CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Wiki > Wilcox's k-omega model

Wilcox's k-omega model

From CFD-Wiki

(Difference between revisions)
Jump to: navigation, search
(Closure Coefficients and Auxilary Relations)
Line 16: Line 16:
==Closure Coefficients and Auxilary Relations==
==Closure Coefficients and Auxilary Relations==
:<math>
:<math>
-
\alpha  = {{13} \over {25}}   
+
\alpha  = {{5} \over {9}}   
</math>
</math>
:<math>
:<math>
-
  \beta  = \beta _0 f_\beta   
+
  \beta  = {{3} \over {40}}  
-
</math>
+
-
:<math>
+
-
\beta ^*  = \beta _0^* f_{\beta ^* }  
+
</math>
</math>
:<math>
:<math>
Line 29: Line 26:
:<math>
:<math>
\sigma ^*  = {1 \over 2}   
\sigma ^*  = {1 \over 2}   
-
</math>
 
-
:<math>
 
-
\beta _0  = {9 \over {125}}
 
-
</math>
 
-
 
-
:<math>
 
-
f_\beta  = {{1 + 70\chi _\omega  } \over {1 + 80\chi _\omega  }}
 
-
</math>
 
-
 
-
:<math>
 
-
\chi _\omega  = \left| {{{\Omega _{ij} \Omega _{jk} S_{ki} } \over {\left( {\beta _0^* \omega } \right)^3 }}} \right|
 
</math>
</math>
Line 46: Line 32:
</math>
</math>
-
:<math>
 
-
f_{\beta ^* }  = \left\{
 
-
 
-
\begin{matrix}
 
-
  {1,} & {\chi _k  \le 0}  \\
 
-
  {{{1 + 680\chi _k^2 } \over {1 + 80\chi _k^2 }},} & {\chi _k  > 0}  \\
 
-
\end{matrix}
 
-
 
-
 
-
  \right.
 
-
</math>
 
-
 
-
:<math>
 
-
\chi _k  \equiv {1 \over {\omega ^3 }}{{\partial k} \over {\partial x_j }}{{\partial \omega } \over {\partial x_j }}
 
-
</math>
 
:<math>
:<math>
\varepsilon  = \beta ^* \omega k
\varepsilon  = \beta ^* \omega k
</math>
</math>
-
 
-
:<math>
 
-
l = {{k^{{1 \over 2}} } \over \omega }
 
-
</math>
 
-
 
== 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-book|author=Wilcox, D.C. |year=2004|title=Turbulence Modeling for CFD|rest=ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.}}

Revision as of 09:53, 6 October 2005

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  = {{5} \over {9}}

 \beta  = {{3} \over {40}}

\sigma  = {1 \over 2}

\sigma ^*  = {1 \over 2}

\beta _0^*  = {9 \over {100}}



\varepsilon  = \beta ^* \omega k

References

  1. Wilcox, D.C. (2004), Turbulence Modeling for CFD, ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc..
My wiki