Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-19T11:40:40.622Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulations of non-spherical bubble collapse

Published online by Cambridge University Press:  15 June 2009

ERIC JOHNSEN  and
TIM COLONIUS
ERIC JOHNSEN*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
TIM COLONIUS
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Present address: Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A high-order accurate shock- and interface-capturing scheme is used to simulate the collapse of a gas bubble in water. In order to better understand the damage caused by collapsing bubbles, the dynamics of the shock-induced and Rayleigh collapse of a bubble near a planar rigid surface and in a free field are analysed. Collapse times, bubble displacements, interfacial velocities and surface pressures are quantified as a function of the pressure ratio driving the collapse and of the initial bubble stand-off distance from the wall; these quantities are compared to the available theory and experiments and show good agreement with the data for both the bubble dynamics and the propagation of the shock emitted upon the collapse. Non-spherical collapse involves the formation of a re-entrant jet directed towards the wall or in the direction of propagation of the incoming shock. In shock-induced collapse, very high jet velocities can be achieved, and the finite time for shock propagation through the bubble may be non-negligible compared to the collapse time for the pressure ratios of interest. Several types of shock waves are generated during the collapse, including precursor and water-hammer shocks that arise from the re-entrant jet formation and its impact upon the distal side of the bubble, respectively. The water-hammer shock can generate very high pressures on the wall, far exceeding those from the incident shock. The potential damage to the neighbouring surface is quantified by measuring the wall pressure. The range of stand-off distances and the surface area for which amplification of the incident shock due to bubble collapse occurs is determined.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 231 - 262
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Abgrall, R. 1996 How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125, 150–160.CrossRefGoogle Scholar
Ball, G. J., Howell, B. P., Leighton, T. G. & Schofield, M. J. 2000 Shock-induced collapse of a cylindrical air cavity in water: a free-Lagrange simulation. Shock Waves 10, 265–276.CrossRefGoogle 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. A 260, 221–240.Google Scholar
Best, J. P. 1993 The formation of toroidal bubbles upon the collapse of transient cavities. J. Fluid Mech. 251, 79–107.CrossRefGoogle Scholar
Best, J. P. & Kucera, A. 1992 A numerical investigation of non-spherical rebounding bubbles. J. Fluid Mech. 245, 137–154.CrossRefGoogle Scholar
Blake, J. R., Taib, B. B. & Doherty, G. 1986 Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid Mech. 170, 479–497.CrossRefGoogle Scholar
Bourne, N. K. & Field, J. E. 1992 Shock-induced collapse of single cavities in liquids. J. Fluid Mech. 244, 225–240.CrossRefGoogle Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.CrossRefGoogle Scholar
Brennen, C. E. 2002 Fission of collapsing cavitation bubbles. J. Fluid Mech. 472, 153–166.CrossRefGoogle Scholar
Chang, C. H. & Liou, M. S. 2007 A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM+-up scheme. J. Comput. Phys. 225, 840–873.CrossRefGoogle Scholar
Cocchi, J. P., Saurel, R. & Loraud, J. C. 1996 Treatment of interface problems with Godunov-type schemes. Shock Waves 5, 347–357.CrossRefGoogle Scholar
Cole, R. 1948 Underwater Explosions. Princeton University Press.CrossRefGoogle Scholar
Fujikawa, S. & Akamatsu, T. 1980 Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid. J. Fluid Mech. 97, 481–512.CrossRefGoogle Scholar
Gottlieb, S. & Shu, C. W. 1998 Total variation diminishing Runge–Kutta schemes. Math. Comput. 67, 73–85.CrossRefGoogle Scholar
Haas, J. F. & Sturtevant, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41–76.CrossRefGoogle Scholar
Hansson, I., Kedrinskii, V. & Mørch, K. A. 1982 On the dynamics of cavity clusters. J. Phys. D: Appl. Phys. 12, 1725–1734.CrossRefGoogle Scholar
Harlow, F. & Amsden, A. 1971 Fluid dynamics. Tech Rep. LANL Monograph LA-4700. Los Alamos National Labs.CrossRefGoogle Scholar
Herring, C. 1941 Theory of the pulsations of the gas bubble produced by an underwater explosion. Tech Rep. NDRC Division 6 Report C4-sr20. National Defense Research Committee.Google Scholar
Hickling, R. & Plesset, M. S. 1964 Collapse and rebound of a spherical bubble in water. Phys. Fluids 7, 7–14.CrossRefGoogle Scholar
Hu, X. Y., Khoo, B. C., Adams, N. A. & Huang, F. L. 2006 A conservative interface method for compressible flows. J. Comput. Phys. 219, 553–578.CrossRefGoogle Scholar
Huang, Y. C., Hammitt, F. G. & Mitchell, T. M. 1973 Note on shock-wave velocity in high-speed liquid–solid impact. J. Appl. Phys. 44, 1868–1869.CrossRefGoogle Scholar
