Stability analysis of shock-mixing interaction based on dynamic mode decomposition

Abstract

Air-fuel mixing under high-speed, compressible conditions is one of the difficulties in scramjet design, and the use of shock wave enhancement is an effective technical approach. Shock-mixing interaction leads to an increase in the thickness and the turbulence intensity of the mixing layer, thus enhancing the mixing. In this paper, shock-mixing interaction with a convective Mach number of 0.6 is simulated by direct numerical simulation, and the mechanism of shock wave enhancement is studied for the first time from the perspective of flow stability. The dynamic mode decomposition technique is used to decompose the three simulated cases: shock-free mixing, steady shock-mixing interaction, and unsteady shock-mixing interaction. The results show that the flow status is dominated by inlet disturbance in both shock-free mixing and steady shock-mixing interaction, but the flow under unsteady shock-mixing interaction is dominated by the unsteady shock wave. The dominant modes are generally lower in frequency and account for a higher energy proportion; on the contrary, the unstable modes are usually higher in frequency and account for a lower energy proportion. The effect of steady shock wave will substantially increase the growth rate of the unstable modes, while the unsteady shock wave will increase the growth rate of the unstable modes and excite more unstable modes simultaneously, thus promoting flow instability and improving mixing efficiency.