ANSYS FLUENT 12.0 Theory Guide - 4.3.7 Wall Boundary Conditions

4.3.7 Wall Boundary Conditions

At walls, the modified turbulent kinematic viscosity, $\widetilde{\nu}$ , is set to zero.

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

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

(4.3-16)

If the mesh is too coarse to resolve the viscous sublayer, then 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:

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

(4.3-17)

where is the velocity parallel to the wall, $u_{\tau}$ is the shear velocity, is the distance from the wall, $\kappa$ is the von Kármán constant (0.4187), and .

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