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Some Nonlinear Interactive Effects in Bubbly Clouds

Kumar, Sanjay and Brennen, Christopher E. (1993) Some Nonlinear Interactive Effects in Bubbly Clouds. Journal of Fluid Mechanics, 253 . pp. 565-591. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:KUMjfm93b

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Abstract

Nonlinear interactive effects in a bubbly cloud have been studied by investigating the frequency response of a bubble layer bounded by a wall oscillating normal to itself. Averaged equations of motion are used and the Rayleigh-Plesset equation is used to include the bubble dynamics. Energy dissipation due to viscous and thermal effects are included while relative motion between the two phases, liquid compressibility and viscous dissipation in the liquid have been ignored. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear response of a single bubble in an infinite fluid. This is used in an approximate calculation of the nonlinear frequency response of a bubble layer. Finite thickness of the bubble layer results in characteristic natural frequencies of the layer all of which are less than the natural frequency of a single bubble. The presence of bubbles of different sizes in the layer causes a phenomenon called harmonic cascading. This phenomenon consists of a large response at twice the excitation frequency when the mixture contains bubbles with a natural frequency equal to twice the excitation frequency. The details of these results along with the most important limitations of theory are presented.


Item Type:Article
Additional Information:(Received 2 January 1992 and in revised form 11 August 1992) The authors are grateful for the support of Office of Naval Research under contract N000167-85-K-0165. The authors are also grateful to the reviewers for their helpful comments and suggestions included in the paper. "Reprinted with the permission of Cambridge University Press."
Record Number:CaltechAUTHORS:KUMjfm93b
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KUMjfm93b
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118
Collection:CaltechAUTHORS
Deposited By: Christopher Brennen
Deposited On:13 Oct 2004
Last Modified:26 Dec 2012 08:39

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