Difference between revisions of "Contrib/turbFoamAverage with k-omega SST SAS"

Revision as of 09:22, 2 July 2009

1 k- $\omega$ SST-SAS Equations

$\frac{\partial \omega}{\partial t}+\nabla \cdot (\vec{u}\omega) = \nabla^2[(\nu+\nu_t\sigma_\omega)\omega] + \frac{\gamma \omega}{k}\tau_{ij}\frac{\partial u_i}{\partial x_j}-\beta\omega^2 + 2(1-F_1)\sigma_{\omega2}\frac{1}{\omega}\nabla k \cdot \nabla \omega + P_{sas}$

$\frac{\partial k}{\partial t}+\nabla \cdot (\vec{u}k) = \nabla^2[(\nu+\nu_t\sigma_k)k] + \tau_{ij}\frac{\partial u_i}{\partial x_j}-\beta^*\omega k$

$P_{sas}=1.25 \mbox{max}\left(T_1-T_2,0\right)$

$T_1=1.755 \kappa S^2\frac{L}{L_{vK}}$

$T_2=3 k \mbox{max}\left(\frac{1}{\omega^2}\nabla \omega \cdot \nabla \omega , \frac{1}{k^2}\nabla k \cdot \nabla k \right)$

$L=\frac{k^{\frac{1}{2}}}{\omega c_\mu^{\frac{1}{4}}}$

$L_{vK}=\kappa \frac{S}{|\nabla^2 \vec{u}|}$

$\nu _T = {a_1 k \over \mbox{max}(a_1 \omega, \Omega F_2) }$

$F_2=\mbox{tanh} \left[ \left[ \mbox{max} \left( { 2 \sqrt{k} \over \beta^* \omega y } , { 500 \nu \over y^2 \omega } \right) \right]^2 \right]$

$F_1=\mbox{tanh} \left\{ \left\{ \mbox{min} \left[ \mbox{max} \left( {\sqrt{k} \over \beta ^* \omega y}, {500 \nu \over y^2 \omega} \right) , {4 \sigma_{\omega 2} k \over CD_{k\omega} y^2} \right] \right\} ^4 \right\}$

$CD_{k\omega}=\mbox{max} \left( 2\rho\sigma_{\omega 2} {1 \over \omega} {{\partial k} \over {\partial x_i}} {{\partial \omega} \over {\partial x_i}}, 10 ^{-10} \right )$

$\phi = \phi_1 F_1 + \phi_2 (1 - F_1)$

$\alpha_1 = {{5} \over {9}}, \alpha_2 = 0.44$

$\beta_1 = {{3} \over {40}}, \beta_2 = 0.0828$

$\beta^* = {9 \over {100}}$

$\sigma_{k1} = 0.85, \sigma_{k2} = 1$

$\sigma_{\omega 1} = 0.5, \sigma_{\omega 2} = 0.856$

1.1 References

A Scale Adaptive Simulation Model using Two-Equation Models
F. Menter and Y. Egorov, ANSYS CFX, Otterfing, Germany, AIAA-2005-1095
43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 10-13, 2005
Revisiting The Turbulent Scale Equation
F.R. Menter and Y. Egorov, ANSYS CFX, Otterfing, Germany,
IUTAM Symposium, 'One Hundred Years of Boundary Layer Research', Goettingen 2004.
Steady and Unsteady Flow Modelling Using the $k-\sqrt{k}L$ Model
F.R. Menter, Y. Egorov and D. Rusch, Turbulence, Heat and Mass Transfer 5, K. Hanjalic, Y. Nagano and S. Jakirlic (Editors)
Evaluation of the SST-SAS Model: Channel Flow, Asymmetric Diffuser and Axi-symmetric Hill
L. Davidson, ECCOMAS CFD 2006.

2 Solver

The openFoam solver is a modified version of turbFoam. Since the k- $\omega$ SST sas turbulence model, in unstable flow situations, gives LES-like solution fields, the modifications were introduced to handle the omega field and to allow the time averaging of pressure and velocity quantities. The averaging has been done in analogy with the openFoam LES solver oodles.

The solver files are available here: Media:turbFoamAverage.tar.gz

2.1 How to install the solver

3 Turbulence Model Files

Note: This library was obviously developed with 1.4.1 or older and won't compile with 1.5 or newer The turbulence models files are available here: Media:KOmegaTurbulenceModels.tar.gz

3.1 How to install the turbulence models files

4 Test Cases

4.1 Flow Past a Long Square Cylinder

Details about the test case are available at the ERCOFTAC NEXUS data base (ErcoftacLESig)

Test case files are available here:Media:LESigSquareCylSSTsas.tar.gz

@@ Line 83: / Line 83: @@
 == Turbulence Model Files ==
+'''Note: This library was obviously developed with 1.4.1 or older and won't compile with 1.5 or newer'''
 The turbulence models files are available here: [[Media:KOmegaTurbulenceModels.tar.gz]]