Wilcox's k-omega model

(Difference between revisions)
 Revision as of 09:54, 6 October 2005 (view source) (→Closure Coefficients and Auxilary Relations)← Older edit Revision as of 09:54, 6 October 2005 (view source) (→Closure Coefficients and Auxilary Relations)Newer edit → Line 30: Line 30: \sigma  = {1 \over 2} \sigma  = {1 \over 2} [/itex] [/itex] + :[itex] :[itex] \sigma ^*  = {1 \over 2} \sigma ^*  = {1 \over 2}

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

$\alpha = {{5} \over {9}}$
$\beta = {{3} \over {40}}$
$\beta^* = {9 \over {100}}$
$\sigma = {1 \over 2}$
$\sigma ^* = {1 \over 2}$
$\varepsilon = \beta ^* \omega k$

References

1. Wilcox, D.C. (2004), Turbulence Modeling for CFD, ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc..