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Simulation of cavitation bubbles in a convergent–divergent nozzle water jet

Published online by Cambridge University Press:  05 February 2007

Z. QIN ,
K. BREMHORST ,
H. ALEHOSSEIN  and
T. MEYER
Z. QIN
Affiliation:
Division of Mining and Minerals Process Engineering, The University of Queensland, Brisbane, QLD, Australia, 4072 CRCMining, The University of Queensland, Brisbane, QLD, Australia, 4072
K. BREMHORST
Affiliation:
Division of Mechanical Engineering, The University of Queensland, Brisbane, QLD, Australia, 4072
H. ALEHOSSEIN
Affiliation:
CSIRO Exploration and Mining, Brisbane, Queensland 4069, Australia
T. MEYER
Affiliation:
Division of Mining and Minerals Process Engineering, The University of Queensland, Brisbane, QLD, Australia, 4072 CRCMining, The University of Queensland, Brisbane, QLD, Australia, 4072
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Abstract

A model for simulating the process of growth, collapse and rebound of a cavitation bubble travelling along the flow through a convergent–divergent nozzle producing a cavitating water jet is established. The model is based on the Rayleigh–Plesset bubble dynamics equation using as inputs ambient pressure and velocity profiles calculated with the aid of computational fluid dynamics (CFD) flow modelling. A variable time-step technique is applied to solve the highly nonlinear second-order differential equation. This technique successfully solves the Rayleigh–Plesset equation for wide ranges of pressure variation and bubble original size and saves considerable computing time. Inputs for this model are the pressure and velocity data from CFD calculation. To simulate accurately the process of bubble growth, collapse and rebound, a heat transfer model, which includes the effects of conduction plus radiation, is developed to describe the thermodynamics of the incondensable gas inside the bubble. This heat transfer model matches previously published experimental data well. Assuming that single bubble behaviour also applies to bubble clouds, the calculated distance from the nozzle exit travelled by the bubble to the point where the bubble size becomes invisible is taken to be equal to the bubble cloud length observed. The predictions are compared with experiments carried out in a cavitation cell and show good agreement for different nozzles operating at different pressure conditions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 1 - 25
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Apfel, R. 1999 And there was light. Nature 398, 378–379.CrossRefGoogle Scholar
Barber, B. P. & Putterman, S. J. 1991 Observations of synchronous picosecond sonoluminescence. Nature 352, 318.CrossRefGoogle Scholar
Bogoyavlenskiy, V. A. 1999 Differential criterion of a bubble collapse in viscous liquids. Phys. Rev. E 60, 504.Google Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.CrossRefGoogle Scholar
Chahine, G. L. 1994 Strong interactions bubble/bubble and bubble/flow. Bubble Dynamics and Interface Phenomena (ed. Blake, J. R., Boulton-Stone, J. M. & Thomas, N. H.), pp. 195–206. Kluwer.Google Scholar
Csanady, G. T. 1964 Theory of Turbomachines. McGraw–Hill.Google Scholar
Flannigan, D. J. & Suslick, K. S. 2005 Plasma formation and temperature measurement during single-bubble cavitation. Nature 434, 52–55.Google Scholar
Flint, E. B. & Suslick, K. S. 1991 The temperature of cavitation. Science 253, 1397–1399.CrossRefGoogle ScholarPubMed
Fujikawa, S. & Akamatsu, T. 1980 Effects of the non-equilibrium condensation of vapour on the pressure wave produces by the collapse of a bubble in a liquid. J. Fluid Mech. 97, 481–512.Google Scholar
Gong, C. L. & Hart, D. P. 1999 Interactions of bubble dynamics and chemistry in cavitation bubbles induced by ultrasound. Proc. 3rd ASME/JSME Joint Fluids Engineering Conf., San Francisco, USA, pp. 1–5.Google Scholar
Hilgenfeldt, S., Grossmann, S. & Lohse, D. 1999 A simple explanation of light emission sonoluminescence. Nature 398, 402–405.CrossRefGoogle Scholar
Jarman, P. D. 1960 Sonoluminescence – A Discussion. J. Acoust. Soc. Am. 32, 1459–1462.Google Scholar
