High-Pass Filtered Eddy-Viscosity Models for Large-Eddy Simulations of Compressible Wall-Bounded Flows

Abstract

In this contribution we consider large-eddy simulation (LES) using the high-pass filtered (HPF) Smagorinsky model of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.5 and momentum-thickness Reynolds numbers at inflow of ∼4500. The HPF eddy-viscosity models employ high-pass filtered quantities instead of the full velocity field for the computation of the subgrid-scale (SGS) model terms. This approach has been proposed independently by Vreman (, 2003, Phys. Fluids, 15, pp. L61–L64) and (, , , and , 2003, in Direct and Large Eddy Simulation V, Kluwer, Dordrecht, pp. 81–88). Different from classical eddy-viscosity models, such as the Smagorinsky model (, 1963, Mon. Weath. Rev, 93, pp. 99–164) or the structure-function model ( and , 1992, J. Fluid Mech., 239, pp. 157–194) which are among the most often employed SGS models for LES, the HPF eddy-viscosity models do need neither van Driest wall damping functions for a correct prediction of the viscous sublayer of wall-bounded turbulent flows nor a dynamic determination of the coefficient. Furthermore, the HPF eddy-viscosity models are formulated locally and three-dimensionally in space. For compressible flows the model is supplemented by a HPF eddy-diffusivity ansatz for the SGS heat flux in the energy equation. Turbulent inflow conditions are generated by a rescaling and recycling technique in which the mean and fluctuating part of the turbulent boundary layer at some distance downstream of inflow is rescaled and reintroduced at the inflow position ( and , 2003, Phys. Fluids, 15, pp. 2389–2412).