Skip to main content
Log in

Interaction of two spark-generated bubbles near a confined free surface

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

In this paper, the oscillation of two spark-generated bubbles placed on a vertical column in close proximity to a confined free surface is considered. The confined free surface is accorded by the top opening of different configurations. These configurations include (i) a centrally perforated horizontal flat plate (\({\theta=90^{\circ})}\), (ii) vertically placed cylinder (\({\theta=0^{\circ})}\) and (iii) nozzle (\({\theta >0^{\circ})}\). The main objective of the present work is to study the effects of key parameters such as the nozzle geometry, the locations of the energy input (i.e., initial position of the bubbles with respect to each other and relative to the free surface) on the dynamics of the two bubbles and the free surface. It was found that the lifetime of the upper bubble decreases from the vertical cylinder to the flat plate case. In addition, by reducing the inter-bubble distance, the lifetime of the upper bubble becomes longer and the repulsion between two bubbles during the expansion phase is stronger. Finally, by reducing the upper bubble-free surface distance, the repulsion between two bubbles during expansion phase increases, the tendency of the upper bubble to rebound and initiate another oscillation cycle decreases, and the amplitude of elevation of the free surface increases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Rayleigh L.: On the pressure developed in a liquid during the collapse of a spherical cavity. Philos. Mag. 34, 94–98 (1917)

    Article  MATH  Google Scholar 

  2. Benjamin T.B., Ellis A.T.: The collapse of cavitation bubbles and pressure thereby produced against solid boundary. Philos. Trans. R, Soc. Lond. A 260, 221–240 (1966)

    Article  Google Scholar 

  3. Best J.P.: The formation of toroidal bubbles upon the collapse of transient cavities. J. Fluid Mech. 251, 79–107 (1993)

    Article  MATH  Google Scholar 

  4. Plesset M.S., Chapman R.B.: Collapse of an initial spherical vapor cavity in the neighbourhood of a solid boundary. J. Fluid Mech. 47, 283–290 (1971)

    Article  Google Scholar 

  5. Plesset M.S., Prosperetti A.: Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9, 145–185 (1977)

    Article  MATH  Google Scholar 

  6. Chahine G.L.: Interaction between an oscillating bubble and a free surface. ASME I: J. Fluid Eng. 99, 709–716 (1977)

    Google Scholar 

  7. Blake J.R., Gibson D.C.: Growth and collapse of a vapour cavity near a free surface. J. Fluid Mech. 111, 123–140 (1981)

    Article  Google Scholar 

  8. Blake J.R., Taib B.B., Doherty G.: Transient cavities near boundaries, Part 1, rigid boundary. J. Fluids Mech. 170, 479–497 (1986)

    Article  MATH  Google Scholar 

  9. Blake J.R., Taib B.B., Doherty G.: Transient cavities near boundaries, Part 2, free surface. J. Fluids Mech. 181, 197–212 (1987)

    Article  Google Scholar 

  10. Dommermuth D.G., Yue D.K.P.: Numerical simulation of nonlinear axisymmetric flows with a free surface. J. Fluid Mech. 178, 195–219 (1987)

    Article  MATH  Google Scholar 

  11. Chahine, G.L., Perdue, T.O.: Simulation of the three dimensional behaviour of an unsteady large bubble near a structure. In: Proceedings of AIP conference, vol. 197, pp. 188–199 (1990)

  12. Baker G.R., Moore D.W.: The rise and distortion of a two-dimensional gas bubble in an inviscid liquid. Phys. Fluids A 1(9), 1451–1459 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wilkerson, S.A.: Boundary integral technique for explosion bubble collapse analysis. In: Proceedings of ASME energy-source technology conference and exhibition, Houston, Texas (1989)

  14. Wilkerson, S.A.: A boundary integral approach to three dimensional underwater explosion bubble dynamics. Ph.D. thesis, Johns Hopkins University, Baltimore (1990)

  15. Chahine, G.L.: Numerical modelling of dynamic behavior of bubble in nonuniform flow fields. In: ASME symposium on numerical method for multiphase flows, Toronto vol. 91, pp. 57–65 (1990)

  16. Harris P.J.: A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid. Int. J. Numer. Methods Eng. 33(9), 1813–1822 (1992)

    Article  MATH  Google Scholar 

  17. Best J.P., Kucera A.: A numerical investigation of non—spherical rebounding bubbles. J. Fluid Mech. 245, 137–154 (1992)

    Article  MATH  Google Scholar 

  18. Zhang S., Duncan J.H., Chanine G.L.: The final stage of the collapse of a cavitation bubble near a rigid wall. J. Fluid Mech. 257, 147–181 (1993)

    Article  MATH  Google Scholar 

  19. Harris P.J.: A numerical method for predicting the motion of a bubble close to a moving rigid structure. Commun. Numer. Methods Eng. 9(1), 81–86 (1993)

    Article  MATH  Google Scholar 

  20. Shervani-Tabar, M.T.: Computer study of a cavity bubble near a rigid boundary, a free surface and a compliant wall. Ph.D. thesis, University of Wollongong, Wollongong, Australia (1995)

