ANSYS FLUENT 14.0 Theory Guide

826 Pages·2016·24.75 MB·English

ANSYS FLUENT Theory Guide
ANSYS, Inc. Release 14.0
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Table of Contents
Using This Manual..................................................................................................................................... xxv
1.The Contents of This Manual............................................................................................................. xxv
2.The Contents of the FLUENT Manuals............................................................................................... xxvi
3.Typographical Conventions............................................................................................................ xxvii
4. Mathematical Conventions............................................................................................................. xxvii
5.Technical Support ........................................................................................................................... xxix
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................................................................................................................................. 7
1.4.2. Limitations............................................................................................................................... 7
1.4.3. Physics of Periodic Flows.......................................................................................................... 8
1.4.3.1. Definition of the Periodic Velocity.................................................................................... 8
1.4.3.2. Definition of the Streamwise-Periodic Pressure................................................................ 8
1.5. Swirling and Rotating Flows.............................................................................................................. 9
1.5.1. Overview of Swirling and Rotating Flows................................................................................ 10
1.5.1.1. Axisymmetric Flows with Swirl or Rotation..................................................................... 10
1.5.1.1.1. Momentum Conservation Equation for Swirl Velocity............................................. 11
1.5.1.2.Three-Dimensional Swirling Flows.................................................................................. 11
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............................................................................ 14
1.6.2. Physics of Compressible Flows................................................................................................ 14
1.6.2.1. Basic Equations for Compressible Flows......................................................................... 15
1.6.2.2.The Compressible Form of the Gas Law.......................................................................... 15
1.7. Inviscid Flows ................................................................................................................................. 16
1.7.1. Euler Equations...................................................................................................................... 16
1.7.1.1.The Mass Conservation Equation.................................................................................... 16
1.7.1.2. Momentum Conservation Equations.............................................................................. 17
1.7.1.3. Energy Conservation Equation....................................................................................... 17
2. Flows with Moving Reference Frames................................................................................................... 19
2.1. Introduction ................................................................................................................................... 19
2.2. Flow in a Moving Reference Frame.................................................................................................. 21
2.2.1. Equations for a Moving Reference Frame................................................................................ 21
2.2.1.1. Relative Velocity Formulation......................................................................................... 22
2.2.1.2. Absolute Velocity Formulation....................................................................................... 23
2.2.1.3. Relative Specification of the Reference Frame Motion..................................................... 24
2.3. Flow in Multiple Reference Frames.................................................................................................. 24
2.3.1.The Multiple Reference Frame Model...................................................................................... 25
2.3.1.1. Overview....................................................................................................................... 25
2.3.1.2. Examples....................................................................................................................... 25
2.3.1.3.The MRF Interface Formulation...................................................................................... 27
2.3.1.3.1. Interface Treatment: Relative Velocity Formulation................................................. 27
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2.3.1.3.2. Interface Treatment: Absolute Velocity Formulation............................................... 28
2.3.2.The Mixing Plane Model......................................................................................................... 28
2.3.2.1. Overview....................................................................................................................... 29
2.3.2.2. Rotor and Stator Domains.............................................................................................. 29
2.3.2.3.The Mixing Plane Concept............................................................................................. 30
2.3.2.4. Choosing an Averaging Method..................................................................................... 31
2.3.2.4.1. Area Averaging..................................................................................................... 31
2.3.2.4.2. Mass Averaging .................................................................................................... 31
2.3.2.4.3. Mixed-Out Averaging............................................................................................ 32
2.3.2.5. Mixing Plane Algorithm of ANSYS FLUENT ..................................................................... 33
2.3.2.6. Mass Conservation ........................................................................................................ 33
2.3.2.7. Swirl Conservation......................................................................................................... 33
2.3.2.8.Total Enthalpy Conservation.......................................................................................... 34
3. Flows Using Sliding and Dynamic Meshes............................................................................................ 35
3.1. Introduction ................................................................................................................................... 35
3.2. Dynamic Mesh Theory.................................................................................................................... 36
3.2.1. Conservation Equations ......................................................................................................... 37
