Numerical study on Rayleigh-Taylor effect on cylindrically converging Richtmyer-Meshkov instability

Abstract

Evolution of a two-dimensional air/SF₆ single-mode interface is numerically investigated by an upwind CE/SE method under a cylindrically converging circumstance. The Rayleigh-Taylor effect caused by the flow deceleration on the phase inversion (RTPI) is highlighted. The RTPI was firstly observed in our previous experiment, but the related mechanism remains unclear. By isolating the three-dimensional effect, it is found here that the initial amplitude (a₀), the azimuthal mode number (k₀) and the re-shocking moment are the three major parameters which determine the RTPI occurrence. In the variable space of (k₀, a₀), a critical a0 for the RTPI occurrence is solved for each k₀, and there exists a threshold value of k₀ below which the RTPI will not occur no matter what a₀ is. There exists a special k₀ corresponding to the largest critical a₀, and the reduction rule of critical a₀ with k₀ can be well described by an exponential decay function. The results show that the occurrence of the RTPI requires a small a₀ which should be less than a critical value, a large k₀ which should exceed a threshold, and a right im**ing moment of the re-shock which should be later than the RTPI occurrence. Finally, the effects of the incident shock strength, the density ratio and the initial position of the interface on the threshold value of k₀ and on the maximum critical a₀ are examined. These new findings would facilitate the understanding of the converging Richtmyer-Meshkov instability and would be helpful for designing an optimal structure of the inertia confinement fusion capsule.