Journal of Hydrodynamics

, Volume 30, Issue 4, pp 573–591 | Cite as

Numerical simulation of transient turbulent cavitating flows with special emphasis on shock wave dynamics considering the water/vapor compressibility

  • Chang-chang Wang (王畅畅)
  • Biao Huang (黄彪)Email author
  • Guo-yu Wang (王国玉)
  • Zhong-ping Duan (段忠平)
  • Bin Ji (季斌)


The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed at α = 6° and σ =1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages: (1) the growth of the attached cavity sheet, (2) development of re-entrant flow and attached cavity sheet breakup, (3) attached cavity sheet rolling up and cavity cloud shedding, and (4) cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.

Key words

Turbulent cavitating flows compressibility re-entrant flow shock wave cavitation instability OpenFOAM 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the Open Foundation of State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, the Graduate Technological Innovation Project of Beijing Institute of Technology (Grant No. 2017CX10017).


  1. [1]
    Wang G., Senocak I., Shyy W., et al. Dynamics of attached turbulent cavitating flows [J]. Progress in Aerospace Sciences, 2012, 37 (6): 551–581.CrossRefGoogle Scholar
  2. [2]
    Huang B., Young Y., Wang G., Shyy W. Combined experimental and computational investigation of unsteady structure of sheet/cloud cavitation [J]. Journal of Fluids Engineering, 2013, 135 (7): 071301.CrossRefGoogle Scholar
  3. [3]
    Huang B., Zhao Y., Wang G. Large eddy simulation of turbulent vortex-cavitation interactions in transient sheet/ cloud cavitating flows [J]. Computers and Fluids, 2014, 92: 113–124.CrossRefzbMATHGoogle Scholar
  4. [4]
    Huang B., Wang G., Zhao Y. Numerical simulation unsteady cloud cavitating flow with correction model [J]. Journal of Hydrodynamics, 2014, 26 (1): 26–36.CrossRefGoogle Scholar
  5. [5]
    Gopalan S., Katz J. Flow structure and modeling issues in the closure region of attached cavitation [J]. Physics and Fluids, 2000, 12 (4): 895–911.CrossRefzbMATHGoogle Scholar
  6. [6]
    Chen G., Wang G., Hu C. et al. Observations and measurements on unsteady cavitating flows using a simultaneous sampling approach [J]. Experiments in Fluids, 2015 56 (2): 1–11.CrossRefGoogle Scholar
  7. [7]
    Joseph D. D. Cavitation in a flowing liquid [J]. Physical Review E, 1995, 51 (3): 1649–1650.CrossRefGoogle Scholar
  8. [8]
    Wang G., Wu Q., Huang B. Dynamics of cavitation-structure interaction [J]. Acta Mechanica Sinica, 2017, 33 (4): 685–708.CrossRefGoogle Scholar
  9. [9]
    Wu Q., Huang B., Wang G. et al. Experimental and numerical investigation of hydroelastic response of a flexible hydrofoil in cavitating flow [J]. International Journal of Multiphase Flow, 2015, 74: 19–33.CrossRefGoogle Scholar
  10. [10]
    Reisman G. E. Dynamics, acoustics and control of cloud cavitation on hydrofoils [D]. Doctoral Thesis, Pasadena, USA: California Institute of Technology, 1997.Google Scholar
  11. [11]
    Soyama H., Kato H., Oba R. Cavitation observations of severely erosive vortex cavitation arising in a centrifugal pump [C]. Proceedings of the third IMechE International Conference on Cavitation, Cambridge, UK,1992.Google Scholar
  12. [12]
    Wang C., Huang B., Wang G. et al. Unsteady pressure fluctuation characteristics in the process of breakup and shedding of sheet/cloud cavitation [J]. International Journal of Heat and Mass Transfer, 2017, 114: 769–785.CrossRefGoogle Scholar
  13. [13]
    Zhang W., Bai X., Ma Z. et al., Compressible effect on the cavitating flow: A numerical study [J]. Journal of Hydrodynamics, 2017, 29 (6): 1089–1092.CrossRefGoogle Scholar
  14. [14]
    Wallis G. One-dimensional two-phase flow [M]. New York, USA: McGraw-Hill, 1967.Google Scholar
