Journal of Hydrodynamics

, Volume 30, Issue 6, pp 975–991 | Cite as

Bubble dynamics and its applications

  • Shi-Ping Wang (王诗平)
  • A-Man Zhang (张阿漫)Email author
  • Yun-Long Liu (刘云龙)
  • Shuai Zhang (张帅)
  • Pu Cui (崔璞)
Review Article


Bubbles have very important applications in many fields such as shipbuilding engineering, ocean engineering, mechanical engineering, environmental engineering, chemical engineering, medical science and so on. In this paper, the research status and the development of the bubble dynamics in terms of theory, numerical simulation and experimental technique are reviewed, which cover the underwater explosion bubble, airgun bubble, spark bubble, laser bubble, rising bubble, propeller cavitation bubble, water entry/exit cavitation bubble and bubble dynamics in other fields. Former researchers have done a lot of researches on bubble dynamics and gained fruitful achievements. However, due to the complexity of the bubble motion, many tough mechanical problems remain to be solved. Based on the research progress of bubble dynamics, this paper gives the future research direction of bubble dynamics, aiming to provide references for researches related to bubble dynamics.

Key words

Bubble cavitation underwater explosion bubble high pressure airgun bubble spark bubble laser bubble rising bubble 


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The authors would like to thank Fu-ren Ming, Shuai Li, Xiao Huang for their great help on this work.


  1. [1]
    Liu Y. L., Zhang A. M., Tian Z. L. et al. Numerical investigation on global responses of surface ship subjected to underwater explosion in waves [J]. Ocean Engineering, 2018, 161: 277–290.Google Scholar
  2. [2]
    Klaseboer E., Khoo B. C. Hung K. C. Dynamics of an oscillating bubble near a floating structure [J]. Journal of Fluids and Structures, 2005, 10(2): 1–10.Google Scholar
  3. [3]
    Hsiao C. T., Chahine G. L. Effect of a propeller and gas diffusion on bubble nuclei distribution in a liquid [J]. Journal of Hydrodynamics, 2012, 24(6): 809–822.Google Scholar
  4. [4]
    Vahaji S., Chen L., Cheung S. C. P. et al. Numerical investigation on bubble size distribution around an underwater vehicle [J]. Applied Ocean Research, 2018. 78: 254–266.Google Scholar
  5. [5]
    de Graaf K. L., Brandner P. A. Penesis I. Bubble dynamics of a seismic airgun [J]. Experimental Thermal and Fluid Science, 2014, 55: 228–238.Google Scholar
  6. [6]
    Deane G. B., Stokes M. D. Scale dependence of bubble creation mechanisms in breaking waves [J]. Nature, 2002, 418(6900): 839–844.Google Scholar
  7. [7]
    Zhang S., Wang S. P., Zhang A. M. et al. Numerical study on motion of the air-gun bubble based on boundary integral method [J]. Ocean Engineering, 2018, 154: 70–80.Google Scholar
  8. [8]
    Zhang Y. N., Zhang Y. N., Qian Z. D. et al. A review of microscopic interactions between cavitation bubbles and particles in silt-laden flow [J]. Renewable and Sustainable Energy Reviews, 2016, 56: 303–318.Google Scholar
  9. [9]
    Sedlar M., Ji B., Kratky T. et al. Numerical and experimental investigation of three-dimensional cavitating flow around the straight NACA2412 hydrofoil [J]. Ocean Engineering, 2016, 123: 357–382.Google Scholar
  10. [10]
    Yang D. D., Yu A., Ji B. et al. Numerical analyses of ventilated cavitation over a 2-D NACA0015 hydrofoil using two turbulence modeling methods [J]. Journal of Hydrodynamics, 2018, 30(2): 345–356.Google Scholar
  11. [11]
    Wang Z. Y., Huang B., Zhang M. D. et al. Experimental and numerical investigation of ventilated cavitating flow structures with special emphasis on vortex shedding dynamics [J]. International Journal of Multiphase Flow, 2018, 98: 79–95.Google Scholar
  12. [12]
    Ji B., Luo X. W., Arndt R. E. A. et al. Large eddy simulation and theoretical investigations of the transient cavitating vortical flow structure around a NACA66 hydrofoil [J]. International Journal of Multiphase Flow, 2015, 68: 121–134.MathSciNetGoogle Scholar
  13. [13]
    Chen L. M., Yang X. G., Li G. et al. Prediction of bubble fluidisation during chemical looping combustion using CFD simulation [J]. Computers and Chemical Engineering, 2017, 99: 82–95.Google Scholar
  14. [14]
    Sarhan A. R., Naser J., Brooks G. CFD modeling of bubble column: Influence of physico-chemical properties of the gas/liquid phases properties on bubble formation [J]. Separation and Purification Technology, 2018, 201: 130–138.Google Scholar
  15. [15]
    Huang Z. B., McClure D. D., Barton G. W. et al. Assessment of the impact of bubble size modelling in CFD simulations of alternative bubble column configurations operating in the heterogeneous regime [J]. Chemical Engineering Science, 2018, 186: 88–101.Google Scholar
  16. [16]
    Chen H., Kreider W., Brayman A. A. et al. Blood vessel deformations on microsecond time scales by ultrasonic cavitation [J]. Physical Review Letters, 2011, 106: 034301.Google Scholar
  17. [17]
    Liu Y. Q., Sugiyama K., Takagi S. et al. Surface instability of an encapsulated bubble induced by an ultrasonic pressure wave [J]. Journal of Fluid Mechanics, 2012, 691: 315–340.MathSciNetzbMATHGoogle Scholar
  18. [18]
