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Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study

Published online by Cambridge University Press:  11 May 2012

N. A. Hawker  and
Y. Ventikos
N. A. Hawker
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
Y. Ventikos*
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
*
†Email address for correspondence: yiannis.ventikos@eng.ox.ac.uk
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Abstract

The interaction of a shockwave with a gas bubble in a liquid medium is of interest in a variety of areas, e.g. shockwave lithotripsy, cavitation damage and the study of sonoluminescence. This study employs a high-resolution front-tracking framework to numerically investigate this phenomenon. The modelling paradigm is validated extensively and then used to explore the parametric space of interest. We provide a comprehensive qualitative analysis of the collapse process, which we categorize into three phases, based on the principal feature dominating each phase. This results in the characterization of numerous previously unidentified features important in the evolution of the process and in the emergence of peak temperatures and pressures. For example, we discover that the peak pressure does not occur as a result of the impact of the main transverse jet (also called the re-entrant jet) but later in the collapse. We perform fully three-dimensional simulations, showing that three-dimensional instabilities are limited to the small-scale details of collapse, and continue by comparing collapse of cylindrical and spherical bubbles. We detail a parametric investigation varying the shock strength from 100 MPa to 100 GPa. A counter-intuitive discovery is that the maximum gas density decreases with increasing shock strength.

JFM classification

Drops and Bubbles: Bubble dynamics Compressible Flows: Shock waves Drops and Bubbles: Sonoluminescence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 701 , 25 June 2012 , pp. 59 - 97
Copyright
Copyright © Cambridge University Press 2012

