Cavitation Bubble Collapse in Viscous, Compressible Liquids—Numerical Analysis

[+] Author and Article Information
R. D. Ivany

Nuclear Engineering Department, Laboratory for Fluid Flow and Heat Transport Phenomena, Nuclear Engineering Department, University of Michigan, Ann Arbor, Mich.

F. G. Hammitt

Nuclear Engineering Department, University of Michigan, Ann Arbor, Mich.

J. Basic Eng 87(4), 977-985 (Dec 01, 1965) (9 pages) doi:10.1115/1.3650853 History: Received February 26, 1965; Online November 03, 2011


Collapse of a spherical bubble in a compressible liquid, including the effects of surface tension, viscosity, and an adiabatic compression of gas within the bubble is investigated by numerical solutions of the hydrodynamic equations. A limiting value of shear viscosity causes the bubble collapse to slow down markedly, for both compressible and incompressible liquids, whereas moderate viscosities have very little effect on the rate of collapse. The inclusion of surface tension and viscosity introduces two scaling parameters into the solution, so that a single normalized solution is no longer sufficient to describe collapse behavior. The magnitude of the density changes calculated for the compressible liquid and the extremely rapid changes with time suggest that the usual Navier-Stokes equation of motion may not be appropriate. The possibility of liquid relaxational phenomenon and its contribution to sonoluminescence is considered. Shock waves or damagingly high pressures are not generated during collapse at a distance in the liquid equal to the initial radius from the center of collapse, although they will appear at such a distance if the bubble rebounds.

Copyright © 1965 by ASME
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