A priori testing of wall models for separated flows

Databases from numerical simulation of wall-bounded flows with closed reverse flow regions were examined in order to derive models, which relate the mean wall shear stress to flow quantities in a certain distance from the wall. The approach makes use of the particular shape of the profiles of turbulent shear stress which balances the streamwise pressure gradient outside the viscosity-affected near-wall region. One model version requires as input the streamwise pressure gradient and a velocity scale $UW$ which results from linear extrapolation of the mean flow to the wall. Its application is restricted to the part of the reverse flow region with nonvanishing adverse pressure gradient. A more general applicable skin-friction law is derived from the observation that near-wall mean velocity profiles approximately collapse if they are scaled in a defect form. This scaling holds up to approximately half a bubble length downstream of attachment. Numerical values for model coefficients vary slightly from flow to flow and seem to depend on the Reynolds number.