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12.8.3 SST $k$- $\omega$ RANS Model

The dissipation term of the turbulent kinetic energy (see Section  12.5.1) is modified for the DES turbulence model as described in Menter's work [ 238] such that

 Y_k = \rho \beta^* k \omega f_{\beta^*} (12.8-6)

where $f_{\beta^*}$ is no longer a constant equal to 1 as in the SST $k$- $\omega$ model (see Section  12.5.1), but is now expressed as
 f_{\beta^*} = max \left(\frac{L_t}{C_{\rm des}\Delta},1 \right) (12.8-7)

where $C_{\rm des}$ is a calibration constant used in the DES model and has a value of 0.61, $\Delta$ is the maximum local grid spacing ( $\Delta x, \Delta y, \Delta z$) and $f_{\beta^*}$ is defined in Equation  12.5-16.

The turbulent length scale is the parameter that defines this RANS model:
 L_t = \frac{\sqrt{k}}{\beta^* \omega} (12.8-8)

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