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.
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References
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.
Arndt R. E. A. Cavitation in vortical flows [J]. Annual Review of Fluid Mechanics, 2002, 34: 143–175.
Arndt R. E. A., Arakeri V. H., Higuchi H. Some observations of tip-vortex cavitation [J]. Journal of Fluid Mechanics, 1991, 229: 269–289.
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.
Arndt R. E. A. Cavitation in fluid machinery and hydraulic structures [J]. Annual Review of Fluid Mechanics, 1981, 13: 273–328.
Stutz B., Reboud J. L. Experiments on unsteady cavitation [J]. Experiments in Fluids, 1997, 22(3): 191–198.
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.
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.
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.
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.
Aeschlimann V., Barre S., Djeridi H. Velocity field analysis in an experimental cavitating mixing layer [J]. Physics of Fluids, 2011, 23(5): 055105.
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.
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.
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.
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.
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.
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.
Kolář V. Vortex identification: New requirements and limitations [J]. International Journal of Heat and Fluid Flow, 2007, 28(4): 638–652.
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.
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.
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.
Haller G. Lagrangian coherent structures [J]. Annual Review of Fluid Mechanics, 2015, 47: 137–162.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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Project supported by the National Natural Science Foundation of China (Project Nos. 11772239, 51576143 and 91752105), the Outstanding Youth Foundation of Natural Science Foundation of Hubei Province (Grant No. 2017CFA048).
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Cheng, Hy., Long, Xp., Ji, B. et al. 3-D Lagrangian-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis. J Hydrodyn 30, 122–130 (2018). https://doi.org/10.1007/s42241-018-0013-x
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DOI: https://doi.org/10.1007/s42241-018-0013-x