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Shock waves in dilute bubbly liquids

Published online by Cambridge University Press:  26 April 2006

M. Watanabe  and
A. Prosperetti
M. Watanabe
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
A. Prosperetti
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

The propagation of weak shock waves in liquids containing a small concentration of gas bubbles is studied theoretically on the basis of a mathematical model that contains all — and only — the effects that contribute to first order in the gas volume fraction. In particular, the thermal exchange between the gas bubbles and the liquid is described accurately. This aspect of the theory emerges as its most significant component, relegating effects such as the relative motion between the phases to roles of minor importance. Comparison with experimental results substantiates the accuracy of the model for shock waves that have had time to broaden from an initial sharp front to a more diffuse profile. For shock waves closer to inception, marked differences are found between theory and experiment. The same problem affects all other published theoretical treatments. It is concluded that some as yet poorly understood mechanism governs the early-time behaviour of shock waves in bubbly liquids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 349 - 381
Copyright
© 1994 Cambridge University Press

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References

Aidagulov, R. R., Khabeev, N. S. & Shagapov, V. Sh., 1977 Shock structure in a liquid containing gas bubbles with nonsteady interphase heat transfer. J. Appl. Mech. Tech. Phys. 18, 334–340.Google Scholar
Beam, R. M. & Warming, R. F. 1976 An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. J. Comput. Phys. 22, 87–110.Google Scholar
Beylich, A. E. & Gülhan, A. 1990 On the structure of nonlinear waves in liquids with gas bubbles. Phys. Fluids A 2, 1412–1428.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985 Effective equations for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259–273.Google Scholar
Campbell, I. J. & Pitcher, A. S. 1958 Shock waves in a liquid containing gas bubbles. Proc. R. Soc. Lond. A 243, 534–545.Google Scholar
Commander, K. W. & Prosperetti, A. 1989 Linear pressure waves in bubbly liquids: Comparison between theory and experiments. J. Acoust. Soc. Am. 85, 732–746.Google Scholar
Devin, C. 1959 Survey of thermal, radiation and viscous damping of pulsating air bubbles. J. Acoust. Soc. Am. 31, 1654–1667.Google Scholar
Drumheller, D. S., Kipp, M. E. & Bedford, A. 1982 Transient wave propagation in bubbly liquids. J. Fluid Mech. 119, 347–365.Google Scholar
Flynn, H. G. 1975 Cavitation dynamics I. A mathematical formulation. J. Acoust. Soc. Am. 57, 1379–1396.Google Scholar
Gasenko, V. G., Nakoryakov, V. E. & Shreyber, I. R. 1979 Nonlinear disturbances in a liquid containing gas bubbles. Sov. Phys. Acoust. 25, 385–388.Google Scholar
Jeffrey, A. & Kawahara, T. 1982 Asymptotic Methods in Nonlinear Wave Phenomena. Pitman.
Kamath, V., Oguz, H. N. & Prosperetti, A. 1992 Bubble oscillations in the nearly adiabatic limit. J. Acoust. Soc. Am. 92, 2016–2023.Google Scholar
Kamath, V. & Prosperetti, A. 1989 Numerical integration methods in gas-bubble dynamics. J. Acoust. Soc. Am. 85, 1538–1548.Google Scholar
Kamath, V., Prosperetti, A. & Egolfopoulos, F. N. 1993 A theoretical study of sonoluminescence. J. Acoust. Soc. Am. 94, 248–260.Google Scholar
Kedrinskii, V. K. 1968 Propagation of perturbations in a liquid containing gas bubbles. J. Appl. Mech. Tech. Phys. 9, 370–376.Google Scholar
Kedrinskii, V. K. 1980 Shock waves in liquid containing gas bubbles. Combust. Expl. Shock Waves 16, 495–504.Google Scholar