3.2.2. Six DOF (6DOF) Solver Theory................................................................................................. 38
3.3. Sliding Mesh Theory....................................................................................................................... 39
4.Turbulence............................................................................................................................................. 41
4.1. Underlying Principles of Turbulence Modeling................................................................................. 41
4.1.1. Reynolds (Ensemble) Averaging.............................................................................................. 41
4.1.2. Filtered Navier-Stokes Equations............................................................................................. 42
4.1.3. Hybrid RANS-LES Formulations............................................................................................... 44
4.1.4. Boussinesq Approach vs. Reynolds Stress Transport Models..................................................... 44
4.2. Spalart-Allmaras Model................................................................................................................... 44
4.2.1. Overview............................................................................................................................... 45
4.2.2.Transport Equation for the Spalart-Allmaras Model................................................................. 45
4.2.3. Modeling the Turbulent Viscosity............................................................................................ 46
4.2.4. Modeling the Turbulent Production........................................................................................ 46
4.2.5. Modeling the Turbulent Destruction....................................................................................... 47
4.2.6. Model Constants.................................................................................................................... 48
4.2.7.Wall Boundary Conditions...................................................................................................... 48
4.2.8. Convective Heat and Mass Transfer Modeling.......................................................................... 49
4.3. Standard, RNG, and Realizable k- ε Models....................................................................................... 49
4.3.1. Standard k- ε Model............................................................................................................... 49
4.3.1.1. Overview....................................................................................................................... 49
4.3.1.2. Transport Equations for the Standard k- ε Model............................................................. 50
4.3.1.3. Modeling the Turbulent Viscosity................................................................................... 50
4.3.1.4. Model Constants........................................................................................................... 51
4.3.2. RNG k- ε Model....................................................................................................................... 51
4.3.2.1. Overview....................................................................................................................... 51
4.3.2.2. Transport Equations for the RNG k- ε Model.................................................................... 51
4.3.2.3. Modeling the Effective Viscosity..................................................................................... 52
4.3.2.4. RNG Swirl Modification.................................................................................................. 53
4.3.2.5. Calculating the Inverse Effective Prandtl Numbers.......................................................... 53
4.3.2.6. The R-ε Term in the ε Equation........................................................................................ 53
4.3.2.7. Model Constants........................................................................................................... 54
4.3.3. Realizable k- ε Model.............................................................................................................. 54
4.3.3.1. Overview....................................................................................................................... 54
4.3.3.2. Transport Equations for the Realizable k- ε Model........................................................... 56
4.3.3.3. Modeling the Turbulent Viscosity................................................................................... 57
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4.3.3.4. Model Constants........................................................................................................... 58
4.3.4. Modeling Turbulent Production in the k- ε Models.................................................................. 58
4.3.5. Effects of Buoyancy on Turbulence in the k- ε Models.............................................................. 59
4.3.6. Effects of Compressibility on Turbulence in the k- ε Models..................................................... 60
4.3.7. Convective Heat and Mass Transfer Modeling in the k- ε Models.............................................. 60
4.4. Standard and SST k- ω Models......................................................................................................... 62
4.4.1. Standard k- ω Model............................................................................................................... 62
4.4.1.1. Overview....................................................................................................................... 62
4.4.1.2. Transport Equations for the Standard k- ω Model............................................................ 63
4.4.1.3. Modeling the Effective Diffusivity................................................................................... 63
4.4.1.3.1. Low-Reynolds-Number Correction........................................................................ 63
4.4.1.4. Modeling the Turbulence Production............................................................................. 64
4.4.1.4.1. Production of k..................................................................................................... 64
4.4.1.4.2. Production of ω..................................................................................................... 64
4.4.1.5. Modeling the Turbulence Dissipation............................................................................. 65
4.4.1.5.1. Dissipation of k..................................................................................................... 65
4.4.1.5.2. Dissipation of ω..................................................................................................... 66
4.4.1.5.3. Compressibility Correction.................................................................................... 67
4.4.1.6. Model Constants........................................................................................................... 67
4.4.2. Shear-Stress Transport (SST) k- ω Model.................................................................................. 68
4.4.2.1. Overview....................................................................................................................... 68
4.4.2.2. Transport Equations for the SST k- ω Model.................................................................... 68