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References

1. Arora, M., Junge, L. & Ohl, C. D. 2005 Cavitation cluster dynamics in shock-wave lithotripsy. Part 1. Free field. Ultrasound Med. Biol. 31 (6), 827–839.CrossRefGoogle ScholarPubMed
2. 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 (4), 265–276.CrossRefGoogle Scholar
3. Barber, B. P., Hiller, R. A., Lofstedt, R., Putterman, S. J. & Weninger, K. R. 1997 Defining the unknowns of sonoluminescence. Phys. Rep. 281 (2), 65–143.Google Scholar
4. Benjamin, T. B. & Ellis, A. T. 1966 The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries. Phil. Trans. R. Soc. Lond. A 260 (1110), 221–240.Google Scholar
5. Bjerknes, V. F. K. 1906 Fields of Force. Columbia University Press.Google Scholar
6. Bourne, N. K. 2002 On the collapse of cavities. Shock Waves 11 (6), 447–455.CrossRefGoogle Scholar
7. Bourne, N. K. & Field, J. E. 1992 Shock-induced collapse of single cavities in liquids. J. Fluid Mech. 244, 225–240.CrossRefGoogle Scholar
8. Bourne, N. K. & Field, J. E. 1999 Shock-induced collapse and luminescence by cavities. Phil. Trans. R. Soc. Lond. A 357, 295–311.CrossRefGoogle Scholar
9. Bourne, N. K. & Milne, A. M. 2003 The temperature of a shock-collapsed cavity. Proc. R. Soc. Lond. A 459 (2036), 1851–1861.CrossRefGoogle Scholar
10. Bowden, F. & Gurton, O. 1948 Birth and growth of the explosion in solids initiated by impact. Nature 161, 348.CrossRefGoogle Scholar
11. Brackbil, J., Kothe, D. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354.Google Scholar
12. Brenner, M., Hilgenfeldt, S. & Lohse, D. 2002 Single-bubble sonoluminescence. Rev. Mod. Phys. 74 (2), 425–484.CrossRefGoogle Scholar
13. 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 (1), 85–92.Google Scholar
14. 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 (1), 840–873.Google Scholar
15. Colella, P. 1985 A direct Eulerian MUSCL scheme for gas dynamics. SIAM J. Sci. Stat. Comput. 6 (1), 104–117.CrossRefGoogle Scholar
16. Coley, G. D. & Field, J. E. 1973 The role of cavities in the initiation and growth of explosion in liquids. Proc. R. Soc. Lond. A 335 (1600), 67–86.Google Scholar
17. Cook, S. S. 1928 Erosion by water-hammer. Proc. R. Soc. Lond. A 119 (783), 481–488.Google Scholar
18. Courant, R., Friedrichs, K. & Lewy, H. 1967 On the partial difference equations of mathematical physics. IBM J. Res. Dev. 11 (2), 215–234.Google Scholar
19. Dear, J. & Field, J. E. 1988 A study of the collapse of arrays of cavities. J. Fluid Mech. 190, 409–425.CrossRefGoogle Scholar
20. Didenko, Y. T. & Gordeychuk, T. 2000 Multibubble sonoluminescence spectra of water which resemble single-bubble sonoluminescence. Phys. Rev. Lett. 84 (24), 5640–5643.Google Scholar
21. Ding, Z. & Gracewski, S. M. 1996 The behaviour of a gas cavity impacted by a weak or strong shock wave. J. Fluid Mech. 309, 183–209.Google Scholar
22. Du, J., Fix, B., Glimm, J., Jia, X., Li, X., Li, Y. & Wu, L. 2006 A simple package for front tracking. J. Comput. Phys. 213 (2), 613–628.CrossRefGoogle Scholar
23. Fix, B., Glimm, J., Kaufman, R., Li, X. & Wu, L. 2008 Verification and validation of FronTier code and application to fluid interfacial instabilities. Phys. Scr. T132, 1–6.Google Scholar
24. Flannigan, D. J. & Suslick, K. S. 2005 Plasma formation and temperature measurement during single-bubble cavitation. Nature 434, 52–55.CrossRefGoogle ScholarPubMed
25. Frenzel, H. & Schultes, H. 1934 Luminescenz im ultraschallbeschickten Wasser. Z. Phys. Chem. 27b, 421.CrossRefGoogle Scholar
26. Gaitan, D. F., Crum, L. A., Church, C. C. & Roy, R. A. 1992 Sonoluminescence and bubble dynamics for a single, stable, cavitation bubble. J. Acoust. Soc. Am. 91 (6), 3166–3183.CrossRefGoogle Scholar
27. Gilmore, F. R. 1952. The growth or collapse of a spherical bubble in a viscous compressible liquid. Hydrodynamics Lab. Rep. 26-4. California Institute of Technology.Google Scholar
28. Glimm, J. 1988 The interaction of nonlinear hyperbolic waves. Commun. Pure Appl. Maths 41 (5), 569–590.CrossRefGoogle Scholar
29. Glimm, J. 1998 Front tracking in two and three dimensions. Comput. Maths Applics. 35 (7), 1–11.CrossRefGoogle Scholar
30. Glimm, J., Grove, J. W., Li, X., Shyue, K.-M., Zeng, Y. & Zhang, Q. 1998 Three-dimensional front tracking. SIAM J. Sci. Comput. 19 (3), 703–723.Google Scholar
