Numerical investigations of shock–bubble interactions in mercury

Abstract

The bubble collapse induced by the shock–bubble interactions in mercury is investigated numerically to evaluate the cavitation damage. The ghost fluid method (GFM) is applied to the present analysis. Riemann solutions are utilized to correct the values at boundary nodes to suppress the pressure oscillations near the interface. The interactions between an air bubble and a plane shock wave in mercury with the infinite boundary are compared with those in water. It is shown that the collapse time of a bubble in mercury is longer than that in water. The interaction with the incident shock wave leads to the bubble deformation and the formation of liquid jet in the final stage of collapse. Higher impulsive pressure is generated in the mercury when the jet impacts the bubble surface. Also, the interactions between an air bubble and a plane shock wave in mercury in the vicinity of a glass wall are simulated. The mercury and glass are evaluated by using the stiffened gas equations. The motions of three phases for air, mercury, and glass are solved directly coupling the GFM with the level set method. Since the acoustic impedance of glass is smaller than the mercury, the expansion waves are reflected at the glass wall when the shock wave hits the glass wall. Consequently, the bubble takes a similar motion to that near a compliant wall; the glass wall is attracted toward the bubble during the bubble collapse; the collapse time of a bubble becomes shorter than that of an isolated bubble; the jet impacts the bubble surface in the later stage of collapse. Strong shock waves are formed from the bubble when the bubble rebounds as well as when the jet impacts the bubble surface. The shock waves hit the glass wall and lead to the depression of the glass surface.