Journal of Hydrodynamics

, Volume 30, Issue 1, pp 122–130 | Cite as

3-D Lagrangian-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis

  • Huai-yu Cheng (程怀玉)
  • Xin-ping Long (龙新平)
  • Bin Ji (季斌)
  • Qi Liu (刘琪)
  • Xiao-rui Bai (白晓蕊)
Article

Abstract

In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model (FBDCM), a turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures (LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet, the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage III, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.

Keywords

Cavitation CFD Lagrangian coherent structures (LCSs) Clark-Y hydrofoil vortical flow 

References

  1. [1]
    Wang Y., Wu X., Huang C. et al. Unsteady characteristics of cloud cavitating flow near the free surface around an axisymmetric projectile [J]. International Journal of Multiphase Flow, 2016, 85: 48–56.CrossRefGoogle Scholar
  2. [2]
    Arndt R. E. A. Cavitation in vortical flows [J]. Annual Review of Fluid Mechanics, 2002, 34: 143–175.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Arndt R. E. A., Arakeri V. H., Higuchi H. Some observations of tip-vortex cavitation [J]. Journal of Fluid Mechanics, 1991, 229: 269–289.CrossRefGoogle Scholar
  4. [4]
    Wang Y., Xu C., Wu X. et al. Ventilated cloud cavitating flow around a blunt body close to the free surface [J]. Physical Review Fluids, 2017, 2(8): 084303.CrossRefGoogle Scholar
  5. [5]
    Arndt R. E. A. Cavitation in fluid machinery and hydraulic structures [J]. Annual Review of Fluid Mechanics, 1981, 13: 273–328.CrossRefGoogle Scholar
  6. [6]
    Stutz B., Reboud J. L. Experiments on unsteady cavitation [J]. Experiments in Fluids, 1997, 22(3): 191–198.CrossRefMATHGoogle Scholar
  7. [7]
    Coutier-Delgosha O., Devillers J. F., Pichon T. et al. Internal structure and dynamics of sheet cavitation [J]. Physics of Fluids, 2006, 18(1): 017103.CrossRefGoogle Scholar
  8. [8]
    Makiharju S. A., Gabillet C., Paik B. G. et al. Timeresolved two-dimensional X-ray densitometry of a twophase flow downstream of a ventilated cavity [J]. Experiments in Fluids, 2013, 54(7): 1561.CrossRefGoogle Scholar
  9. [9]
    Iyer C. O., Ceccio S. L. The influence of developed cavitation on the flow of a turbulent shear layer [J]. Physics of Fluids, 2002, 14(10): 3414–3431.CrossRefMATHGoogle Scholar
  10. [10]
    Gopalan S., Katz J. Flow structure and modeling issues in the closure region of attached cavitation [J]. Physics of Fluids, 2000, 12(4): 895–911.CrossRefMATHGoogle Scholar
  11. [11]
    Aeschlimann V., Barre S., Djeridi H. Velocity field analysis in an experimental cavitating mixing layer [J]. Physics of Fluids, 2011, 23(5): 055105.CrossRefGoogle Scholar
  12. [12]
    Ji B., Luo X., Arndt R. E. A. et al. Numerical simulation of three dimensional cavitation shedding dynamics with special emphasis on cavitation-vortex interaction [J]. Ocean Engineering, 2014, 87: 64–77.CrossRefGoogle Scholar
  13. [13]
    Long X., Cheng H., Ji B. et al. Numerical investigation of attached cavitation shedding dynamics around the Clark-Y hydrofoil with the FBDCM and an integral method [J]. Ocean Engineering, 2017, 137: 247–261.CrossRefGoogle Scholar
  14. [14]
    Dittakavi N., Chunekar A., Frankel S. Large eddy simulation of turbulent-cavitation interactions in a venturi nozzle [J]. Journal of Fluids Engineering, 2010, 132(12): 121301.CrossRefGoogle Scholar
  15. [15]
    Callenaere M., Franc J. P., Michel J. M. et al. The cavitation instability induced by the development of a re-entrant jet [J]. Journal of Fluid Mechanics, 2001, 444: 223–256.CrossRefMATHGoogle Scholar
  16. [16]
    Peng X. X., Ji B., Cao Y. T. et al. Combined experimental observation and numerical simulation of the cloud cavitation with U-type flow structures on hydrofoils [J]. International Journal of Multiphase Flow, 2016, 79: 10–22.CrossRefGoogle Scholar
  17. [17]