  15. [15]
    Brennen C. E. Cavitation and bubble dynamics [M]. Oxford, UK: Oxford University Press, 1995.Google Scholar
  16. [16]
    Shamsborhan H., Coutier-Delgosha O., Caignaert G. et al. Experimental determination of the speed of sound in cavitating flows [J]. Experiments in Fluids, 2010, 49 (6): 1359–1373.CrossRefGoogle Scholar
  17. [17]
    Prosperetti A. The equation of bubble dynamics in a compressible liquid [J]. Physics of Fluids, 1987, 30 (11): 3626–3628.CrossRefzbMATHGoogle Scholar
  18. [18]
    Prosperetti A. The speed of sound in a gas-vapor bubbly liquid [J]. Interface Focus, 2015, 5 (5): 20150024.CrossRefGoogle Scholar
  19. [19]
    Franc J. P., Michel J. M. Fundamentals of cavitation [M]. Dordrecht, The Netherlands: Kluwer Academic Publishers, 2005.Google Scholar
  20. [20]
    Noordij L., Wijngaarden L. Relaxation effects, caused by relative motion, on shock waves in gas-bubble/liquid mixtures [J]. Journal of Fluid Mechanics, 1974, 66: 115–143.CrossRefzbMATHGoogle Scholar
  21. [21]
    Mørch K. A. On the collapse of cavity cluster in flow cavitation [C]. Proceedings of the First International Conference on Cavitation and Inhomogenieties in Under-water Acoustics, Gottingen, Germany, 1979, 95–100.Google Scholar
  22. [22]
    Mørch K. A. Cavity cluster dynamics and cavitation erosion [C]. Proceedings of ASME Cavitation and Polyphase Flow Forum, Boulder, Colorado, USA, 1981.Google Scholar
  23. [23]
    Hanson I., Kedrinskii V. K., Mørch K. A. On the dynamics of cavity clusters [J]. Journal of Physics D Appled Physics, 1982, 15 (15): 1725–1734.CrossRefGoogle Scholar
  24. [24]
    Reisman G. E., Wang Y., Brennen C. E. Observations of shock waves in cloud caviatation [J]. Journal of Fluid Mechanics, 1998, 335: 255–283.CrossRefzbMATHGoogle Scholar
  25. [25]
    Leroux J. B., Astolfi J. A., Billard J. Y. An experimental study of unsteady partial cavitation [J]. Journal of Fluids Engineering, 2004, 126 (1): 94–101.CrossRefGoogle Scholar
  26. [26]
    Ganesh H., Mäkiharju S. A., Ceccio S. L. Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities [J]. Journal of Fluid Mechanics, 2016, 802: 37–78.MathSciNetCrossRefGoogle Scholar
  27. [27]
    Ganesh H., Mäkiharju S. A., Ceccio S. L. Bubbly shock propagation as s mechanism of shedding in separated cavitating flows [J]. Journal of Hydrodynamics, 2017, 29 (6): 907–916.CrossRefGoogle Scholar
  28. [28]
    Mäkiharju S. A., Ganesh H., Ceccio S. L. The dynamics of partial cavity formation shedding and influence of dissolved and injected non-dondensable gas [J]. Journal of Fluid Mechanics, 2017, 829: 420–458.CrossRefGoogle Scholar
  29. [29]
    Budich B., Schmidt S., Adams N. A. Numerical simulation and analysis of condensation shocks in cavitating flow [J]. Journal of Fluid Mechanics, 2018, 838: 759–813.MathSciNetCrossRefGoogle Scholar
  30. [30]
    Leroux J. B., Coutier-Delgosha O., Astolfi J. A. A joint experimental and numerical study of mechanisms associated to instability of partial cavitation on two-dimensional hydrofoil [J]. Physics of Fluids, 2005, 17 (5): 052101.CrossRefzbMATHGoogle Scholar
  31. [31]
    Ji B., Luo X., Arndt R. E. A. et al. Large eddy simulation and theoretical investigations of the transient cavitating vertical flow structure around a NACA66 hydrofoil [J]. International Journal of Multiphase Flow, 2015, 68: 121–134.MathSciNetCrossRefGoogle Scholar
  32. [32]
    Schnerr G. H., Sezal I. H., Schmidt S. J. Numerical investigation of three-dimensional cloud cavitation with special emphasis on collapse induced shock wave dynamics [J]. Physics of Fluids, 2008, 20 (4): 040703.CrossRefzbMATHGoogle Scholar
  33. [33]
    Venkateswaran S., Lindau J. W., Kunz R. F. et al. Computational of multiphase mixture flows with compressibility effects [J]. Journal of Computational Physics, 2002, 180 (1): 54–77.CrossRefzbMATHGoogle Scholar
