ANSYS FLUENT 12.0 Theory Guide - 4.12.6 LES Near-Wall Treatment

4.12.6 LES Near-Wall Treatment

When the mesh is fine enough to resolve the laminar sublayer, the wall shear stress is obtained from the laminar stress-strain relationship:

$\frac{\overline{u}}{u_{\tau}} = \frac{ \rho u_{\tau} y}{\mu}$

(4.12-44)

If the mesh is too coarse to resolve the laminar sublayer, it is assumed that the centroid of the wall-adjacent cell falls within the logarithmic region of the boundary layer, and the law-of-the-wall is employed:

$\frac{\overline{u}}{u_{\tau}} = \frac{1}{\kappa} \ln E \left(\frac{\rho u_{\tau} y}{\mu} \right)$

(4.12-45)

where $\kappa$ is the von Kármán constant and . If the mesh is such that the first near-wall point is within the buffer region, then two above laws are blended in accordance with the Equation 4.12-30.

For the LES simulations in ANSYS FLUENT, there is an alternative near-wall approach based on the work of Werner and Wengle [ 375], who proposed an analytical integration of the power-law near-wall velocity distribution resulting in the following expressions for the wall shear stress:

$\vert \tau_{w} \vert = \left \{ \begin{array}{ll} \frac{2 \m... ...ac{\mu}{2 \rho \Delta z} A^{\frac{2}{1-B}} \end{array} \right.$

(4.12-46)

where $u_{p}$ is the wall-parallel velocity, are the constants, and $\Delta z$ is the near-wall control volume length scale.

The Werner-Wengle wall functions can be enabled using the define/models/viscous/ near-wall-treatment/werner-wengle-wall-fn? text command.

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