Liquid compressibility effects during the collapse of a single cavitating bubble

Journal of the Acoustical Society of America

Volumn 129, Issue 1, 2011, Pages 122-131

  Fuster, D ^a   Dopazo, C ^b   Hauke, G ^b  

^a California Institute of Technology   (United States)

^b UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLE INTERFACES; CAVITATING BUBBLES; COMPRESSIBILITY EFFECTS; COMPRESSIBLE LIQUID; CONSERVATION OF MASS; FULL MODEL; PEAK PRESSURE; PRESSURE WAVES; RAYLEIGH; RAYLEIGH-PLESSET EQUATION;

CAVITATION; DIFFERENTIAL EQUATIONS; LIQUIDS;

COMPRESSIBILITY OF LIQUIDS;

ARTICLE; COMPARATIVE STUDY; COMPUTER SIMULATION; MATHEMATICAL COMPUTING; MICROBUBBLE; OSCILLOMETRY; PRESSURE; SURFACE PROPERTY; TEMPERATURE; THEORETICAL MODEL; ULTRASOUND;

COMPUTER SIMULATION; MICROBUBBLES; MODELS, THEORETICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; OSCILLOMETRY; PRESSURE; SURFACE PROPERTIES; TEMPERATURE; ULTRASONICS;

EID: 79551670395     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.3502464     Document Type: Article

References (43)

