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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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References

Arakeri, V. H. & Acosta A. J. 1973 Viscous effects in the inception of cavitation on axisymmetric bodies. Trans. ASME I: J. Fluids Engng 95, 519.Google Scholar
Arakeri, V. H. & Shanmuganathan V. 1985 On the evidence for the effect of bubble interference on cavitation noise. J. Fluid Mech. 159, 131–150.Google Scholar
Carstensen, E. L. & Foldy L. L. 1947 Propagation of sound through a liquid containing bubbles. J. Acoust. Soc. Am. 19, 481–501.Google Scholar
d'Agostino, L. & Brennen C. E. 1983 On the acoustical dynamics of bubble clouds, ASME Cavitation and Multiphase Flow Forum, pp. 72–75.
d'Agostino L., Brennen, C. E. & Acosta A. J. 1984 On the linearized dynamics of two-dimensional bubbly flows over wave-shaped surfaces. ASME Cavitation and Multiphase Flow Forum, pp. 8–13.
Foldy L. L. 1945 The multiple scattering of waves. Phys. Rev. 67, 107–119.Google Scholar
Fox S. E., Curley, S. R. & Larson G. S. 1955 Phase velocity and absorption measurements in water containing air bubbles. J. Acoust. Soc. Am. 27, 534–539.Google Scholar
Gates E. M. 1977 The influence of free stream turbulence, free stream nuclei population and a drag reducing polymer on cavitation inception on two axisymmetric bodies, Ph.D. thesis, Calif. Inst. of Tech.
Knapp R. T., Daily, J. W. & Hammit F. G. 1970 Cavitation. McGraw Hill.
Macpherson J. D. 1957 The effect of gas bubbles on sound propagation in water. Proc. Phys. Soc. Lond. 70 B, 85–92.Google Scholar
Muir, T. F. & Eichhorn R. 1963 Compressible flow of an air-water mixture through a vertical two-dimensional converging-diverging nozzle. Proc. Heat Transfer. Fluid Mech. Inst., Stanford. Stanford University Press.
Noordzij L. 1973 Shock waves in mixtures of liquids and air bubbles. Doctoral thesis, Technische Hogeschool, Twente, Netherlands.
Noordzij L. & van Wijngaärden, L. 1974 Relaxation effects, caused by relative motion, on shock waves in gas-bubble/liquid mixtures. J. Fluid Mech. 66, 115–143.Google Scholar
Plesset, M. S. & Prosperetti A. 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid. Mech. 9, 145–185.Google Scholar
Prosperetti A. 1984 Bubble phenomena in sound fields: part one. Ultrasonics March 1984, 69–78.Google Scholar
Silberman E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 18, 925–933.Google Scholar
Tangren R. F., Dodge, C. H. & Seifert H. S. 1949 Compressibility effects in two-phase flows. J. Appl. Phys. 20, 637–645.Google Scholar
Voinov O. V. 1973 Force acting on a sphere in an inhomogeneous flow of an ideal incompressible fluid. Plenum. (Transl. from Z. Prikl. Mekh. i Tekh. Fiz. 4, 182–184, July-August 1973.)
Wijngaarden L. van 1964 On the collective collapse of a large number of gas bubbles in water. In Proc. 11th Intl Congr. Appl. Mech., pp. 854–861. Springer.
Wijngaarden L. van, 1968 On the equations of motion of mixtures of liquid and gas bubbles. J. Fluid Mech. 33, 465–474.Google Scholar
Wijngaarden L. van 1972 One dimensional flow of liquids containing small gas bubbles Ann. Rev. Fluid. Mech. 4, 369–396.Google Scholar
Wijngaarden L. van 1980 Sound and Shock Waves in B. bubbly Liquids. In Cavitation and Inhomogeneities in Underwater Acoustics, pp. 127–140. Springer.
Wijngaarden L. van 1983 Waves in gas-liquid flows In Theory of Dispersed Multiphase Flow, pp. 251–269, Academic.