Generalized wall-functions for high-Reynolds-number turbulence models

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 a 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, 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 a wall is suggested. Although the generalized wall-functions are realized for the k-epsilon model, generalization to other turbulence models looks quite clear. 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. Preliminary test results made for a channel flow showed good accuracy and a weak dependence of the solution on the location of the intermediate boundary where the boundary conditions are set.