Turbulent energy flux generated by shock/homogeneous-turbulence interaction

Abstract

High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modelling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the postshock turbulent energy flux is predicted to be strongly dependent on the angle of incidence of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available data from direct numerical simulations. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.