4.4.2.3. Modeling the Effective Diffusivity................................................................................... 69
4.4.2.4. Modeling the Turbulence Production............................................................................. 70
4.4.2.4.1. Production of k..................................................................................................... 70
4.4.2.4.2. Production of ω..................................................................................................... 70
4.4.2.5. Modeling the Turbulence Dissipation............................................................................. 71
4.4.2.5.1. Dissipation of k..................................................................................................... 71
4.4.2.5.2. Dissipation of ω..................................................................................................... 71
4.4.2.6. Cross-Diffusion Modification.......................................................................................... 72
4.4.2.7. Model Constants........................................................................................................... 72
4.4.3.Turbulence Damping.............................................................................................................. 72
4.4.4.Wall Boundary Conditions...................................................................................................... 73
4.5. k- kl- ω Transition Model.................................................................................................................. 74
4.5.1. Overview............................................................................................................................... 74
4.5.2. Transport Equations for the k- kl- ω Model............................................................................... 74
4.5.2.1. Model Constants........................................................................................................... 79
4.6.Transition SST Model....................................................................................................................... 79
4.6.1. Overview............................................................................................................................... 80
4.6.2.Transport Equations for the Transition SST Model.................................................................... 80
4.6.2.1. Separation Induced Transition Correction....................................................................... 81
4.6.2.2. Coupling the Transition Model and SST Transport Equations........................................... 83
4.6.2.3.Transition SST and Rough Walls...................................................................................... 84
4.6.3. Specifying Inlet Turbulence Levels.......................................................................................... 84
4.7.The V2F Model................................................................................................................................ 86
4.8. Reynolds Stress Model (RSM)........................................................................................................... 87
4.8.1. Overview............................................................................................................................... 87
4.8.2. Reynolds Stress Transport Equations....................................................................................... 87
4.8.3. Modeling Turbulent Diffusive Transport.................................................................................. 88
4.8.4. Modeling the Pressure-Strain Term......................................................................................... 89
4.8.4.1. Linear Pressure-Strain Model.......................................................................................... 89
4.8.4.2. Low-Re Modifications to the Linear Pressure-Strain Model.............................................. 90
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4.8.4.3. Quadratic Pressure-Strain Model.................................................................................... 91
4.8.4.4. Low-Re Stress-Omega Model......................................................................................... 92
4.8.5. Effects of Buoyancy on Turbulence......................................................................................... 93
4.8.6. Modeling the Turbulence Kinetic Energy................................................................................. 94
4.8.7. Modeling the Dissipation Rate................................................................................................ 95
4.8.8. Modeling the Turbulent Viscosity............................................................................................ 95
4.8.9.Wall Boundary Conditions...................................................................................................... 96
4.8.10. Convective Heat and Mass Transfer Modeling........................................................................ 96
4.9. Scale-Adaptive Simulation (SAS) Model........................................................................................... 97
4.9.1. Overview............................................................................................................................... 97
4.9.2.Transport Equations for the SAS Model................................................................................... 98
4.10. Detached Eddy Simulation (DES)................................................................................................. 100
4.10.1. Overview ........................................................................................................................... 101
4.10.2. Spalart-Allmaras Based DES Model...................................................................................... 101
4.10.3. Realizable k- ε Based DES Model......................................................................................... 102
4.10.4. SST k- ω Based DES Model................................................................................................... 103
4.10.5. Improved Delayed Detached Eddy Simulation (IDDES)........................................................ 104
4.10.5.1. Overview of IDDES..................................................................................................... 104
4.10.5.2. IDDES Model Formulation.......................................................................................... 104
4.11. Large Eddy Simulation (LES) Model.............................................................................................. 105
4.11.1. Overview ........................................................................................................................... 105
4.11.2. Subgrid-Scale Models......................................................................................................... 106
4.11.2.1. Smagorinsky-Lilly Model............................................................................................ 107
4.11.2.2. Dynamic Smagorinsky-Lilly Model.............................................................................. 108
4.11.2.3.Wall-Adapting Local Eddy-Viscosity (WALE) Model...................................................... 109
4.11.2.4. Algebraic Wall-Modeled LES Model (WMLES).............................................................. 110
4.11.2.4.1. Algebraic WMLES Model Formulation................................................................ 111
