Wilcox's k-omega model
From CFD-Wiki
(Difference between revisions)
| Line 36: | Line 36: | ||
:<math> | :<math> | ||
f_\beta = {{1 + 70\chi _\omega } \over {1 + 80\chi _\omega }} | 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> | ||
| + | \beta _0^* = {9 \over {100}} | ||
</math> | </math> | ||
| Line 49: | Line 57: | ||
\right. | \right. | ||
</math> | </math> | ||
| + | |||
| + | :<math> | ||
| + | \chi _k \equiv {1 \over {\omega ^3 }}{{\partial k} \over {\partial x_j }}{{\partial \omega } \over {\partial x_j }} | ||
| + | </math> | ||
| + | |||
| + | :<math> | ||
| + | \varepsilon = \beta ^* \omega k | ||
| + | </math> | ||
| + | |||
| + | :<math> | ||
| + | l = {{k^{{1 \over 2}} } \over \omega } | ||
| + | </math> | ||
Revision as of 10:33, 26 September 2005
Contents |
![{{\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]](/W/images/math/1/a/4/1a436edcf81f2ccbdf53dfa7dd9e0550.png)
![{{\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]](/W/images/math/b/3/6/b361dbe1c46fcbcbf1795a2997a00e09.png)
