A wall-law for the mean velocity in the inner part of turbulent boundary layers at adverse pressure and application for RANS turbulence modelling

Abstract

We present a strategy to modify turbulence models based on the Reynolds averaged Navier-Stokes (RANS) equations for flow separation on smooth surfaces due to an adverse pressure gradient. We describe two new turbulent boundary layer experiments to study the behaviour of the mean velocity profile at adverse pressure gradients and at high Re. We observe that the log-law in the mean velocity profile is a robust feature, but its region is much thinner than in zero-pressure gradient flows, and its slope is altered. A square-root law emerges above the log-law extending to the wall-ward distance the log-law typically occupies. Then we modify a differential Reynolds stress turbulence model. The modified model accounts for a change of the log-law slope and the formation of a square-root law at adverse pressure gradient, improving the agreement with the experimental data for both experiments.