2013 1(12)

BEHAVIOR OF BUBBLES IN A CLUSTER UNDER ACOUSTIC INFLUENCE

Gubaydullin A.A.^1,2, Gubkin A.S.^1,2

¹ Khristianovich Institute Of Theoretical And Applied Mechanics SB RAS, Tyumen Branch, Tumen, Russia
² Tyumen State University, Tumen, Russia

Introduction

Currently, the relevance of research of the phenomenon of sonoluminescence as a single bubble, and a set of bubbles (the so-called bubble clouds or clusters) is determined by the application of cavitation in nanotechnology, the synthesis of new substances, the development of new ways of processing of complex ores and petroleum products. Experimental study of the dynamics of bubbles in the cluster is complicated, therefore the development of models describing the oscillations of a bubble cluster under the influence of the acoustic field is very important. The study of the spherically symmetric collapse of bubbles and clusters is also interesting from the point of view of possibility of obtaining high values of the temperature and pressure, and even thermonuclear fusion. The acoustic cavitation is an effective tool for the conversion of low density energy of sound waves to high density energy associated with oscillations and collapse cavitation bubbles.

Purpose

The purpose of this work is the computer simulation of the dynamics of a bubble cluster, depending on its configuration and the type of external influence.

Method

The paper presents a numerical investigation of the dynamics of bubble clusters. For numerical experiment the program was written in C++ with employment of the OpenMP API. The system of equations was solved by the fourth order Runge–Kutta method with a variable step by time. To bring the system to Cauchy type we used the iterative Gauss – Seidel method. The initial state of a bubble cluster was determined by the initial coordinates, velocities, radii, the radial velocities of the bubbles, the pressure of the gas into the bubble. The low of variation of the liquid pressure away from the cluster also was specified.

Results

In the case of the «step» compression wave the pressure and temperature achieved in the central bubble of the cluster with three embedded dodecahedrons is many times greater than the pressure and temperature in a similar bubble of linear cluster – streamer, which is in qualitative agreement with the experimental data. The characteristic duration of the peak is about 10^-8 – 10^-9 s.

In all cases, the pressure and temperature of gas in the peripheral bubbles did not exceed the same parameters for the central bubble of the cluster.

The pressure in the central bubble of the cluster with three embedded dodecahedrons is much higher than in the  central bubble of the streamer in the case of harmonic disturbances. It was revealed that the frequency of disturbance affects the amplitude of oscillations of bubbles. The amplitude increases with the approach of the frequency to the eigenfrequency of the bubble oscillations in liquid.

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