  34. [34]
    Gnanaskandan A., Mahesh K. Large eddy simulation of the transition from sheet to cloud cavitation over a wedge [J]. International Journal of Multiphase Flow, 2016, 83: 86–102.MathSciNetCrossRefGoogle Scholar
  35. [35]
    Egerer A. P., Schmidt S. J., Hickel S. et al. Efficient implicit LES method for the simulation of turbulent cavitating flows [J]. Journal of Computational Physics, 2016, 316 (1): 453–469.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    Victor H., Luo X. W., Xavier E. et al. Implicit large eddy simulation of unsteady cloud cavitation around a plane-convex hydrofoil [J]. Journal of Hydrodynamics, 2015, 27 (6): 815–823.CrossRefGoogle Scholar
  37. [37]
    Core R. H. Underwater explosion [M]. Princeton, USA: Princeton University Press, 1948.Google Scholar
  38. [38]
    Semenov E., Kosterin S. Results of studying the speed of sound in moving gas-liquid systems [J]. Teploenergetika, 1964, 11 (6): 46–51.Google Scholar
  39. [39]
    Henry R. E., Grolmes M., Fauske H. K. Pressure-pulse propagation in two-phase one- and two-component mixtures [R]. Technical Report Argonne and Image Library, 1971.Google Scholar
  40. [40]
    Karplus H. B. Velocity of sound in a liquid containing gas bubbles [J]. Journal of the Acoustical Society of America, 1957, 29 (11): 1261–1262.CrossRefGoogle Scholar
  41. [41]
    Saito Y., Takami R., Nakamori I. et al. Numerical analysis of unsteady behavior of cloud cavitation around a NACA0015 foil [J]. Computational Mechanics, 2007, 40 (1): 85–96.CrossRefzbMATHGoogle Scholar
  42. [42]
    Meier G. E. A., Thompson P. A. Adiabatic waves in liquid-vapor systems [M]. Berlin Heidelberg, Germany: Springer, 1990.Google Scholar
  43. [43]
    Schmidt E., Grigull U. Properties of water and stream in SI-Units [M]. Berlin Heidelberg, Germany: Springer, 1981.Google Scholar
  44. [44]
    Decaix J., Goncalves E. Time-dependent simulation of cavitating flow with k–l turbulence models [J]. International Journal for Numerical Methods in Fluids, 2012, 68 (8): 1053–1072.MathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    Egorov Y., Menter F. R. Development and application of SST-SAS turbulence model in the DESIBER project (Peng S. H., Haase W. Advances in hybrid RANS-LES modeling. Notes on numerical fluid mechanics and multi-disciplinary design) [M]. Berlin Heidelberg, Germany: Springer, 2008, 97: 261–270.Google Scholar
  46. [46]
    Wang C., Wu Q., Huang B. et al. Numerical investigation of cavitation vortex dynamics in unsteady cavitating flow with shock wave propagation [J]. Ocean Engineering, 2018, 156: 424–434.CrossRefGoogle Scholar
  47. [47]
    Sagaut P. Large eddy simulation for incompressible flows [M]. Berlin Heidelberg, Germany: Springer, 2002.Google Scholar
  48. [48]
    Chen Y., Chen X., Li J. et al. Large eddy simulation and investigation on the flow structure of the cascading cavitation shedding regime around 3D twisted hydrofoil [J]. Ocean Engineering, 2017, 129: 1–19.CrossRefGoogle Scholar
  49. [49]
    Wang B. L., Liu Z. H., Li H. Y. et al. On the numerical simulations of vertical cavitating flows around various hydrofoils [J]. Journal of Hydrodynamics, 2017, 29 (6): 926–938.CrossRefGoogle Scholar
  50. [50]
    Eddington R. B. Investigation of supersonic phenomena in a two-phase (liquid-gas) tunnel [D]. Doctoral Thesis, Pasadena, USA: California Institute of Technology, 1967Google Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Chang-chang Wang (王畅畅)
    • 1
  • Biao Huang (黄彪)
    • 1
    Email author
  • Guo-yu Wang (王国玉)
    • 1
  • Zhong-ping Duan (段忠平)
    • 1
  • Bin Ji (季斌)
    • 2
  1. 1.School of Mechanical EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina

Personalised recommendations