A compressible wall model for large-eddy simulation with application to prediction of aerothermal quantities

Abstract

Large-eddy simulation (LES) of compressible flow with wall modelling is assessed on a quasi-isothermal and supersonic plane channel. The derivation of a quasi-analytical wall model based on empirical laws appears very difficult for combined physical effects like compressibility with pressure gradient. A wall model based on the compressible thin boundary layer equations constitutes a more general approach toward the simulation of multiphysical wall bounded flows with LES. In this work, such a wall model is derived and solved thanks to a new meshless method. An adequate scaling of the wall distance is introduced in the Van-Driest damping function of the wall model to handle compressibility effects. The choice of the proper wall distance scaling is shown to be crucial as soon as compressibility effects become significant. Additionally, some sources of error inherent to this wall-modelling approach are treated by appropriate corrections, and show non-negligible impact on the results. On a quasi-isothermal plane channel flow, the mean wall fluxes, primitive variable profiles and velocity fluctuations compare well to Direct Numerical Simulation (DNS) and empirical correlations for a wide range of Reynolds number. Then the DNS of supersonic isothermal-wall plane channel of Coleman at Mach = 1.5 and Mach = 3 are used as a more discriminant test case. The results agree well with the DNS data in terms of mean wall friction and wall heat flux. Finally, a specific analysis of the wall model accuracy is performed outside of the LES solver. This analysis allows to discriminate the error due to the wall model itself from the error due to the interaction between the wall model and the LES solver.