Growth rate predictions of single- and multi-mode Richtmyer–Meshkov instability with reshock

Abstract

The single- and multi-mode Richtmyer–Meshkov instabilities (RMI) with reshock are numerically analyzed in two- and three-dimensional domains. Four different types of air/SF6 interface shapes are investigated in a shock tube configuration, and the predicted post-reshock growth rates are compared with available empirical models of Mikaelian’s (Physica D 36(3):343–347, 1989) and Charakhch’an’s (J Appl Mech Tech Phys 41(1):23–31, 2000). The simulation of 3D multi-mode RMI shows good agreement with a past experimental study, but other interface types (2D single-mode, 2D multi-mode and 3D single-mode) result in different growth rates after reshock. Parametric studies are therefore performed to investigate the sensitivities of the post-reshock growth rates to model the empirical parameters. For single-mode RMI configurations, the interface shape is found to be only a weak function of the post-reshock growth rate, as also predicted by previous reshock models. The post-reshock growth rate shows a linear correlation to the velocity jump due to reshock; however, it is only about a half of the prediction of Charakhch’an’s model even though the growth before reshock compares well with pre-reshock models. The 3D single-mode post-reshock RMI growth rate is nearly 1.6 times larger than the 2D single-mode RMI. The parametric studies of multi-mode RMI show two distinctly different growth rates depending on the mixing conditions at reshock. If the interface remains sharp at the time of reshock, the post-reshock growth rate is as large as the single-mode cases. However, if the interface is mixed due to non-linear interactions of bubbles and spikes, the growth rates becomes slow and independent of the interface shapes. Overall, this study provides new insights into the flow features of reshocked RMI for different initial perturbation types.