    Wang S. P., Wang Q. X., Leppinen D. M. et al. Acoustic bubble dynamics in a microvessel surrounded by elastic material [J]. Physics of Fluids, 2018, 30(1): 012104.Google Scholar
  19. [19]
    Zhang A. M., Zeng L. Y., Cheng X. D. et al. The evaluation method of total damage to ship in underwater explosion [J]. Applied Ocean Research, 2011, 33(4): 240–251.Google Scholar
  20. [20]
    Korkut E., Atlar M. An experimental investigation of the effect of foul release coating application on performance, noise and cavitation characteristics of marine propellers [J]. Ocean Engineering, 2012, 41: 1–12.Google Scholar
  21. [21]
    Lohse D. Bubble puzzles [J]. Physics Today, 2003, 56(2): 36–41.Google Scholar
  22. [22]
    Ziolkowski A. A method for calculating the output pressure waveform from an air gun [J]. Geophysical Journal Royal Astronomical Society, 1970, 21: 137–161.Google Scholar
  23. [23]
    Zhang S., Wang S. P., Zhang A. M. et al. Numerical study on attenuation of bubble pulse through tuning the air-gun array with the particle swarm optimization method [J]. Applied Ocean Research, 2017, 66: 13–22.Google Scholar
  24. [24]
    Alizadeh M., Seyyedi S. M., Taeibi Rahni M. et al. Threedimensional numerical simulation of rising bubbles in the presence of cylindrical obstacles, using lattice Boltzmann method [J]. Journal of Molecular Liquids, 2017, 236: 151–161.Google Scholar
  25. [25]
    Zhang A., Sun P., Ming F. An SPH modeling of bubble rising and coalescing in three dimensions [J]. Computer Methods in Applied Mechanics and Enginee-ring, 2015, 294: 189–209.MathSciNetGoogle Scholar
  26. [26]
    Brennen C. E. Cavitation and bubble dynamics [M]. New York, USA: Oxford University Press, 1995.zbMATHGoogle Scholar
  27. [27]
    Tripathi M. K., Sahu K. C. Govindarajan R. Dynamics of an initially spherical bubble rising in quiescent liquid [J]. Nature communications, 2015, 6: 6268.Google Scholar
  28. [28]
    Sun C., Can E., Dijkink R. et al. Growth and collapse of a vapour bubble in a microtube: The role of thermal effects [J]. Journal of Fluid Mechanics, 2009, 632: 5–16.zbMATHGoogle Scholar
  29. [29]
    Kuijpers M. W. A., van Eck D., Kemmere M. F. et al. Cavitation-induced reactions in high-pressure carbon dioxide [J]. Science, 2002, 298(5600): 1969–1971.Google Scholar
  30. [30]
    Debrégeas G., de Gennes P. G., Brochard-Wyart F. The life and death of “bare” viscous bubbles [J]. Science, 1998, 279(5357): 1704–1707.Google Scholar
  31. [31]
    Klaseboer E., Manica R., Chan D. Y. C. et al. BEM simulations of potential flow with viscous effects as applied to a rising bubble [J]. Engineering Analysis With Boundary Elements, 2011, 35: 489–494.zbMATHGoogle Scholar
  32. [32]
    Mougin G., Magnaudet J. Path instability of a rising bubble [J]. Physical Review Letters, 2001, 88(1): 014502.Google Scholar
  33. [33]
    Lind S. J., Phillips T. N. The effect of viscoelasticity on a rising gas bubble [J]. Journal of Non-Newtonian Fluid Mechanics, 2010, 165(15-16): 852–865.zbMATHGoogle Scholar
  34. [34]
    Wang Q. X. Non-spherical bubble dynamics of underwater explosions in a compressible fluid [J]. Physics of Fluids, 2013, 25(7): 072104.zbMATHGoogle Scholar
  35. [35]
    Wang Q. X., Yeo K. S., Khoo B. C. et al. Strong interaction between a buoyancy bubble and a free surface [J]. Theoretical and Computational Fluid Dynamics, 1996, 8: 73–88.zbMATHGoogle Scholar
  36. [36]
    Zhang A. M., Wang S. P., Wu G. X. Simulation of bubble motion in a compressible liquid based on the three dimensional wave equation [J]. Engineering Analysis with Boundary Elements, 2013, 37(9): 1179–1188.MathSciNetzbMATHGoogle Scholar
  37. [37]
    Blake J. R., Gibson D. C. Cavitation bubbles near boundaries [J]. Annual Review of Fluid Mechanics, 1987, 19: 99–123.Google Scholar
  38. [38]
    Zhang Y. L., Yeo K. S., Khoo B. C. et al. 3D jet impact and toroidal bubbles [J]. Journal of Computational Physics, 2001, 16(6): 336–360.zbMATHGoogle Scholar
  39. [39]
    Zhang A. M., Liu Y. L. Improved three-dimensional bubble dynamics model based on boundary element method [J]. Journal of Computational Physics, 2015. 294: 208–223.MathSciNetzbMATHGoogle Scholar
  40. [40]
    Liu Y. L., Zhang A. M., Tian Z. L. et al. Investigation of free-field underwater explosion with Eulerian finite element method [J]. Ocean Engineering, 2018, 166: 182–190.Google Scholar
  41. [41]
    Tian Z. L., Liu Y. L., Zhang A. M. et al. Analysis of breaking and re-closure of a bubble near a free surface based on the Eulerian finite element method [J]. Computers and Fluids, 2018, 170: 41–52.MathSciNetzbMATHGoogle Scholar
  42. [42]
    Li T., Wang S., Li S. et al. Numerical investigation of an underwater explosion bubble based on FVM and VOF [J]. Applied Ocean Research, 2018, 74: 49–58.Google Scholar
  43. [43]
    Koukouvinis P., Gavaises M., Supponen O. et al. Simulation of bubble expansion and collapse in the vicinity of a free surface [J]. Physics of Fluids, 2016, 28(5): 052103.Google Scholar
  44. [44]
    Amaya-Bower L., Lee T. Single bubble rising dynamics for moderate Reynolds number using lattice Boltzmann method [J]. Computers and Fluids, 2010, 39(7): 1191–1207.zbMATHGoogle Scholar
  45. [45]
