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Concentration waves and the instability of bubbly flows

Published online by Cambridge University Press:  26 April 2006

J. H. Lammers  and
A. Biesheuvel
J. H. Lammers
Affiliation:
J. M. Burgers Centre for Fluid Mechanics, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands Present address: Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven. The Netherlands.
A. Biesheuvel
Affiliation:
J. M. Burgers Centre for Fluid Mechanics, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands
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Abstract

This paper examines whether G. K. Batchelor's (1988) theory of the propagation of planar concentration disturbances and the occurrence of instabilities in uniform fluidized beds can be applied to bubbly flows. According to this theory the propagation of long weakly nonlinear gas volume concentration waves is governed by the Burgers equation. Experiments on the propagation of weak concentration shock waves and small, but finite, amplitude periodic waves are presented; good agreement is found with classic solutions of Burgers’ equation. For example, the phenomenon of amplitude saturation, familiar from nonlinear acoustics, is established here for concentration waves. Batchelor's instability conditions are given for bubbly flows, and his model for the bulk modulus of elasticity of the dispersed phase is used to obtain estimates of the critical volume concentration at which a uniform bubbly flow becomes unstable to planar disturbances. Observations of the onset of instabilities of bubbly flow in a pipe are described, and compared with what would be expected from Batchelor's theory.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 328 , 10 December 1996 , pp. 67 - 93
Copyright
© 1996 Cambridge University Press

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References

Batchelor, G. K. 1988 A new theory of the instability of a uniform fluidized bed. J. Fluid Mech. 193, 75–110.Google Scholar
Batchelor, G. K. 1991 The formation of bubbles in fluidized beds. In Proc. Symp. Honoring John W. Miles on his 70th birthday. Scripps Institution of Oceanography. Ref. Series 91–24.
Batchelor, G. K. 1993 Secondary instability of a gas-fluidized bed. J. Fluid Mech. 257, 359–371.Google Scholar
Blackstock, D. T. 1966 Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude. J. Acoust. Soc. Am. 39, 1019–1026.Google Scholar
Cole, J. D. 1951 On a quasi-linear parabolic equation occurring in aerodynamics. Q. Appl. Maths 9, 225–236.Google Scholar
Crighton, D. G. 1992 Nonlinear acoustics. In Modern Methods in Analytical Acoustics (ed. D. G. Crighton), pp. 684–670. Springer.
Crighton, D. G. & Scott, J. F. 1979 Asymptotic solutions of model equations in nonlinear acoustics. Proc. R. Soc. Lond. A 292, 101–134.Google Scholar
Didwania, A. K. & Homsy, G. M. 1981 Flow regimes and flow transitions in liquid fluidized beds. Intl J. Multiphase Flow 7, 563–580.Google Scholar
Didwania, A. K. & Homsy, G. M. 1982 Resonant sideband instabilities in wave propagation in fluidized beds. J. Fluid Mech. 122, 433–438.Google Scholar
Duineveld, P. C. 1994 Bouncing and coalescence of two bubbles in water. PhD thesis, University of Twente.
El-Kaissy, M. M. & Homsy, G. M. 1976 Instability waves and the origin of bubbles in fluidized beds. Part 1: Experiments. Intl J. Multiphase Flow 2, 379–395.Google Scholar
Ganser, G. H. & Drew, D. A. 1990 Nonlinear stability analysis of a uniformly fluidized bed. Intl J. Multiphase Flow 16, 447–460.Google Scholar
Haberman, W. L. & Morton, R. K. 1953 An experimental investigation of the drag and shape of air bubbles rising in various liquids. David Taylor Model Basin Rep. 802.Google Scholar
Harris, S. E. & Crighton, D. G. 1994 Solitons, solitary waves, and voidage disturbances in gas-fluidized beds. J. Fluid Mech. 266, 243–276.Google Scholar
Hayakawa, H., Komatsu, T. S. & Tsuzuki, T. 1994 Pseudo-solitons in fluidized beds. Physica A 204, 277–289.Google Scholar
Kynch, G. J. 1952 A theory of sedimentation. Trans. Faraday Soc. 48, 166–176.Google Scholar
Lammers, J. H. 1994 The stability of bubbly flows. PhD thesis, University of Twente.
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies), pp. 250–351. Cambridge University Press.
Liu, J. T. C. 1983 Nonlinear unstable wave disturbances in fluidized beds. Proc. R. Soc. Lond. A 389, 331–347.Google Scholar
Moore, D. W. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749–766.Google Scholar
Nimmo, J. J. C. & Crighton, D. G. 1986 Geometrical and diffusive effects in nonlinear acoustic propagation over long ranges. Phil. Trans. R. Soc. Lond. A 320, 1–35.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley & Sons.
Wijngaarden, L. van & Biesheuvel, A. 1988 Voidage waves in mixtures of liquid and gas bubbles. In Transient Phenomena in Multiphase Flow (ed. N. Afgan), pp. 275–289. Hemisphere.
Wijngaarden, L. van & Kapteyn, C. 1990 Concentration waves in dilute bubble/liquid mixtures. J. Fluid Mech. 212, 111–137.Google Scholar