Evolution of perturbations in the spherical shape of a cavitation bubble during its implosive collapse

R. I. Nigmatulin ; A. A. Aganin ; M. A. Ilgamov ; D. Yu. Toporkov

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 1, pp. 79-108

Résumé

We study the growth of small deviations in the spherical shape of a cavitation bubble during its single strong compression. At the beginning of compression, the vapor in the bubble cavity is in the state of saturation. The deviations from sphericity are taken in the form of spherical harmonics of degree $n=2,3,\dots$. The dynamics of the vapor in the bubble and the surrounding liquid is presented as a superposition of the spherical component and its nonspherical perturbation. The spherical component of the liquid and vapor dynamics is described by gas dynamics equations since shock waves may arise in the bubble during the final high-speed stage of compression and the liquid compressibility becomes significant. The nonstationary heat conductivity of the liquid and vapor and the nonequilibrium of evaporation/condensation on the interface are taken into account. Realistic wide-range equations of state are applied. The nonspherical component is described allowing for the effects of liquid viscosity, surface tension, density of the vapor in the bubble and inhomogeneity of its pressure. The collapse of the cavitation bubble in water and acetone is considered at the liquid pressure $p_\infty$, the initial radius $R_0$ and the liquid temperature $T_0$, which vary in the ranges $250\leq R_0\leq1000$ mcm, $1\leq p_\infty\leq50$ bar, $20\leq T_0\leq40\,^\circ$ C for water and $0\leq T_0\leq20\,^\circ$ C for acetone. It is found that in the case of $R_0=500$ mcm, $p_\infty\leq50$ bar, $T_0=20\,^\circ$ C for water and $T_0=0\,^\circ$ C for acetone, the amplitude of the small nonsphericity of the bubble in the form of individual spherical harmonics may increase during compression up to 2000 times in water and up to 150 times in acetone. The growth of nonsphericity is studied as a function of a number of important factors such as the initial bubble radius, liquid pressure, liquid viscosity, evaporation/condensation on the bubble surface, the presence of vapor in the bubble, heat conductivity in the vapor and liquid, etc.

Détail

Keywords: cavitation bubble, vapor bubble, collapse of a bubble, compression of a bubble, distortion from a spherical shape, deformation of a bubble.