    Peng C., Tian S., Li G. et al. Single-component multiphase lattice Boltzmann simulation of free bubble and crevice heterogeneous cavitation nucleation [J]. Physical Review E, 2018, 98(2): 023305.MathSciNetGoogle Scholar
  46. [46]
    Wang Z., Shi D., Zhang A. Three-dimensional lattice Boltzmann simulation of bubble behavior in a flapinduced shear flow [J]. Computers and Fluids, 2015, 123: 44–53.MathSciNetzbMATHGoogle Scholar
  47. [47]
    Sun P. N., Li Y. B. Ming F. R. Numerical simulation on the motion characteristics of freely rising bubbles using smoothed particle hydrodynamics method [J]. Acta Physica Sinica, 2015, 64(17): 174701.Google Scholar
  48. [48]
    Rahmat A., Tofighi N., Yildiz M. Numerical simulation of the electrohydrodynamic effects on bubble rising using the SPH method [J]. International Journal of Heat and Fluid Flow, 2016, 62: 313–323.Google Scholar
  49. [49]
    Fan H., Li S. A Peridynamics-SPH modeling and simulation of blast fragmentation of soil under buried explosive loads [J]. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 349–381.MathSciNetGoogle Scholar
  50. [50]
    Hung C. F. Hwangfu J. J. Experimental study of the behaviour of mini-charge underwater explosion bubbles near different boundaries [J]. Journal of Fluid Mechanics, 2010, 651: 55–80.zbMATHGoogle Scholar
  51. [51]
    Graaf K. L. D., Brandner P. A., Penesis I. The pressure field generated by a seismic airgun [J]. Experimental Thermal and Fluid Science, 2014, 55: 239–249.Google Scholar
  52. [52]
    Peters A., Lantermann U., el Moctar O. Numerical prediction of cavitation erosion on a ship propeller in model-and full-scale [J]. Wear, 2018, 408-409: 1–12.Google Scholar
  53. [53]
    Cui P., Zhang A. M., Wang S. et al. Ice breaking by a collapsing bubble [J]. Journal of Fluid Mechanics, 2018, 841: 287–309.Google Scholar
  54. [54]
    Philipp A., Lauterborn W. Cavitation erosion by single laser-produced bubbles [J]. Journal of Fluid Mechanics, 1998, 361: 75–116.zbMATHGoogle Scholar
  55. [55]
    Cole R. H. Underwater explosion [M]. Princeton USA: Princeton University Press, 1948.Google Scholar
  56. [56]
    Brett J. M. Yiannakopolous G. A study of explosive effects in close proximity to a submerged cylinder [J]. International Journal of Impact Engineering, 2008, 35(4): 206–225.Google Scholar
  57. [57]
    Geers T. L. Residual potential and approximation methods for three dimensional fluid-structure interaction problems [J]. Journal of the Acoustical Society of America, 1971, 49: 1505–1510.Google Scholar
  58. [58]
    Geers T. L. Doubly asympotic approximation for transient motions of submerged structures [J]. Journal of the Acoustical Society of America, 1978, 64: 1500–1508.zbMATHGoogle Scholar
  59. [59]
    Huang H. Transient interaction of plane acoustic waves with a spherical elastic shell [J]. Journal of the Acoustical Society of America, 1969, 45(3): 85–98.Google Scholar
  60. [60]
    Wang P. P., Zhang A. M., Ming F. R. et al. A novel nonreflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics [J]. Journal of Fluid Mechanics, 2018, 10.1017/jfm.2018.852.Google Scholar
  61. [61]
    Wang C., Khoo B. C. An indirect boundary element method for three-dimensional explosion bubbles [J]. Journal of Computational Physics, 2004, 19(4): 451–480.zbMATHGoogle Scholar
  62. [62]
    Klaseboer E., Hung K. C., Wang C. W. et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure [J]. Journal of Fluid Mechanics, 2005, 53(7): 387–413.zbMATHGoogle Scholar
  63. [63]
    Prosperetti A., Lezzi A. Bubble dynamics in a compressible liquid. Part 1. First-order theory [J]. Journal of Fluid Mechanics, 1986, 168: 457–478.zbMATHGoogle Scholar
  64. [64]
    Rayleigh L. On the pressure developed in a liquid during the collapse of a spherical cavity [J]. Philosophical Magazine, 1917, 34(200): 94–98.zbMATHGoogle Scholar
  65. [65]
    Plesset M. S., Pasadena C. The dynamics of cavitation bubbles [J]. Journal of Applied Mechanics, 1949, 16: 277–282.Google Scholar
  66. [66]
    Noltingk B. E., Neppiras E. A. Caviation produced by ultrasonics [J]. Proceedings of the Physical Society. Section B, 1950, 63: 674–685.Google Scholar
  67. [67]
    Gilmore F. R. The growth and collapse of a spherical bubble in a viscous compressible liquid [R]. Pasadena, CA: California Institute of Technology, 1952.Google Scholar
  68. [68]
    Prosperetti A. Bubbles [J]. Physics of Fluids, 2004, 16(6): 1852–1865.MathSciNetzbMATHGoogle Scholar
  69. [69]
    Zhang Y. N., Min Q., Zhang Y. N. et al. Effects of liquid compressibility on bubble-bubble interactions between oscillating bubbles [J]. Journal of Hydrodynamics, 2016, 28(5): 832–839.Google Scholar
  70. [70]
    Smith W. R., Wang Q. Radiative decay of the nonlinear oscillations of an adiabatic spherical bubble at small Mach number [J]. Journal of Fluid Mechanics, 2018, 837: 1–18.MathSciNetGoogle Scholar
  71. [71]
    Plesset M. S., Prosperetti A. Bubble dynamics and cavitation [J]. Annual Review Of Fluid Mechanics, 1977, 9: 145–185.zbMATHGoogle Scholar
  72. [72]
    Lauterborn W. Numerical investigation of nonlinear oscillations of gas bubbles in liquids [J]. Journal of the Acoustical Society of America, 1976, 59: 283–293.Google Scholar
  73. [73]
    Geers T. L., Lagumbay R. S., Vasilyev O. V. Acousticwave effects in violent bubble collapse [J]. Journal of Applied Physics, 2012, 112: 054910.Google Scholar
