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Dynamics of cavitating tip vortex

Published online by Cambridge University Press:  20 July 2023

Qingqing Ye Open the ORCID record for Qingqing Ye [Opens in a new window] ,
Yuwei Wang  and
Xueming Shao
Qingqing Ye
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Yuwei Wang
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Xueming Shao*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
*
†Email address for correspondence: mecsxm@zju.edu.cn
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Abstract

The three-dimensional dynamic behaviour of a tip vortex generated by a NACA $66_2$-415 hydrofoil is investigated under wetted flow and cavitating conditions using time-resolved tomographic particle image velocimetry. Two main cavitation modes are studied, namely the breathing and double-helical modes. The time-averaged flow field consists of a system of two streamwise vortices for all three conditions. The shape of the tip vortex resembles that of the cavitation mode, instead of a circular cylinder. Multi-scale vortical structures are captured in the instantaneous flow field. The surface oscillation of the cavity contributes to the growth of Kelvin–Helmholtz instability over the tip vortex, leading to the onset of hairpin vortices. Stronger spanwise interaction between the tip vortex and flow separation of the hydrofoil is produced by cavitation, further intensifying the perturbation growth. The proper orthogonal decomposition analysis gives insight into the relationship between cavity oscillation and vortex instability. Two major types of unstable modes of the tip vortex are obtained, leading to serpentine centreline displacement and elliptical deformation motion. The selection of the dominant unstable mode is associated with cavity surface oscillation. For the wetted flow condition, the displacement mode dominates the growth of vortex perturbation, while for breathing mode cavitation, the most energetic unstable mode changes into an elliptical deformation pattern, the disturbance energy of which is negligible in the wetted flow condition. Consistency is found between the peak frequency of the deformation mode and the cavity resonance frequency, indicating the contribution of cavity oscillation to the disturbance growth and breakdown of the tip vortex.

JFM classification

Drops and Bubbles: Cavitation Vortex Flows: Vortex dynamics Vortex Flows: Vortex instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 967 , 25 July 2023 , A30
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Amini, A., Reclari, M., Sano, T., Iino, M., Dreyer, M. & Farhat, M. 2019 On the physical mechanism of tip vortex cavitation hysteresis. Exp. Fluids 60 (7), 1–15.CrossRefGoogle Scholar
Arndt, R.E.A. 2002 Cavitation in vortical flows. Annu. Rev. Fluid Mech. 34 (1), 143–175.CrossRefGoogle Scholar
Arndt, R.E.A., Arakeri, V.H. & Higuchi, H. 1991 Some observations of tip-vortex cavitation. J. Fluid Mech. 229, 269–289.CrossRefGoogle Scholar
Arndt, R.E.A. & Keller, A.P. 1992 Water quality effects on cavitation inception in a trailing vortex. Trans. ASME J. Fluids Engng. 114 (3), 430–438.CrossRefGoogle Scholar
Arndt, R., Pennings, P., Bosschers, J. & Van Terwisga, T. 2015 The singing vortex. Interface Focus 5, 1–11.CrossRefGoogle ScholarPubMed
Asnaghi, A., Svennberg, U. & Bensow, R.E. 2020 a Large eddy simulations of cavitating tip vortex flows. Ocean Engng 195, 106703.CrossRefGoogle Scholar
Asnaghi, A., Svennberg, U., Gustafsson, R. & Bensow, R.E. 2020 b Investigations of tip vortex mitigation by using roughness. Phys. Fluids 32 (6), 065111.CrossRefGoogle Scholar
Atkinson, C. & Soria, J. 2009 An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp. Fluids 47 (4), 553–568.CrossRefGoogle Scholar
Batchelor, G.K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20 (4), 645–658.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Bertényi, T. & Graham, W.R. 2007 Experimental observations of the merger of co-rotating wake vortices. J. Fluid Mech. 586, 397–422.CrossRefGoogle Scholar
Bosschers, J. 2008 Analysis of inertial waves on inviscid cavitating vortices in relation to low-frequency radiated noise. In Proceedings of the Warwick Innovative Manufacturing Research Centre (WIMRC) Cavitation: Turbo-machinery and Medical Applications Forum, pp. 1–7. Warwick University.Google Scholar
Bosschers, J. 2019 Mechanisms of low-frequency broadband noise by cavitating tip-vortices on marine propellers. In Sixth International Symposium on Marine Propulsors SMP, vol. 19.Google Scholar
Caflisch, R. & Lamb, H. 1993 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Canny, J. 1986 A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8 (6), 679–698.CrossRefGoogle ScholarPubMed
Chang, N.A., Choi, J., Yakushiji, R. & Ceccio, S.L. 2012 Cavitation inception during the interaction of a pair of counter-rotating vortices. Phys. Fluids 24 (1), 014107.CrossRefGoogle Scholar
Chang, N.A., Yakushiji, R., Dowling, D.R. & Ceccio, S.L. 2007 Cavitation visualization of vorticity bridging during the merger of co-rotating line vortices. Phys. Fluids 19 (5), 058106.CrossRefGoogle Scholar
Chen, C., Wang, Z. & Gursul, I. 2018 Experiments on tip vortices interacting with downstream wings. Exp. Fluids 59 (5), 1–24.CrossRefGoogle Scholar
Cheng, H., Long, X., Ji, B., Peng, X. & Farhat, M. 2021 A new Euler–Lagrangian cavitation model for tip-vortex cavitation with the effect of non-condensable gas. Intl J. Multiphase Flow 134, 103441.CrossRefGoogle Scholar
Cheng, Z.-P., Qiu, S.-Y., Xiang, Y. & Liu, H. 2019 Quantitative features of wingtip vortex wandering based on the linear stability analysis. AIAA J. 57 (7), 2694–2709.CrossRefGoogle Scholar
Choi, J., Hsiao, C.-T., Chahine, G. & Ceccio, S. 2009 Growth, oscillation and collapse of vortex cavitation bubbles. J. Fluid Mech. 624, 255–279.CrossRefGoogle Scholar
Choi, J., Oweis, G. & Ceccio, S. 2003 Vortex-vortex interactions and cavitation inception. In Fifth International Symposium on Cavitation (CAV2003), Osaka, Japan.Google Scholar
Del Pino, C., Lopez-Alonso, J.M., Parras, L. & Fernandez-Feria, R. 2011 Dynamics of the wing-tip vortex in the near field of a NACA 0012 aerofoil. Aeronaut. J. 115 (1166), 229–239.CrossRefGoogle Scholar
Devenport, W.J., Rife, M.C., Liapis, S.I. & Follin, G.J. 1996 The structure and development of a wing-tip vortex. J. Fluid Mech. 312, 67–106.CrossRefGoogle Scholar
Dreyer, M. 2015 Mind the gap: tip leakage vortex dynamics and cavitation in axial turbines. PhD thesis, Swiss Federal Institute of Technology in Lausanne (EPFL) Lausanne, Switzerland.Google Scholar
Dreyer, M., Decaix, J., Münch-Alligné, C. & Farhat, M. 2014 Mind the gap: a new insight into the tip leakage vortex using stereo-PIV. Exp. Fluids 55 (11), 1–13.CrossRefGoogle Scholar
Duarte, C.M., et al. 2021 The soundscape of the anthropocene ocean. Science 371 (6529).CrossRefGoogle ScholarPubMed
Edstrand, A.M., Davis, T.B., Schmid, P.J., Taira, K. & Cattafesta, L.N. 2016 On the mechanism of trailing vortex wandering. J. Fluid Mech. 801, R1.CrossRefGoogle Scholar
Edstrand, A.M., Sun, Y., Schmid, P.J., Taira, K. & Cattafesta, L.N. 2018 Active attenuation of a trailing vortex inspired by a parabolized stability analysis. J. Fluid Mech. 855, R2.CrossRefGoogle Scholar
Ergin, F.G. & White, E.B. 2006 Unsteady and transitional flows behind roughness elements. AIAA J. 44 (11), 2504–2514.CrossRefGoogle Scholar
Fabre, D., Sipp, D. & Jacquin, L. 2006 Kelvin waves and the singular modes of the Lamb–Oseen vortex. J. Fluid Mech. 551, 235–274.CrossRefGoogle Scholar
Felli, M., Camussi, R. & Di Felice, F. 2011 Mechanisms of evolution of the propeller wake in the transition and far fields. J. Fluid Mech. 682, 5–53.CrossRefGoogle Scholar
Ganesh, H., Schot, J. & Ceccio, S.L. 2014 Stationary cavitation bubbles forming on a delta wing vortex. Phys. Fluids 26 (12), 127102.CrossRefGoogle Scholar