4.11.2.4.1.1. Reynolds Number Scaling......................................................................... 111
4.11.2.5. Dynamic Kinetic Energy Subgrid-Scale Model............................................................. 113
4.11.3. Inlet Boundary Conditions for the LES Model....................................................................... 113
4.11.3.1.Vortex Method........................................................................................................... 114
4.11.3.2. Spectral Synthesizer................................................................................................... 115
4.12. Embedded Large Eddy Simulation (ELES)..................................................................................... 116
4.12.1. Overview ........................................................................................................................... 116
4.12.2. Selecting a Model............................................................................................................... 116
4.12.3. Interfaces Treatment........................................................................................................... 117
4.12.3.1. RANS-LES Interface.................................................................................................... 117
4.12.3.2. LES-RANS Interface.................................................................................................... 118
4.12.3.3. Internal Interface Without LES Zone........................................................................... 118
4.12.3.4. Grid Generation Guidelines ....................................................................................... 119
4.13. Near-Wall Treatments for Wall-Bounded Turbulent Flows.............................................................. 119
4.13.1. Overview ........................................................................................................................... 119
4.13.1.1.Wall Functions vs. Near-Wall Model............................................................................. 120
4.13.1.2.Wall Functions........................................................................................................... 122
4.13.2. Standard Wall Functions..................................................................................................... 122
4.13.2.1. Momentum............................................................................................................... 122
4.13.2.2. Energy....................................................................................................................... 123
4.13.2.3. Species...................................................................................................................... 125
4.13.2.4.Turbulence ................................................................................................................ 126
4.13.3. Scalable Wall Functions ...................................................................................................... 127
4.13.4. Non-Equilibrium Wall Functions.......................................................................................... 127
4.13.4.1. Standard Wall Functions vs. Non-Equilibrium Wall Functions....................................... 129
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4.13.4.2. Limitations of the Wall Function Approach................................................................. 129
4.13.5. Enhanced Wall Treatment ε-Equation (EWT-ε)...................................................................... 129
4.13.5.1.Two-Layer Model for Enhanced Wall Treatment........................................................... 130
4.13.5.2. Enhanced Wall Treatment for Momentum and Energy Equations ................................ 132
4.13.6. Enhanced Wall Treatment ω-Equation (EWT-ω).................................................................... 135
4.13.7. User-Defined Wall Functions............................................................................................... 135
4.13.8. LES Near-Wall Treatment..................................................................................................... 135
4.14. Curvature Correction for the Spalart-Allmaras and Two-Equation Models..................................... 136
5. Heat Transfer....................................................................................................................................... 139
5.1. Introduction ................................................................................................................................. 139
5.2. Modeling Conductive and Convective Heat Transfer...................................................................... 139
5.2.1. Heat Transfer Theory............................................................................................................. 139
5.2.1.1.The Energy Equation.................................................................................................... 139
5.2.1.2.The Energy Equation in Moving Reference Frames........................................................ 140
5.2.1.3.The Energy Equation for the Non-Premixed Combustion Model.................................... 141
5.2.1.4. Inclusion of Pressure Work and Kinetic Energy Terms.................................................... 141
5.2.1.5. Inclusion of the Viscous Dissipation Terms.................................................................... 141
5.2.1.6. Inclusion of the Species Diffusion Term........................................................................ 142
5.2.1.7. Energy Sources Due to Reaction................................................................................... 142
5.2.1.8. Energy Sources Due To Radiation................................................................................. 143
5.2.1.9. Interphase Energy Sources........................................................................................... 143
5.2.1.10. Energy Equation in Solid Regions............................................................................... 143
5.2.1.11. Anisotropic Conductivity in Solids.............................................................................. 143
5.2.1.12. Diffusion at Inlets....................................................................................................... 143
5.2.2. Natural Convection and Buoyancy-Driven Flows Theory........................................................ 144
5.3. Modeling Radiation ...................................................................................................................... 144
5.3.1. Overview and Limitations..................................................................................................... 145
5.3.1.1. Advantages and Limitations of the DTRM..................................................................... 145
5.3.1.2. Advantages and Limitations of the P-1 Model............................................................... 146
5.3.1.3. Advantages and Limitations of the Rosseland Model.................................................... 146
5.3.1.4. Advantages and Limitations of the DO Model............................................................... 146
5.3.1.5. Advantages and Limitations of the S2S Model.............................................................. 147
5.3.2. Radiative Transfer Equation.................................................................................................. 147
