Dynamics of a Spherical Cavity in a Cavitating Liquid with a Continuously Changing Concentration of Cavitation Nuclei

Abstract

The study derives an equation and solves for the first time the problem on the formation and radiation dynamics of a quasi-empty pulsating spherical cavity in a cavitating liquid under the influence of variable sound velocity in a cavitation and cavitation nuclei concentration zone. The data on the cavity dynamics, radiation, and collapsing velocity for a spectrum of initial internal pressures show that, at a maximum gas phase concentration, pulsations are different in the degree of their compression. They have almost identical character: after the first collapse, only a single half-cycle is completed to attain different constant equilibrium radii. The condition of equality between the pressures in a cavitation zone and inside a spherical cavity at its boundary makes it possible to establish a dynamic relation between the volumetric concentration (sound speed) in the cavitation zone and the radius of this spherical cavity for the first time. When calculating and constructing the solution, the condition that the initial cavity size takes a value corresponding to the initial pressure is changed. The dependences of radiation amplitudes over the entire range of applied pressures are plotted. It turns out that the radiation amplitude increases by five orders of magnitude, when the initial pressure inside a cavity changes by three orders of magnitude from 10^–2 to 10^–5 atm.