Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-19T05:02:31.690Z Has data issue: false hasContentIssue false

Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid

Published online by Cambridge University Press:  19 April 2006

Shigeo Fujikawa
Affiliation:
Department of Mechanical Engineering, Kyoto University, Kyoto
Teruaki Akamatsu
Affiliation:
Department of Mechanical Engineering, Kyoto University, Kyoto

Abstract

Analytical and numerical analyses have been made of the physical behaviour of a collapsing bubble in a liquid. The mathematical formulation takes into account the effects of compressibility of the liquid, non-equilibrium condensation of the vapour, heat conduction and the temperature discontinuity at the phase interface. Numerical solutions for the collapse of the bubble are obtained beyond the time when the bubble reaches its minimum radius up to the stage when a pressure wave forms and propagates outward into the liquid. The numerical results indicate that evaporation and condensation strongly influence the dynamical behaviour of the bubble.

In addition, the propagation of the stress wave, both in a solid and a liquid, due to the collapse of the bubble has been observed by means of the dynamic photoelasticity. It is clearly demonstrated that the stress wave in a photoelastic specimen is caused by impact of the pressure wave radiated from the bubble.

Type
Research Article
Copyright
© 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alty, T. 1936 Sci. Prog. Lond. 31, 436.
Alty, T. & Mackay, C. A. 1935 Proc. Roy. Soc. A 149, 104.
Benjamin, T. B. 1958 Proc. 2nd Symp. on Naval Hydrodyn., Washington, p. 207.
Benjamin, T. B. & Ellis, A. T. 1966 Phil. Trans. R. Soc. A 260, 221.
Cole, R. H. 1948 Underwater Explosions. New York: Dover.
Ebeling, K. J. & Lauterborn, W. 1977 Paper presented at Euromech 98, Eindhoven.
Efimov, A. V., 1976 Proc. IAHR Symp. Grenoble, p. 159.
Ellis, A. T. 1956 Proc. Symp. Cavitation in Hydrodyn., N.P.L., paper 8. London: H.M.S.O.
Flynn, H. G. 1975a J. Acoust. Soc. Am. 57, 1379.
Flynn, H. G. 1975b J. Acoust. Soc. Am. 58, 1160.
Fujikawa, S. & Akamatsu, T. 1975 Proc. 10th Int. Shock Tube Symp., Kyoto, p. 174.
Fujikawa, S. & Akamatsu, T. 1978 Bull. Japan Soc. Mech. Eng. 21, 223.
Hatsopoulos, G. N. & Keenan, J. H. 1965 Principles of General Thermodynamics. Wiley.
Herring, C. 1941 Office of Sci. Res. & Develop. Rep. no. 236.
Hickling, R. 1963 J. Acoust. Soc. Am. 35, 7.
Hickling, R. & Plesset, M. S. 1964 Phys. Fluids 7, 7.
Hill, P. G. 1966 J. Fluid Mech. 25, 593.
Hsieh, D. Y. 1965 Trans. A.S.M.E. D, J. Basic Engng 87, 991.
Jahsman, W. E. 1968 Trans. A.S.M.E. E, J. Appl. Mech. 35, 579.
Jones, I. R. & Edwards, D. H. 1960 J. Fluid Mech. 7, 596.
Kennard, E. H. 1938 Kinetic Theory of Gases. McGraw-Hill.
Kling, C. L. & Hammitt, F. G. 1972 Trans. A.S.M.E. D, J. Basic Engng 94, 825.
Knacke, A. & Stranski, I. N. 1956 Prog. Metal Phys. 6, 181.
Kogan, M. N. 1969 Rarefied Gas Dynamics. Plenum.
Kornfeld, M. & Suvorov, L. 1944 J. Appl. Phys. 15, 495.
Kuttruff, H. 1962 Acustica 6, 526.
Lauterborn, W. & Bolle, H. 1975 J. Fluid Mech. 72, 391.
Mitchell, T. M. 1970 Ph.D. Thesis, Depart. of Nuclear Engng, Univ. of Michigan.
Mitchell, T. & Hammitt, F. G. 1974 Nucl. Sci. Engng 53, 263.
Mori, Y. 1973 Trans. Japan Soc. Mech. Eng. 39, 694.
Naudé, C. F. & Ellis, A. T. 1961 Trans. A.S.M.E. D, J. Basic Engng 83, 648.
Plesset, M. S. 1949 J. Appl. Mech. 16, 277.
Plesset, M. S. & Chapman, R. B. 1971 J. Fluid Mech. 47, 283.
Plesset, M. S. & Prosperetti, A. 1976 J. Fluid Mech. 78, 433.
Plesset, M. S. & Prosperetti, A. 1977 Ann. Rev. Fluid Mech. 9, 145.
Plesset, M. S. & Zwick, S. A. 1952 J. Appl. Phys. 23, 95.
Rayleigh, LORD 1917 Phil. Mag. 34, 94.
Schrage, R. W. 1953 A Theoretical Study of Interphase Mass Transfer. Columbia University Press.
Shima, A. & Nakajima, K. 1977 J. Fluid Mech. 80, 369.
Theofanus, T. G. 1969 Paper presented at 11th Nat. Heat Transfer Conf., Mineapolis.
Tomita, Y. & Shima, A. 1977 Bull. Japan Soc. Mech. Eng. 20, 1453.
Trilling, L. 1952 J. Appl. Phys. 23, 14.
Zwick, S. A. & Plesset, M. S. 1955 J. Math. Phys. 33, 308.