Modeling and Numerical Simulation of Single Bubble Dynamics and Shock Wave Propagation

Abstract

Cavitation is a formation of bubbles in liquid with high-speed, where a phase transition from liquid phase to gas phase occurs when the pressure of the liquid is reduced to the saturated vapor pressure. The Rayleigh-Plesset equation is well known mathematical model of a spherical single cavitation bubble. However, there have not been proposed an appropriate mathematical model of such a single bubble including the shock wave phenomenon associated with the collapse of the bubble. In this study, we propose a coupled model of the Rayleigh-Plesset equation and the wave equation associated with pressure. In this model, these equations are combined by a bubble surface boundary condition, which is defined by solutions of the Rayleigh-Plesset equation. Further, by using our coupled model, we make a numerical test of the rebounding behavior of the single bubble in an ultrasonic field and the shock wave emission. As a results, we show that the shock wave phenomenon associated with the collapse of the bubble, namely, an intensive pressure on the bubble surface and the shock wave propagation are reproduced.