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SST k-omega model

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Revision as of 07:37, 11 October 2005 by Jonas Bredberg (Talk | contribs)
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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 )
Failed to parse (syntax error): F_2=\mbox{tanh} \right[ \right[ \mbox{max} { 2 \sqrt{k} \over \beta^* \omega y } , { 500 \nu \over y^2 \omega } \right]^2 \right]


Failed to parse (syntax error): 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 ]



\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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