31. Glimm, J., Grove, J. W., Li, X. & Tan, D. C. 2000 Robust computational algorithms for dynamic interface tracking in three dimensions. SIAM J. Sci. Comput. 21 (6), 2240–2256.Google Scholar
32. Glimm, J., Grove, J. W., Li, X. & Zhao, N. 1999 Simple front tracking. Contemp. Maths 238, 133–149.Google Scholar
33. Glimm, J., Grove, J. W., Lindquist, B., McBryan, O. A. & Tryggvason, G. 1988 The bifurcation of tracked scalar waves. SIAM J. Sci. Stat. Comput. 9 (1), 61–79.CrossRefGoogle Scholar
34. Glimm, J., Grove, J. W. & Zhang, Y. 2002 Interface tracking for axisymmetric flows. SIAM J. Sci. Comput. 24 (1), 208–236.CrossRefGoogle Scholar
35. Glimm, J., Isaacson, E., Marchesin, D. & McBryan, O. A. 1981 Front tracking for hyperbolic systems. Adv. Appl. Maths 2, 91–119.CrossRefGoogle Scholar
36. Glimm, J., Li, X., Liu, Y., Xu, Z. & Zhao, N. 2003 Conservative front tracking with improved accuracy. SIAM J. Numer. Anal. 41 (5), 1926–1947.Google Scholar
37. Glimm, J. & McBryan, O. A. 1985 A computational model for interfaces. Adv. Appl. Maths 6, 422–435.Google Scholar
38. Glimm, J., McBryan, O. A., Menikoff, R. & Sharp, D. H. 1986 Front tracking applied to Rayleigh–Taylor instability. SIAM J. Sci. Stat. Comput. 7 (1), 230–251.CrossRefGoogle Scholar
39. Grove, J. W. 1994 Applications of front tracking to the simulation of shock refractions and unstable mixing. Appl. Numer. Maths 14 (1–3), 213–237.Google Scholar
40. Grove, J. W. & Menikoff, R. 1990 Anomalous reflection of a shock wave at a fluid interface. J. Fluid Mech. 219, 313–336.CrossRefGoogle Scholar
41. 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
42. Haller, K. K., Poulikakos, D., Ventikos, Y. & Monkewits, P. 2003 Shock wave formation in droplet impact on a rigid surface: lateral liquid motion and multiple wave structure in the contact line region. J. Fluid Mech. 490, 1–14.CrossRefGoogle Scholar
43. Haller, K. K., Ventikos, Y. & Poulikakos, D. 2003 Wave structure in the contact line region during high speed droplet impact on a surface: solution of the Riemann problem for the stiffened gas equation of state. J. Appl. Phys. 93 (5), 3090–3097.CrossRefGoogle Scholar
44. Haller, K. K., Ventikos, Y., Poulikakos, D. & Monkewitz, P. 2002 Computational study of high-speed liquid droplet impact. J. Appl. Phys. 92 (5), 2821–2828.CrossRefGoogle Scholar
45. Hansson, I., Kedrinskii, V. & Morch, K. A. 1982 On the dynamics of cavity clusters. J. Phys. D: Appl. Phys. 15 (9), 1725–1734.CrossRefGoogle Scholar
46. Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (12), 2182–2189.Google Scholar
47. Hiller, R. A., Putterman, S. J. & Barber, B. P. 1992 Spectrum of synchronous picosecond sonoluminescence. Phys. Rev. Lett. 69 (8), 1182–1184.CrossRefGoogle ScholarPubMed
48. Hirt, C. & Nichols, B. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225.Google Scholar
49. Jiao, X. & Zha, H. 2008 Consistent computation of first- and second-order differential quantities for surface meshes. In Proceedings of the 2008 ACM Symposium on Solid and Physical Modelling. pp. 159–170. ACM.Google Scholar
50. Johnsen, E. & Colonius, T. 2006 Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219 (2), 715–732.Google Scholar
51. Johnsen, E. & Colonius, T. 2008 Shock-induced collapse of a gas bubble in shockwave lithotripsy. J. Acoust. Soc. Am. 124 (4), 2011–2020.Google Scholar
52. Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231–262.Google Scholar
53. Keller, J. B. & Miksis, M. 1980 Bubble oscillations of large amplitude. J. Acoust. Soc. Am. 68 (2), 628–633.CrossRefGoogle Scholar
54. Klaseboer, E., Fong, S. W., Turangan, C. K., Khoo, B. C., Szeri, A. J., Calvisi, M. L. & Sankin, G. N. et al. 2007 Interaction of lithotripter shockwaves with single inertial cavitation bubbles. J. Fluid Mech. 593, 33–56.Google Scholar
55. Kodama, T. & Tomita, Y. 2000 Cavitation bubble behaviour and bubble-shock wave interaction near a gelatin surface as a study of in vivo bubble dynamics. Appl. Phys. B 70 (1), 139–149.Google Scholar
56. Kornfeld, M. & Suvorov, L. 1944 On the destructive action of cavitation. J. Appl. Phys. 15, 495–506.CrossRefGoogle Scholar
57. Kröninger, D., Köhler, K., Kurz, T. & Lauterborn, W. 2010 Particle tracking velocimetry of the flow field around a collapsing cavitation bubble. Exp. Fluids 48 (3), 395–408.CrossRefGoogle Scholar
58. Lauterborn, W. & Bolle, H. 1975 Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 72 (02), 391–399.CrossRefGoogle Scholar
