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12.7.9 Wall Boundary Conditions

The RSM model in FLUENT requires boundary conditions for individual Reynolds stresses, $\overline{u'_i u'_j}$, and for the turbulence dissipation rate, $\epsilon$ (or $\omega$ if the low-Re stress-omega model is used). These quantities can be input directly or derived from the turbulence intensity and characteristic length, as described in Section  12.20.3.

At walls, FLUENT computes the near-wall values of the Reynolds stresses and $\epsilon$ from wall functions (see Section  12.10.2, Section  12.10.3, and Section  12.10.4). FLUENT applies explicit wall boundary conditions for the Reynolds stresses by using the log-law and the assumption of equilibrium, disregarding convection and diffusion in the transport equations for the stresses (Equation  12.7-1). Using a local coordinate system, where $\tau$ is the tangential coordinate, $\eta$ is the normal coordinate, and $\lambda$ is the binormal coordinate, the Reynolds stresses at the wall-adjacent cells (assuming standard wall functions or non-equilibrium wall functions) are computed from

 \frac{\overline{u_{\tau}^{'2}}}{k} = 1.098, \; \; \frac{\o... ...5, \; \; - \frac{\overline{u'_{\tau}u'_{\eta}}}{k} = 0.255 (12.7-34)

To obtain $k$, FLUENT solves the transport equation of Equation  12.7-29. For reasons of computational convenience, the equation is solved globally, even though the values of $k$ thus computed are needed only near the wall; in the far field $k$ is obtained directly from the normal Reynolds stresses using Equation  12.7-28. By default, the values of the Reynolds stresses near the wall are fixed using the values computed from Equation  12.7-34, and the transport equations in Equation  12.7-1 are solved only in the bulk flow region.

Alternatively, the Reynolds stresses can be explicitly specified in terms of wall-shear stress, instead of $k$:
 \frac{\overline{u_{\tau}^{'2}}}{u_{\tau}^2} = 5.1, \; \; \... ...; - \frac{\overline{u'_{\tau}u'_{\eta}}}{u_{\tau}^2} = 1.0 (12.7-35)

where $u_{\tau}$ is the friction velocity defined by $u_{\tau} \equiv \sqrt {\tau_w/\rho}$, where $\tau_{w}$ is the wall-shear stress. When this option is chosen, the $k$ transport equation is not solved.

When using enhanced wall treatments as the near-wall treatment, FLUENT applies zero flux wall boundary conditions to the Reynolds stress equations.


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