CAVITATION DYNAMICS: I. A MATHEMATICAL FORMULATION.
HARVARD UNIV CAMBRIDGE MASS ACOUSTICS RESEARCH LAB
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A central problem in the study of acoustic cavitation is that of understanding the dynamics of small, isolated bubbles set in motion in a liquid by a sound field. The complicated, nonlinear nature of such motions has served in the past to limit investigations to the study of very simple models of such bubbles. However, the advent of large digital computers now makes it possible to construct more realistic models with a reasonable expectation that numerical calculation of their motions will give a deepter insight into cavitation phenomena. In order to exploit this possibility, a mathematical formulation has been constructed in the form of a set of nonlinear ordinary differential and algebraic equations that can be solved simultaneously, and economically, on a digital computer. Two objectives of this program of computation have been to obtain numerical solutions of this formulation that give reliable estimates of physical quantities associated with bubbles in violent motion and to assess the effects of heat conduction, viscosity, sound radiation, and surface tension of such quantities. In this report, the formulation is derived and an assessment of the reliability of its predictions made. Author
- Fluid Mechanics