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12.10.6 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} (12.10-42)

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) (12.10-43)

where $\kappa$ is the von Kármán constant and $E = 9.793$. If the mesh is a such that the first near wall point is within the buffer region, then two above laws are blended in accordance with equation Equation  12.10-28.

For the LES simulations in FLUENT, there is an alternative near wall approach based on the work of Werner and Wengle [ 398], who proposed analytical integration of 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... ...mu}{2 \rho \Delta z} A^{\frac{2}{1-B}} \end{array} \right. (12.10-44)

where $u_{p}$ is velocity parallel to the wall, $A=8.3, B=1/7$ 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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© Fluent Inc. 2006-09-20