Skip to main content
Log in

Acoustic radiation induced by bubble motion in compressible fluid

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Based on the theory of compressible fluid, a three-dimension boundary element method is utilized to research the motion of bubble. The far-field noise radiation during the growth and contraction is calculated by the Kirchhoff formula and the Ffowcs Williams-Hawkings (FW-H) formula with a fixed radiation surface being arranged at the near-field of bubble as a new acoustic source. The results show that the amplitude of the sound pressure induced by non-spherical bubble is lower than that of spherical bubble in the contraction phase. The retardance effect is more obvious when the observer is farther away from the bubble. In the anaphase of contraction, the observer with the maximum amplitude of sound pressure moves up with the obvious jet. Larger buoyance parameters will generate lower sound pressure amplitudes in the anaphase, while larger intensive parameters will cause higher sound pressure amplitudes in the whole procedure of bubble motion.

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. Blake, J. R. and Gibson, D. C. Cavitation bubbles near boundaries. Annual Review of Fluid Mechanics, 19, 99–123 (1987)

    Article  Google Scholar 

  2. Zhang, A. M., Yang, W. S., Huang, C., and Ming, F. R. Numerical simulation of column charge underwater explosion based on SPH and BEM combination. Computers and Fluids, 71, 169–178 (2013)

    Article  MathSciNet  Google Scholar 

  3. Zhang, A. M., Zeng, L. Y., Wang, S. P., Yang, S. T., Yao, X. L., and Wen, X. Y. Study on fusion dynamics of underwater explosion bubbles. Applied Mathematics and Mechanics (English Edition), 31(2), 163–170 (2010) DOI 10.1007/s10483-010-0205-z

    MathSciNet  Google Scholar 

  4. Li, Y. B., Wu, X. Y., Ma, Y., and Wang, J. G. A method based on potential theory for calculating air cavity formation of an air cavity resistance reduction ship. Journal of Marine Science Application, 7, 98–101 (2008)

    Article  Google Scholar 

  5. 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)

    Article  MATH  Google Scholar 

  6. Ni, B. Y., Zhang, A. M., Yao, X. L., and Wang, B. Numerical simulation of trajectory and deformation of bubble in tip vortex. Applied Mathematics and Mechanics (English Edition), 33(6), 1–16 (2012) DOI 10.1007/s10483-012-1581-9

    Article  MathSciNet  Google Scholar 

  7. Qi, D. M. The Study of Bubble Collapse and Cavitation Noise (in Chinese), Ph. D. dissertation, Shanghai Jiao Tong University, 1–8 (1999)

    Google Scholar 

  8. Prosperetti, A. and Lezzi, A. Bubble dynamics in a compressible liquid, part I-first-order theory. Journal of Fluid Mechanics, 168, 457–478 (1986)

    Article  MATH  Google Scholar 

  9. Prosperetti, A. and Lezzi, A. Bubble dynamics in a compressible liquid, part II-second-order theory. Journal of Fluid Mechanics, 185, 289–321 (1986)

    Google Scholar 

  10. Wang, S. P. Study on Dynamics of Underwater Explosion Bubbles near Structures (in Chinese), Ph. D. dissertation, Harbin Engineering University, 31–33 (2011)

    Google Scholar 

  11. Wang, Q. X. and Blake, J. R. Non-spherical bubble dynamics in a compressible liquid, part 1-travelling acoustic wave. Journal of Fluid Mechanics, 659, 191–224 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  12. Wang, Q. X. and Blake, J. R. Non-spherical bubble dynamics in a compressible liquid, part 2-acoustic standing wave. Journal of Fluid Mechanics, 679, 559–581 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. Geers, T. L. Doubly asymptotic approximation for transient motions of submerged structure. Journal of the Acoustical Society of America, 64, 1500–1508 (1978)

    Article  MATH  Google Scholar 

  14. Geers, T. L. Residucal potential and approximation methods for three dimensional fluid-structure interaction problems. Journal of the Acoustical Society of America, 49, 1505–1510 (1971)

    Article  Google Scholar 

  15. Geers, T. L. Doubly asymptotic approximations for vibration analysis of submerged structure. Journal of Acoustical Society of America, 73, 1152–1159 (1983)

    Article  Google Scholar 

  16. Zhang, A. M., Wang, S. P., and Wu, G. X. Simulation of bubble motion in a compressible liquid based on the three dimensional wave equation. Engineering Analysis with Boundary Element, 37, 1179–1188 (2013)

    Article  Google Scholar 

  17. Rose, D. Mechanices of Underwater Noise, Peninsula Publishing Ltd., New York (1987)

    Google Scholar 

  18. Huang, J. Q. Noise at inception and collapse of a cavity. Applied Mathematics and Mechanics (English Edition), 11, 773–778 (1990) DOI 10.1007/BF02015152

    Article  Google Scholar 

  19. Choi, J. K. and Georges, L. C. Non-spherical bubble behavior in vortex flow fields. International Association for Boundary Element Method, Austin, U. S.A. (2002)

    Google Scholar 

  20. Choi, J. K. and Georges, L. C. A numerical study on the bubble noise and the tip vortex cavitation inception. The 8 th International Conference on Numerical Ship Hydrodynamics, Busan, Korea (2003)

    Google Scholar 

  21. Qi, D. M. and Lu, C. J. Numerical study of cavity noise (in Chinese). Journal of Hydrodynamics, 16, 9–17 (2001)

    Google Scholar 

  22. Jamaluddin, A. R. and Ball, G. J. The collapse of single bubbles and approximation of the far-field acoustic emissions for cavitation induced by shock wave lithotripsy. Journal of Fluid Mechanics, 677, 305–341 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  23. Turangan, C. K. and Jamaluddin, A. R. Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water. Journal of Fluid Mechanics, 598, 1–25 (2008)

    Article  MATH  Google Scholar 

  24. Lyrintzis, A. S. and Mankbadi, R. R. Prediction of the far-field jet noise using Kirchhoff’s formulation. AIAA Journal, 34, 413–416 (1996)

    Article  MATH  Google Scholar 

  25. Farassat, F. Extension of Kirchhoff formula to radiation from moving surface. Journal of Sound and Vibration, 123, 451–460 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  26. Farassat, F. and Succi, G. P. The prediction of helicopter descrete frequency noise. Vertica, 7, 309–320 (1983)

    Google Scholar 

  27. Di Francescantonio, P. A new boundary integral formulation for the prediction of sound radiation. Journal of Sound and Vibration, 202, 491–509 (1997)

    Article  Google Scholar 

  28. Jeffreys, H. and Jeffreys, B. Methods of Mathematical Physics, Cambridge University Press, Cambridge (1998)

    Google Scholar 

  29. Rayleigh, J. W. On the pressure developed in a liquid during the collapse of a spherical cavity. Philosophical Magazine, 34, 94–98 (1917)

    Article  MATH  Google Scholar 

  30. Wang, B., Zhang, Y. P., and Wang, Y. P. Experimental study on bubble oscillation formed during underwater explosions (in Chinese). Explosion and Shock Wave, 28, 572–576 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A-man Zhang  (张阿漫).

Additional information

Project supported by the Key Program of the National Natural Science Foundation of China (No. 50939002), the National Defense Basic Scientific Research Program of China (No. 613157), and the Excellent Young Science Foundation of the National Natural Science Foundation of China (No. 51222904)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ye, X., Pang, Fz. & Zhang, Am. Acoustic radiation induced by bubble motion in compressible fluid. Appl. Math. Mech.-Engl. Ed. 35, 177–190 (2014). https://doi.org/10.1007/s10483-014-1782-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-014-1782-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Navigation