A generalised wall function including compressibility and pressure-gradient terms for the Spalart–Allmaras turbulence model

Abstract

Spalart-Allmaras (SA) model is a low Reynolds number (Re) model, which means that the first off-wall grid point should be placed in the viscous sub-layer with y+≃1. This restriction of placing the first off-wall grid point so close to the wall leads to an increase in the mesh size, and thus the computation. The wall function approach is an alternative to this problem. The standard wall function method usually employed has a limitation for cases that involve high adverse pressure gradient and compressibility. This limits its use to the non-separated flows only. The present work focuses on the formulation of the generalised wall function given by Shih et al. [A generalized wall function; 1999] and applies it to the SA turbulence model, with some modification. The proposed modification was found to remove the oscillation and inaccuracy found in the result when directly using the Shih et al. model. Several flows, with zero pressure gradient to those with adverse pressure gradient leading to flow separation, are solved with the proposed wall treatment, with relatively coarse grids involving y+ beyond 50 and up to 100 for certain cases. It is concluded that the results in each case are close to those obtained by the low-Re SA model, despite the use of much coarser meshes.