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12.3.7 Wall Boundary Conditions

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

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

 \frac{u}{u_{\tau}} = \frac{ \rho u_{\tau} y}{\mu} (12.3-16)

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{u}{u_{\tau}} = \frac{1}{\kappa} \ln E \left( \frac{\rho u_{\tau} y}{\mu} \right) (12.3-17)

where $u$ is the velocity parallel to the wall, $u_{\tau}$ is the shear velocity, $y$ is the distance from the wall, $\kappa$ is the von Kármán constant (0.4187), and $E = 9.793$.


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