Numerical Study of Hydrodynamic Instabilities in Converging Geometry

This work presents simulations of a heavy gas, SF₆, immersed within a light gas, air, under the effect of a converging shock wave. Upon interaction of the shock wave with the perturbed interface between air and SF6, Richtmyer-Meshkov instability (RMI) and, later, Rayleigh-Taylor instability (RTI) take place. More precisely, a succession of RMI and RTI occurs due to multiple shock and rarefaction waves, and gives rise to mixing between the heavy and light fluids. The problem of hydrodynamic instability-induced mixing in converging geometry is particularly relevant to engineering applications such as the process of nuclear fusion by the inertial confinement approach. This study is motivated by the need to better understand the relation between the initial perturbations at the interface between the fluids and the development of the instabilities and mixing in a converging geometry. Using the Flash Code, a PPM hydrodynamic solver developed by the ASC center at the University of Chicago [1], this study focuses on the growth rate of instabilities and the subsequent mixing associated with various carefully designed initial interfacial perturbations in the implosion configuration described above. In cylindrical geometry, comparisons between the growth of high and low frequency single mode perturbations are presented. It is found that at later times, after RMI and RTI take place, the width of the mixing layer is the largest for the low-wavenumber initial interface perturbation. Also, simulations show that the SF₆ target with the highest wavenumber perturbation presents the most mixing at the later times but the lowest wavenumber initial interface perturbation presents the most mixing before reshock.