Skip to main content Accessibility help

The behaviour of a gas cavity impacted by a weak or strong shock wave

  • Zhong Ding (a1) and S. M. Gracewski (a1)


Two-dimensional simulations of gas cavity responses to both weak shocks (p ≤ 30 MPa) and strong shocks (p ranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. A weak shock is defined in the present context as one that does not cause liquid jet formation upon impact with the bubble. For this case, a large pressure is created within the gas upon collapse due to rapid compression of the gas, ultimately causing the re-expansion of the bubble. The bubble collapse and re-expansion time predicted by this model agree well with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liquid jet is formed that propagates through the bubble to the opposite bubble wall. Jet speeds as high as 2000 m s−1 are predicted by this model.



Hide All
Bailey, M. R., Dalecki, D., Child, S. Z., Raeman, C. H., Blackstock, D. T. & Carstensen, E. L. 1995 Bioeffect of positive and negative acoustic pressure in vivo. Submitted for publication.
Benson, D. J. 1991 A new two-dimensional flux-limited shock viscosity for impact calculation. Comput. Meth. Appl. Mech. Engng 93, 3995.
Blake, J. R. & Gibson, D. C. 1987 Cavitation bubbles near boundaries. Ann. Rev. Fluid Mech. 19, 99123.
Bourne, N. & Field, J. 1990 Collapsing cavities in reactive and non-reactive media. In 19th International Congress on High-Speed Photography and Photonics, vol. SPIE 1358, pp. 10461056.
Brackbill, J. U. & Saltzman, J. S. 1982 Adaptive zoning for singular problems in two dimensions. J. Comput. Phys. 46, 342368.
Carstensen, E. L., Campbell, D. S., Hoffman, D., Child, S. Z. & Aymé-Bellegarda, E. J. 1990 Killing of drosophila larvae by the fields of an electrohydraulic lithotripter. Ultrasound Med. Biol. 16, 687698.
Crum, L. A. 1988 Cavitation microjets as a contributory mechanism for renal calculi disintegration in ESWL. J. Urology 140, 15871590.
Dear, J. P. & Field, J. E. 1987 Applications of the two-dimensional gel techniques to erosion problems. In Proc. 7th Intl Conf. on Erosion by Liquid and Solid Impact, pp. 4.14.11.
Dear, J. P. & Field, J. E. 1988 A study of the collapse of arrays of cavities. J. Fluid Mech. 190, 409425.
Delius, M., Enders, G., Heine, G., Stark, J., Remberger, K. & Brendel, W. 1987 Biological effects of shock waves: Lung hemorrhage by shock waves in dogs - Pressure dependence. Ultrasound Med. Biol. 13, 6167.
Delius, M., Jordan, M., Eizenhoefer, H., Marlinghaus, E., Heine, G., Liebich, H. G. & Brendel, W. 1988 Biological effects of shock waves: Kidney hemorrhage by shock waves in dogs - Administration rate dependence. Ultrasound Med. Biol. 14, 689694.
Demuth, R. B., Margolin, L. G, Nichols, B. D., Adams, T. F. & Smith, B. W. 1985 SHALE: A computer program for solid dynamics. Tech. Rep. LA-10236. Los Alamos National Laboratory.
Ding, Z. & Gracewski, S. 1994 Response of constrained and unconstrained bubbles to lithotripter shock wave pulses. J. Acoust. Soc. Am. 96, 36363644.
Dwyer, H. A., Kee, R. J. & Sanders, B. R. 1980 Adaptive grid method for problems in fluid mechanics and heat transfer. AIAA J. 18, 12051212.
Evans, M. W., Harlow, F. H. & Meixner, B. D. 1962 Interaction of shock or rarefaction with a bubble. Phys. Fluids 5, 651656.
Flynn, H. G. 1964 Physics of acoustic cavitation in liquids. In Physical Acoustics (ed.W. P. Mason), vol. 1, Part B, pp. 58172. Academic.
Gilmore, F. R. 1952 The growth or collapse of a spherical bubble in a viscous compressible liquid. Rep. 26–4, pp. 140. California Institute of Technology, Pasadena, CA.
Gracewski, S. M., Dahake, G., Ding, Z., Burns, S. J. & Everbach, E. C. 1993 Internal stress wave measurements in solid subjected to lithotripter pulses. J. Acoust. Soc. Am. 94, 652661.
Grove, J. W. & Menikoff, R. 1990 Anomalous reflection of a shock wave at a fluid interface. J. Fluid Mech. 219, 313336.
Hansson, I. & Morch, K. A. 1980 The dynamics of cavity clusters in ultrasonic (vibratory) cavitation erosion. J. Appl. Phys. 51, 46514658.