  74. [74]
    Zamyshlyayev B. V. Dynamic loads in underwater explosion [R]. Washington DC, USA: Naval Intelligence Support Center, 1973.Google Scholar
  75. [75]
    Kedrinskiy V. K. Hydrodynamics of explosion experiments and models [M]. Novosibirsk, Russia: Springer, 2005.Google Scholar
  76. [76]
    White L. R., Carnie S. L. The drag on a flattened bubble moving across a plane substrate [J]. Journal of Fluid Mechanics, 2012, 696: 345–373.MathSciNetzbMATHGoogle Scholar
  77. [77]
    Cui P., Zhang A. M., Wang S. P. Small-charge underwater explosion bubble experiments under various boundary conditions [J]. Physics of Fluids, 2016, 28(11): 117103.Google Scholar
  78. [78]
    Zhang A. M., Li S., Cui J. Study on splitting of a toroidal bubble near a rigid boundary [J]. Physics of Fluids, 2015, 27: 062102.Google Scholar
  79. [79]
    Blake J. R., Taib B. B., Doherty G. Transient cavities near boundaries. Part 1. Rigid boundary [J]. Journal of Fluid Mechanics, 1986, 170: 479–497.zbMATHGoogle Scholar
  80. [80]
    Blake J. R., Taib B. B., Doherty G. Transient cavities near boundaries. Part 2. Free surface [J]. Journal of Fluid Mechanics, 1987, 181: 197–212.zbMATHGoogle Scholar
  81. [81]
    Wang Q. X., Yeo K. S., Khoo B. C. et al. Nonlinear interaction between gas bubble and free surface [J]. Computer and Fluids, 1996, 25(7): 607–628.zbMATHGoogle Scholar
  82. [82]
    Ni B. Y., Zhang A. M., Wu G. X. Simulation of a fully submerged bubble bursting through a free surface [J]. European Journal of Mechanics /B Fluids, 2016, 55(4): 1–14.MathSciNetzbMATHGoogle Scholar
  83. [83]
    Benson D. J., Okazawa S. Contact in a multi-material Eulerian finite element formulation [J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(39): 4277–4298.zbMATHGoogle Scholar
  84. [84]
    Benson D. J. Computational methods in Lagrangian and Eulerian hydrocodes [J]. Computer Methods in Applied Mechanics and Engineering, 1992, 99(2): 235–394.MathSciNetzbMATHGoogle Scholar
  85. [85]
    Hirt C. W., Nichols B. D. Volume of fluid (VOF) method for the dynamics of free boundaries [J]. Journal of Computational Physics, 1981, 39(1): 201–225.zbMATHGoogle Scholar
  86. [86]
    Miller S. T., Jasak H., Boger D. A. et al. A pressure-based, compressible, two-phase flow finite volume method for underwater explosions [J]. Computers and Fluids, 2013, 87: 132–143.MathSciNetzbMATHGoogle Scholar
  87. [87]
    Koch M., Lechner C., Reuter F. et al. Numerical modeling of laser generated cavitation bubbles with the finite volume and volume of fluid method, using OpenFOAM [J]. Computers and Fluids, 2016, 126: 71–90.MathSciNetzbMATHGoogle Scholar
  88. [88]
    Jasak H., Gosman A. D. Element residual error estimate for the finite volume method [J]. Computers and Fluids, 2003, 32(2): 223–248.MathSciNetzbMATHGoogle Scholar
  89. [89]
    Blake J. R., Gibson D. C. Growth and collapse of a vapour cavity near a free surface [J]. Journal of Fluid Mechanics, 1981, 111: 123–140.Google Scholar
  90. [90]
    Gibson D. C., Blake J. R. The growth and collapse of bubbles near deformable surfaces [J]. Applied Scientific Research, 1982, 38(1): 215–224.Google Scholar
  91. [91]
    Zhang Y. L., Yeo K. S., Khoo B. C. et al. Three dimensional computation of bubbles near a free surface [J]. Journal of Computational Physics, 1998, 146: 105–123.MathSciNetzbMATHGoogle Scholar
  92. [92]
    Tu Q., Li S. An updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluids [J]. Journal of Computational Physics, 2017, 348: 493–513.MathSciNetzbMATHGoogle Scholar
  93. [93]
    Zhang A. M., Wang S. P., Huang C. et al. Influences of initial and boundary conditions on underwater explosion bubble dynamics [J]. European Journal of Mechanics B-Fluids, 2013, 42: 69–91.zbMATHGoogle Scholar
  94. [94]
    Wang B., Zhang Y. P., Wang Y. P. Experimental study on bubble oscillation formed during underwater explosions [J]. Explosion and Shock Waves, 2008, 28: 572–576.Google Scholar
  95. [95]
    Gauch E., Leblanc J., Shukla A. Near field underwater explosion response of polyurea coated composite cylinders [J]. Composite Structures, 2018, 202: 836–852.Google Scholar
  96. [96]
    Chahine G. L. Interaction between an oscillating bubble and a free surface [J]. Journal of Fluids Engineering, 1977, 99(4): 709–716.Google Scholar
  97. [97]
    Turangan C. K., Ong G. P., Klaseboer E. et al. Experimental and numerical study of transient bubble-elastic membrane interaction [J]. Journal of Applied Physics, 2006, 100: 054910.Google Scholar
  98. [98]
    Cui P., Wang Q. X., Wang S. P. et al. Experimental study on interaction and coalescence of synchronized multiple bubbles [J]. Physics of Fluids, 2016, 28(1): 012103.Google Scholar
  99. [99]
    Lauterborn W., Bolle H. Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary [J]. Journal of Fluid Mechanics, 1975, 72(2): 391–399.Google Scholar
  100. [100]
    Supponen O., Kobel P., Obreschkow D. et al. The inner world of a collapsing bubble [J]. Physics of Fluids, 2015, 27(9): 94–98.Google Scholar
  101. [101]
    Menon S. Lal M. On the dynamics and instability of bubbles formed during underwater explosions [J]. Experimental Thermal and Fluid Science, 1998, 16(4): 305–321.Google Scholar
