Investigation of Numerical Wall Functions Based on the 1D Boundary Layer Equations for Flows with Significant Pressure Gradient

In this paper we present a numerical wall function method for the simulation of isothermal flows with separation and reattachment based on the Reynolds averaged Navier-Stokes equations using an unstructured flow solver. The method is applied to the one-equation turbulencemodel by Spalart and Allmaras and is implemented in OpenFOAM®. For each wall node, a system of one-dimensional boundary-layer equations for the wall-parallel velocity component and for the turbulence quantity is integrated numerically on an embedded sub-grid in the nearwall region. The method is applied to the flow over a flat plate, over a backward facing step, and over a smoothly contoured ramp. The improvement of the results compared to universal wall functions become significant in case of separation and reattachment. © Springer International Publishing Switzerland 2015