Advertisement

Applied Mathematics and Mechanics

, Volume 33, Issue 6, pp 701–716 | Cite as

Numerical simulation of trajectory and deformation of bubble in tip vortex

  • Bao-yu Ni (倪宝玉)
  • A-man Zhang (张阿漫)Email author
  • Xiong-liang Yao (姚熊亮)
  • Bin Wang (汪 斌)
Article

Abstract

According to the behaviors of a bubble in the ship wake flow, the numerical simulation is divided into two stages, quasi-spherical motion and non-spherical motion, based on whether the bubble is captured by the vortex or not. The one-way coupled particle tracking method (PTM) and the boundary element method (BEM) are adopted to simulate these two stages, respectively. Meanwhile, the initial condition of the second stage is taken as the output of the first one, and the entire simulation is connected and completed. Based on the numerical results and the published experimental data, the cavitation inception is studied, and the wake bubble is tracked. Besides, the split of the bubble captured by the vortex and the following sub-bubbles are simulated, including motion, deformation, and collapse. The results provide some insights into the control on wake bubbles and optimization of the wake flow.

Key words

wake bubble tip vortex split reverse jet 

Chinese Library Classification

O351.2 

2010 Mathematics Subject Classification

76B07 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Carrica, M., Bonetto, F., Drew, D. A., and Lahey, R. T. A polydisperse model for bubbly two-phase flow around a surface ship. International Journal of Multiphase Flow, 25, 257–305 (1999)zbMATHCrossRefGoogle Scholar
  2. [2]
    Hsiao, C. T. and Pauley, L. L. Numerical computation of the tip vortex flow generated by a marine propeller. Journal of Fluids Engineering, 121(3), 638–645 (1999)CrossRefGoogle Scholar
  3. [3]
    Johnson, V. E. and Hsieh, T. The influence of the trajectories of gas nuclei on cavitation inception. Sixth Symposium on Naval Hydrodynamics, 163–179 (1966)Google Scholar
  4. [4]
    Hsiao, C. T. and Pauley, L. L. Study of tip vortex cavitation inception using Navier-Stokes computation and bubble dynamics model. Journal of Fluids Engineering, 121, 198–204 (1999)CrossRefGoogle Scholar
  5. [5]
    Hsiao, C. T. and Chahine, G. L. Scaling effect on prediction of cavitation inception in a line vortex flow. Journal of Fluid Engineering, 125, 53–60 (2003)CrossRefGoogle Scholar
  6. [6]
    Hsiao, C. T. and Chahine, G. L. Prediction of tip vortex cavitation inception using coupled spherical and nonspherical bubble models and Navier-Stokes computations. Journal of Marine Science Technology, 8, 99–108 (2004)CrossRefGoogle Scholar
  7. [7]
    Hsiao, C. T., Jain, A., and Chahine, G. L. Effect of gas diffusion on bubble entrainment and dynamics around a propeller. 26th Symposium on Naval Hydrodynamics, September, Rome, 17–22 (2006)Google Scholar
  8. [8]
    Rebow, M., Choi, J., Choi, J. K., Chahine, G. L., and Ceccio, S. L. Experimental validation of BEM code analysis of bubble splitting in a tip vortex flow. 11th International Symposium on Flow Visualization, August, Indiana, 9–12 (2004)Google Scholar
  9. [9]
    Oweis, G. F., Choi, J., and Ceccio, S. L. Dynamics and noise emission of laser induced cavitation bubbles in a vortical flow field. Acoustical Society of America, 115(3), 1049–1058 (2004)CrossRefGoogle Scholar
  10. [10]
    Choi, J., Hsiao, C. T., Chahine, G. L., and Ceccio, S. L. Growth, oscillation and collapse of vortex cavitation bubbles. Journal of Fluid Mechanics, 624, 255–279 (2009)zbMATHCrossRefGoogle Scholar
  11. [11]
