A new adaptive wall-function method for subsonic and transonic turbulent flows

This report is dedicated to a new wall-function approach for RANS turbulence modelling of subsonic and transonic turbulent flows. The objective is to obtain solutions independent of the wall-normal grid spacing, provided the first grid node above the wall is located in the logarithmic layer or below. For this purpose two means are employed, i.e., (i) new hybrid wall-functions and (ii) a near-wall grid adaptation technique in wall-normal direction. The wall-function method is formulated as a domain-decomposition method with full overlap in the near-wall region. This reveals a necessary criterion for ensuring (wall-normal) grid-independent wall-functions, i.e., wall-functions have to be turbulence model specific. Thereby the novel wall-function approach devised in Kalitzin(2005) is covered as a special strategy. New analytical wall-functions valid for all variants of the Spalart-Allmaras model and the k-omega model respectively are devised. Although the method is designed for fully developed turbulent boundary-layer flows with zero-pressure gradient, it is applied successfully to flows with separation due to abrupt and smooth adverse pressure gradients. The influence of the wall-normal grid resolution and the pressure gradient parameter is investigated. In order to reduce the slight grid-dependence in regions of strong surface curvature, large pressure gradients and separation, we apply a near-wall grid adaptation in such regions.