    Akhatov I., Lindau O., Topolnikov A. et al. Collapse and rebound of a laser-induced cavitation bubble [J]. Physics of Fluids, 2001, 13(10): 2805–2819.CrossRefMATHGoogle Scholar
  18. [18]
    Kolář V. Vortex identification: New requirements and limitations [J]. International Journal of Heat and Fluid Flow, 2007, 28(4): 638–652.CrossRefGoogle Scholar
  19. [19]
    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.CrossRefGoogle Scholar
  20. [20]
    Ji B., Luo X., Wu Y. et al. Numerical analysis of unsteady cavitating turbulent flow and shedding horseshoe vortex structure around a twisted hydrofoil [J]. International Journal of Multiphase Flow, 2013, 51(5): 33–43.CrossRefGoogle Scholar
  21. [21]
    Kubota A., Kato H., Yamaguchi H. A new modeling of cavitating flows-a numerical study of unsteady cavitation on a hydrofoil section [J]. Journal of Fluid Mechanics, 1992, 240: 59–96.CrossRefGoogle Scholar
  22. [22]
    Haller G. Lagrangian coherent structures [J]. Annual Review of Fluid Mechanics, 2015, 47: 137–162.MathSciNetCrossRefGoogle Scholar
  23. [23]
    Green M. A., Rowley C. W., Haller G. Detection of Lagrangian coherent structures in three-dimensional turbulence [J]. Journal of Fluid Mechanics, 2007, 572: 111–120.MathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    Hu C., Wang G., Chen G. et al. Three-dimensional unsteady cavitating flows around an axisymmetric body with a blunt headform [J]. Journal of Mechanical Science and Technology, 2015, 29(3): 1093–1101.CrossRefGoogle Scholar
  25. [25]
    Tseng C. C., Liu P. B. Dynamic behaviors of the turbulent cavitating flows based on the Eulerian and Lagtangian viewpoints [J]. International Journal of Heat and Mass Transfer, 2016, 102: 479–500.CrossRefGoogle Scholar
  26. [26]
    Cheng H. Y., Long X. P., Ji B. et al. Numerical investigation of unsteady cavitating turbulent flows around twisted hydrofoil from the Lagrangian viewpoint [J]. Journal of Hydrodynamics, 2016, 28(4): 709–712.CrossRefGoogle Scholar
  27. [27]
    Tang W., Chan P. W., Haller G. Lagrangian coherent structure analysis of terminal winds detected by lidar. Part I: Turbulence structures [J]. Journal of Applied Meteorology and Climatology, 2011, 50(2): 325–338.CrossRefGoogle Scholar
  28. [28]
    Dular M., Bachert R., Schaad C. Investigation of a reentrant jet reflection at an inclined cavity closure line [J]. European Journal of Mechanics B-Fluids, 2007, 26(5): 688–705.CrossRefMATHGoogle Scholar
  29. [29]
    Zhao Y., Wang G., Huang B. et al. Lagrangian investigations of vortex dynamics in time-dependent cloud cavitating flows [J]. International Journal of Heat and Mass Transfer, 2016, 93: 167–174.CrossRefGoogle Scholar
  30. [30]
    Haller G. Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence [J]. Physics of Fluids, 2001, 13(11): 3365–3385.MathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    Huang B., Wang G. Y., Zhao Y. Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model [J]. Journal of Hydrodynamics, 2014, 26(1): 26–36.CrossRefGoogle Scholar
  32. [32]
    Zwart P. J., Gerber A. G., Belamri T. A two phase flow model for predicting cavitation dynamics [C]. ICMF 2004 International Conference on Multiphase Flow, Yokohama, Japan, 2004.Google Scholar
  33. [33]
    Long Y., Long X. P., Ji B. et al. Verification and validation of URANS simulations of the turbulent cavitating flow around the hydrofoil [J]. Journal of Hydrodynamics, 2017, 29(4): 610–620.CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Huai-yu Cheng (程怀玉)
    • 1
    • 2
  • Xin-ping Long (龙新平)
    • 1
    • 2
  • Bin Ji (季斌)
    • 1
  • Qi Liu (刘琪)
    • 3
  • Xiao-rui Bai (白晓蕊)
    • 1
    • 2
  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Hubei Key Laboratory of Waterjet Theory and New TechnologySchool of Power and Mechanical EngineeringWuhanChina
  3. 3.China Ship Development and Design CenterWuhanChina

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