The method of boundary condition transfer in application to modeling near-wall turbulent flows

Abstract

Generalized wall functions in application to high-Reynolds-number turbulence models are derived. The wall functions are based on transfer of a boundary condition from a wall to some intermediate boundary near the wall (usually the first nearest to the wall mesh point but that is not obligatory). The boundary conditions on the intermediate boundary are of Robin-type and represented in a differential form. The wall functions are obtained in an analytical easy-to-implement form, can take into account source terms such as pressure gradient and buoyancy forces, and do not include free parameters. The log-profile assumption is not used in this approach. Both Dirichlet and Newman boundary-value problems are considered. A method for complementing solution near the wall is suggested. Although the generalized wall functions are obtained for the k– ϵ model, generalization to other turbulence models is straightforward. The general approach suggested is applicable to studying high-temperature regimes with variable laminar viscosity and density. A robust numerical algorithm is proposed for implementation of Robin-type wall functions. Test results made for a channel flow and axisymmetric impinging jet have showed reasonably good accuracy, reached without any case-dependent turning, and a weak dependence of the solution on the location of the intermediate boundary where the boundary conditions are set. It is demonstrated that the method of boundary condition transfer applied to low-Reynolds-number turbulence models can be used as a decomposition method.