Garmann, D.J. & Visbal, M.R. 2017 a Analysis of tip vortex near-wake evolution for stationary and oscillating wings. AIAA J. 55 (8), 2686–2702.CrossRefGoogle Scholar
Garmann, D.J. & Visbal, M.R. 2017 b Investigation of the unsteady tip vortex structure on a naca0012 wing at fixed incidence. AIAA Paper 2017-1002.CrossRefGoogle Scholar
Gentile, V., Schrijer, F.F.J., Van Oudheusden, B.W. & Scarano, F. 2016 Low-frequency behavior of the turbulent axisymmetric near-wake. Phys. Fluids 28 (6), 065102.CrossRefGoogle Scholar
Gursul, I. & Wang, Z. 2018 Flow control of tip/edge vortices. AIAA J. 56 (5), 1731–1749.CrossRefGoogle Scholar
Hall, M.G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4, 195–218.CrossRefGoogle Scholar
Humble, R.A., Scarano, F. & Van Oudheusden, B.W. 2007 Unsteady flow organization of compressible planar base flows. Phys. Fluids 19 (7), 076101.CrossRefGoogle Scholar
Jahangir, S., Ghahramani, E., Neuhauser, M., Bourgeois, S., Bensow, R.E. & Poelma, C. 2021 Experimental investigation of cavitation-induced erosion around a surface-mounted bluff body. Wear 480, 203917.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Ji, B., Luo, X., Arndt, R.E.A. & Wu, Y. 2014 Numerical simulation of three dimensional cavitation shedding dynamics with special emphasis on cavitation–vortex interaction. Ocean Engng 87, 64–77.CrossRefGoogle Scholar
Kerswell, R.R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83.CrossRefGoogle Scholar
Lacaze, L., Ryan, K. & Le Dizes, S. 2007 Elliptic instability in a strained batchelor vortex. J. Fluid Mech. 577, 341–361.CrossRefGoogle Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221–246.CrossRefGoogle Scholar
Leweke, T., Le Dizes, S. & Williamson, C.H.K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 507–541.CrossRefGoogle Scholar
Leweke, T. & Williamson, C.H.K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85–119.CrossRefGoogle Scholar
Liu, Y. & Wang, B. 2019 Dynamics and surface stability of a cylindrical cavitation bubble in a rectilinear vortex. J. Fluid Mech. 865, 963–992.CrossRefGoogle Scholar
Long, Y., Long, X. & Ji, B. 2020 LES investigation of cavitating flows around a sphere with special emphasis on the cavitation–vortex interactions. Acta Mechanica Sin. 36 (6), 1238–1257.CrossRefGoogle Scholar
Lynch, K.P. & Scarano, F. 2015 An efficient and accurate approach to MTE-MART for time-resolved tomographic PIV. Exp. Fluids 56 (3), 1–16.CrossRefGoogle Scholar
Ma, B.-F., Wang, Z. & Gursul, I. 2017 Symmetry breaking and instabilities of conical vortex pairs over slender delta wings. J. Fluid Mech. 832, 41–72.CrossRefGoogle Scholar
Maines, B. & Arndt, R.E.A. 1997 a The case of the singing vortex. Trans. ASME J. Fluids Engng. 119 (2), 271–276.CrossRefGoogle Scholar
Maines, B.H. & Arndt, R.E.A. 1997 b Tip vortex formation and cavitation. Trans. ASME J. Fluids Engng. 119 (2), 413–419.CrossRefGoogle Scholar
Moore, D.W. & Saffman, P.G. 1973 Axial flow in laminar trailing vortices. Proc. R. Soc. Lond. A 333 (1595), 491–508.Google Scholar
Moore, D.W. & Saffman, P.G. 1975 The instability of a straight vortex filament in a strain field. Proc. R. Soc. Lond. A 346 (1646), 413–425.Google Scholar
Novara, M., Batenburg, K.J. & Scarano, F. 2010 Motion tracking-enhanced mart for tomographic PIV. Meas. Sci. Technol. 21 (3), 035401.CrossRefGoogle Scholar
Park, I., Kim, J., Paik, B. & Seol, H. 2021 Numerical study on tip vortex cavitation inception on a foil. Appl. Sci. 11 (16), 7332.CrossRefGoogle Scholar
Peng, X., Wang, B., Li, H., Xu, L. & Song, M. 2017 a Generation of abnormal acoustic noise: singing of a cavitating tip vortex. Phys. Rev. Fluids 2 (5), 053602.CrossRefGoogle Scholar
Peng, X.-X., Xu, L.-H., Liu, Y.-W., Zhang, G.-P., Cao, Y.-T., Hong, F.-W. & Yan, K. 2017 b Experimental measurement of tip vortex flow field with/without cavitation in an elliptic hydrofoil. J. Hydrodyn. 29 (6), 939–953.CrossRefGoogle Scholar
