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Temperatures produced by inertially collapsing bubbles near rigid surfaces

Published online by Cambridge University Press:  02 August 2018

S. A. Beig Open the ORCID record for S. A. Beig [Opens in a new window] ,
B. Aboulhasanzadeh  and
E. Johnsen Open the ORCID record for E. Johnsen [Opens in a new window]
S. A. Beig*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
B. Aboulhasanzadeh
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
E. Johnsen
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of bubbles inertially collapsing in water near solid objects have been the subject of numerous studies in the context of cavitation erosion. While non-spherical bubble collapse, re-entrant jet dynamics and emitted shock waves have received significant interest, less is known about the temperatures thereby produced and their possible connection to damage. In this article, we use highly resolved numerical simulations of a single bubble inertially collapsing near a rigid surface to measure the temperatures produced in the fluid and estimate those in the solid, as well as to identify the responsible mechanisms. In particular, we find that elevated temperatures along the wall can be produced by one of two mechanisms, depending on the initial stand-off distance of the bubble from the wall and the driving pressure: for bubbles initially far from the wall, the shock generated by the bubble collapse is the source of the high temperature, while bubbles starting initially closer migrate towards the wall and eventually come into contact with it. A scaling is introduced to describe the maximum fluid temperature along the wall as a function of the initial stand-off distance and driving pressure. To predict the temperature of the solid, we develop a semianalytical heat transfer model, which supports recent experimental observations that elevated temperatures achieved during collapse could play a role in cavitation damage to soft heat-sensitive materials.

JFM classification

Drops and Bubbles: Bubble dynamics Compressible Flows: Compressible Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 105 - 125
Copyright
© 2018 Cambridge University Press 

