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Linearized Dynamics of Spherical Bubble Clouds

d'Agostino, Luca and Brennen, Christopher E. (1989) Linearized Dynamics of Spherical Bubble Clouds. Journal of Fluid Mechanics, 199 . pp. 155-176. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:DAGjfm89

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Abstract

The present work investigates the dynamics of the one-dimensional, steady flow of a spherical bubble cloud subject to harmonic far-field pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility and relative motion of the two phases are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. The results are then generalized by means of Fourier synthesis to the case of arbitrary far-field pressure excitation. The flow displays various regimes (sub-resonant, trans-resonant and super-resonant) with different properties depending on the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms. Finally the results for the case of Gaussian-shaped far-field pressure change are presented and the most important limitations of the theory are briefly discussed. The simple linearized dynamical analysis developed so far clearly deminstrates the importance of the complex phenomena connected to the interaction of the dynamics of the bubbles with the flow and provides an introduction to the more realistic study of the same flows with nonlinear bubble dynamics.


Item Type:Article
Additional Information:Received 22 December 1987 and in revised form 27 May 1988. The authors would like to thank Cecilia Lin for her help in drawing the pictures. This work was supported by the Naval Sea System Command General Hydromechanics Research Program admninistered by the David Taylor Naval Ship Research and Development Center under Contract No. N00167-85-K-0165, by the Office of Naval Research under contract No. N0014-83-K-0506 and by a Fellowship for Technological Research administered by the North Atlantic Treaty Organization - Consiglio Nazionale delle Ricerche, Italy, Competition No. 215.15/11 of 11.5.1982. Their support is gratefully acknowledged. "Reprinted with the permission of Cambridge University Press."
Record Number:CaltechAUTHORS:DAGjfm89
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:DAGjfm89
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87
Collection:CaltechAUTHORS
Deposited By: Christopher Brennen
Deposited On:21 Sep 2004
Last Modified:26 Dec 2012 08:39

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