SST k-omega model

From CFD-Wiki

(Difference between revisions)

Revision as of 07:39, 11 October 2005

Kinematic Eddy Viscosity

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

Turbulence Kinetic Energy

${{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = \tau _{ij} {{\partial U_i } \over {\partial x_j }} - \beta ^* k\omega + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma_{k1} \nu _T } \right){{\partial k} \over {\partial x_j }}} \right]$

Specific Dissipation Rate

${{\partial \omega } \over {\partial t}} + U_j {{\partial \omega } \over {\partial x_j }} = \alpha {\omega \over k}\tau _{ij} {{\partial U_i } \over {\partial x_j }} - \beta \omega ^2 + {\partial \over {\partial x_j }}\left[ {\left( {\nu + \sigma_{\omega 1} \nu _T } \right){{\partial \omega } \over {\partial x_j }}} \right] + 2( 1 - F_1 ) \sigma_{\omega 2} {1 \over \omega} {{\partial k } \over {\partial x_i}} {{\partial \omega } \over {\partial x_i}}$

Closure Coefficients and Auxilary Relations

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

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

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

$P_k=\mbox{min} \left(\tau _{ij} {{\partial U_i } \over {\partial x_j }} , 10\beta^* k \omega \right)$

$\alpha = {{5} \over {9}}$

$\beta = {{3} \over {40}}$

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

$\sigma = {1 \over 2}$

$\sigma ^* = {1 \over 2}$

$\varepsilon = \beta ^* \omega k$

References

Wilcox, D.C. (1988), "Re-assessment of the scale-determining equation for advanced turbulence models", AIAA Journal, vol. 31, pp. 1414-1421.

SST k-omega model

From CFD-Wiki

Revision as of 07:39, 11 October 2005

Contents

Kinematic Eddy Viscosity

Turbulence Kinetic Energy

Specific Dissipation Rate

Closure Coefficients and Auxilary Relations

References

Views

My wiki

wiki navigation

wiki search

wiki toolbox

@@ Line 27: / Line 27: @@
 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_2=\mbox{tanh} \right[ \right[ \mbox{max} \left( { 2 \sqrt{k} \over \beta^* \omega y} , { 500 \nu \over y^2 \omega } \right ) \right ] ^2 \right ]
+P_k=\mbox{min} \left(\tau _{ij} {{\partial U_i } \over {\partial x_j }} , 10\beta^* k \omega \right)
 </math>
 :<math>