  102. [102]
    Ren S., Song Y., Zhang A. M. et al. Experimental study on dynamic buckling of submerged grid-stiffened cylindrical shells under intermediate-velocity impact [J]. Applied Ocean Research, 2018, 74: 237–245.Google Scholar
  103. [103]
    Caldwell J., Dragoset W. A brief overview of seismic air-gun arrays [J]. Leading Edge, 2000, 19(8): 898–902.Google Scholar
  104. [104]
    Schulze-Gattermann R. Physical aspects of the “airpulser” as a seismic energy source [J]. Geophysical Prospecting, 1972, 20(1): 155–192.Google Scholar
  105. [105]
    Johnson D. T. Understanding air-gun bubble behavior [J]. Geophysics, 1994, 59: 1729–1734.Google Scholar
  106. [106]
    Johnston R. C. Performance of 2000 and 6000 psi air guns: Theory and experiment [J]. Geophysical Prospecting, 1980, 28(5): 700–715.Google Scholar
  107. [107]
    Fontana P. M., Haugland T. A. Compact sleeve-gun source arrays [J]. Geophysics, 1991, 56(3): 1359.Google Scholar
  108. [108]
    Allen T. J., Jeffery S. J., Mansfield G. C. Sleeve guns and wide tow [J]. Exploration Geophysics, 1987, 18(2): 1–3.Google Scholar
  109. [109]
    Langhammer J., Landrø M. Experimental study of viscosity effects on air-gun signatures [J]. Geophysics, 1993, 58(12): 1801–1808.Google Scholar
  110. [110]
    Vaage S., Ursin B. Computation of signatures of linear airgun arrays [J]. Geophysical Prospecting, 1987, 35: 281–287.Google Scholar
  111. [111]
    Landrø M. Modelling of GI gun signatures [J]. Geophysical Prospecting, 1992, 40(7): 721–747.Google Scholar
  112. [112]
    Ziolkowski A. Review of vibroseis data acquisition and processing for better amplitudes: adjusting the sweep and deconvolving for the time-derivative of the true groundforce [J]. Geophysical Prospecting, 2010, 58: 41–54.Google Scholar
  113. [113]
    Giles B. F., Johnston R. C. System approach to air-gun array design [J]. Geophysical Prospecting, 1973, 21(1): 77–101.Google Scholar
  114. [114]
    Ursin B. Attenuation of coherent noise in marine seismic exploration using very long arrays [J]. Geophysical Prospecting, 1978, 26(4): 722–749.Google Scholar
  115. [115]
    Ziolkowski A., Parkes G., Hatton L. et al. The signature of an air gun array: Computation from near-field measurements including interactions [J]. Geophysics, 1982, 47: 1413–1421.Google Scholar
  116. [116]
    Safar M. H. The radiation of acoustic waves from an airgun [J]. Geophysical Prospecting, 1976, 24(4): 756–772.Google Scholar
  117. [117]
    Landrø M. Source signature determination from ministreamer data [J]. Geophysics, 1994, 59(8): 1261–1269.Google Scholar
  118. [118]
    Landrø M., Sollie R. Source signature determination by inversion [J]. SEG Technical Program Expanded Abstracts, 1992, 57(11): 1633–1640.Google Scholar
  119. [119]
    Li G., Liu Z., Wang J. et al. Air-gun signature modelling considering the influence of mechanical structure factors [J]. Journal of Geophysics and Engineering, 2014, 11(2): 25005–25012.Google Scholar
  120. [120]
    Li G. F., Cao M. Q., Chen H. L. et al. Modeling air gun signatures in marine seismic exploration considering multiple physical factors [J]. Applied Geophysics, 2010, 7(2): 158–165.Google Scholar
  121. [121]
    Laws R. M., Hatton L., Haartsen M. Computer modelling of clustered airguns [J]. First Break, 1990, 8(9): 331–338.Google Scholar
  122. [122]
    Schrage R. W. A theoretical study of interface mass transfer [M]. New York, USA: Columbia University Press, 1953.Google Scholar
  123. [123]
    Graaf K. L. D., Penesis I., Brandner P. A. Modelling of seismic airgun bubble dynamics and pressure field using the Gilmore equation with additional damping factors [J]. Ocean Engineering, 2014, 76(1): 32–39.Google Scholar
  124. [124]
    Huang X., Zhang A. M., Liu Y. L. Investigation on the dynamics of air-gun array bubbles based on the dual fast multipole boundary element method [J]. Ocean Engineering, 2016, 124: 157–167.Google Scholar
  125. [125]
    Cox E., Pearson A., Blake J. R. et al. Comparison of methods for modelling the behaviour of bubbles produced by marine seismic airguns [J]. Geophysical Prospecting, 2004, 52: 451–477.Google Scholar
  126. [126]
    Langhammer J. Landrø M. Temperature effects on airgun signatures [J]. Geophysical Prospecting, 1993, 41(6): 737–750.Google Scholar
  127. [127]
    Laws R., Landrø M. Amundsen L. An experimental comparison of three direct methods of marine source signature estimation [J]. Geophysical Prospecting, 1998, 46(4): 353–389.Google Scholar
  128. [128]
    Langhammer J., Landrø M., Martin J. et al. Air-gun bubble damping by a screen [J]. Geophysics, 1995, 60(6): 1765–1772.Google Scholar
  129. [129]
    Langhammer J., Landrø M. High-speed photography of the bubble generated by an airgun [J]. Geophysical Prospecting, 1996, 44(1): 153–172.Google Scholar
  130. [130]
    Zhang S., Wang S. P., Zhang A. M. Experimental study on the interaction between bubble and free surface using a high-voltage spark generator [J]. Physics of Fluids, 2016, 28(3): 032109.Google Scholar
  131. [131]
    Thompson P. R. Shock testing of naval vessels using seismic airgun arrays [P]. USA, US6662624B1, 2003.Google Scholar
  132. [132]
    Zhang A. M., Cui P., Cui J. et al. Experimental study on bubble dynamics subject to buoyancy [J]. Journal of Fluid Mechanics, 2015, 776: 137–160.Google Scholar
