ANSYS_2020_Fluent_Theory_Guide

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ANSYS Fluent Theory Guide

Release 2020 R1ANSYS, Inc.

January 2020Southpointe

2600 ANSYS Drive

Canonsburg, PA 15317

ANSYS, Inc. and

ANSYS Europe,

ansysinfo@ansys.com

Ltd. are UL

http://www.ansys.com

registered ISO

(T) 724-746-3304

(F) 724-514-9494

9001: 2015

companies.

Table of Contents

Using This Manual ................................................................................................................................... xxxix

1.The Contents of This Manual .......................................................................................................... xxxix

2.Typographical Conventions ................................................................................................................. xl

3. Mathematical Conventions ............................................................................................................... xliii

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 ................................................................................................ 14

1.6.2.1. Basic Equations for Compressible Flows ......................................................................... 14

1.6.2.2.The Compressible Form of the Gas Law .......................................................................... 15

1.7. Inviscid Flows ................................................................................................................................. 15

1.7.1. Euler Equations ...................................................................................................................... 15

1.7.1.1.The Mass Conservation Equation .................................................................................... 16

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 .................................................................................................. 19

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

2.3.1.3.2. Interface Treatment: Absolute Velocity Formulation ............................................... 25

2.3.2.The Mixing Plane Model ......................................................................................................... 25

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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 .................................................................................................... 29

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 .................................................................................................................... 35

3.2.1. Conservation Equations ......................................................................................................... 36

3.2.2. Six DOF Solver Theory ............................................................................................................ 37

3.3. Sliding Mesh Theory ....................................................................................................................... 38

4.Turbulence ............................................................................................................................................. 39

4.1. Underlying Principles of Turbulence Modeling ................................................................................. 39

4.1.1. Reynolds (Ensemble) Averaging .............................................................................................. 40

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 ............................................................................................................................... 43

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

4.2.7.1.Treatment of the Spalart-Allmaras Model for Icing Simulations ....................................... 46

4.2.8. Convective Heat and Mass Transfer Modeling .......................................................................... 46

4.3. Standard, RNG, and Realizable k-ε Models ........................................................................................ 47

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 ............................................................. 48

4.3.1.3. Modeling the Turbulent Viscosity ................................................................................... 48

4.3.1.4. Model Constants ........................................................................................................... 48

4.3.2. RNG k-ε Model ....................................................................................................................... 49

4.3.2.1. Overview ....................................................................................................................... 49

4.3.2.2. Transport Equations for the RNG k-ε Model ..................................................................... 49

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 ........................................................................................ 51

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 ............................................................ 53

4.3.3.3. Modeling the Turbulent Viscosity ................................................................................... 54

4.3.3.4. Model Constants ........................................................................................................... 54

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Theory Guide

4.3.4. Modeling Turbulent Production in the k-ε Models ................................................................... 55

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, BSL, and SST k-ω Models ................................................................................................... 58

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 ............................................................. 59

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 Effects .......................................................................................... 61

4.4.1.6. Model Constants ........................................................................................................... 62

4.4.2. Baseline (BSL) k-ω Model ........................................................................................................ 62

4.4.2.1. Overview ....................................................................................................................... 62

4.4.2.2. Transport Equations for the BSL k-ω Model ..................................................................... 62

4.4.2.3. Modeling the Effective Diffusivity ................................................................................... 63

4.4.2.4. Modeling the Turbulence Production ............................................................................. 63

4.4.2.4.1. Production of k ..................................................................................................... 63

4.4.2.4.2. Production of ω ..................................................................................................... 63

4.4.2.5. Modeling the Turbulence Dissipation ............................................................................. 64

4.4.2.5.1. Dissipation of k ..................................................................................................... 64

4.4.2.5.2. Dissipation of ω ..................................................................................................... 64

4.4.2.6. Cross-Diffusion Modification .......................................................................................... 64

4.4.2.7. Model Constants ........................................................................................................... 64

4.4.3. Shear-Stress Transport (SST) k-ω Model ................................................................................... 65

4.4.3.1. Overview ....................................................................................................................... 65

4.4.3.2. Modeling the Turbulent Viscosity ................................................................................... 65

4.4.3.3. Model Constants ........................................................................................................... 65

4.4.3.4.Treatment of the SST Model for Icing Simulations ........................................................... 65

4.4.4. Effects of Buoyancy on Turbulence in the k-ω Models .............................................................. 66

4.4.5.Turbulence Damping .............................................................................................................. 67

4.4.6. Wall Boundary Conditions ...................................................................................................... 68

4.5. Generalized k-ω (GEKO) Model ........................................................................................................ 68

4.5.1. Model Formulation ................................................................................................................. 69

4.5.2. Limitations ............................................................................................................................. 71

4.6. k-kl-ω Transition Model ................................................................................................................... 71

4.6.1. Overview ............................................................................................................................... 71

4.6.2. Transport Equations for the k-kl-ω Model ................................................................................ 71

4.6.2.1. Model Constants ........................................................................................................... 74

4.7.Transition SST Model ....................................................................................................................... 74

4.7.1. Overview ............................................................................................................................... 75

4.7.2.Transport Equations for the Transition SST Model .................................................................... 75

4.7.2.1. Separation-Induced Transition Correction ...................................................................... 77

4.7.2.2. Coupling the Transition Model and SST Transport Equations ........................................... 78

4.7.2.3.Transition SST and Rough Walls ...................................................................................... 78

4.7.3. Mesh Requirements ............................................................................................................... 79

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Theory Guide

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