Shock-induced collapse of a cylindrical air cavity in water: a Free-Lagrange simulation

Abstract. A Free-Lagrange CFD code is used to simulate the collapse of a cylindrical air cavity in water by a 1.9 GPa incident shock. The Lagrangian treatment allows the air/water interface to be tracked throughout the interaction. The incident shock is partially transmitted into the cavity, within which it experiences multiple reflections. The upstream cavity wall involutes to form a high-speed jet which, on impact with the far cavity wall, produces an intense blast wave. Heating of the gas within the cavity is highly non-isentropic, and is dominated by shock heating. The predicted final gas temperature is of order 12000 K, although the modelling assumptions used here lead to over-prediction of temperature during the later stages of collapse.

[1]  John E. Field,et al.  Shock-induced collapse of single cavities in liquids , 1992, Journal of Fluid Mechanics.

[2]  M.Munawar Chaudhri,et al.  High Speed Photography Of The Interaction Of Shocks With Voids In Condensed Media , 1983, Other Conferences.

[3]  F. P. Bowden,et al.  Initiation and Growth of Explosion in Liquids and Solids , 1985 .

[4]  John E. Field,et al.  A study of the collapse of arrays of cavities , 1988, Journal of Fluid Mechanics.

[5]  John E. Field,et al.  Bubble collapse and the initiation of explosion , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[6]  J. Field,et al.  The role of localized plastic flow in the impact initiation of explosives , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  James J. Quirk,et al.  On the dynamics of a shock–bubble interaction , 1994, Journal of Fluid Mechanics.

[8]  R. Apfel,et al.  Gauging the likelihood of cavitation from short-pulse, low-duty cycle diagnostic ultrasound. , 1991, Ultrasound in medicine & biology.

[9]  C. Church,et al.  A theoretical study of cavitation generated by an extracorporeal shock wave lithotripter. , 1988, The Journal of the Acoustical Society of America.

[10]  J. Blake,et al.  Transient cavities near boundaries. Part 1. Rigid boundary , 1986, Journal of Fluid Mechanics.

[11]  M. M. Chaudhri,et al.  The role of rapidly compressed gas pockets in the initiation of condensed explosives , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[12]  G. J. Ball,et al.  A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave , 1996 .

[13]  W. Lauterborn,et al.  Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary , 1975, Journal of Fluid Mechanics.

[14]  J. Field,et al.  The role of cavities in the initiation and growth of explosion in liquids , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[15]  C. H. Johansson.  The initiation of liquid explosives by shock and the importance of liquid break up , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[16]  E. Toro,et al.  Restoration of the contact surface in the HLL-Riemann solver , 1994 .

[17]  M. Kornfeld,et al.  On the Destructive Action of Cavitation , 1944 .

[18]  C. Mader,et al.  THEORETICAL AND EXPERIMENTAL TWO-DIMENSIONAL INTERACTIONS OF SHOCKS WITH DENSITY DISCONTINUITIES. , 1966 .

[19]  S. Tanaka,et al.  A study of cavitation bubble collapse pressures and erosion part 2: Estimation of erosion from the distribution of bubble collapse pressures , 1989 .

[20]  Ernst Brinkmeyer,et al.  Investigation Of Very Short Cavitation Shock Waves By Coherent Optical Methods , 1977, Other Conferences.

[21]  J. F. Davidson,et al.  The initial motion of a gas bubble formed in an inviscid liquid Part 1. The two-dimensional bubble , 1962, Journal of Fluid Mechanics.

[22]  J. D. Kershner,et al.  The heterogeneous explosive reaction zone , 1989 .

[23]  Herbert Herman,et al.  Treatise on Materials Science and Technology , 1979 .

[24]  G. J. Ball,et al.  Damping of mesh-induced errors in Free-Lagrange simulations of Richtmyer-Meshkov instability , 2000 .

[25]  J. Haas,et al.  Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities , 1987, Journal of Fluid Mechanics.

[26]  W. Lauterborn,et al.  Cavitation erosion by single laser-produced bubbles , 1998, Journal of Fluid Mechanics.

[27]  R. Frey.  Cavity Collapse in Energetic Materials. , 1986 .

[28]  M. Holt,et al.  Glimm's method applied to underwater explosions , 1981 .

[29]  A. Shima,et al.  Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse , 1986, Journal of Fluid Mechanics.

[30]  R. A. East,et al.  Shock and blast attenuation by aqueous foam barriers: influences of barrier geometry , 1999 .

[31]  Werner Lauterborn,et al.  Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary , 1989, Journal of Fluid Mechanics.

[32]  A. T. Ellis,et al.  On the Mechanism of Cavitation Damage by Nonhemispherical Cavities Collapsing in Contact With a Solid Boundary , 1961 .

[33]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[34]  John R. Blake,et al.  Cavitation Bubbles Near Boundaries , 1987 .

[35]  Y. Iwai,et al.  A study of cavitation bubble collapse pressures and erosion part 1: A method for measurement of collapse pressures , 1989 .

[36]  G. M. Swallowe,et al.  Ignition mechanisms of explosives during mechanical deformation , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[37]  R. Apfel,et al.  An improved theory for the prediction of microcavitation thresholds , 1989, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[38]  S. N. Heavens,et al.  The ignition of a thin layer of explosive by impact , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[39]  J. Field,et al.  Gas compression and jet formation in cavities collapsed by a shock wave , 1988, Nature.

[40]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .