10-rans - 1 Lecture 10 - Turbulence Models Applied...

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Unformatted text preview: 1 Lecture 10 - Turbulence Models Applied Computational Fluid Dynamics Instructor: Andr Bakker http://www.bakker.org Andr Bakker (2002-2006) Fluent Inc. (2002) 2 Turbulence models A turbulence model is a computational procedure to close the system of mean flow equations. For most engineering applications it is unnecessary to resolve the details of the turbulent fluctuations. Turbulence models allow the calculation of the mean flow without first calculating the full time-dependent flow field. We only need to know how turbulence affected the mean flow. In particular we need expressions for the Reynolds stresses. For a turbulence model to be useful it: must have wide applicability, be accurate, simple, and economical to run. 3 Common turbulence models Classical models. Based on Reynolds Averaged Navier-Stokes (RANS) equations (time averaged): 1. Zero equation model: mixing length model. 2. One equation model: Spalart-Almaras. 3. Two equation models: k- style models (standard, RNG, realizable), k- model, and ASM. 4. Seven equation model: Reynolds stress model. The number of equations denotes the number of additional PDEs that are being solved. Large eddy simulation. Based on space-filtered equations. Time dependent calculations are performed. Large eddies are explicitly calculated. For small eddies, their effect on the flow pattern is taken into account with a subgrid model of which many styles are available. 4 Prediction Methods l = l/ Re L 3/4 Direct numerical simulation ( DNS ) Large eddy simulation ( LES ) Reynolds averaged Navier-Stokes equations ( RANS ) 5 Boussinesq hypothesis Many turbulence models are based upon the Boussinesq hypothesis. It was experimentally observed that turbulence decays unless there is shear in isothermal incompressible flows. Turbulence was found to increase as the mean rate of deformation increases. Boussinesq proposed in 1877 that the Reynolds stresses could be linked to the mean rate of deformation. Using the suffix notation where i, j, and k denote the x-, y-, and z- directions respectively, viscous stresses are given by: Similarly, link Reynolds stresses to the mean rate of deformation: + = = i j j i ij ij x u x u e + =- = i j j i t j i ij x U x U u u ' ' 6 Turbulent viscosity A new quantity appears: the turbulent viscosity t . Its unit is the same as that of the molecular viscosity: Pa.s. It is also called the eddy viscosity. We can also define a kinematic turbulent viscosity: t = t / . Its unit is m 2 /s....
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10-rans - 1 Lecture 10 - Turbulence Models Applied...

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