Outgoing shock waves at collapse of a cavitation bubble in water

Abstract

Formation and propagation of a shock pulse arising at collapse of a cavitation bubble in water are numerically studied. The initial bubble radius R0 is varied in the range 1–4 mm, the liquid pressure p∞ in the range 1–20 bar, and the liquid temperature T∞ in the range 20–80 °C. The dynamics of the vapor in the bubble and the surrounding liquid is governed by the equations of gas dynamics with allowing for the heat conductivity, heat and mass exchange on the bubble surface. Wide-range equations of state are applied. The numerical technique is based on the Godunov method on moving grids thickened to the bubble surface. A discontinuous approximation of the numerical shock pulse in the vicinity of its front part is used. The case of R0=1 mm, p∞=1 bar, T∞=20 °C is considered as a reference one. It is revealed that the influence of R0 in terms of the dimensionless distance from the collapse center r/R0 is not large and is mainly realized during the shock pulse formation. The variation in p∞ mostly leads to quantitative changes of the pulse characteristics. In particular, the maximum rate of decrease in the pulse pressure peak grows with r (the distance to the collapse center) from that of a regression proportional to r−3/2 to that of a regression according to r−4/3. With rising T∞, the pulse gets weaker and becomes pronounced at larger distance from the collapse center. With increasing T∞ to about 45 °C at R0=1.92 mm and p∞=1 bar, the pulse turns out to be shockless. With the increase of T∞ to approximately 40 °C, the maximum rate of decay in the pulse pressure amplitude is reduced to that of a regression proportional to r−1. It is shown that the obtained results are in good agreement with known experimental data.