A numerical study of shock-interface interaction and prediction of the mixing zone growth in inhomogeneous medium

The growth of mixing zone on an interface induced by Richtmyer-Meshkov (RM) instability occurs frequently in natural phenomena and in engineering applications. Usually, the medium on which the RM instability happens is inhomogeneous, the effect of medium inhomogeneity on the growth of the mixing zone during the RM instability is still not clear. Therefore, it is necessary to investigate the RM instability in inhomogeneous medium. Based on a high-order computational scheme, the interactions of a density interface with an incident shock wave (ISW) in inhomogeneous medium are numerically simulated by solving the compressible Navier-Stokes equations. The effect of the inhomogeneity on the interface evolution after the passage of ISW through the interface is investigated. The results show that the interface morphology develops in a distinctive “spike-spike” structure in inhomogeneous medium. Particularly, the spike structure on the bottom of the interface is due to the reverse induction of RM instability by curved ISW or reflected shock wave. With the increase of inhomogeneity, the growth rate of the mixing zone width on interface increases, and the wave patterns caused by interaction between the shock wave and interface are more complex. Compared with RM instability in homogeneous medium, the inhomogeneous distribution of the density in medium further enhances the baroclinic effect and induces larger vorticity in flow field. Therefore, the interface is stretched much more significantly under the induction of enhanced vorticity in inhomogeneous medium. Based on above analyses, a model for predicting the growth of mixing zone width on the interface after the passage of ISW is proposed, in order to provide a useful method for evaluations of perturbation growth behavior during the RM instability in inhomogeneous medium.