Theoretical and numerical studies on shock reflection at water/air two-phase interface: Fast-slow case

Abstract

The wave patterns of shock wave interaction with multi-material interface have been studied in the past decades. Interactions between shock waves and interfaces can be classified as slow-fast and fast-slow case depending on the relative acoustic impedance of two mediums as shock passes from one to another. In this paper, the fast-slow case of shock passes from water to air is studied and the refraction wave patterns includes regular and irregular types, which have been identified from previous studies. The analytical solutions are emphasized with the incident shock angle ranging from 0∘ to 90∘ and the shock strength from 0.2 GPa to 5.0 GPa. By applying the Tait equation, the shock relations as well as the Prandtl-Meyer relations in water is obtained, both of which are used to complete the polar diagrams for the incident shock wave, the reflected Prandtl-Meyer fan and the transmitted shock wave for the fast-slow case. This has not yet been reported in previous studies. The critical angle is obtained when the reflection transits from a regular to an irregular type and the inclination angle of the incident shock wave at the interaction point after the reflection is found for irregular reflection. The interface deflection angle, the pressure ratio across the transmitted shock wave and the post-shock velocity of the transmitted shock wave are derived analytically with varying incident shock angles and strengths. Numerical simulations are performed to compare with the analytical solutions and the refraction wave patterns are consistent with the analytical results. The analytical interface deflection angles and transmitted shock angles overlap well with the numerical results.