Deformation of cavitation bubbles at their strong expansion and collapse in a streamer

Abstract

Deformation of initially spherical cavitation bubbles is considered in the case of their strong single expansion and subsequent collapse in a streamer consisting of three bubbles located in one straight line. The central bubble is equidistant from the others. The influence of the distance between the bubbles is studied in the range, in which the non-sphericity of the central bubble during the collapse does not exceed 20%. The expansion of the bubbles and the most part of their collapse is governed by the ordinary differential equations of the second order in the radii of the bubbles, the positions of their centers on the line of their interaction, and the amplitudes of their axisymmetric non-sphericity in the form of spherical harmonics. In doing so, the interaction between bubbles is taken into account, the assumptions of weak liquid compressibility, homobaricity of bubbles, and their small non-sphericity are used. The final of the collapse of each bubble is governed by the partial differential equations of gas dynamics. In doing so, the interaction of bubbles is ignored, but the axial symmetry of bubbles, liquid compressibility, non-uniformity of vapor, heat conductivity of vapor and liquid are taken into account, wide-range equation of states for vapor and liquid are applied. It is shown that with decreasing the distance between the bubbles, the non-sphericity of the central bubble at the end of its collapse first slowly increases from zero and then quite rapidly grows. Along with that, the central bubble non-sphericity level of 1% is attained at the distance between the bubbles equal to about 20 times their radius at the moment of their maximal expansion. Simulation of the final high-speed stage of the bubble collapse by the model destined to the low-speed stage of expansion and collapse leads to significant overestimation of the non-sphericity of the central bubble at the end of its collapse.