Wall-Modelled Large-Eddy Simulation of a Mach 7.5 Hypersonic Boundary Layer

Large-Eddy Simulation (LES) has proven to be a computationally valuable tool to simulate unsteady turbulent flows. However, restrictive resolution requirements high-Reynolds number wall-bounded flows necessitate the use of wall models or approximate wall boundary conditions in addition to a subgrid-scale (SGS) model. Inoue and Pullin~(J. Fluid Mech. 2011) developed a virtual wall model for incompressible boundary layer flows. This model dynamically couples the outer resolved region with the wall region, and imposes a slip velocity boundary condition for the filtered velocity field on a ``virtual'' wall. An extension of the previous wall model is presented for LES of compressible turbulent boundary layer flows. The new virtual wall model is combined with the stretched spiral vortex sub-grid scale model in a self-consistent framework. Both models are incorporated in a fourth order finite volume compressible Navier-Stokes solver. A wall-modeled LES (WMLES) of a Mach 7.5 turbulent boundary layer is performed. We present results of mean profiles, turbulence intensity and Reynolds shear stress and compare these with the experimental results of Williams et al. (J. Fluid Mech, 2018).