  133. [133]
    Vogel A., Lauterborn W. Acoustic transient generation by laser-produced cavitation bubbles near solid boundaries [J]. Journal of the Acoustical Society of America, 1988, 84(2): 719–713.Google Scholar
  134. [134]
    Zhang Y. N., Chen F. P., Zhang Y. N. et al. Experimental investigations of interactions between a laser-induced cavitation bubble and a spherical particle [J]. Experimental Thermal and Fluid Science, 2018, 98: 645–661.Google Scholar
  135. [135]
    Zhang S., Zhang A. M., Wang S. P. et al. Dynamic characteristics of large scale spark bubbles close to different boundaries [J]. Physics of Fluids, 2017, 29(9): 092107.Google Scholar
  136. [136]
    Buogo S. Vokurka K. Intensity of oscillation of sparkgenerated bubbles [J]. Journal of Sound and Vibration, 2010, 329(20): 4266–4278.Google Scholar
  137. [137]
    Xu W. L., Bai L. X., Zhang F. X. Interaction of a cavitation bubble and an air bubble with a rigid boundary [J]. Journal of Hydrodynamics, 2010, 22(4): 503–512.Google Scholar
  138. [138]
    Luo J., Xu W. L., Niu Z. P. et al. Experimental study of the interaction between the spark-induced cavitation bubble and the air bubble [J]. Journal of Hydrodynamics, 2013, 25(6): 895–902.Google Scholar
  139. [139]
    Hajizadeh Aghdam A., Khoo B. C., Farhangmehr V. et al. Experimental study on the dynamics of an oscillating bubble in a vertical rigid tube [J]. Experimental Thermal and Fluid Science, 2015. 60: 299–307.Google Scholar
  140. [140]
    Cui P., Zhang A. M., Wang S. P. et al. Experimental investigation of bubble dynamics near the bilge with a circular opening [J]. Applied Ocean Research, 2013, 41(6): 65–75.Google Scholar
  141. [141]
    Ma X. J., Huang B. A., Zhao X. et al. Comparisons of spark-charge bubble dynamics near the elastic and rigid boundaries [J]. Ultrasonics Sonochemistry, 2018, 43: 80–90.Google Scholar
  142. [142]
    Lauterborn W., Kurz T. Physics of bubble oscillations [J]. Reports on Progress in Physics, 2010, 73: 106501.Google Scholar
  143. [143]
    Lauterborn W., Vogel A. Shock wave emission by laser generated bubbles (Delale C. F. Bubble dynamics and shock waves) [M]. Berlin Heidelberg: Springer, 2013, 67–103.Google Scholar
  144. [144]
    Lindau O., Lauterborn W. Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall [J]. Journal of Fluid Mechanics, 2003, 479: 327–348.zbMATHGoogle Scholar
  145. [145]
    Bhaga D., Weber M. E. Bubbles in viscous liquids: Shapes, wakes and velocities [J]. Journal of Fluid Mechanics, 2006, 105: 61–85.Google Scholar
  146. [146]
    Fernandez Rivas D., Stricker L., Zijlstra A. G. et al. Ultrasound artificially nucleated bubbles and their sonochemical radical production [J]. Ultrasonics Sonochemistry, 2013, 20(1): 510–524.Google Scholar
  147. [147]
    Biesheuvel A., Heijst G. F. V. In fascination of fluid dynamics [M]. Rotterdam, The Netherlands: Springer, 1998.Google Scholar
  148. [148]
    Walters J. K., Davidson J. F. The initial motion of a gas bubble formed in an inviscid liquid. Part 2. The three-dimensional bubble and the toroidal bubble [J]. Journal of Fluid Mechanics, 1963, 17(3): 321–336.zbMATHGoogle Scholar
  149. [149]
    Deike L., Ghabache E., Ligerbelair G. et al. Dynamics of jets produced by bursting bubbles [J]. Physical Review Fluids, 2018, 3: 013603.Google Scholar
  150. [150]
    Shew W. L., Pinton J. F. Dynamical model of bubble path instability [J]. Physical Review Letters, 2006, 97(14): 144508.Google Scholar
  151. [151]
    Wu W. B., Liu Y. L., Zhang A. M. Numerical investigation of 3D bubble growth and detachment [J]. Ocean Engineering, 2017, 138: 86–104.Google Scholar
  152. [152]
    Zenit R., Magnaudet J. Path instability of rising spheroidal air bubbles: A shape-controlled process [J]. Physics of Fluids, 2008, 20(6): 061702.zbMATHGoogle Scholar
  153. [153]
    Sanada T., Sato A., Shirota M. et al. Motion and coalescence of a pair of bubbles rising side by side [J]. Chemical Engineering Science, 2009, 64(11): 2659–2671.Google Scholar
  154. [154]
    Takemura F. Yabe A. Rising speed and dissolution rate of a carbon dioxide bubble in slightly contaminated water [J]. Journal of Fluid Mechanics, 1999, 378: 319–334.Google Scholar
  155. [155]
    Maxworthy T. Bubble rise under an inclined plate [J]. Journal of Fluid Mechanics, 2006, 229: 659–674.Google Scholar
  156. [156]
    de Vries A. W. G., Biesheuvel A., van Wijngaarden L. Notes on the path and wake of a gas bubble rising in pure water [J]. International Journal of Multiphase Flow, 2002, 28(11): 1823–1835.zbMATHGoogle Scholar
  157. [157]
    Maxworthy T. A note on the existence of wakes behind large, rising bubbles [J]. Journal of Fluid Mechanics, 2006, 27(2): 367–368.Google Scholar
  158. [158]
    Miksis M. J., Vanden-Broeck J. M., Keller J. B. Rising bubbles [J]. Journal of Fluid Mechanics, 2006, 123: 31–41.MathSciNetzbMATHGoogle Scholar
  159. [159]
    Li S., Sun L. Q., Zhang A. M. Dynamic behavior of rising bubble [J]. Acta Physica Sinica, 2014, 63(18): 291–303.Google Scholar
  160. [160]
    Albert C., Kromer J., Robertson A. M. et al. Dynamic behaviour of buoyant high viscosity droplets rising in a quiescent liquid [J]. Journal of Fluid Mechanics, 2015, 778: 485–533.MathSciNetzbMATHGoogle Scholar