  21. Wang Q.X., Yeo K.S., Khoo B.C., Lam K.Y.: Strong interaction between a buoyancy bubble and a free surface. J. Theor. Comput. Fluid Dyn. 8, 73–88 (1996)

    Article  MATH  Google Scholar 

  22. Wang Q.X., Yeo K.S., Khoo B.C., Lam K.Y.: Nonlinear interaction between gas bubble and free surface. J. Comput. Fluids 25(7), 607–628 (1996)

    Article  MATH  Google Scholar 

  23. Lu C.J., He Y.S., Zhu S.Q.: Transient cavity collapse in the vicinity of a flexible boundary. J. Hydrodynam 142, 1305–1310 (1996)

    Google Scholar 

  24. Blake J.R., Hooton M.C., Robinson P.B., Tong P.R.: Collapsing cavities, toroidal bubbles and jet impact. Philos. Trans. R. Soc. Lond. A 355, 537–550 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  25. Dingman, Q.I., Chuanjing, L.U.: Growth and collapse of single bubble and its noise. J. Shanghai Jiaotong Univ. 32(12), 50–54 (in Chinese) (1998)

  26. Zhang Y.L., Yeo K.S., Khoo B.C. et al.: Three-dimensional bubbles near a free surface. J. Comput. Phys. 146(1), 105–123 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  27. Wang Q.X.: The evolution of a gas bubble near an inclined wall. Theor. Comput. Fluid Dyn. 12(1), 29–51 (1998)

    Article  MATH  Google Scholar 

  28. Zhang Y.L., Yeo K.S., Khoo B.C., Wang C.: 3D jet impact and toroidal bubbles. J. Comput. Phys. 166(2), 336–360 (2001)

    Article  MATH  Google Scholar 

  29. Brujan E.A., Keen G.S., Vogel A., Blake J.R.: The final stage of the collapse of a cavitation bubble close to a rigid boundary. Phys. Fluids 14(1), 85–92 (2002)

    Article  MATH  Google Scholar 

  30. Shervani-Tabar, M.T.: Dynamics of a pulsating bubble beneath a free surface. In: Proceeding of DETC02, ASME, design engineering technical conferences and computers and information in engineering conference, Montreal, Canada, vol. 1, pp. 515–519 (2002)

  31. Wang C., Khoo B.C., Yeo K.S.: Elastic mesh technique for 3D BIM simulation with an application to underwater explosion bubbles, J. Comput. Fluids 32(9), 1195–1212 (2003)

    Article  MATH  Google Scholar 

  32. Tomita Y., Kodama T.: Interaction of laser-induced cavitation bubbles with composite surfaces. J. Appl. Phys. 94(5), 2809–2816 (2003)

    Article  Google Scholar 

  33. Harris P.J.: An investigation into the use of the boundary integral method to model the motion of a single gas or vapour bubble in a liquid. Eng. Anal. Bound. Elem. 28(4), 325–332 (2004)

    Article  MATH  Google Scholar 

  34. Wang Q.X.: Numerical simulation of violent bubble motion. Phys. Fluids 16(5), 1610–1619 (2004)

    Article  MATH  Google Scholar 

  35. Wang C., Khoo B.C.: An indirect boundary element method for three-dimensional explosion bubbles. J. Comput. Phys. 194(2), 451–480 (2004)

    Article  MATH  Google Scholar 

  36. Klaseboer E., Hung K.C., Wang C., Wang C.W., Khoo B.C., Boyce P., Debono S., Charlier H.: Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J. Fluid Mech. 537, 387–413 (2005)

    Article  MATH  Google Scholar 

  37. Klaseboer E., Khoo B.C., Hung K.C.: Dynamics of an oscillating bubble near a floating structure. J. Fluid Struct. 21(4), 395–412 (2005)

    Article  Google Scholar 

  38. Zhang A.M., Yao X.L., Yu X.B.: The dynamics of three-dimensional underwater explosion bubble. J. Sound Vib. 311(3-5), 1196–1212 (2008)

    Article  Google Scholar 

  39. Shervani-Tabar M.T., Mobadersany N., Mahmoudi S.M.S., Rezaee-Barmi A.: Velocity field and pressure distribution around a collapsing cavitation bubble during necking and splitting. J Eng. Math. 71(4), 349–366 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Ohl S.W., Klaseboer E., Khoo B.C.: The dynamics of a non-equilibrium bubble near bio-materials. Phys. Med. Biol. 54(20), 6313–6336 (2009)

    Article  Google Scholar 

  41. Gibson D.C., Blake J.R.: The growth and collapse of bubbles near deformable surfaces. Appl. Sci. Res. 38(1), 215–224 (1982)

    Article  Google Scholar 

  42. Blake J.R., Gibson D.C.: Cavitation bubbles near boundaries. Annu. Rev. Fluid Mech. 19, 99–123 (1987)

    Article  Google Scholar 

  43. Shima A., Tomita Y., Gibson D.C., Blake J. R.: The growth and collapse of cavitation bubbles near composite surfaces. J. Fluid Mech. 203, 199–214 (1989)