1. W. Besant, A Treatise on Hydrostatics and Hydrodynamics (Deighton, Bell, London, 1859), p. 228.
2. L. Rayleigh, On the pressure developed in a liquid during the collapse of a spherical cavity., Philos. Mag. 34, 94 (1917).
3. F. R. Gilmore, The growth of collapse of a spherical bubble in viscous compressible liquid., Technical Report No. 26-4, California Institute of Technology (1952).
4. J. Keller and M. Miksis, Bubble oscillations of large amplitude., J. Acoust. Soc. Am. 68, 628-633 (1980). 10.1121/1.384720
5. M. Plesset and A. Prosperetti, Bubble dynamics and cavitation., Annu. Rev. Fluid Mech. 9, 145 (1977). 10.1146/annurev.fl.09.010177.001045
6. A. Prosperetti, Bubble phenomena in sound fields: Part one., Ultrasonics 22, 69-77 (1984). 10.1016/0041-624X(84)90024-6 (Pubitemid 14549223)
7. A. Prosperetti, A new mechanism for sonoluminescence., J. Acoust. Soc. Am. 101, 2003-2007 (1997). 10.1121/1.418133 (Pubitemid 27163962)
8. R. Toegel and D. Lohse, Phase diagrams for sonoluminescing bubbles: A comparison between experiment and theory., J. Chem. Phys. 118, 1863-1875 (2003). 10.1063/1.1531610
9. Y. An and C. Ying, Model of single bubble sonoluminescence., Phys. Rev. E 71, 1-12 (2005).
10. K. Yasui, T. Tuziuti, M. Sivakumar, and Y. Iida, Theoretical study of single-bubble sonochemistry., J. Chem. Phys. 122, 1-12 (2005). 10.1063/1.1925607 (Pubitemid 40850286)
11. G. Hauke, D. Fuster, and C. Dopazo, Dynamics of a single cavitating and reacting bubble., Phys. Rev. E 75, 1-14 (2007). 10.1103/PhysRevE.75.066310 (Pubitemid 47140266)
12. W. Moss, Understanding the periodic driving pressure in the Rayleigh-Plesset equation., J. Acoust. Soc. Am. 101, 1187-1190 (1997). 10.1121/1.418111 (Pubitemid 27079902)
13. S. Hilgenfeldt, M. Brenner, S. Grossmann, and D. Lohse, Analysis of the Rayleigh-Plesset dynamics for sonoluminescing bubbles., J. Fluid Mech. 365, 171-204 (1998). 10.1017/S0022112098001207
14. H. Lin, B. D. Storey, and A. J. Szeri, Inertially driven in homogeneities in violently collapsing bubbles: The validity of the Rayleigh-Plesset equation., J. Fluid Mech. 452, 145-162 (2002). 10.1017/S0022112001006693
15. A. Preston, T. Colonius, and C. Brennen, A reduced order model of diffusive effects on the dynamics of bubbles., Phys. Fluids 19, 1-19 (2007). 10.1063/1.2825018
16. R. Nigmatulin, I. Akhatov, N. Vakhitova, and R. Lahey, On the forced oscillations of a small gas bubble in a spherical liquid-filled flask., J. Fluid Mech. 414, 47-73 (2000). 10.1017/S0022112000008338
17. E. Johnson and T. Colonius, Compressible multicomponent flow calculations and shock-wave interactions., in Sixth International Symposium on Cavitation (2006).
18. A. Prosperetti and A. Lezzi, Bubble dynamics in a compressible liquid. Part 1. First-order theory., J. Fluid Mech. 168, 457-478 (1986). 10.1017/S0022112086000460
19. A. Lezzi and A. Prosperetti, Bubble dynamics in a compressible liquid. Part 2. Second-order theory., J. Fluid Mech. 185, 289-321 (1987). 10.1017/S0022112087003185
20. E. Johnsen and T. Colonius, Implementation of WENO schemes in compressible multi-component flow problems., J. Comput. Phys. 219, 715-732 (2006). 10.1016/j.jcp.2006.04.018
21. Z. Wang, R. Pecha, B. Gompf, and W. Eisenmenger, Single bubble sonoluminescence: Investigations of the emitted pressure wave with a fiber optic probe hydrophone., Phys. Rev. E 59, 1777 (1999). 10.1103/PhysRevE.59.1777
22. R. Pecha and B. Gompf, Microimplosions: Cavitation collapse and shock wave emission on a nanosecond time scale., Phys. Rev. Lett. 84, 1328-1330 (2000). 10.1103/PhysRevLett.84.1328
23. W. Lauterborn, T. Kurz, R. Geisler, D. Schanz, and O. Lindau, Acoustic cavitation, bubble dynamics and sonoluminiescence., Ultrason. Sonochem. 14, 484-491 (2007). 10.1016/j.ultsonch.2006.09.017 (Pubitemid 46330096)
24. G. Reisman, Y. Wang, and C. Brennen, Observations of shock waves in cloud cavitation., J. Fluid. Mech. 344, 255 (1998). 10.1017/S0022112097007830 (Pubitemid 28284067)
25. Y. Wang, Shock waves in bubbly cavitating flows., Ph.D. thesis, California Institute of Technology, Pasadena, CA, 1996.
26. A. Colussi, L. Weavers, and M. Hoffmann, Chemical bubble dynamics and quantitative sonochemistry., J. Phys. Chem. A 102, 6927-6934 (1998). 10.1021/jp980930t
27. G. Puente and F. Bonetto, Proposed method to estimate the liquid-vapor accommodation coefficient based on experimental sonoluminescence data., Phys. Rev. E 71 (2005). 10.1103/PhysRevE.71.056309 (Pubitemid 43272543)
28. D. Fuster, Modeling and numerical simulation of the dynamics of liquid-bubble cavitating systems with chemical reaction processes., Ph.D. thesis, Centro Politecnico Superior, Zaragoza, Spain, 2007.
29. D. Fuster, G. Hauke, and C. Dopazo, Influence of accommodation coefficient on nonlinear bubble oscillations., J. Acoust. Soc. Am. 128, 5-10 (2010). 10.1121/1.3436520
30. W. Press, S. Teulkolsky, W. Vetterling, and B. Flannery, Numerical Recipes in Fortran 77 (Press Syndicate of the University of Cambridge, The Pitt Building, Trumpington Street, Cambridge CB2 1RP, 1992), Chap..
31. T. Hughes, W. Liu, and T. Zimmerman, Langrangian-eulerian finite element formulation for incompressible viscous flows., Comput. Methods Appl. Mech. Eng. 29, 329-349 (1981). 10.1016/0045-7825(81)90049-9 (Pubitemid 12509257)
32. G. Hauke and T. Hughes, A unified approach to compressible and incompressible flows., Comput. Methods Appl. Mech. Eng. 113, 389-395 (1994). 10.1016/0045-7825(94)90055-8
33. G. Hauke and T. Hughes, A comparative study of different sets of variables for solving compressible and incompressible flows., Comput. Methods Appl. Mech. Eng. 153, 1-44 (1998). 10.1016/S0045-7825(97)00043-1 (Pubitemid 28161649)
34. T. Hughes and M. Mallet, A new finite element formulation for computational fluid dynamics: III. the generalized streamline operator for multidimensional advection-diffusion systems., Comput. Methods Appl. Mech. Eng. 58, 305-328 (1986). 10.1016/0045-7825(86)90152-0 (Pubitemid 17466105)
35. F. Shakib, T. Hughes, and Z. Johan, A new finite element formulation for fluid dynamics formulation: X. the compressible Euler and Navier-Stokes equations., Comput. Methods Appl. Mech. Eng. 89, 141-219 (1991). 10.1016/0045-7825(91)90041-4 (Pubitemid 21721603)
36. G. Hauke, Simple stabilizing matrices for the computation of compressible flows in primitive variables., Comput. Methods Appl. Mech. Eng. 190, 6881-6893 (2001). 10.1016/S0045-7825(01)00267-5 (Pubitemid 33079939)
37. G. Hauke, A. Landaberea, I. Garmendia, and J. Canales, A segregated method for compressible flow computation part I: Isothermal compressible flows., Int. J. Numer. Methods Fluids 190, 271-323 (2004).
38. G. Hauke, A. Landaberea, I. Garmendia, and J. Canales, A segregated method for compressible flow computation. Part II: General divariant compressible flows., Int. J. Numer. Methods Fluids 49, 183-209 (2005). 10.1002/fld.v49:2 (Pubitemid 41183946)
39. W. Press, S. Teulkolsky, W. Vetterling, and B. Flannery, Numerical Recipes in For tran 77 (Press Syndicate of the University of Cambridge, The Pitt Building, Trumpington Street, Cambridge CB2 1RP, 1992), Chap..
40. P. Morse and K. Ingard, Theoretical Acoustics, 927 (Princenton University Press, Princeton, NJ, 1986).
41. C. Brennen, Cavitation and Bubble Dynamics (Oxford University Press, New York, 1995), p. 254.
42. Z. Wang, R. Pecha, B. Gompf, and W. Eisenmenger, Single bubble sonoluminescence: Investigations of the emitted pressure wave with a fiber optic probe hydrophone., Phys. Rev. E 59, 1777-1780 (1999). 10.1103/PhysRevE.59.1777
43. Y. Tomita and A. Shima, On the behavior of a spherical bubble and the impulse pressure in a viscous compressible liquid., Bull. JSME 20, 1453-1460 (1977).