5.3.8.3.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................................................................................................ 175
6.1.1. Overview of the Macro Heat Exchanger Models.................................................................... 175
6.1.2. Restrictions of the Macro Heat Exchanger Models................................................................. 176
6.1.3. Macro Heat Exchanger Model Theory.................................................................................... 177
6.1.3.1. Streamwise Pressure Drop........................................................................................... 178
6.1.3.2. Heat Transfer Effectiveness........................................................................................... 179
6.1.3.3. Heat Rejection............................................................................................................. 180
6.1.3.4. Macro Heat Exchanger Group Connectivity.................................................................. 182
6.2.The Dual Cell Model...................................................................................................................... 183
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6.2.1. Overview of the Dual Cell Model........................................................................................... 183
6.2.2. Restrictions of the Dual Cell Model........................................................................................ 183
6.2.3. Dual Cell Model Theory......................................................................................................... 183
6.2.3.1. NTU Relations.............................................................................................................. 184
6.2.3.2. Heat Rejection............................................................................................................. 184
7. Species Transport and Finite-Rate Chemistry..................................................................................... 187
7.1.Volumetric Reactions .................................................................................................................... 187
7.1.1. Species Transport Equations................................................................................................. 187
7.1.1.1. Mass Diffusion in Laminar Flows................................................................................... 188
7.1.1.2. Mass Diffusion in Turbulent Flows................................................................................ 188
7.1.1.3.Treatment of Species Transport in the Energy Equation................................................. 188
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..................................................................................... 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
7.1.2.5.The Eddy-Dissipation-Concept (EDC) Model................................................................. 195
7.1.2.6.The Thickened Flame Model......................................................................................... 196
7.1.2.7.The Relaxation to Chemical Equilibrium Model............................................................. 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-Solid Reactions............................................................................................................ 207
7.3.5. Solid Decomposition Reactions............................................................................................ 207
7.3.6. Solid Deposition Reactions................................................................................................... 207
7.3.7. Gaseous Solid Catalyzed Reactions on the Particle Surface.................................................... 208
7.4. Reacting Channel Model............................................................................................................... 208
7.4.1. Overview and Limitations..................................................................................................... 208
7.4.2. Reacting Channel Model Theory........................................................................................... 208
7.4.2.1. Flow Inside the Reacting Channel................................................................................. 209
7.4.2.2. Surface Reactions in the Reacting Channel................................................................... 210
7.4.2.3. Porous Medium Inside Reacting Channel...................................................................... 211
7.4.2.4. Outer Flow in the Shell................................................................................................. 211
7.5. Reactor Network Model................................................................................................................ 212
7.5.1. Reactor Network Model Theory............................................................................................ 212
7.5.1.1. Reactor network temperature solution......................................................................... 213
8. Non-Premixed Combustion................................................................................................................. 215
8.1. Introduction ................................................................................................................................. 215
8.2. Non-Premixed Combustion and Mixture Fraction Theory............................................................... 215
8.2.1. 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................................................................................. 219
8.2.1.4. 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
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Theory Guide
8.2.2.1. Description of the Probability Density Function............................................................ 221
8.2.2.2. Derivation of Mean Scalar Values from the Instantaneous Mixture Fraction................... 222
8.2.2.3.The Assumed-Shape PDF............................................................................................. 222
8.2.2.3.1.The Double Delta Function PDF........................................................................... 223
8.2.2.3.2. The β-Function PDF............................................................................................. 223
8.2.3. Non-Adiabatic Extensions of the Non-Premixed Model.......................................................... 224
8.2.4. Chemistry Tabulation ........................................................................................................... 227
8.2.4.1. Look-Up Tables for Adiabatic Systems........................................................................... 227
8.2.4.2. 3D Look-Up Tables for Non-Adiabatic Systems.............................................................. 228
8.2.4.3. 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...................................................................... 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
8.3.4.1. Mixture Composition................................................................................................... 237
8.3.4.1.1. Property Evaluation............................................................................................. 238
8.4.The Diffusion Flamelet Models Theory........................................................................................... 238
8.4.1. Restrictions and Assumptions............................................................................................... 238
8.4.2.The Flamelet Concept........................................................................................................... 239
8.4.2.1. Overview..................................................................................................................... 239
8.4.2.2. Strain Rate and Scalar Dissipation................................................................................. 240
8.4.2.3. 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................................................................................. 244
8.5.1. Overview ............................................................................................................................. 244
8.5.2. Multiple Steady Flamelet Libraries........................................................................................ 245
8.5.3. Steady Diffusion Flamelet Automated Grid Refinement......................................................... 245
8.5.4. Non-Adiabatic Steady Diffusion Flamelets............................................................................. 246
8.6.The Unsteady Diffusion Flamelet Model Theory............................................................................. 246
8.6.1.The Eulerian Unsteady Laminar Flamelet Model.................................................................... 247
8.6.1.1. Liquid Reactions.......................................................................................................... 249
8.6.2.The Diesel Unsteady Laminar Flamelet Model....................................................................... 249
8.6.3. Multiple Diesel Unsteady Flamelets....................................................................................... 250
8.6.4. Multiple Diesel Unsteady Flamelets with Flamelet Reset........................................................ 251
8.6.4.1. Resetting the Flamelets................................................................................................ 251
9. Premixed Combustion......................................................................................................................... 253
9.1. Overview and Limitations............................................................................................................. 253
9.1.1. Overview ............................................................................................................................. 253
9.1.2. Limitations........................................................................................................................... 254
9.2. C-Equation Model Theory.............................................................................................................. 254
9.2.1. Propagation of the Flame Front............................................................................................ 254
9.3. G-Equation Model Theory............................................................................................................. 255
9.3.1. Numerical Solution of the G-equation................................................................................... 257
9.4.Turbulent Flame Speed Models..................................................................................................... 257
9.4.1. Zimont Turbulent Flame Speed Closure Model...................................................................... 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.Wall Damping.............................................................................................................. 260
9.4.2. Peters Flame Speed Model.................................................................................................... 260
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x of ANSYS, Inc. and its subsidiaries and affiliates.