Passive scalar mixing induced by the formation of compressible vortex rings

Abstract

This study aims to determine the relationship between the physical features of a compressible vortex and the mixing process. Such relationship is of significant importance to design combustors that can achieve optimal or most effective mixing. The passive scalar mixing induced by the formation of a canonical compressible vortex ring (CVR) generated at the end of a shock tube is investigated by using numerical simulation. In addition, the method of finite-time Lyapunov exponent (FTLE) field are detected to identify the region of CVR, as well as to analyze the passive scalar mixing during the CVR formation. As the CVR rolls up, the ambient fluid outside the shock tube is entrained into the ring. The entrainment fraction (the mass of entrained fluid to the total mass of CVR) is found to strongly depend on two features of CVRs. One is the compressibility of CVRs, which is characterized by the Mach number of the incident shock denoted by Mach number (Ma). The other is pinch-off of CVRs, which happens at a certain timescale with narrow range of 2–4. As Ma increases, the entrainment fraction of the leading CVR decreases linearly due to smaller vortex core and weaker radial diffusion of vorticity generated by larger compressibility. After CVRs pinch off, trailing vortices appear and show less effective at entrainment than the leading CVRs do. Moreover, the tendency of the rate of entrainment is examined. The results indicate that increasing compressibility and total fluid flux are in favor of the rate of entrainment but restrain the entrainment fraction of total jet.