Knapp, R. T. 1952 Proc. Inst. Mech. Engrs Lond. 166, 150.CrossRefGoogle Scholar
Knapp, R. T., Daily, J. W. & Hammit, F. G. 1970 Cavitation. McGraw–Hill.Google Scholar
Lauterborn, W. & Bolle, H. 1975 Experimental investigations of cavitation bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 72, 391–399.Google Scholar
Lauterborn, W. & Ohl, C. 1997 Cavitation bubble dynamics. Ultrasonics Sonochem. 4, 65–75.Google Scholar
Lauterborn, W., Eick, I. & Philipp, A. 1994 Approaching bubble dynamics with lasers, holography and computers. Bubble Dynamics and Interface Phenomena (ed. Blake, J. R., Boulton-Stone, J. M. & Thomas, N. H.), pp. 299–310. Kluwer.CrossRefGoogle Scholar
Lohse, D. 2005 Cavitation hots up. Nature 434, 33–34.CrossRefGoogle ScholarPubMed
Marinesco, M. & Trillat, J. J. 1933 Action des ultrasons sur les plaques photographiques. CR Acad. Sci. Paris. 196, 858–860.Google Scholar
Meyer, T., Carnavas, P., Alehossein, H., Hood, M., Adam, S. & Gledhill, M. 1999 The effect of nozzle design on erosion performance of cavitating water jets. Intl Symp. on New Applications of Water Jet Technology, Japan, pp. 33–41.Google Scholar
Moss, W. C., Clarke, D. B., White, J. W. & Young, D. A. 1994 Hydrodynamic simulations of bubble collapse and picosecond sonoluminescence. Phys. Fluids 6, 2979–2985.Google Scholar
Moss, W. C., Clarke, D. B. & Young, D. A. 1997 Calculated pulse widths and spectra of a single sonoluminescing bubble. Science 276, 1398–1401.Google Scholar
Philipp, A. & Lauterborn, W. 1998 Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 361, 75–116.Google Scholar
Plesset, M. S. 1949 The dynamics of cavitation bubbles. Trans. ASME J. Appl. Mech. 16, 228–231.CrossRefGoogle Scholar
Plesset, M. S. & Prosperetti, A. 1997 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9, 1451–185.Google Scholar
Popinet, S. & Zaleski, S. 2002 Bubble collapse near a solid boundary: a numerical study of the influence of viscosity. J. Fluid Mech. 464, 137–163.CrossRefGoogle Scholar
Prosperetti, A. 1994 Some things we did not know 10 years ago. Bubble Dynamics and Interface Phenomena (ed. Blake, J. R., Boulton-Stone, J. M. & Thomas, N. H.), pp. 3–16. Kluwer.CrossRefGoogle Scholar
Qin, Z. 2004 Investigation of the cavitation mechanism and erosion of submerged high pressure water jets. PhD thesis, The University of Queensland, Australia.Google Scholar
Rayleigh, Lord 1917 On the pressure developed in a liquid during collapse of a spherical cavity. Phil. Mag. 34, 94–98.CrossRefGoogle Scholar
Shima, A. & Tsujino, T. 1994 The dynamics of cavity clusters in polymer aqueous solutions subjected to an oscillating pressure. Bubble Dynamics and Interface Phenomena (ed. Blake, J. R., Boulton-Stone, J. M. & Thomas, N. H.), pp. 81–92. Kluwer.Google Scholar
Shima, A., Tomita, Y. & Ohno, T. 1988 Temperature effects on single bubble collapse and induced impulsive pressure. Trans. ASME I: J. Fluids Engng 110, 194–199.Google Scholar
Shima, A., Tomita, Y., Gibson, D. C. & Blake, J. R. 1989 The growth and collapse of cavitation bubbles near composite surfaces. J. Fluid Mech. 203, 199–214.CrossRefGoogle Scholar
Taylor, K. J. & Jarman, P. D. 1970 The spectra of sonoluminescence. Austral. J. Phys. 23, 319–334.Google Scholar
Tomita, Y. & Shima, A. 1990 High speed photographic observations of laser-induced cavitation bubbles in water. Acustica 71 (3), 161–171.Google Scholar
Trilling, L. 1952 The collapse and rebound of a gas bubble. J. Appl. Phys. 23, 14–17.CrossRefGoogle Scholar
Vargaftik, N. B., Vinogradov, Y. K. & Yargin, V. S. 1996 Handbook of Physical Properties of Liquids and Gases. Begell House.CrossRefGoogle Scholar
Vogel, A., Lauterborn, W. & Timm, R. 1989 Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary. J. Fluid Mech. 206, 299–338.CrossRefGoogle Scholar
Wang, Y. C. & Brennen, C. E. 1999 Numerical computation of shock waves in a spherical cloud of cavitation bubbles. Trans. ASME I: J. Fluids Engng 121, 872–880.Google Scholar
Wu, C. C. & Roberts, P. H. 1993 Shock-wave propagation in a sonoluminescing gas bubble. Phys. Rev. Lett. 70, 3424–3427.CrossRefGoogle Scholar
Young, F. R. 1989 Cavitation. McGraw–Hill.Google Scholar