Implementation of a Generalized Wall Function for the Spalart Allmaras Turbulence Model

Accurately capturing of turbulence has been a challenging problem for both the academic study and industrial applications. The method generally employed for prediction of turbulence is by using Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling, which are time-averaged equations for fluid flow. The Spalart-Allmaras turbulence model is a one-equation model that uses RANS to solve the equation for the kinematic eddy viscosity. It is a low Reynolds number model, which means that the first grid point should be placed in the viscous sub-layer with y + ' 1. This restriction of placing the first grid so close to wall leads to increase the mesh size, which further increases the computation and also delays the convergence due to the CFL criteria. The wall function approach is used for the SA turbulence model to achieve similar accuracy as obtained by the low Reynolds number model with an increased first grid distance. The region from wall to the first grid is modelled by a certain analytical function. The standard wall function method usually employed in the study of general incompressible flows 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 generalized wall function given by Shih et al (1999) for SA turbulence model, with a proposed modification. The proposed modification was found to remove the oscillation and inaccuracy found in the result when using the Shih et al model for the cases considered in this work. Several cases are validated with relatively coarse grids, involving y + beyond 50 and up to 100 for certain cases. The cases include both flows with zero pressure gradient to those with adverse pressure gradient leading to flow separatio