5.3.3. P-1 Radiation Model Theory.................................................................................................. 149
5.3.3.1.The P-1 Model Equations............................................................................................. 149
5.3.3.2. Anisotropic Scattering................................................................................................. 150
5.3.3.3. Particulate Effects in the P-1 Model.............................................................................. 151
5.3.3.4. Boundary Condition Treatment for the P-1 Model at Walls............................................. 152
5.3.3.5. Boundary Condition Treatment for the P-1 Model at Flow Inlets and Exits...................... 153
5.3.4. Rosseland Radiation Model Theory....................................................................................... 154
5.3.4.1.The Rosseland Model Equations................................................................................... 154
5.3.4.2. Anisotropic Scattering................................................................................................. 154
5.3.4.3. Boundary Condition Treatment at Walls........................................................................ 155
5.3.4.4. Boundary Condition Treatment at Flow Inlets and Exits................................................. 155
5.3.5. Discrete Transfer Radiation Model (DTRM) Theory................................................................. 155
5.3.5.1.The DTRM Equations.................................................................................................... 155
5.3.5.2. Ray Tracing.................................................................................................................. 156
5.3.5.3. Clustering.................................................................................................................... 157
5.3.5.4. Boundary Condition Treatment for the DTRM at Walls................................................... 158
5.3.5.5. Boundary Condition Treatment for the DTRM at Flow Inlets and Exits............................ 158
5.3.6. Discrete Ordinates (DO) Radiation Model Theory................................................................... 158
5.3.6.1.The DO Model Equations............................................................................................. 159
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5.3.6.2. Energy Coupling and the DO Model............................................................................. 160
5.3.6.2.1. Limitations of DO/Energy Coupling..................................................................... 161
5.3.6.3. Angular Discretization and Pixelation........................................................................... 161
5.3.6.4. Anisotropic Scattering................................................................................................. 164
5.3.6.5. Particulate Effects in the DO Model.............................................................................. 165
5.3.6.6. Boundary and Cell Zone Condition Treatment at Opaque Walls..................................... 165
5.3.6.6.1. Gray Diffuse Walls............................................................................................... 167
5.3.6.6.2. Non-Gray Diffuse Walls........................................................................................ 167
5.3.6.7. Cell Zone and Boundary Condition Treatment at Semi-Transparent Walls...................... 168
5.3.6.7.1. Semi-Transparent Interior Walls........................................................................... 168
5.3.6.7.2. Specular Semi-Transparent Walls......................................................................... 169
5.3.6.7.3. Diffuse Semi-Transparent Walls............................................................................ 172
5.3.6.7.4. Partially Diffuse Semi-Transparent Walls............................................................... 173
5.3.6.7.5. Semi-Transparent Exterior Walls........................................................................... 173
5.3.6.7.6. Limitations.......................................................................................................... 175
5.3.6.7.7. Solid Semi-Transparent Media............................................................................. 176
5.3.6.8. Boundary Condition Treatment at Specular Walls and Symmetry Boundaries................. 176
5.3.6.9. Boundary Condition Treatment at Periodic Boundaries................................................. 176
5.3.6.10. Boundary Condition Treatment at Flow Inlets and Exits............................................... 176
5.3.7. Surface-to-Surface (S2S) Radiation Model Theory.................................................................. 176
5.3.7.1. Gray-Diffuse Radiation................................................................................................. 176
5.3.7.2.The S2S Model Equations............................................................................................. 177
5.3.7.3. Clustering.................................................................................................................... 178
5.3.7.3.1. Clustering and View Factors................................................................................ 178
5.3.7.3.2. Clustering and Radiosity...................................................................................... 179
5.3.8. Radiation in Combusting Flows............................................................................................ 179
5.3.8.1.The Weighted-Sum-of-Gray-Gases Model..................................................................... 179
5.3.8.1.1.When the Total (Static) Gas Pressure is Not Equal to 1 atm.................................... 181
5.3.8.2.The Effect of Soot on the Absorption Coefficient........................................................... 181
5.3.8.3.The Effect of Particles on the Absorption Coefficient..................................................... 182
5.3.9. Choosing a Radiation Model................................................................................................. 182
5.3.9.1. External Radiation ....................................................................................................... 183
6. Heat Exchangers.................................................................................................................................. 185
6.1.The Macro Heat Exchanger Models................................................................................................ 185
6.1.1. Overview of the Macro Heat Exchanger Models.................................................................... 185
6.1.2. Restrictions of the Macro Heat Exchanger Models................................................................. 186
6.1.3. Macro Heat Exchanger Model Theory.................................................................................... 187
6.1.3.1. Streamwise Pressure Drop........................................................................................... 188
6.1.3.2. Heat Transfer Effectiveness........................................................................................... 190
6.1.3.3. Heat Rejection............................................................................................................. 190
6.1.3.4. Macro Heat Exchanger Group Connectivity.................................................................. 192
6.2.The Dual Cell Model...................................................................................................................... 193
