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Wilcox's k-omega model

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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  ^* = 1 ;         = {{0.025 + 10 R_t / 27} \over {1 + 10 R_t / 27}}

\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. 31, pp. 1414-1421.
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