Reshocked Richtmyer-Meshkov instability: Numerical study and modeling of random multi-mode experiments

Abstract

The evolution of the three-dimensional planar Richtmyer-Meshkov (RM) instability during a two shock wave interaction (i.e., reshock) is investigated by means of comparing numerical simulations and analytical modelling with experimental results of low Mach numbers (M < 1.5) and fairly high Atwood numbers (A ∼ 0.7). The study discusses and analyses the differences in the evolution of the mixing zone for two different types of initial perturbations, namely, multi-mode random initial perturbation with a narrow or wide bubble size distribution. More specifically, the study is focused on the agreement between numerical simulations and experiments performed with an unknown random initial perturbation. Using a large set of experimental results with different reshock arrival times and Mach numbers, the numerical simulations results are compared to the experimental results for a variety of different scenarios. This methodology allows a constrained comparison, while requiring good agreement for all cases. A comprehensive parametric study is conducted, examining the evolution of the mixing zone (MZ) for different initial amplitudes and wavelengths. It is found that in order to achieve a good agreement, the numerical simulation must be performed using a wide enough initial spectrum, which enables a dominant, efficient bubble merging process to take place within the MZ. The numerical simulation results are compared to a model, based on classic single bubble RM evolution formulation, combined with high amplitude effects consideration and phase reversal treatment in case of heavy to light reshock passage. The model is also extended for the case of multi-mode fronts, accounting for a bubble merging process, determining that the MZ evolution after the reshock can be classified with high confidence as governed by an inverse cascade bubble merger, approaching self-similarity.