6.2.1. Overview of the Dual Cell Model........................................................................................... 193
6.2.2. Restrictions of the Dual Cell Model........................................................................................ 194
6.2.3. Dual Cell Model Theory......................................................................................................... 194
6.2.3.1. NTU Relations.............................................................................................................. 195
6.2.3.2. Heat Rejection............................................................................................................. 195
7. Species Transport and Finite-Rate Chemistry..................................................................................... 197
7.1.Volumetric Reactions .................................................................................................................... 197
7.1.1. Species Transport Equations................................................................................................. 197
7.1.1.1. Mass Diffusion in Laminar Flows................................................................................... 198
7.1.1.2. Mass Diffusion in Turbulent Flows................................................................................ 198
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7.1.1.3.Treatment of Species Transport in the Energy Equation................................................. 198
7.1.1.4. Diffusion at Inlets......................................................................................................... 199
7.1.2.The Generalized Finite-Rate Formulation for Reaction Modeling............................................ 199
7.1.2.1.The Laminar Finite-Rate Model..................................................................................... 199
7.1.2.2. Pressure-Dependent Reactions.................................................................................... 202
7.1.2.3.The Eddy-Dissipation Model......................................................................................... 204
7.1.2.4.The Eddy-Dissipation Model for LES............................................................................. 205
7.1.2.5.The Eddy-Dissipation-Concept (EDC) Model................................................................. 206
7.1.2.6.The Thickened Flame Model......................................................................................... 207
7.1.2.7.The Relaxation to Chemical Equilibrium Model............................................................. 209
7.2.Wall Surface Reactions and Chemical Vapor Deposition.................................................................. 210
7.2.1. Surface Coverage Reaction Rate Modification....................................................................... 212
7.2.2. Reaction-Diffusion Balance for Surface Chemistry................................................................. 213
7.2.3. Slip Boundary Formulation for Low-Pressure Gas Systems..................................................... 214
7.3. Particle Surface Reactions............................................................................................................. 216
7.3.1. General Description.............................................................................................................. 216
7.3.2. ANSYS FLUENT Model Formulation....................................................................................... 217
7.3.3. Extension for Stoichiometries with Multiple Gas Phase Reactants.......................................... 219
7.3.4. Solid-Solid Reactions............................................................................................................ 219
7.3.5. Solid Decomposition Reactions............................................................................................ 219
7.3.6. Solid Deposition Reactions................................................................................................... 220
7.3.7. Gaseous Solid Catalyzed Reactions on the Particle Surface.................................................... 220
7.4. Reacting Channel Model............................................................................................................... 220
7.4.1. Overview and Limitations..................................................................................................... 220
7.4.2. Reacting Channel Model Theory........................................................................................... 221
7.4.2.1. Flow Inside the Reacting Channel................................................................................. 221
7.4.2.2. Outer Flow in the Shell................................................................................................. 223
8. Non-Premixed Combustion................................................................................................................. 225
8.1. Introduction ................................................................................................................................. 225
8.2. Non-Premixed Combustion and Mixture Fraction Theory............................................................... 225
8.2.1. Mixture Fraction Theory....................................................................................................... 226
8.2.1.1. Definition of the Mixture Fraction................................................................................ 226
8.2.1.2.Transport Equations for the Mixture Fraction................................................................ 228
8.2.1.3.The Non-Premixed Model for LES................................................................................. 229
8.2.1.4. Mixture Fraction vs. Equivalence Ratio.......................................................................... 229
8.2.1.5. Relationship of Mixture Fraction to Species Mass Fraction, Density, and Temperature..... 230
8.2.2. Modeling of Turbulence-Chemistry Interaction..................................................................... 231
8.2.2.1. Description of the Probability Density Function............................................................ 231
8.2.2.2. Derivation of Mean Scalar Values from the Instantaneous Mixture Fraction................... 232
8.2.2.3.The Assumed-Shape PDF............................................................................................. 233
8.2.2.3.1.The Double Delta Function PDF........................................................................... 233
8.2.2.3.2. The β-Function PDF............................................................................................. 234
8.2.3. Non-Adiabatic Extensions of the Non-Premixed Model.......................................................... 235
8.2.4. Chemistry Tabulation ........................................................................................................... 237
8.2.4.1. Look-Up Tables for Adiabatic Systems........................................................................... 237
8.2.4.2. 3D Look-Up Tables for Non-Adiabatic Systems.............................................................. 239
8.3. Restrictions and Special Cases for Using the Non-Premixed Model................................................. 241
8.3.1. Restrictions on the Mixture Fraction Approach...................................................................... 242
8.3.2. Using the Non-Premixed Model for Liquid Fuel or Coal Combustion...................................... 244
