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12.8.2 Realizable $k$- $\epsilon$ RANS Model

This RANS model is similar to the Realizable $k$- $\epsilon$ model discussed in Section  12.4.3, with the exception of the dissipation term in the $k$ equation. In the DES model, the Realizable $k$- $\epsilon$ RANS dissipation term is modified such that:

 Y_k = \frac{\rho k^{\frac{3}{2}}}{l_{des}} (12.8-2)

$\displaystyle l_{des} = min (l_{rke}, l_{les})$     (12.8-3)
$\displaystyle l_{rke} = \frac{k^{\frac{3}{2}}}{\epsilon}$     (12.8-4)
$\displaystyle l_{les} = C_{\rm des} \Delta$     (12.8-5)

where $C_{\rm des}$ is a calibration constant used in the DES model and has a value of 0.61 and $\Delta$ is the maximum local grid spacing ( $\Delta x, \Delta y, \Delta z$).

For the case where $l_{des} = l_{rke}$, you will obtain an expression for the dissipation of the $k$ formulation for the Realizable $k$- $\epsilon$ model (Section  12.4.3):
$Y_k = \rho \epsilon$

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