A semi-locally scaled eddy viscosity formulation for LES wall models and flows at high speeds

Abstract

We show that the mean wall-shear stresses in wall-modeled large-eddy simulations (WMLES) of high-speed flows can be off by up to $$\approx 100\%$$ with respect to a DNS benchmark when using the van-Driest-based damping function, i.e., the conventional damping function. Errors in the WMLES-predicted wall-shear stresses are often attributed to the so-called log-layer mismatch, which, albeit also an error in wall-shear stresses $$\tau _\mathrm{w}$$ , is an error of about $$15\%$$ . The larger error identified here cannot be removed using the previously developed remedies for the log-layer mismatch. This error may be removed by using the semi-local scaling, i.e., $$l_\nu =\mu /\sqrt{\rho \tau _\mathrm{w}}$$ , in the damping function, where $$\mu $$ and $$\rho $$ are the local mean dynamic viscosity and density, respectively.