A new wall-law for adverse pressure gradient flows and modification of k-omega type RANS turbulence models

Abstract

We present an attempt to improve the predictive accuracy of RANS turbulence models for low-speed flow separation on airfoils and wings near stall. It is based on a proposal for a new wall-law for the mean velocity in the inner layer of a turbulent boundary layer at adverse pressure gradient. The wall-law is a composite law with a log-law in the inner part and a half-power (or sqrt-) law in the outer part of the inner layer. The wall law is calibrated using a large experimental database. The slope coefficient for log-law and sqrt-law and the wall distance for transition between them depends on the pressure gradient parameter. We describe the corresponding wall law for the turbulent viscosity and for k and omega in k-omega RANS turbulence models. We propose a modification for the k- and omega-equation such that the wall law for the inner layer is satisfied. We apply the modified SST model to a new turbulent boundary layer experiment and to airfoil flows near maximum lift at different Reynolds numbers. The modification leads to a reduction of the skin-friction coefficient in the adverse pressure gradient region and causes an upstream shift of the separation line.