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SST k-omega model

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\alpha_1  = {{5} \over {9}}  \alpha_2  = 0.44
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\phi = \phi_1 F_1 + \phi_2 (1 - F_1)
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  \beta_1  = {{3} \over {40}}  \beta_2  = 0.0828  
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\alpha_1  = {{5} \over {9}},  \alpha_2  = 0.44
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  \beta_1  = {{3} \over {40}}, \beta_2  = 0.0828  
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\sigma_{k1}  = 0.85  \sigma_{k2}  = 1
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\sigma_{k1}  = 0.85, \sigma_{k2}  = 1
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\sigma_{\omega 1}  = 0.5  \sigma_{\omega 2}  = 0.856
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\sigma_{\omega 1}  = 0.5, \sigma_{\omega 2}  = 0.856
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Revision as of 08:16, 11 October 2005

Contents

Kinematic Eddy Viscosity

\nu _T = {a_1 k \over \mbox{max}(a_1 \omega, \Omega F_2) }

Turbulence Kinetic Energy

{{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = P_k - \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 S^2 - \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_2=\mbox{tanh} \left[ \left[ \mbox{max} \left( { 2 \sqrt{k} \over \beta^* \omega y } , { 500 \nu \over y^2 \omega } \right) \right]^2 \right]
P_k=\mbox{min} \left(\tau _{ij} {{\partial U_i } \over {\partial x_j }} , 20\beta^* k \omega \right)
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\rho\sigma_{\omega 2} {1 \over \omega} {{\partial k} \over {\partial x_i}} {{\partial \omega} \over {\partial x_i}}, 10 ^{-10} \right )
\phi = \phi_1 F_1 + \phi_2 (1 - F_1)
\alpha_1 = {{5} \over {9}}, \alpha_2 = 0.44
\beta_1 = {{3} \over {40}}, \beta_2 = 0.0828
\beta^* = {9 \over {100}}
\sigma_{k1} = 0.85, \sigma_{k2} = 1
\sigma_{\omega 1} = 0.5, \sigma_{\omega 2} = 0.856

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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