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

Abstract

This paper presents an improved wall function method for unstructured flow solvers using the DLR TAU Code based on the one-dimensional boundary-layer equations for wall-parallel velocity, including pressure gradient term and convective term, and turbulence quantities in wall normal direction. For each wall node, this system of equations is integrated numerically on an embedded subgrid between wall node and first node above the wall. The method is verified for a flat plate turbulent boundary layer flow at zero pressure gradient. Then the method is applied to the flow in a diffusor at adverse pressure gradient without separation to assess different levels of approximation of the boundary layer model for wall-parallel velocity and to demonstrate the improvement of results compared to universal wall-functions.