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Linearized dynamics of two-dimensional bubbly and cavitating flows over slender surfaces

Published online by Cambridge University Press:  21 April 2006

Luca D'Agostino ,
Christopher E. Brennen  and
Allan J. Acosta
Luca D'Agostino
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
Christopher E. Brennen
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
Allan J. Acosta
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

The present work investigates the dynamics of two-dimensional, steady bubbly flows over a surface and inside a symmetric channel with sinusoidal profiles. Bubble dynamics effects are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. Energy dissipation due to viscous, thermal and liquid compressibility effects in the dynamics of the bubbles is included, while the relative motion of the two phases and viscous effects at the flow boundaries are neglected. The results are then generalized by means of Fourier synthesis to the case of surfaces with slender profiles of arbitrary shape. The flows display various flow regimes (subsonic, supersonic and super-resonant) with different properties according to 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 on the flows subject to harmonic excitation. Finally the results for a flow over a surface with a Gaussian-shaped bump are presented and the most important limitations of the theory are briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 192 , July 1988 , pp. 485 - 509
Copyright
© 1988 Cambridge University Press

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