  161. [161]
    Hallez Y., Legendre D. Interaction between two spherical bubbles rising in a viscous liquid [J]. Journal of Fluid Mechanics, 2011, 673: 406–431.MathSciNetzbMATHGoogle Scholar
  162. [162]
    Aktas B., Atlar M., Turkmen S. et al. Systematic cavitation tunnel tests of a propeller in uniform and inclined flow conditions as part of a round robin test campaign [J]. Ocean Engineering, 2016, 120: 136–151.Google Scholar
  163. [163]
    Duttweiler M. E., Brennen C. E. Surge instability on a cavitating propeller [J]. Journal of Fluid Mechanics, 2002, 458: 133–152.zbMATHGoogle Scholar
  164. [164]
    Zhang L. X., Zhang N., Peng X. X. et al. A review of studies of mechanism and prediction of tip vortex cavitation inception [J]. Journal of Hydrodynamics, 2015, 27(4): 488–495.Google Scholar
  165. [165]
    Chen L. Y., Zhang L. X., Shao X. M. The motion of small bubble in the ideal vortex flow [J]. Procedia Engineering, 2015, 126: 228–231.Google Scholar
  166. [166]
    Dular M., Stoffel B., Širok B. Development of a cavitation erosion model [J]. Wear, 2006, 261(5): 642–655.Google Scholar
  167. [167]
    Greeley D. S., Kerwin J. E. Numerical methods for propeller design and analysis in steady flow [J]. Transactions-Society of Naval Architects and Marine Engineers, 1982, 90: 415–453.Google Scholar
  168. [168]
    Zeng Z. B., Kuiper G. Blade section design of marine propellers with maximum cavitation inception speed [J]. Journal of Hydrodynamics, 2012, 24(1): 65–75.Google Scholar
  169. [169]
    Ye J. M., Xiong Y. Prediction of podded propeller cavitation using an unsteady surface panel method [J]. Journal of Hydrodynamics, 2008, 20(6): 790–796.Google Scholar
  170. [170]
    Baltazar J., Falcao de Campos J. A. C. An iteratively coupled solution of the cavitating flow on marine propellers using BEM [J]. Journal of Hydrodynamics, 2010, 22(5): 838–843.Google Scholar
  171. [171]
    Yari E., Ghassemi H. Numerical analysis of sheet cavitation on marine propellers, considering the effect of cross flow [J]. International Journal of Naval Architecture and Ocean Engineering, 2013, 5(4): 546–558.Google Scholar
  172. [172]
    Ji B., Long Y., Long X. P. et al. Large eddy simulation of turbulent attached cavitating flow with special emphasis on large scale structures of the hydrofoil wake and turbulence-cavitation interactions [J]. Journal of Hydrodynamics, 2017, 29(1): 27–39.Google Scholar
  173. [173]
    Huang B., Wang G. Y., Zhao Y. Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model [J]. Journal of Hydrodynamics, 2014, 26(1): 26–36.Google Scholar
  174. [174]
    Zhang Y. N., Qiu X., Chen F. P. et al. A selected review of vortex identification methods with applications [J]. Journal of Hydrodynamics, 2018, 30(5): 767–779.Google Scholar
  175. [175]
    Carnelli D., Karimi A., Franc J. P. Application of spherical nanoindentation to determine the pressure of cavitation impacts from pitting tests [J]. Journal of Materials Research, 2011, 27(1): 91–99.Google Scholar
  176. [176]
    Foeth E. J., Doorne C. W. H. V., Terwisga T. V. et al. Time resolved PIV and flow visualization of 3D sheet cavitation [J]. Experiments in Fluids, 2006, 40(4): 503–513.Google Scholar
  177. [177]
    Chow Y. C. Experimental investigation and numerical prediction of cavitation incurred on propeller surfaces [J]. Journal of Hydrodynamics, 2010, 22(5): 764–769.Google Scholar
  178. [178]
    Asnaghi A., Svennberg U., Bensow R. E. Numerical and experimental analysis of cavitation inception behaviour for high-skewed low-noise propellers [J]. Applied Ocean Research, 2018, 79: 197–214.Google Scholar
  179. [179]
    Aktas B., Atlar M., Turkmen S. et al. Propeller cavitation noise investigations of a research vessel using medium size cavitation tunnel tests and full-scale trials [J]. Ocean Engineering, 2016, 120: 122–135.Google Scholar
  180. [180]
    Faltinsen O. M. Hydrodynamics of marine and offshore structures [J]. Journal of Hydrodynamics, 2015, 26(6): 835–847.Google Scholar
  181. [181]
    Wu G. X. Numerical simulation of water entry of twin wedges [J]. Journal of Fluids and Structures, 2006, 22(1): 99–108.Google Scholar
  182. [182]
    Korobkin A. A., Pukhnachov V. V. Initial stage of water impact [J]. Annual Review of Fluid Mechanics, 1988, 20(1): 159–185.Google Scholar
  183. [183]
    de Graaf K. L., Brandner P. A., Pearce B. W. Spectral content of cloud cavitation about a sphere [J]. Journal of Fluid Mechanics, 2016, 812: R1.MathSciNetzbMATHGoogle Scholar
  184. [184]
    Wan C. R., Liu H. Shedding frequency of sheet cavitation around axisymmetric body at small angles of attack [J]. Journal of Hydrodynamics, 2017, 29(3): 520–523.Google Scholar
  185. [185]
    Truscott T. T., Epps B. P., Belden J. Water entry of projectiles [J]. Annual Review of Fluid Mechanics, 2014, 46(1): 355–378.MathSciNetzbMATHGoogle Scholar
  186. [186]
    Truscott T. T., Techet A. H. A spin on cavity formation during water entry of hydrophobic and hydrophilic spheres [J]. Physics of Fluids, 2009, 21(12): 121703.zbMATHGoogle Scholar
  187. [187]
    Jiang Y., Bai T., Gao Y. et al. Water entry of a constraint posture body under different entry angles and ventilation rates [J]. Ocean Engineering, 2018, 153: 53–59.Google Scholar
