Computational turbulent stress closure for large-eddy simulation of compressible flow

Abstract

Large-eddy simulation (LES) focuses on the primary features of a turbulent flow with length scales larger than an externally specified filter width Δ. Scales smaller than Δ are removed from the simulation by spatial filtering which allows the use of a grid spacing h on the order of Δ. In most LES, the subgrid resolution r = Δ/h is rather coarse (r≈ 1–2) and an additional filtering is induced by the spatial discretization method. This modifies the dynamics of the smaller resolved scales. The computational turbulent stress tensor ξ _ij expresses this modification and incorporates the regular turbulent stress as well as numerical high-pass filter contributions. We consider the computational turbulent stress for three-dimensional compressible flow. Compressibility motivates a decomposition of ξ _ij in a part that is primarily associated with velocity variations and a part associated with density variations. The density variations depend strongly on the Mach number while the velocity variations remain much closer to their incompressible level, even in low supersonic flow. An a priori investigation of a turbulent mixing layer quantifies the significance of the density variations at sufficiently high Mach number with a magnitude of up to 20% of ξ _ij . An explicit modelling of density variations in terms of approximate deconvolution is proposed and shown to accurately follow the Mach number dependence.