Effects of Density Stratification on Mixing Enhancement by Shock Wave in Supersonic Shear Layer Flows

We analyze the response of passive mixing to shock wave in a density-stratified supersonic shear layer by means of direct numerical simulation with a high-order hybrid compact-WENO scheme. The coexistence gradients of density and pressure have a complex influence on generation of baroclinic vorticity, depending on the gradient directions. The growth rate of mixing layer thickness is increased by the presence of shock wave, but the mixing layer thickness is not always increased. The passive mixing can be enhanced in a thickened shear layer by the incident shock wave if the homodromous vortexes are induced by the baroclinic torque. The mixing efficiency is also enhanced by increasing the density difference of two streams. The present study can be helpful to take measures to strengthen the mixing process in supersonic shear flows. 1. Introduction Acquirement of fast and highly efficient mixing is a very challenging problem in supersonic flows. Shear layer flows are widely applied in scramjet to increase the mixing of two supersonic streams. Moreover, it has been found that the introduction of shock wave into a supersonic shear layer flow may enhance the mixing performance [1–3]. Due to the incident shock wave, the mixing process is much changed with the compression of vortexes and the generation of baroclinic vorticity. Some researchers have studied the interactions between shock wave and vortexes to explain the mechanisms of mixing enhancement [4–6]. And it has been shown that the complex shock wave refraction contributes to the mixing increase [7]. Hermanson and Cetegen [8] have experimentally studied shock-induced mixing of nonhomogeneous density turbulent jets and indicated that the reversal of the density ratio between the jet and the surroundings, and the consequent change in the sign of baroclinic vorticity, does not yield similar effects in terms of flow structure or mixing enhancement. However, passive mixing induced by shock wave in density-stratified shear flows has not been well studied. Therefore, in the present paper, the shocked mixing layer flows are numerically simulated considering the effects of density stratification of two streams. The thickness of mixing layer and the mixing efficiency are then carefully compared. The physics of mixing enhancement by the oblique shock wave is then discussed. 2. Numerical Methods The shocked density-stratified supersonic mixing layers are simulated by means of direct numerical simulation. The three-dimensional conserved compressible Navier-Stokes equations, together with a passive scalar conserved