Numerical simulation of strong expansion and collapse of cavitation bubbles with centers located in a straight line

Abstract

A technique for numerical investigation of strong expansion and collapse of cavitation bubbles is presented. The bubbles are located on a straight line, radially convergent shock waves are supposed to appear inside the bubbles in the final stage of their collapse. The efficiency of the technique is achieved by using different models for simulating the expansion of the bubbles and the beginning of their collapse where the interaction between the bubbles is essential, and for simulating the end of the collapse of the bubbles where their interaction is insignificant. The first model is that of joint dynamics of weakly-nonspherical bubbles. In that model, it is assumed that the liquid is weakly compressible, its motion is potential, the vapor in the bubbles is homobaric, the pressure inside the bubbles is equal to the saturated vapor pressure at the ambient liquid temperature. The second model is that of dynamics of a single axisymmetric bubble. It takes into account the liquid compressibility, the nonstationary heat conductivity of liquid and vapor, the nonequilibrium evaporation and condensation at the interphase boundaries, the considerable nonsphericity of the bubble and the strong non-uniformity of the vapor in the final stage of the bubble collapse. It utilizes realistic equations of state for liquid and vapor. An example illustrating the effect of peripheral bubbles on the dynamics of the central one is given in the case of three bubbles located on a straight line.