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References

Barajas, C. & Johnsen, E. 2017 The effects of heat and mass diffusion on freely oscillating bubbles in a viscoelastic, tissue-like medium. J. Acoust. Soc. Am. 141, 908–918.Google Scholar
Barber, B. P. & Putterman, S. J. 1991 Observation of synchronous picosecond sonoluminescence. Nature 352, 318–320.Google Scholar
Beig, S. A. & Johnsen, E. 2015a Maintaining interface equilibrium conditions in compressible multiphase flows using interface capturing. J. Comput. Phys. 302, 548–566.Google Scholar
Beig, S. A. & Johnsen, E. 2015b Temperature considerations in non-spherical bubble collapse near a rigid wall. J. Phys.: Conf. Ser. 656, 012044.Google Scholar
Beig, S. A. & Johnsen, E.2018 Inertial collapse of a gas bubble near a rigid boundary. In preparation.Google Scholar
Benjamin, T. B. & Ellis, A. T. 1966 The collapse of cavitation bubbles and the pressure thereby produced against solid boundaries. Phil. Trans. R. Soc. Lond. 260, 221–240.Google Scholar
Blake, J. R. & Gibson, D. C. 1987 Cavitation bubbles near boundaries. Annu. Rev. Fluid Mech. 19, 99–123.Google Scholar
Böhm, H., Betz, S. & Ball, A. 1990 The wear resistance of polymers. Tribol. Intl 23, 399–406.Google Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.Google Scholar
Brenner, M. P., Hilgenfeldt, S. & Lohse, D. 2002 Single-bubble sonoluminescence. Rev. Mod. Phys. 74, 425–484.Google Scholar
Brujan, E. A., Hecht, D. S., Lee, F. & Williams, G. A. 2005 Properties of luminescence from laser-created bubbles in pressurized water. Phys. Rev. E 72, 066310.Google Scholar
Brujan, E. A., Keen, G. S., Vogel, A & Blake, J. R. 2002 The final stage of the collapse of a cavitation bubble close to a rigid boundary. Phys. Fluids 14, 85–92.Google Scholar
Deplancke, T., Lame, O., Cavaille, J. Y., Fivel, M., Riondet, M. & Franc, J. P. 2015 Outstanding cavitation erosion resistance of ultra high molecular weight polyethylene (UHMWPE) coatings. Wear 328, 301–308.Google Scholar
Didenko, Y. T., McNamara, W. B. & Suslick, K. S. 2000 Molecular emission from single-bubble sonoluminescence. Nature 407, 877–879.Google Scholar
Duplat, J. & Villermaux, E. 2015 Luminescence from collapsing centimeter bubbles expanded by chemical reaction. Phys. Rev. Lett. 115, 1–5.Google Scholar
Field, J. E. 1991 The physics of liquid impact, shock wave interactions with cavities, and the implications to shock wave lithotripsy. Phys. Med. Biol. 36, 1475–1484.Google Scholar
Flannigan, D. J., Hopkins, S. D., Camara, C. G., Putterman, S. J. & Suslick, K. S. 2006 Measurement of pressure and density inside a single sonoluminescing bubble. Phys. Rev. Lett. 96, 204301.Google Scholar
Flannigan, D. J. & Suslick, K. S. 2010 Inertially confined plasma in an imploding bubble. Nat. Phys. 6, 598–601.Google Scholar
Franc, J. P., Riondet, M., Karimi, A. & Chahine, G. L. 2011 Impact load measurements in an erosive cavitating flow. Trans. ASME J. Fluids Engng 133, 121301.Google Scholar
Gottlieb, S. & Shu, C. W. 1996 Total variation diminishing Runge–Kutta schemes. Math. Comput. 67, 73–85.Google Scholar
Henry de Frahan, M. T., Varadan, S. & Johnsen, E. 2015 A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces. J. Comput. Phys. 280, 489–509.Google Scholar
Johnsen, E. & Colonius, T. 2006 Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219, 715–732.Google Scholar
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231–262.Google Scholar
Keller, J. B. & Miksis, M. 1980 Bubble oscillations of large amplitude. J. Acoust. Soc. Am. 68, 628–633.Google Scholar
Kim, K. H., Chahine, G., Franc, J. P. & Karimi, A. 2014 Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction. Springer.Google Scholar
Lauer, E., Hu, X. Y., Hickel, S. & Adams, N. A. 2012 Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics. Comput. Fluids 69, 1–19.Google Scholar
Lauterborn, W. & Kurz, T. 2010 Physics of bubble oscillations. Rep. Prog. Phys. 73, 106501.Google Scholar
Le Métayer, O. & Saurel, R. 2016 The Noble–Abel stiffened-gas equation of state. Phys. Fluids 28, 046102.Google Scholar
Legay, M., Gondrexon, N., Le Person, S., Boldo, P. & Bontemps, A. 2011 Enhancement of heat transfer by ultrasound: review and recent advances. Intl J. Chem. Engng 670108, 1–17.Google Scholar
Lindau, O. & Lauterborn, W. 2003 Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall. J. Fluid Mech. 479, 327–348.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
Murrone, A. & Guillard, H. 2005 A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 202, 664–698.Google Scholar
Naudé, C. F. & Ellis, A. T. 1961 On the mechanism of cavitation damage by nonhemispherical cavities collapsing in contact with a solid boundary. Trans. ASME J. Basic Engng 83, 648–656.Google Scholar
Ohl, C. D., Lindau, O. & Lauterborn, W. 1998 Luminescence from spherically and aspherically collapsing laser-induced bubbles. Phys. Rev. Lett. 103, 3077.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. & Chapman, R. B. 1971 Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J. Fluid Mech. 47, 283–290.Google Scholar
Ramsey, M. C. & Pitz, R. W. 2013 Energetic cavitation collapse generates 3.2 Mbar plasma with a 1.4 J driver. Phys. Rev. Lett. 110 (15), 154301.Google Scholar
Rayleigh, L. 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 94–98.Google Scholar
Storey, B. D. & Szeri, A. J. 2000 Water vapour, sonoluminescence and sonochemistry. Proc. R. Soc. Lond. 456, 1685–1709.Google Scholar
Supponen, O., Obreschkow, D., Kobel, P. & Farhat, M. 2017a Luminescence from cavitation bubbles deformed in uniform pressure gradients. Phys. Rev. E 96, 033114.Google Scholar
Supponen, O., Obreschkow, D., Kobel, P., Tinguely, M., Dorsaz, N. & Farhat, M. 2017b Shock waves from nonspherical cavitation bubbles. Phys. Rev. Fluids 2, 093601.Google Scholar
Supponen, O., Obreschkow, D., Tinguely, M., Kobel, P., Dorsaz, N. & Farhat, M. 2016 Scaling laws for jets of single cavitation bubbles. J. Fluid Mech. 802, 263–293.Google Scholar
Suslick, K. S. & Flannigan, D. J. 2008 Inside a collapsing bubble: sonoluminescence and the conditions during cavitation. Annu. Rev. Phys. Chem. 59, 659–683.Google Scholar
Tiwari, A., Pantano, C. & Freund, J. B. 2015 Growth-and-collapse dynamics of small bubble clusters near a wall. J. Fluid Mech. 775, 1–23.Google Scholar
Tomita, Y. & Shima, A. 1986 Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. J. Fluid Mech. 169, 535–564.Google 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.Google Scholar