59. Lauterborn, W. & Kurz, T. 2010 Physics of bubble oscillations. Rep. Prog. Phys. 73 (10) 1–88.Google Scholar
60. Leighton, T. G., Fedele, F., Coleman, A., McCarthy, C., Ryves, S., Hurrell, A. M. & De Stefano, A. et al. 2008. Clinical studies of real-time monitoring of lithotripter performance using passive acoustic ensors. 2nd International Urolithiasis Research Symposium, pp. 256-277. AIP.CrossRefGoogle Scholar
61. Li, X. 1996 Numerical study for the three-dimensional Rayleigh–Taylor Instability through the TVD/AC scheme and parallel computation. J. Comput. Phys. 126 (2), 343–355.CrossRefGoogle Scholar
62. 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
63. Liu, X., Li, Y., Glimm, J. & Li, X. 2007 A front tracking algorithm for limited mass diffusion. J. Comput. Phys. 222 (2), 644–653.CrossRefGoogle Scholar
64. Lu, T., Xu, Z., Samulyak, R., Glimm, J. & Ji, X. M. 2008 Dynamics phase boundaries for compressible fluids. SIAM J. Sci. Comput. 30 (2), 895–915.Google Scholar
65. Mader, C. L. 1965 Initiation of detonation by the interaction of shocks with density discontinuities. Phys. Fluids 8 (10), 1811–1816.Google Scholar
66. Matula, T. & Crum, L. A. 1998 Evidence for gas exchange in single-bubble sonoluminescence. Phys. Rev. Lett. 80 (4), 865–868.Google Scholar
67. McNamara, W. B., Didenko, Y. T. & Suslick, K. S. 1999 Sonoluminescence temperatures during multi-bubble cavitation. Nature 401 (6755), 772–775.Google Scholar
68. Mellen, R. H. 1956 An experimental study of the collapse of a spherical cavity in water. J. Acoust. Soc. Am. 28 (3), 447–454.Google Scholar
69. Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flows of real materials. Rev. Mod. Phys. 61 (1), 75–130.Google Scholar
70. Moss, W. C., Clarke, D. B., White, J. W. & Young, D. A. 1994 Hydrodynamic simulations of bubble collapse and picosecond sonoluminescence. Phys. Fluids 6 (9), 2979–2985.Google Scholar
71. Nagayama, K., Mori, Y., Shimada, K. & Nakahara, M. 2002 Shock Hugoniot compression curve for water up to 1 GPa by using a compressed gas gun. J. Appl. Phys. 91 (1), 476–482.Google Scholar
72. 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
73. Nigmatulin, R. I., Akhatov, I. S., Topolnikov, A. S., Bolotnova, R. K., Vakhitova, N. K., Lahey, R. T. Jr. & Taleyarkhan, R. P. 2005 Theory of supercompression of vapor bubbles and nanoscale thermonuclear fusion. Phys. Fluids 17 (10), 107106.Google Scholar
74. Nourgaliev, R. R., Dinh, T. N. & Theofanous, T. G. 2006 Adaptive characteristics-based matching for compressible multifluid dynamics. J. Comput. Phys. 213 (2), 500–529.CrossRefGoogle Scholar
75. Pelekasis, N. A. & Tsamopoulos, J. A. 1993a Bjerknes forces between two bubbles. Part 1. Response to a step change in pressure. J. Fluid Mech. 254, 467–499.Google Scholar
76. Pelekasis, N. A. & Tsamopoulos, J. A. 1993b Bjerknes forces between two bubbles. Part 2. Response to an oscillatory pressure field. J. Fluid Mech. 254, 501–527.CrossRefGoogle Scholar
77. Philipp, A. & Lauterborn, W. 1998 Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 361, 75–116.CrossRefGoogle Scholar
78. Plesset, M. S. 1949 The dynamics of cavitation bubbles. Trans. ASME: J. Appl. Mech. 16 (3), 227–282.Google Scholar
79. 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 (2), 283–290.CrossRefGoogle Scholar
80. Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9 (1), 145–185.Google Scholar
81. Prosperetti, A. 1997 A new mechanism for sonoluminescence. J. Acoust. Soc. Am. 101 (4), 2003–2007.Google Scholar
82. Quirk, J. J. & Karni, S. 1996 On the dynamics of a shock–bubble interaction. J. Fluid Mech. 318, 129–163.Google Scholar
83. Ranjan, D., Niederhaus, J. H. J., Oakley, J. G., Anderson, M. H., Bonazza, R. & Greenough, J. A. 2008 Shock-bubble interactions: features of divergent shock-refraction geometry observed in experiments and simulations. Phys. Fluids 20 (3), 036101.Google Scholar
84. Ray, J., Samtaney, R. & Zabusky, N. J. 2000 Shock interactions with heavy gaseous elliptic cylinders: two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times. Phys. Fluids 12 (3), 707–716.Google Scholar
85. Rayleigh, Lord 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 94–98.CrossRefGoogle Scholar
86. Samtaney, R., Ray, J. & Zabusky, N. J. 1998 Baroclinic circulation generation on shock accelerated slow/fast gas interfaces. Phys. Fluids 10 (5), 1217–1230.Google Scholar
