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Transient wave propagation in bubbly liquids

Published online by Cambridge University Press:  20 April 2006

D. S. Drumheller ,
M. E. Kipp  and
A. Bedford
D. S. Drumheller
Affiliation:
Sandia National Laboratories, Albuquerque, New Mexico 87185, U.S.A.
M. E. Kipp
Affiliation:
Sandia National Laboratories, Albuquerque, New Mexico 87185, U.S.A.
A. Bedford
Affiliation:
The University of Texas, Austin, Texas 78712, U.S.A.
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Abstract

A theoretical and numerical investigation of the propagation of one-dimensional waves in a bubbly liquid is presented. A variational formulation of the problem is used that yields both the linear-momentum equation and the equation that describes the oscillations of the bubbles. The compressibility of the liquid is taken into account in the formulation. The thermal dissipation is treated by solving the energy-balance equations simultaneously with the mechanical equations. Solutions are obtained by a finite-difference procedure and are compared to the experimental data of Kuznetsov et al. and Noordzij & van Wijngaarden. In some cases quite good agreement is obtained, but in others substantial errors are found. It is suggested that the observed discrepancies may be due to the breakup of the bubbles in the case of very large amplitude disturbances; the fact that the formulation does not include relative motion between the liquid and the bubbles; and possible non-planarity effects in the experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 347 - 365
Copyright
© 1982 Cambridge University Press

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References

Bedford, A. & Drumheller, D. S. 1978 A variational theory of immiscible mixtures. Arch. Rat. Mech. Anal. 68, 37–51.Google Scholar
Benjamin, T. B. 1966 Discussion of van Wijngaarden (1966). In Proc. 6th Symp. on Naval Hydrodynamics (ed. R. D. Cooper & S. W. Doroff), pp. 129–135. U.S. Govt Printing Office, Washington D.C.
Campbell, I. J. & Pitcher, A. S. 1958 Shock waves in liquid containing gas bubbles. Proc. R. Soc. London A 243, 534–545.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
Crespo, A. 1969 Sound and shock waves in liquids containing bubbles. Phys. Fluids 12, 2274–2282.Google Scholar
Devin, C. 1959 Survey of thermal, radiation and viscous damping of pulsating air bubbles in water. J. Acoust. Soc. Am. 31, 1654–1667.Google Scholar
Drumheller, D. S. & Bedford, A. 1979a A theory of bubbly liquids. J. Acoust. Soc. Am. 66, 197–208.Google Scholar
Drumheller, D. S. & Bedford, A. 1979b On the mechanics and thermodynamics of fluid mixtures. Arch. Rat. Mech. Anal. 71, 345–355.Google Scholar
Drumheller, D. S. & Bedford, A. 1980a A theory of liquids with vapor bubbles. J. Acoust. Soc. Am. 67, 186–200.Google Scholar
Drumheller, D. S. & Bedford, A. 1980b A thermomechanical theory for reacting immiscible mixtures. Arch. Rat. Mech. Anal. 73, 257–284.Google Scholar
Eddington, R. B. 1970 Investigation of supersonic phenomena in a two-phase (liquid-gas) tunnel. A.I.A.A.J. 8, 65–74.Google Scholar
Finlayson, B. A. 1972 The Method of Weighted Residuals and Variational Principles. Academic.
Fox, F. 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
Gel'Fand, B. E., Gubin, S. A., Kogarko, B. S. & Kogarko, S. M. 1974 Investigation of compression waves in a mixture of liquid with gas bubbles. Sov. Phys. Dokl. 18, 787–789.Google Scholar
Kieffer, S. W. 1977 Sound speed in liquid-gas mixtures: water-air and water-steam. J. Geophys. Res. 82, 2895–2904.Google Scholar
Kuznetsov, V. V., Nakoryakov, V. E., Pokusaev, B. G. & Shreiber, I. R. 1978 Propagation of perturbations in a gas-liquid mixture. J. Fluid Mech. 85, 85–96.Google Scholar
Lawrence, R. J. & Mason, D. S. 1971 wondy iv — A computer program for one-dimensional wave propagation with rezoning. SandiaLab. Rep. SC-RR-71 0284, Albuquerque, New Mexico.Google Scholar
Macpherson, J. D. 1957 The effect of gas bubbles on sound propagation in water. Proc. Phys. Soc. Lond. 70, 85–92.Google Scholar
Mcwilliam, D. & Duggins, R. K. 1969 Speed of sound in bubbly liquids. Proc. Inst. Mech. Engrs 184, 102–107.Google Scholar
Medwin, H. 1974 Acoustic fluctuations due to microbubbles in the near surface ocean. J. Acoust. Soc. Am. 56, 1100–1104.Google Scholar
Nakoryakov, V. E., Sobolev, V. V. & Shreiber, I. R. 1972 Long-wave disturbances in a gas-liquid mixture. Izv. Akad. Nauk USSR, Mekh. Zhid. i Gaza 5, 71–73.Google Scholar
Nigmatulin, R. I. 1979 Spatial averaging in the mechanics of heterogeneous and dispersed systems. Int. J. Multiphase Flow 5, 353–385.Google Scholar
Noordzij, L. 1973 Shock waves in bubbly liquid mixtures. In Proc. IUTAM Symp. on Non-steady Flow of Water at High Speeds (ed. L. I. Sedov & G. Yu. Stepanov), pp. 369–374. Nauka.
Noordzij, L. & van Wijngaarden, 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
Poritsky, H. 1952 The collapse or growth of a spherical bubble or cavity in a viscous fluid. In Proc. 1st U.S. Nat. Cong. Appl. Mech., pp. 813–821. A.S.M.E.
Shampine, L. F. & Gordon, M. K. 1974 Computer Solution of Ordinary Differential Equations: The Initial Value Problem. Freeman.
Silberman, E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29, 925–933.Google Scholar
Urick, R. J. 1975 Principles of Underwater Sound. McGraw-Hill.
Van Wijngaarden, L. 1966 Linear and nonlinear dispersion of pressure pulses in liquid-bubble mixtures. In Proc. 6th Symp. on Naval Hydrodynamics (ed. R. D. Cooper & S. W. Doroff), pp. 129–135. U.S. Govt Printing Office, Washington D.C.
Van Wijngaarden, L. 1972a One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369–396.Google Scholar
Van Wijngaarden, L. 1972b Propagation of shock waves in bubble-liquid mixtures. Prog. Heat Mass Transfer 6, 637–650.Google Scholar
Walchli, H. & West, J. M. 1964 Heterogeneous water cooled reactors. In Reactor Handbook Vol. IV, Engineering (ed. S. McLain & J. H. Martens), pp. 548–611. Wiley-Interscience.