A wall model for large-eddy simulation of highly compressible flows based on a new scaling of the law of the wall

Wall modelling in large-eddy simulation (LES) is of high importance to allow scale resolving simulations of industrial applications. Numerous models were developed and validated for incompressible flows, including a simple quasi-analytical model based on Reichardt's formula that approximates the law of the wall. In this paper, a scaling is proposed to generalize this wall model to highly compressible flows. First, the results of wall-resolved LES (wrLES) of adiabatic compressible turbulent channel flows at Re-tau = 1000 and at centreline Mach numbers of M-c = 0.76 and 1.5 are presented. Then, three potential scalings of the incompressible wall model are proposed, and their a priori performance is evaluated : (i) the Howarth-Stewartson scaling, (ii) an improved Van Driest scaling and (iii) a new scaling obtained from a blending of those two. The results of wall-modelled LES (wmLES) of compressible channel flows using these three models are compared with the reference wrLES data, showing the superior accuracy of the hybrid scaling. The consistency of the new wall model at low Mach numbers is also verified by comparing the results of a wmLES at M-c = 0.25 with those of reference incompressible DNS data at Re-tau = 1000 and 5200. Finally, the proposed wall model is also applied to a turbulent channel flow at M-c = 1.5 and R-tau = 5200.