  188. [188]
    Lee M., Longoria R. G., Wilson D. E. Cavity dynamics in high-speed water entry [J]. Physics of Fluids, 1997, 9(3): 540–550.MathSciNetzbMATHGoogle Scholar
  189. [189]
    Paryshev E. V. Approximate mathematical models in high-speed hydrodynamics [J]. Journal of Engineering Mathematics, 2006, 55(1): 41–64.MathSciNetzbMATHGoogle Scholar
  190. [190]
    Wang J., Faltinsen O. M. Improved numerical solution of Dobrovol’skaya’s boundary integral equations on similarity flow for uniform symmetrical entry of wedges [J]. Applied Ocean Research, 2017, 66: 23–31.Google Scholar
  191. [191]
    Sun P., Zhang A. M., Marrone S. et al. An accurate and efficient SPH modeling of the water entry of circular cylinders [J]. Applied Ocean Research, 2018, 72: 60–75.Google Scholar
  192. [192]
    Wang Y., Wu X., Huang C. et al. Unsteady characteristics of cloud cavitating flow near the free surface around an axisymmetric projectile [J]. International Journal of Multiphase Flow, 2016, 85: 48–56.Google Scholar
  193. [193]
    Abelson H. I. Pressure measurements in the water-entry cavity [J]. Journal of Fluid Mechanics, 1970, 44: 129–144.Google Scholar
  194. [194]
    Wang J., Lugni C., Faltinsen O. M. Experimental and numerical investigation of a freefall wedge vertically entering the water surface [J]. Applied Ocean Research, 2015, 51: 181–203.Google Scholar
  195. [195]
    Chen C., Yuan X., Liu X. et al. Experimental and numerical study on the oblique water-entry impact of a cavitating vehicle with a disk cavitator [J]. International Journal of Naval Architecture and Ocean Engineering, 2018, Scholar
  196. [196]
    Aristoff J. M., Bush J. W. M. Water entry of small hydrophobic spheres [J]. Journal of Fluid Mechanics, 2009, 619: 45–78.MathSciNetzbMATHGoogle Scholar
  197. [197]
    Truscott T. T., Epps B. P., Techet A. H. Unsteady forces on spheres during free-surface water entry [J]. Journal of Fluid Mechanics, 2012, 704: 173–210.zbMATHGoogle Scholar
  198. [198]
    Yan H., Liu Y., Kominiarczuk J. et al. Cavity dynamics in water entry at low Froude numbers [J]. Journal of Fluid Mechanics, 2009, 641: 441–461.zbMATHGoogle Scholar
  199. [199]
    Truscott T. T. Cavity dynamics of water entry for spheres and ballistic projectiles [D]. Doctoral Thesis, Cambridge, MA, USA: Massachusetts Institute Technology, 2009.Google Scholar
  200. [200]
    Neaves M. D., Edwards J. R. All-speed time-accurate underwater projectile calculations using a preconditioning algorithm [J]. Journal of Fluids Engineering, 2006, 128(2): 284–296.Google Scholar
  201. [201]
    Sanders W. C., Winkel E. S., Dowling D. R. et al. Bubble friction drag reduction in a high-Reynolds-number flatplate turbulent boundary layer [J]. Journal of Fluid Mechanics, 2006. 552: 353–380.zbMATHGoogle Scholar
  202. [202]
    Wu S. J., Ouyang K., Shiah S. W. Robust design of microbubble drag reduction in a channel flow using the Taguchi method [J]. Ocean Engineering, 2008, 35(8-9): 856–863.Google Scholar
  203. [203]
    Li C., Zhang A. M., Wang S. et al. Formation and coalescence of nanobubbles under controlled gas concentration and species [J]. AIP Advances, 2018, 8(1): 015104.Google Scholar
  204. [204]
    Schmidtke E., Nutzel B., Ludwig S. Risk mitigation for sea mammals–The use of air bubbles against shock waves [C]. Proceedings of the International Conference on Acoustics “NAG/DAGA 2009”, Rotterdam, The Netherlands, 2009.Google Scholar
  205. [205]
    Storey B. D., Szeri A. J. Mixture segregation within sonoluminescence bubbles [J]. Journal of Fluid Mechanics, 1999, 396: 203–221.zbMATHGoogle Scholar
  206. [206]
    Jamaluddin A. R., Ball G. J., Turangan C. K. et al. The collapse of single bubbles and approximation of the far-field acoustic emissions for cavitation induced by shock wave lithotripsy [J]. Journal of Fluid Mechanics, 2011, 677: 305–341.MathSciNetzbMATHGoogle Scholar
  207. [207]
    Liu Y. Q., Sugiyama K., Takagi S. On the interaction of two encapsulated bubbles in an ultrasound field [J]. Journal of Fluid Mechanics, 2016, 804: 58–89.MathSciNetzbMATHGoogle Scholar
  208. [208]
    Lindner J. R. Microbubbles in medical imaging: Current applications and future directions [J]. Nature Reviews Drug Discovery, 2004, 3(6): 527–532.Google Scholar
  209. [209]
    Onari H. Fisheries experiments of cultivated shells using micro-bubbles techniques [J]. Journal of Heat Transfer Society of Japan, 2001, 40(160): 2–7.Google Scholar
  210. [210]
    Shen Y., Longo M. L., Powell R. L. Stability and rheological behavior of concentrated monodisperse food emulsifier coated microbubble suspensions [J]. Journal of Colloid and Interface Science, 2008, 327(1): 204–210.Google Scholar
  211. [211]
    Park J. Application of microbubbles to hydroponics solution promotes lettuce growth [J]. Horttechnology, 2009, 19(1): 212–215.Google Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Shi-Ping Wang (王诗平)
    • 1
  • A-Man Zhang (张阿漫)
    • 1
    Email author
  • Yun-Long Liu (刘云龙)
    • 1
  • Shuai Zhang (张帅)
    • 1
  • Pu Cui (崔璞)
    • 1
  1. 1.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinChina

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