Keller, J. B. & Kolodner, I. I. 1956 Damping of underwater explosion bubble oscillations. J. Appl. Phys. 27, 1152–1161.Google Scholar
Keller, J. B. & Miksis, M. J. 1980 Bubble oscillations of large amplitude. J. Acoust. Soc. Am. 68, 628–633.Google Scholar
Kutznetsov, V. V., Nakoryakov, V. E., Pokusaev, B. G. & Shreiber, I. R. 1978a Propagation of disturbances in a gas—liquid mixture. Sov. Phys. Acoust. 23, 153–156.Google Scholar
Kutznetsov, V. V., Nakoryakov, V. E., Pokusaev, B. G. & Shreiber, I. R. 1978b Propagation of perturbations in a gas—liquid mixture. J. Fluid Mech. 85, 85–96.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
Lu, N. Q. & Prosperetti, A. 1994 Active and passive acoustic behavior of bubbly layers. J. Acoust. Soc. Am. (in press).Google Scholar
Miksis, M. J. & Ting, L. 1984 Nonlinear radial oscillations of a gas bubble including thermal effects. J. Acoust. Soc. Am. 76, 897–906.Google Scholar
Nagiev, F. B. & Khabeev, N. S. 1979 Heat-transfer and phase — transition effects associated with oscillations of vapor-gas bubbles. Sov. Phys. Acoust. 25, 148–152.Google Scholar
Nakoryakov, V. E., Shreyber, I. R. & Gasenko, V. G. 1981 Moderate-strength waves in the liquids containing gas bubbles. Fluid Mech. — Sov. Res. 10, 51–66.Google Scholar
Nigmatulin, R. I. 1982 Mathematical modelling of bubbly liquid motion and hydrodynamical effects in wave propagation phenomena. Appl. Sci. Res. 38, 267–289.Google Scholar
Nigmatulin, R. I. 1991 Dynamics of Multiphase Media. Hemisphere.
Nigmatulin, R. I. & Khabeev, N. S. 1974 Heat exchange between a gas bubble and a liquid. Fluid Dyn. 9, 759–764.Google Scholar
Nigmatulin, R. I. & Khabeev, N. S. 1977 Dynamics of vapor-gas bubbles. Fluid Dyn. 12, 867–871.Google Scholar
Nigmatulin, R. I., Khabeev, N. S. & Ngiev, F. B. 1981 Dynamics, heat, and mass transfer in vapor—gas bubbles in a liquid. Intl J. Heat Mass Transfer 24, 1033–1044.Google Scholar
Nigmatulin, R. I. & Shagapov, V. S. 1974 Structure of shock waves in a liquid containing gas bubbles. Fluid Dyn. 9, 890–899.Google Scholar
Noordzij, L. 1973 Shock waves in mixtures of liquids and air bubbles. Doctoral thesis, University of Twente.
Noordzij, L. & Wijngaarden, L. van 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 22, 69–77.Google Scholar
Prospfretti, A. 1991 The thermal behaviour of oscillating gas bubbles. J. Fluid Mech. 222, 587–616.Google Scholar
Prosperetti, A., Crum, L. A. & Commander, K. W. 1988 Nonlinear bubble dynamics. J. Acoust. Soc. Am. 83, 502–514.Google Scholar
Prosperetti, A. & Kim, D. H. 1987 Pressure waves in bubbly liquids at small gas volume fractions. In Fundamentals of Gas—Liquid Flows, FED-Vol. 72 (ed. E. E. Michaelides, & M. P. Sharma), pp. 19–27. ASME.
Prosperetti, A. & Lezzi, A. M. 1986 Bubble dynamics in a compressible liquid. Part 1. First-order theory. J. Fluid Mech. 168, 457–478.Google Scholar
Rubinstein, J. 1985 Bubble interaction effects on waves in bubbly liquids. J. Acoust. Soc. Am. 77, 2061–2066.Google Scholar
Sod, G. A. 1978 A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27, 1–31.Google Scholar
Tan, M. J. & Bankoff, S. G. 1984a Propagation of pressure waves in bubbly mixtures. Phys. Fluids 27, 1362–1369.Google Scholar
Tan, M. J. & Bankoff, S. G. 1984b Strong shock waves propagating through a bubbly mixture. Exp. Fluids 2, 159–165.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Wijngaarden, L. van, 1968 On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33, 465–474.Google Scholar
Wijngaarden, L. van, 1970 On the structure of shock waves in liquid-bubble mixtures. Appl. Sci. Res. 22, 366–381.Google Scholar
Wijngaarden, L. van, 1972 One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369–396.Google Scholar