CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Wiki > Wilcox's k-omega model

Wilcox's k-omega model

From CFD-Wiki

(Difference between revisions)
Jump to: navigation, search
Line 14: Line 14:
</math>
</math>
 +
==Closure Coefficients and Auxilary Relations==
 +
:<math>
 +
\alpha  = {{13} \over {25}} 
 +
</math>
 +
:<math>
 +
\beta  = \beta _0 f_\beta   
 +
</math>
 +
:<math>
 +
\beta ^*  = \beta _0^* f_{\beta ^* } 
 +
</math>
 +
:<math>
 +
\sigma  = {1 \over 2} 
 +
</math>
 +
:<math>
 +
\sigma ^*  = {1 \over 2} 
 +
</math>
 +
:<math>
 +
\beta _0  = {9 \over {125}}
 +
</math>
 +
 +
:<math>
 +
\alpha  = {{13} \over {25}} 
 +
</math>
:<math>
:<math>

Revision as of 10:28, 26 September 2005

Contents

Kinematic Eddy Viscosity

\nu _T = {k \over \omega }

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 ^* \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 \nu _T } \right){{\partial \omega } \over {\partial x_j }}} \right]

Closure Coefficients and Auxilary Relations

\alpha = {{13} \over {25}}
\beta = \beta _0 f_\beta
\beta ^* = \beta _0^* f_{\beta ^* }
\sigma = {1 \over 2}
\sigma ^* = {1 \over 2}
\beta _0 = {9 \over {125}}
\alpha = {{13} \over {25}}
f_{\beta ^* } = \left\{ \begin{matrix} {1,} & {\chi _k \le 0} \\ {{{1 + 680\chi _k^2 } \over {1 + 80\chi _k^2 }},} & {\chi _k > 0} \\ \end{matrix} \right.
Retrieved from "https://openfoam.cfd-online.com/Wiki/Wilcox%27s_k-omega_model"
My wiki