Journal of Pure and Applied Ultrasonics

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Computation of Erosion Potential of Cavitation Bubble in an Ultrasonic Pressure Field


Affiliations
1 Fast Reactor Technology Group, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam-603102, India
2 Materials Technology Division, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam-603102, India
3 Department of Chemical Engineering, Institute of Chemical Technology, Mumbai-400019, India
 

Cavitation is the creation and collapse of a vapor cavity in a liquid. Cavitation can be produced by a sound field and this principle is employed in the ultrasonic vibratory cavitation device. The rapidly fluctuating applied pressure results in cavitation of the liquid. The pressure produced by the collapse of a vapor bubble can be determined by solving equations of bubble dynamics. The fundamental equation of bubble dynamics is the Rayleigh-Plesset- Noltingk-Neppiras-Poritsky equation popularly known as the RP equation. This equation does not account for the effect of liquid compressibility. Gilmore's equation, which considers liquid compressibility, can be used to obtain realistic estimates of bubble wall velocities at the end of bubble collapse. This paper discusses the numerical solution of Gilmore's equation to evaluate the bubble wall velocity at the end of bubble collapse and the pressure imposed on a solid surface from impingement of the resulting jet. The parameters affecting the growth and collapse of a single bubble is are studied. A discussion of results of cavitation damage experiments in sodium is also provided as a confirmation of the theoretical estimate of damage.

Keywords

Ultrasonic Cavitation, Gilmore's Equation, Collapse Pressure.
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  • Benjamin T.B. and Ellis A.T., The collapse of cavitation bubbles and the pressures produced against solid boundaries, Phil. Trans. R. Soc. Lond. A, 260 (1966) 221-240.

  • Rayleigh L., On the pressure developed in a liquid during the collapse of a spherical cavity, Philoso. Mag. Series, 6 (1917) 94-98.

  • Plesset M.S., The dynamics of cavitation bubbles, ASME J. Appl. Mech., 71(1949) 277-282.

  • Noltingk B.E. and Neppiras E.A., Cavitation produced by ultrasonics, Proc. Phys. Soc. Sec. B, 63 (1950) 674-685.

  • Poritsky H., The collapse and growth of a spherical bubble or cavity in a viscous fluid. In Proc. 1st U.S. National Congress on Applied Mechanics (ed. E. Sternberg), New York, NY: American Society of Mechanical Engineers, (1952) pp. 813–821.

  • Flynn H.G., Physics of acoustic cavitation in liquids, Physical Acoustics, 1B, W.P. Mason (ed.), Academic Press, New York (1964), Ch. 9, 76.

  • Herring C., Theory of the pulsations of the gas bubble produced by an underwater explosion, in Underwater Explosion Research (Office of Naval Research, Washington, D.C., 1950), 2 (1941) 35–131.

  • Gilmore F.R, Growth or collapse of a spherical bubble in a viscous compressible liquids, Hydrodynamics laboratory, California Institute of Technology, (1952), Report no 26-4,

  • Franc J.P. and Michel J.M., Fundamentals of Cavitation, Kluwer Academic Publishers, Dordrecht (2004).

  • Akulichev V.A, Pulsations of cavitation voids, in: High Intensity Ultrasonic Fields (Ultrasonic Technology), ed. L.D. Rozenberg, Springer US (1971), pp 201-259.

  • Knapp R.T, Daily J.W. and Hammitt F.G., Cavitation, McGraw Hill, New York, 1970.

  • Fink J. K. and Leibowitz L., Thermodynamic and Transport Properties of Sodium Liquid and Vapor, Argonne National Laboratory, U.S. Department of Energy, Oak Ridge, (1995) ANL/RE-95/2.

  • Ross Macdonald J., Some simple isothermal equations of state, Rev. Mod. Phys., 38 (1966) 669-679.

  • Leighton T., The Acoustic Bubble, Academic Press, New York 1997.

  • Sreedhar B.K, Albert S.K. and Pandit A.B., Cavitation damage: Theory and measurements – A review, Wear, 372-373 (2017) 177-196.


Abstract Views: 294

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  • Computation of Erosion Potential of Cavitation Bubble in an Ultrasonic Pressure Field

Abstract Views: 294  |  PDF Views: 3

Authors

B. K. Sreedhar
Fast Reactor Technology Group, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam-603102, India
S. K. Albert
Materials Technology Division, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam-603102, India
A. B. Pandit
Department of Chemical Engineering, Institute of Chemical Technology, Mumbai-400019, India

Abstract


Cavitation is the creation and collapse of a vapor cavity in a liquid. Cavitation can be produced by a sound field and this principle is employed in the ultrasonic vibratory cavitation device. The rapidly fluctuating applied pressure results in cavitation of the liquid. The pressure produced by the collapse of a vapor bubble can be determined by solving equations of bubble dynamics. The fundamental equation of bubble dynamics is the Rayleigh-Plesset- Noltingk-Neppiras-Poritsky equation popularly known as the RP equation. This equation does not account for the effect of liquid compressibility. Gilmore's equation, which considers liquid compressibility, can be used to obtain realistic estimates of bubble wall velocities at the end of bubble collapse. This paper discusses the numerical solution of Gilmore's equation to evaluate the bubble wall velocity at the end of bubble collapse and the pressure imposed on a solid surface from impingement of the resulting jet. The parameters affecting the growth and collapse of a single bubble is are studied. A discussion of results of cavitation damage experiments in sodium is also provided as a confirmation of the theoretical estimate of damage.

Keywords


Ultrasonic Cavitation, Gilmore's Equation, Collapse Pressure.

References