Jamaluddin, A. R., Ball, G. J. & Leighton, T. J. 2005 Free-Lagrange simulations of shock/bubble interaction in shock wave lithotripsy. In Shock Waves: Proceedings of the 24th Intl Symp. on Shock Waves. Beijing, China. International Shock Wave Institute.Google Scholar
Johnsen, E. 2007 Numerical simulations of non-spherical bubble collapse. PhD thesis, California Institute of Technology.Google Scholar
Johnsen, E. & Colonius, T. 2006 Implementation of WENO schemes for compressible multicomponent flow problems. J. Comput. Phys. 219, 715–732.CrossRefGoogle Scholar
Johnsen, E. & Colonius, T. 2008 Shock-induced collapse of a gas bubble in shockwave lithotripsy. J. Acoust. Soc. Am. 124, 2011–2020.CrossRefGoogle ScholarPubMed
Joseph, D. D. 1989 Fluid Dynamics of Viscoelastic Liquids. Springer.Google Scholar
Klaseboer, E., Fong, S. W., Turangan, C. K., Khoo, B. C., Szeri, A. J., Calvisi, M. L., Sankin, G. N. & Zhong, P. 2007 Interaction of lithotripter shockwaves with single inertial cavitation bubbles. J. Fluid Mech. 593, 33–56.CrossRefGoogle ScholarPubMed
Kling, C. L. & Hammitt, F. G. 1972 A photographic study of spark-induced cavitation bubble collapse. Trans. ASME D: J. Basic Engng 94, 825–833.CrossRefGoogle Scholar
Kornfeld, M. & Suvorov, L. 1944 On the destructive action of cavitation. J. Appl. Phys. 15, 495–506.CrossRefGoogle Scholar
Kreider, W. 2008 Gas–vapor bubble dynamics in therapeutic ultrasound. PhD thesis, University of Washington.Google Scholar
Kumar, S. & Brennen, C. E. 1991 Nonlinear effects in the dynamics of clouds of bubbles. J. Acoust. Soc. Am. 89, 707–714.CrossRefGoogle ScholarPubMed
Lauterborn, W. & Bolle, H. 1975 Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 72, 391–399.CrossRefGoogle 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.CrossRefGoogle Scholar
Nagrath, S., Jansen, K., Lahey, R. T. Jr. & Akhatov, I. 2006 Hydrodynamic simulation of air bubble implosion using a level set approach. J. Comput. Phys. 215, 98–132.CrossRefGoogle Scholar
Niederhaus, J. H. J., Greenough, J. A., Oakley, J. G., Ranjan, D., Anderson, M. H. & Bonazza, R. 2008 A computational parameter study for the three-dimensional shock–bubble interaction. J. Fluid Mech. 594, 85–124.CrossRefGoogle Scholar
Nourgaliev, R. R., Dinh, T. N. & Theofanous, T. G. 2006 Adaptive characteristics-based matching for compressible multifluid dynamics. J. Comput. Phys. 213, 500–529.CrossRefGoogle Scholar
Ohl, C. D. & Ikink, R. 2003 Shock-wave-induced jetting of micron-size bubbles. Phys. Rev. Lett. 90, 1–4.CrossRefGoogle ScholarPubMed
Ohl, C. D., Kurz, T., Geisler, R., Lindau, O. & Lauterborn, W. 1999 Bubble dynamics, shock waves and sonoluminescence. Phil. Trans. R. Soc. Lond. A 357, 269–294.CrossRefGoogle Scholar
Philipp, A., Delius, M., Scheffczyk, C., Vogel, A. & Lauterborn, W. 1993 Interaction of lithotripter-generated shock waves with air bubbles. J. Acoust. Soc. Am. 93, 2496–2509.CrossRefGoogle Scholar
Philipp, A. & Lauterborn, W. 1998 Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 361, 75–116.CrossRefGoogle Scholar
Plesset, M. S. 1969 Cavitating flows. In Topics in Ocean Engineering (ed. Bretschneider, C. I.). Gulf Publishing Company.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.CrossRefGoogle 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
Rattray, M. 1951 Perturbation effects in cavitation bubble dynamics. PhD thesis, California Institute of Technology.Google Scholar
Rayleigh, Lord 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 94–98.CrossRefGoogle Scholar
Samtaney, R. & Pullin, D. I. 1996 On initial-value and self-similar solutions of the compressible Euler equations. Phys. Fluids 8, 2650–2655.CrossRefGoogle Scholar
Sankin, G. N., Simmons, W. N., Zhu, S. L. & Zhong, P. 2005 Shock wave interaction with laser-generated single bubbles. Phys. Rev. Lett. 95, 034501.CrossRefGoogle ScholarPubMed
Shima, A., Tomita, Y. & Takahashi, K. 1984 The collapse of a gas bubble near a solid wall by a shock wave and the induced impulsive pressure. Proc. Inst. Mech. Engng 198C, 81–86.Google Scholar
Shu, C. W. 1997 Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Tech Rep. ICASE Report No. 97-65. NASA Langley Research Center.Google Scholar
Shyue, K. M. 1998 An efficient shock-capturing algorithm for compressible multicomponent problems. J. Comput. Phys. 142, 208–242.CrossRefGoogle Scholar
Thompson, P. A. 1984 Compressible-Fluid Dynamics. Maple Press Company.Google Scholar
Thompson, K. W. 1990 Time-dependent boundary conditions for hyperbolic systems, II. J. Comput. Phys. 89, 439–461.CrossRefGoogle Scholar
Tomita, Y. & Shima, A. 1986 Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. J. Fluid Mech. 169, 535–564.CrossRefGoogle Scholar
Toro, E. F., Spruce, M. & Speares, W. 1994 Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4, 25–34.CrossRefGoogle Scholar
Turangan, C. K., Jamaluddin, A. R., Ball, G. J. & Leighton, T. G. 2008 Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water. J. Fluid Mech. 598, 1–25.CrossRefGoogle Scholar
Vogel, A., Lauterborn, W. & Timm, R. 1988 Acoustic transient generation by laser-produced cavitation bubbles near solid boundaries. J. Acoust. Soc. Am. 84, 719–731.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