Numerical Implementation of Generalized Robin-type Wall Functions and Their Application to Impinging Flows

Abstract

The paper is devoted to the generalized wall functions of Robin-type and their application to near-wall turbulent flows. The wall functions are based on the transfer of a boundary condition from a wall to some intermediate boundary near the wall. The boundary conditions on the intermediate boundary are of Robin-type and represented in a differential form. The wall functions are formulated in an analytical easy-to-implement form, can take into account the source terms of the momentum equation, and do not include free parameters. The log-profile assumption is not used in this approach. A robust numerical algorithm is proposed for implementation of Robin-type wall functions to both finite-difference and finite-volume numerical schemes. The algorithm of implementation of the Robin-type wall functions to existing finite-volume codes is provided. The axisymmetric impinging jet problem is numerically investigated for different regimes on the base of the wall-functions implemented to the high-Reynolds-number k-epsilon model.