Pennings, P.C., Bosschers, J., Westerweel, J. & Van Terwisga, T.J.C. 2015 a Dynamics of isolated vortex cavitation. J. Fluid Mech. 778, 288–313.CrossRefGoogle Scholar
Pennings, P.C., Westerweel, J. & Van Terwisga, T.J.C. 2015 b Flow field measurement around vortex cavitation. Exp. Fluids 56 (11), 1–13.CrossRefGoogle Scholar
Phillips, W.R.C. 1981 The turbulent trailing vortex during roll-up. J. Fluid Mech. 105, 451–467.CrossRefGoogle Scholar
Qiu, S., Cheng, Z., Xu, H., Xiang, Y. & Liu, H. 2021 On the characteristics and mechanism of perturbation modes with asymptotic growth in trailing vortices. J. Fluid Mech. 918, A41.CrossRefGoogle Scholar
Ragab, S. & Sreedhar, M. 1995 Numerical simulation of vortices with axial velocity deficits. Phys. Fluids 7 (3), 549–558.CrossRefGoogle Scholar
Rood, E.P. 1991 Mechanisms of cavitation inception. Trans. ASME J. Fluids Engng. 113 (2), 163–175.CrossRefGoogle Scholar
Roy, C., Leweke, T., Thompson, M.C. & Hourigan, K. 2011 Experiments on the elliptic instability in vortex pairs with axial core flow. J. Fluid Mech. 677, 383–416.CrossRefGoogle Scholar
Saffman, P.G. 1995 Vortex Dynamics. Cambridge University Press.Google Scholar
Sciacchitano, A. & Wieneke, B. 2016 PIV uncertainty propagation. Meas. Sci. Technol. 27 (8), 084006.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45 (3), 561–571.CrossRefGoogle Scholar
Smith, T.A. & Ventikos, Y. 2021 Wing-tip vortex dynamics at moderate Reynolds numbers. Phys. Fluids 33 (3), 035111.CrossRefGoogle Scholar
Stinebring, D.R., Farrell, K.J. & Billet, M.L. 1991 The structure of a three-dimensional tip vortex at high Reynolds numbers. Trans. ASME J. Fluids Engng. 113 (3), 496–503.CrossRefGoogle Scholar
Taira, K. & Colonius, T.I.M. 2009 Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. J. Fluid Mech. 623, 187–207.CrossRefGoogle Scholar
Thomson, W. 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 443–456.CrossRefGoogle Scholar
Tsai, C.-Y. & Widnall, S.E. 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73 (4), 721–733.CrossRefGoogle Scholar
Van Oudheusden, B.W., Scarano, F., Van Hinsberg, N.P. & Watt, D.W. 2005 Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence. Exp. Fluids 39 (1), 86–98.CrossRefGoogle Scholar
Widnall, S.E., Bliss, D.B. & Tsai, C.-Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66 (1), 35–47.CrossRefGoogle Scholar
Wieneke, B. 2008 Volume self-calibration for 3d particle image velocimetry. Exp. Fluids 45 (4), 549–556.CrossRefGoogle Scholar
Xie, C., Liu, J., Jiang, J.-W. & Huang, W.-X. 2021 Numerical study on wetted and cavitating tip-vortical flows around an elliptical hydrofoil: interplay of cavitation, vortices, and turbulence. Phys. Fluids 33 (9), 093316.CrossRefGoogle Scholar
Ye, Q., Schrijer, F.F.J. & Scarano, F. 2016 Boundary layer transition mechanisms behind a micro-ramp. J. Fluid Mech. 793, 132–161.CrossRefGoogle Scholar
Ye, Q., Schrijer, F.F.J. & Scarano, F. 2018 On Reynolds number dependence of micro-ramp-induced transition. J. Fluid Mech. 837, 597–626.CrossRefGoogle Scholar
Zhang, M., Feng, F., Wang, M., Guo, Z., Kang, Z. & Huang, B. 2022 Investigation of hysteresis effect of cavitating flow over a pitching Clark-Y hydrofoil. Acta Mechanica Sin. 38 (6), 321382.CrossRefGoogle Scholar
Zhang, K., Hayostek, S., Amitay, M., He, W., Theofilis, V. & Taira, K. 2020 On the formation of three-dimensional separated flows over wings under tip effects. J. Fluid Mech. 895, A9.CrossRefGoogle Scholar
Zhang, L.-X., Zhang, N., Peng, X.-X., Wang, B.-L. & Shao, X.-M. 2015 A review of studies of mechanism and prediction of tip vortex cavitation inception. J. Hydrodyn. 27 (4), 488–495.CrossRefGoogle Scholar
Zhao, Y., Wang, G. & Huang, B. 2015 A cavitation model for computations of unsteady cavitating flows. Acta Mechanica Sin. 32 (2), 273–283.CrossRefGoogle Scholar

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