Modeling the speed of jet induced by a shock wave

When a shock wave impacts on a curved interface between two fluids, the disturbance will grow as described by Richtmyer-Meshkov instability (RMI). If the shock runs from a heavy fluid to a light fluid, the interface shape may be reversed and a jet could be generated. Although numerical simulations could give more details, as shown in our earlier work on single-mode RMI (Bai, Deng & Jiang, Shock Waves 2018), people often wants a simple analytical model to predict the interface movement. In the current work, under the situation of a planar shock wave impacting a spherical cap interface, we try to use analytical and numerical methods to model the speed of jet and so provide a tool to predict the maximum jet speed. Through theoretical analysis, the formula of interfacial velocity between liquid-gas interface is achieved and applied to the modeling of jet speed. Then numerical simulations with a cut-cell based sharp-interface method (Chang, Deng & Theofanous, JCP 2013) are performed to validate the formula and identify the related parameters. The analytical formula of interfacial velocity and the result model of maximum jet speed could be used to estimate the interfacial behavior in similar situations.