4.9.9 Wall Boundary Conditions

The RSM model in ANSYS 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 ( this section in the separate User's Guide).

At walls, ANSYS FLUENT computes the near-wall values of the Reynolds stresses and $\epsilon$ from wall functions (see Section  4.12.2, Section  4.12.3, and Section  4.12.4). ANSYS 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  4.9-1). 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

To obtain $k$, ANSYS FLUENT solves the transport equation of Equation  4.9-28. 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  4.9-27. By default, the values of the Reynolds stresses near the wall are fixed using the values computed from Equation  4.9-34, and the transport equations in Equation  4.9-1 are solved only in the bulk flow region.

Alternatively, the Reynolds stresses can be explicitly specified in terms of wall-shear stress, instead of $k$:

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, ANSYS FLUENT applies zero flux wall boundary conditions to the Reynolds stress equations.