8.3.3. Using the Non-Premixed Model with Flue Gas Recycle.......................................................... 245
8.3.4. Using the Non-Premixed Model with the Inert Model............................................................ 246
8.3.4.1. Mixture Composition................................................................................................... 246
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ANSYS FLUENT Theory Guide
8.3.4.1.1. Property Evaluation............................................................................................. 247
8.4.The Laminar Flamelet Models Theory............................................................................................. 248
8.4.1. Restrictions and Assumptions............................................................................................... 248
8.4.2.The Flamelet Concept........................................................................................................... 248
8.4.2.1. Overview..................................................................................................................... 248
8.4.2.2. Strain Rate and Scalar Dissipation................................................................................. 250
8.4.2.3. Embedding Laminar Flamelets in Turbulent Flames...................................................... 251
8.4.3. Flamelet Generation............................................................................................................. 252
8.4.4. Flamelet Import ................................................................................................................... 252
8.5.The Steady Laminar Flamelet Model Theory................................................................................... 254
8.5.1. Overview ............................................................................................................................. 254
8.5.2. Multiple Steady Flamelet Libraries........................................................................................ 255
8.5.3. Steady Laminar Flamelet Automated Grid Refinement.......................................................... 255
8.5.4. Non-Adiabatic Steady Laminar Flamelets.............................................................................. 256
8.6.The Unsteady Laminar Flamelet Model Theory............................................................................... 257
8.6.1.The Eulerian Unsteady Laminar Flamelet Model.................................................................... 257
8.6.1.1. Liquid Reactions.......................................................................................................... 259
8.6.2.The Diesel Unsteady Laminar Flamelet Model....................................................................... 260
9. Premixed Combustion......................................................................................................................... 263
9.1. Overview and Limitations............................................................................................................. 263
9.1.1. Overview ............................................................................................................................. 263
9.1.2. Limitations........................................................................................................................... 264
9.2. C-Equation Model Theory.............................................................................................................. 264
9.2.1. Propagation of the Flame Front............................................................................................ 264
9.3. G-Equation Model Theory............................................................................................................. 266
9.3.1. Numerical Solution of the G-equation................................................................................... 267
9.4.Turbulent Flame Speed Models..................................................................................................... 267
9.4.1. Zimont Turbulent Flame Speed Closure Model...................................................................... 268
9.4.1.1. Zimont Turbulent Flame Speed Closure for LES............................................................. 269
9.4.1.2. Flame Stretch Effect..................................................................................................... 269
9.4.1.3. Gradient Diffusion....................................................................................................... 270
9.4.1.4.Wall Damping.............................................................................................................. 271
9.4.2. Peters Flame Speed Model.................................................................................................... 271
9.4.2.1. Peters Flame Speed Model for LES................................................................................ 272
9.5. Extended Coherent Flamelet Model Theory................................................................................... 273
9.5.1. Closure for ECFM Source Terms............................................................................................. 275
9.5.2.Turbulent Flame Speed in ECFM............................................................................................ 278
9.5.3. LES and ECFM...................................................................................................................... 278
9.6. Calculation of Properties............................................................................................................... 281
9.6.1. Calculation of Temperature................................................................................................... 281
9.6.1.1. Adiabatic Temperature Calculation............................................................................... 282
9.6.1.2. Non-Adiabatic Temperature Calculation....................................................................... 282
9.6.2. Calculation of Density.......................................................................................................... 282
9.6.3. Laminar Flame Speed........................................................................................................... 283
9.6.4. Unburnt Density and Thermal Diffusivity............................................................................... 283
10. Partially Premixed Combustion........................................................................................................ 285
10.1. Overview.................................................................................................................................... 285
10.2. Limitations.................................................................................................................................. 285
10.3. Partially Premixed Combustion Theory........................................................................................ 285
10.3.1. Calculation of Scalar Quantities........................................................................................... 286
10.3.2. Laminar Flame Speed......................................................................................................... 287
11. Composition PDF Transport.............................................................................................................. 289
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of ANSYS, Inc. and its subsidiaries and affiliates.