87. Sethian, J. A. 1999 Level Set Methods and Fast Marching Methods. Cambridge University Press.Google Scholar
88. Shapira, D. & Saltmarsh, M. 2002 Nuclear fusion in collapsing bubbles – Is it there? An attempt to repeat the observation of nuclear emissions from sonoluminescence. Phys. Rev. Lett. 89 (10), 2–5.Google Scholar
89. Storey, B. D. & Szeri, A. J. 2000 Water vapour, sonoluminescence and sonochemistry. Proc. R. Soc. Lond. A 456, 1685–1709.Google Scholar
90. Suslick, K. S. 1990 Sonochemistry. Science 247 (4949), 1439–1445.Google Scholar
91. Suslick, K. S., Doktycz, S. & Flint, E. 1990 On the origin of sonoluminescence and sonochemistry. Ultrasonics 28 (5), 280–290.Google Scholar
92. 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
93. Takahira, H., Matsuno, T. & Shuto, K. 2008 Numerical investigations of shock–bubble interactions in mercury. Fluid Dyn. Res. 40 (7-8), 510–520.Google Scholar
94. Taleyarkhan, R. P., West, C. D., Cho, J. S., Lahey, R. T. Jr., Nigmatulin, R. I. & Block, R. C. 2002 Evidence for nuclear emissions during acoustic cavitation. Science 295 (5561), 1868–1873.CrossRefGoogle ScholarPubMed
95. Thompson, L. H. & Doraiswamy, L. K. 1999 Sonochemistry: science and engineering. Ind. Engng Chem. Res. 38 (4), 1215–1249 American Chemical Society.Google Scholar
96. Tong, R. P., Schiffers, W. P., Shaw, S. J., Blake, J. R. & Emmony, D. C. 1999 The role of ‘splashing’ in the collapse of a laser-generated cavity near a rigid boundary. J. Fluid Mech. 380, 339–361.CrossRefGoogle Scholar
97. Tryggvason, G. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2), 708–759.Google Scholar
98. 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.Google Scholar
99. Wagner, W. & Pruss, A. 2002 The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31 (2), 387–535.Google Scholar
100. Wang, Y. & Chen, Y. 2007 Application of piezoelectric PVDF film to the measurement of impulsive forces generated by cavitation bubble collapse near a solid boundary. Exp. Therm. Fluid Sci. 32 (2), 403–414.Google Scholar
101. Weninger, K. R., Camara, C. & Putterman, S. J. 1999 Energy focusing in a converging fluid flow: implications for sonoluminescence. Phys. Rev. Lett. 83 (10), 2081–2084.Google Scholar
102. Woodward, P. & Colella, P. 1984 The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54, 115–173.Google Scholar
103. Wu, C. C. & Roberts, P. H. 1993 Shock-wave propagation in a sonoluminescing gas bubble. Phys. Rev. Lett. 70 (22), 3424–3427.Google Scholar
104. Xu, Z., Glimm, J., Zhang, Y. & Liu, X. 2007 A multiscale front tracking method for compressible free surface flows. Chem. Engng Sci. 62 (13), 3538–3548.Google Scholar
105. Yasui, K. 1997 Alternative model of single-bubble sonoluminescence. Phys. Rev. E 56 (6), 6750–6760.Google Scholar
106. van Leer, B. 1977 Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J. Comput. Phys. 23 (3), 276–299.Google Scholar
107. van Leer, B. 1979 Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101–136.Google Scholar

Hawker and Ventikos supplementary movie

1GPa - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 12.9 MB

Hawker and Ventikos supplementary movie

1GPa - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 8.7 MB

Hawker and Ventikos supplementary movie

1GPa Vorticity - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows a numerical schlieren image whereas the right hand side shows vorticity.

Download Hawker and Ventikos supplementary movie(Video)
Video 8.1 MB

Hawker and Ventikos supplementary movie

1GPa Vorticity - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows a numerical schlieren image whereas the right hand side shows vorticity.

Download Hawker and Ventikos supplementary movie(Video)
Video 8.2 MB

Hawker and Ventikos supplementary movie

100GPa - A 2D simulation of the interaction of 100GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 15.6 MB

Hawker and Ventikos supplementary movie

100GPa - A 2D simulation of the interaction of 100GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 13.1 MB

Hawker and Ventikos supplementary movie

100MPa - A 2D simulation of the interaction of 100MPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 24.6 MB

Hawker and Ventikos supplementary movie

100MPa - A 2D simulation of the interaction of 100MPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 16.8 MB