    Saffman, P. G. Vortex Dynamics, Cambridge University Press, Cambridge (1992)zbMATHGoogle Scholar
  12. [12]
    Park, K., Seol, H., Choi, W., and Lee, S. Numerical prediction of tip vortex cavitation behavior and noise considering nuclei size and distribution. Applied Acoustics, 70, 674–680 (2009)CrossRefGoogle Scholar
  13. [13]
    Rayleigh, J. W. On the pressure developed in a liquid during the collapse of a spherical cavity. Philosophy Magazine, 34, 94–98 (1917)zbMATHCrossRefGoogle Scholar
  14. [14]
    Plesset, M. S. and Chapman, R. B. Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary. Journal of Fluid Mechanics, 47, 283–290 (1971)CrossRefGoogle Scholar
  15. [15]
    Cole, R. H. Underwater Explosion, Princeton University Press, Princeton (1948)Google Scholar
  16. [16]
    Gilmore, F. R. The growth and collapse of a spherical bubble in a viscous compressible liquid. Hydro Lab California Institute Technical Report, 26(4), 117–125 (1952)Google Scholar
  17. [17]
    Maxey, M. R. and Riley, J. J. Equation of motion for a small rigid sphere in a nonuniform flow. Physics of Fluids, 26(4), 883–889 (1983)zbMATHCrossRefGoogle Scholar
  18. [18]
    Haberman, W. L. and Morton, R. K. An Experimental Investigation of the Drag and Shape of Air Bubbles Rising in Various Liquids, David Taylor Model Basin Report, 802, Washington (1953)Google Scholar
  19. [19]
    Oweis, G. F., Hout, I. E., Iyer, C., Tryggvason, G., and Ceccioa, S. L. Capture and inception of bubbles near line vortices. Physics of Fluids, 17, 1–14 (2005)CrossRefGoogle Scholar
  20. [20]
    Borse, G. J. Numerical Methods with MATLAB, PWS, Boston (1997)Google Scholar
  21. [21]
    Choi, J. K. and Chahine, G. L. Non-spherical bubble behavior in vortex flow fields. Computational Mechanics, 32(4–6), 281–290 (2002)Google Scholar
  22. [22]
    Chahine, G. L., Sarkar, K., and Duraiswami, R. Strong Bubble/Flow Interaction and Cavitation Inception, Technical Report, 94003-1ONR, Maryland (1997)Google Scholar
  23. [23]
    Best, J. P. and Kucera, A. A numerical investigation of non-spherical rebounding bubbles. Journal of Fluid Mechanics, 245, 137–154 (1992)zbMATHCrossRefGoogle Scholar
  24. [24]
    Bronshtein, I. N. and Semendyayev, K. A. Handbook of Mathematics, 3rd ed., Springer, Berlin (1997)zbMATHGoogle Scholar
  25. [25]
    Oguz, H. and Zeng, J. Axisymmetric and three-dimensional boundary integral simulations of bubble growth from an underwater orifice. Engineering Analysis with Boundary Elements, 19, 319–330 (1997)CrossRefGoogle Scholar
  26. [26]
    Klaseboer, E. and Khoo, B. C. Boundary integral equations as applied to an oscillating bubble near a fluid-fluid interface. Computational Mechanics, 33, 129–138 (2004)zbMATHCrossRefGoogle Scholar
  27. [27]
    Zhang, A. M. and Yao, X. L. The law of the underwater explosion bubble motion near free surface. Acta Physica Sinica, 57(1), 339–353 (2008)Google Scholar
  28. [28]
    Zhang, A. M., Ni, B. Y., Song, B. Y., and Yao, X. L. Numerical simulation of the bubble breakup phenomena in the narrow flow field. Applied Mathematics and Mechanics (English Edition), 31(4), 449–460 (2010) DOI 10.1007/s10483-010-0405-zMathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bao-yu Ni (倪宝玉)
    • 1
  • A-man Zhang (张阿漫)
    • 1
    Email author
  • Xiong-liang Yao (姚熊亮)
    • 1
  • Bin Wang (汪 斌)
    • 2
  1. 1.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinP. R. China
  2. 2.National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid PhysicsChina Academy of Engineering PhysicsMianyangSichuan Province, P. R. China

Personalised recommendations