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ANSYS Fluent Theory Guide
Release 15.0ANSYS, Inc.
November 2013Southpointe
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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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Theory Guide
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
v
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of ANSYS, Inc. and its subsidiaries and affiliates.
Theory Guide
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