ANSYS FLUENT 12.0 Theory Guide - 4.5.3 Wall Boundary Conditions

4.5.3 Wall Boundary Conditions

The wall boundary conditions for the equation in the - $\omega$ models are treated in the same way as the equation is treated when enhanced wall treatments are used with the - $\epsilon$ models. This means that all boundary conditions for wall-function meshes will correspond to the wall function approach, while for the fine meshes, the appropriate low-Reynolds-number boundary conditions will be applied.

In ANSYS FLUENT the value of $\omega$ at the wall is specified as

$\omega_w = \frac{\rho \, (u^*)^2}{\mu} \omega^+$

(4.5-53)

The asymptotic value of $\omega^+$ in the laminar sublayer is given by

$\omega^+ = \min \left(\omega_w^+, \frac{6}{\beta_i (y^+)^2}\right)$

(4.5-54)

where

$\omega_w^+ = \left\{ \begin{array}{ll} \left(\frac{50}{k_s^+... ...25 \\ \\ \frac{100}{k_s^+} & k_s^+ \ge 25 \end{array}\right.$

(4.5-55)

where

$k_s^+ = \max \left(1.0, \frac{\rho k_s u^*}{\mu}\right)$

(4.5-56)

and is the roughness height.

In the logarithmic (or turbulent) region, the value of $\omega^+$ is

$\omega^+ = \frac{1}{\sqrt{\beta_\infty^*}} \frac{du_{\rm turb}^+}{dy^+}$

(4.5-57)

which leads to the value of $\omega$ in the wall cell as

$\omega = \frac{u^*}{\sqrt{\beta_\infty^*} \kappa y}$

(4.5-58)

Note that in the case of a wall cell being placed in the buffer region, ANSYS FLUENT will blend $\omega^+$ between the logarithmic and laminar sublayer values.

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