Study on Richtmyer-Meshkov instability at heavy/lightsingle-mode interface

Abstract

The Richtmyer-Meshkov (RM) instability at a heavy/light single-mode interface is studied both experimentally and numerically in this work, focusing on the interface structure evolution and the perturbation amplitude growth. The difference between the RM instability of the heavy/light interface and the light/heavy case (J. Fluid Mech., 2018, 853: R2) is discussed. Experimentally, an advanced soap film technique is adopted to generate an SF6/air gaseous interface with a controllable shape such that the instability development can be accurately examined. Detailed evolutions of the interface morphology and the wave pattern are captured by a high-speed video camera combined with schlieren photography. It is observed that the interfacial morphology presents an evident stratification after the phase inversion of the interface (the bubble (spike) reverses to be a spike (bubble)), which is mainly ascribed to the droplet cloud produced by the rupture of the soap film impacted by an incident shock wave. Numerically, a high-order accurate solver for compressible multi-phase flow, which has been thoroughly validated in previous shock-interface interaction studies, is employed to simulate the present heavy/light RM instability. The numerical results show good agreements with the experimental ones, which enables us to perform a detailed flow analysis. Different from the light/heavy case, after the shock impact, the heavy/light interface immediately enters the phase reversal process. After the phase reversal, the interface experiences successively the linear and nonlinear growths, which is similar to the light/heavy case. The reliable experimental and numerical results here allow us to examine the validity of the previous linear and nonlinear models for the heavy/light RM instability growth. It is found that the linear model of Meyer & Blewett (Phys. Fluids, 1972, 15: 753–759) gives a good prediction of the perturbation growth at linear stage up to a dimensionless time of 0.7, and the empirical model of Dimonte & Ramaprabhu (Phys. Fluids, 2010, 22: 014104) reasonably predicts the perturbation growth at the nonlinear stage, which is different from the light/heavy case where the model of Zhang & Guo (J Fluid Mech., 2016, 786: 47–61) gives the best prediction as suggested by an elaborate experimental study. Our study may facilitate the thorough understanding of the heavy/light RM instability and also can serve as a benchmark for new models.