Wilcox's k-omega model
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+ | {{Turbulence modeling}} | ||
==Kinematic Eddy Viscosity == | ==Kinematic Eddy Viscosity == | ||
:<math> | :<math> | ||
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</math> | </math> | ||
+ | == Turbulence Kinetic Energy == | ||
+ | :<math> | ||
+ | {{\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] | ||
+ | </math> | ||
+ | == Specific Dissipation Rate== | ||
+ | :<math> | ||
+ | {{\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] | ||
+ | </math> | ||
+ | |||
+ | ==Closure Coefficients and Auxilary Relations== | ||
:<math> | :<math> | ||
- | + | \alpha = {{5} \over {9}} | |
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \beta = {{3} \over {40}} | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \beta^* = {9 \over {100}} | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \sigma = {1 \over 2} | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \sigma ^* = {1 \over 2} | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \varepsilon = \beta ^* \omega k | ||
+ | </math> | ||
- | + | == References == | |
- | + | ||
- | + | ||
- | + | ||
+ | #{{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]] | |
- | + |
Latest revision as of 16:52, 8 March 2011
Contents |
Kinematic Eddy Viscosity
Turbulence Kinetic Energy
Specific Dissipation Rate
Closure Coefficients and Auxilary Relations
References
- Wilcox, D.C. (1988), "Re-assessment of the scale-determining equation for advanced turbulence models", AIAA Journal, vol. 26, no. 11, pp. 1299-1310.