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Prandtl's one-equation model

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<i> Return to [[Turbulence modeling]] </i>
<i> Return to [[Turbulence modeling]] </i>
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[[Category:Turbulence models]]

Revision as of 07:53, 4 October 2006

Contents

Kinematic Eddy Viscosity

 
\nu _t  = k^{{1 \over 2}} l = C_D {{k^2 } \over \varepsilon }

Model


{{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = \tau _{ij} {{\partial U_i } \over {\partial x_j }} - C_D {{k^{{3 \over 2}} } \over l} + {\partial  \over {\partial x_j }}\left[ {\left( {\nu  + {{\nu _T } \over {\sigma _k }}} \right){{\partial k} \over {\partial x_j }}} \right]


Closure Coefficients and Auxilary Relations


 \varepsilon  = C_D {{k^{{3 \over 2}} } \over l}

    C_D  = 0.3

   \sigma _k  = 1


where


\tau _{ij}  = 2\nu _T S_{ij}  - {2 \over 3}k\delta _{ij}

References

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



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