Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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IssuesArchive of Issues2014-3pp.298-304

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M.A. Ilgamov, "Strong expansion-contraction of a cavity in a fluid under acoustic action," J. Appl. Math. Mech. 78 (3), 298-304 (2014)
Year 2014 Volume 78 Issue 3 Pages 298-304
Title Strong expansion-contraction of a cavity in a fluid under acoustic action
Author(s) M.A. Ilgamov (Ufa, Russia,
Abstract The simplest model of the strong expansion-contraction of a spherical evacuated cavity in an unbounded ideal incompressible fluid under acoustic action is constructed. It is assumed that the cavity is formed at the instant of maximum dilatation of the fluid as the result of the breakdown in its continuity by elementary particles, and the amplitude of the induced acoustic oscillations exceed the mean pressure in the fluid by an order of magnitude or more. The trajectory of the motion of the interface is divided into three stages, in each of which it is assumed that there is a certain constant value of the pressure. This enables an approximate analytical solution of the problem to be obtained. It is shown that there is an agreement with the numerical solution of the initial problem that is sufficient for qualitative estimates. The solution obtained enables a parametric analysis of the expansion-contraction processes of a cavity to be carried out and enables the volume of calculations in the numerical modelling to be reduced when taking account of additional factors.
Received 19 January 2012
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