2.3.2.The Mixing Plane Model ......................................................................................................... 28
2.3.2.1. Overview ....................................................................................................................... 28
2.3.2.2. Rotor and Stator Domains .............................................................................................. 28
2.3.2.3. The Mixing Plane Concept ............................................................................................. 30
2.3.2.4. Choosing an Averaging Method ..................................................................................... 30
2.3.2.4.1. Area Averaging ..................................................................................................... 31
2.3.2.4.2. Mass Averaging .................................................................................................... 31
2.3.2.4.3. Mixed-Out Averaging ............................................................................................ 31
2.3.2.5. Mixing Plane Algorithm of Ansys Fluent ......................................................................... 32
2.3.2.6. Mass Conservation ........................................................................................................ 32
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 .................................................................................................................... 37
3.2.1. Conservation Equations ......................................................................................................... 38
3.2.2. Six DOF Solver Theory ............................................................................................................ 39
3.3. Sliding Mesh Theory ....................................................................................................................... 40
4.Turbulence ............................................................................................................................................. 41
4.1. Underlying Principles of Turbulence Modeling ................................................................................. 41
4.1.1. Reynolds (Ensemble) Averaging .............................................................................................. 42
4.1.2. Filtered Navier-Stokes Equations ............................................................................................. 42
4.1.3. Hybrid RANS-LES Formulations ............................................................................................... 43
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 .................................................................................................................... 47
4.2.7. Wall Boundary Conditions ...................................................................................................... 47
4.2.7.1.Treatment of the Spalart-Allmaras Model for Icing Simulations ....................................... 48
4.2.8. Convective Heat and Mass Transfer Modeling .......................................................................... 48
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 ........................................................................................................... 50
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 .................................................................................................. 52
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 ........................................................................................................... 53
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 ............................................................ 55
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Theory Guide
