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

Latest revision as of 19:51, 21 March 2015

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

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 1: / Line 1: @@
 == k-<math>\omega</math> SST-SAS Equations ==
-=== References ===
+<math>\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}</math>
-A Scale Adaptive Simulation Model using Two-Equation Models
+<math>\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 </math>
-F. Menter and Y. Egorov, ANSYS CFX, Otterfing, Germany
-AIAA-2005-1095
+<math>
-rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 10-13, 2005
+P_{sas}=1.25 \mbox{max}\left(T_1-T_2,0\right)
+</math>
+<math>
+T_1=1.755 \kappa S^2\frac{L}{L_{vK}}
+</math>
+<math>
+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)
+</math>
+<math>
+L=\frac{k^{\frac{1}{2}}}{\omega c_\mu^{\frac{1}{4}}}
+</math>
+<math>
+L_{vK}=\kappa \frac{S}{|\nabla^2 \vec{u}|}
+</math>
+<math>
+\nu _T  = {a_1 k \over \mbox{max}(a_1 \omega, \Omega F_2) }
+</math>
+<math>
+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]
+</math>
+<math>
+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\}
+</math>
+<math>
+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 )
+</math>
+<math>
+\phi = \phi_1 F_1 + \phi_2 (1 - F_1)
+</math>
+<math>
+\alpha_1  = {{5} \over {9}},   \alpha_2  = 0.44
+</math>
+<math>
+\beta_1  = {{3} \over {40}},  \beta_2  = 0.0828
+</math>
+<math>
+\beta^*  = {9 \over {100}}
+</math>
+<math>
+\sigma_{k1}  = 0.85,  \sigma_{k2}  = 1
+</math>
+<math>
+\sigma_{\omega 1}  = 0.5,  \sigma_{\omega 2}  = 0.856
+</math>
+=== References ===
 == Solver ==
@@ Line 18: / Line 78: @@
 == 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]]
@@ Line 29: / Line 90: @@
 Test case files are available here:[[Media:LESigSquareCylSSTsas.tar.gz]]
+[[Category:Solvers]]