# 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 Latest revision as of 16:52, 8 March 2011 (view source)m (→References) (13 intermediate revisions not shown) Line 1: Line 1: + {{Turbulence modeling}} ==Kinematic Eddy Viscosity == ==Kinematic Eddy Viscosity == :[itex] :[itex] Line 15: Line 16: ==Closure Coefficients and Auxilary Relations== ==Closure Coefficients and Auxilary Relations== + :[itex] :[itex] \alpha  = {{5} \over {9}} \alpha  = {{5} \over {9}} Line 41: Line 43: == References == == References == - #{{reference-book|author=Wilcox, D.C. |year=2004|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}} + #{{reference-paper|author=Wilcox, D.C. |year=1988|title=Re-assessment of the scale-determining equation for advanced turbulence models|rest=AIAA Journal, vol. 26, no. 11, pp. 1299-1310}} + + [[Category:Turbulence models]]

## 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. (1988), "Re-assessment of the scale-determining equation for advanced turbulence models", AIAA Journal, vol. 26, no. 11, pp. 1299-1310.