    Article  Google Scholar 

  44. Duncan J.H., Zhang S.: On the interaction of a collapsing cavity and a compliant wall. J. Fluid Mech. 226, 401–423 (1991)

    Article  MATH  Google Scholar 

  45. Duncan J.H., Milligan C.D., Zhang S.: On the interaction between a bubble and a submerged compliant structure. J Sound Vib. 197(1), 17–44 (1996)

    Article  Google Scholar 

  46. Shervani-Tabar, M.T.: Dynamics of a pulsating bubble near a compliant surface. In: The international conference on boundary element methods in engineering (BEM,21). Oxford University, Oxford (1999)

  47. Klaseboer E., Turangan C.K., Khoo B.C.: Dynamic behavior of a bubble near an elastic infinite interface. Int. J. Multiphase Flow 32(9), 1110–1122 (2006)

    Article  MATH  Google Scholar 

  48. Blake J.R., Robinson P.B., Shima A., Tomita Y.: Interaction of two cavitation bubbles with a rigid boundary. J. Fluid Mech. 255, 707–721 (1993)

    Article  Google Scholar 

  49. Tomita, Y., Kodama, T.: Some aspects of the motion of two laser produced cavitation bubbles near a free surface. In: IUTAM symposium on free surface flows. Springer, Netherlands vol. 62, pp. 303–310 (2001)

  50. Robinson P.B., Blake J.R., Kodama T., Shima A., Tomita Y.: Interaction of cavitation bubbles with a free surface. J. Appl. Phys. 89(1), 8225–8237 (2001)

    Article  Google Scholar 

  51. Pearson A., Cox E., Blake J.R., Otto S.R.: Bubble interactions near a free surface. Eng. Anal. Bound. Elem. 28(4), 295–313 (2004)

    Article  MATH  Google Scholar 

  52. Zhang Z., Zhang H.: Surface tension effects on the behavior of two cavities near a rigid wall. Phys. Rev. E. 71(6), 066302 (2005)

    Article  Google Scholar 

  53. Lind S.J.: A numerical study of the effect of viscoelasticity on cavitation and bubble dynamics, Ph.D. thesis, Department of Mathematics, Cardiff University, UK (2010)

  54. Li Z.R., Sun L., Zong Z., Dong J.: A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface. J. Acta. Mecha. Sini. 28(1), 51–65 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  55. Dadvand A., Khoo B.C., Shervani-Tabar M.T.: A collapsing bubble induced microinjector: an experimental study. Exp. Fluids 46(3), 419–434 (2009)

    Article  MATH  Google Scholar 

  56. Dadvand A., Shervani-Tabar M.T., Khoo B.C.: A note on spark bubble drop-on-demand droplet generation: simulation and experiment. Int. J. Adv. Manuf. Technol. 56(1–4), 245–259 (2011)

    Article  Google Scholar 

  57. Saleki-Haselghoubi N., Shervani-Tabar M.T., Taeibi-Rahni M., Dadvand A.: Numerical study on the oscillation of a transient bubble near a confined free surface for droplet generation. Theor. Comput. Fluid Dyn. 28(4), 449–472 (2014)

    Article  Google Scholar 

  58. Paris F., Canas J.: Boundary element method fundamentals and applications. Oxford University Press, Oxford (1997)

    MATH  Google Scholar 

  59. Taib, B.B.: Boundary integral methods applied to cavitation bubble dynamics. Ph.D. thesis, University of Wollongong, NSW, Australia (1985)

  60. Hastings C.: Approximations for digital computers. Princeton University Press, Princeton (1955)

    Book  MATH  Google Scholar 

  61. Abramowitz M., Stegun I.A.: Handbook of mathematical functions. Dover, New York (1965)

    MATH  Google Scholar 

  62. Shervani-Tabar M.T., Maghsoudi K.: Numerical study on the splitting of a vapour bubble in the process of EDM. Int. J. Adv. Manuf. Technol. 38(7/8), 657–673 (2008)

    Article  Google Scholar 

  63. Shervani-Tabar M.T., Dadvand A., Khoo B.C., Nobari M.R.H.: A numerical and experimental study of a collapsing bubble-induced droplet ejector. Theor. Comput. Fluid Dyn. 23(4), 297–316 (2009)

    Article  MATH  Google Scholar 

  64. Longuet-Higgins M.S., Cokelet E.D.: The deformation of steep waves on water: I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  65. Best, J. P.: The dynamics of underwater explosions, Ph.D. thesis, University of Wollongong, Wollongong, Australia (1991)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Noureyeh Saleki-Haselghoubi.

Additional information

Communicated by S. Balachandar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saleki-Haselghoubi, N., Shervani-Tabar, M.T., Taeibi-Rahni, M. et al. Interaction of two spark-generated bubbles near a confined free surface. Theor. Comput. Fluid Dyn. 30, 185–209 (2016). https://doi.org/10.1007/s00162-015-0373-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-015-0373-6

Keywords

Navigation