Modeling strong compression of a gas bubble in fluid

Abstract

A technique for calculating strong adiabatic compression of a gas bubble in fluid is proposed. The compression results from the pressure applied to the outer surface of the fluid. The motion of the fluid and gas is described by two-dimensional dynamic equations of compressed fluid and gas with realistic equations of its state. The effects of viscosity and thermal conductivity are not allowed for. The bubble surface is defined as a contact interface where there is a surface tension. Coupled Euler-Lagrange coordinates are used, with the bubble surface serving as a coordinate system. A spherical system of coordinates is used as a fixed reference. Equations of gas and fluid dynamics are solved by Godunov’s equations with second-order accuracy in space and time. The economic feasibility of the technique is illustrated by some model problems. The proposed method has been proven to be much more efficient than the classic first-order-approximation Godunov’s schemes traditionally used in solving problems of a highly compressed bubble. One of the scenarios is used to show the influence of slight spherical-shape distortions of the bubble on the evolution of the radially converged shock wave resulting from the strong compression.