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 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 ..................................................... 41
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 ........................................................................................ 43
4.2.5. Modeling the Turbulent Destruction ....................................................................................... 44
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 ....................................... 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 .................................................................................................. 49
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
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Theory Guide
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