Haas, J. F. & Sturtevant, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 4176.
Hirt, C. W., Amsden, A. A. & Cook, J. L. 1974 An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14, 227253.
Jordan, S. A. & Spaulding, M. L. 1993 A fast algorithm for grid generation. J. Comput. Phys. 104, 118128.
Kornfeld, M. & Suvorov, L. 1944 On the destructive action of cavitation. J. Appl. Phys. 15, 495506.
Landshoff, R. 1955 A numerical method for treating fluid flow in the presence of shocks. Tech. Rep. LA-1930. Los Alamos Scientific Lab.
Leer, B. V. 1977 Towards the ultimate conservative difference scheme. IV. A new approach to numerical conservationJ. Comput. Phys. 23, 276299.
Leer, B. V. 1979 Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 32, 101136.
Madar, C. L. 1965 Initiation of detonation by the interaction of shocks with density discontinuities. Phys. Fluids 8, 18111816.
Margolin, L. G. 1988 A centered artificial viscosity for cells with large aspect ratio. Tech. Rep. UCRL-53882. Lawrence Livermore National Laboratory.
Matsuno, K. & Dwyer, H. A. 1988 Adaptive methods for elliptic grid generation. J. Comput. Phys. 77, 4052.
Neumann, J. V. & Richtmyer, R. D. 1950 A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21, 232237.
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, 24962509.
Picone, J. M. & Boris, J. P. 1988 Vorticity generated by shock propagation through bubbles in gas. J. Fluid Mech. 189, 2351.
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 145.
Prosperetti, A. 1982 Bubble dynamics: a review and some recent results. Appl. Sci. Res. 38, 14564.
Quirk, J. J. & Karni, S. 1994 On the dynamics of a shock-bubble interaction. NASA CR-194978; ICASE Rep. pp. 9475.
Rayleigh, Lord. 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 9498.
Sass, W., Braunlich, M., Dreyer, H., Matura, E., Folberth, W., Priesmeyer, H. Seifert, J. 1991 The mechanisms of stone disintegration by shock waves. Ultrasound Med. Biol. 17, 239243.
Sato, K., Tomita, Y. & Shima, A. 1994 Numerical analysis of a gas bubble near a rigid boundary in an oscillatory pressure field. J. Acoust. Soc. Am. 95, 24162424
Schwendeman, S. D. 1986 Numerical shock propagation in non-uniform media. J. Fluid Mech. 188, 383410.
Steinberg, D. J. 1987 Spherical explosions and the equation of state of water. Tech. Rep. UCID- 20974. Lawrence Livermore National Laboratory.
Steinberg, D. J. 1993 A brief review on cavitation bubble collapse near a rigid boundary. J. Stone Disease 5(1), 4959.
Thompson, J. F, Warsi, Z. U. A. & Mastin, C. W. 1985 Numerical Grid Generation - Foundations and Applications. North-Holland.
Thompson, P. A. 1988 Compressible-Fluid Dynamics. Rensselaer Polytechnic Institute, New York.
Tipton, R. E., Steinberg, D. J. & Tomita, Y. 1992 Bubble expansion and collapse near a rigid wall. JSME Intl J. II 35(1), 6775.
Trilling, L. 1952 The collapse and rebound of a gas bubble. J. Appl. Phys. 23, 1417.
Vakil, N. & Everbach, E. C. 1991 Gas in gallstones: quantitative determinations and possible effects on fragmentation by shock waves. Gastroenterology 101, 16281634.
Vogel, A., Lauterborn, W. & Timm, R. 1989 Optical and acoustic investigations of the dynamics of laser-produced cavitating bubbles near a solid boundary. J. Fluid Mech. 206, 299338.
Wilkins, M. L. 1964 Calculation of elastic-plastic flow. Meth. Comput. Phys. 3, 211263.
Wilkins, M. L. 1980 Use of artificial viscosity in multidimensional fluid dynamics. J. Comput. Phys. 36, 281303.
Winslow, A. M. 1963 Equipotential zoning of two-dimensional meshes. Tech. Rep. UCRL-7312. Lawrence Livermore Radiation Laboratory.
Zhang, S., Duncan, J. H. & Chahine, G. L. 1993 The final stage of the collapse of a cavitation bubble near a rigid wall. J. Fluid Mech 257, 147181.
MathJax is a JavaScript display engine for mathematics. For more information see

The behaviour of a gas cavity impacted by a weak or strong shock wave

  • Zhong Ding (a1) and S. M. Gracewski (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed