Dynamics of a spherical enclosure in a liquid during ultrasonic cavitation

Abstract

The paper investigates the process of pulsation of a spherical cavity (bubble) in a liquid under the influence of a source of ultrasonic vibrations. The pulsation of a spherical cavity is described by the Kirkwood-Bethe equations, which are one of the most accurate mathematical models of pulsation processes at an arbitrary velocity of the cavity boundary. The Kirkwood-Bethe equations are essentially non-linear, therefore, to construct solutions and parametric analysis of the bubble collapse process under the influence of ultrasound, a numerical algorithm based on the Runge-Kutta method in the Felberg modification of the 4-5th order with an adaptive selection of the integration step in time has been developed and implemented. The proposed algorithm makes it possible to fully describe the process of cavitation pulsations, to carry out comprehensive parametric studies, and to evaluate the influence of various process parameters on the intensity of cavitation. As an example, the results of calculating the process of pulsation of the cavitation pocket in water are given and the influence of the amplitude of ultrasonic vibrations and the initial radius on the process of cavitation of a single bubble is estimated.