Research progresses and prospects of vortex cavitation dynamics

CHENG Huaiyu; JI Bin; LONG Xinping; PENG Xiaoxing

doi:10.6052/1000-0992-23-045

Volume 54 Issue 1

Mar. 2024

Turn off MathJax

Article Contents

Article Navigation > Advances in Mechanics > 2024 > 54(1): 86-137

Cheng H Y, Ji B, Long X P, Peng X X. Research progresses and prospects of vortex cavitation dynamics. Advances in Mechanics, 2024, 54(1): 86-137 doi: 10.6052/1000-0992-23-045

Citation:

Cheng H Y, Ji B, Long X P, Peng X X. Research progresses and prospects of vortex cavitation dynamics. Advances in Mechanics, 2024, 54(1): 86-137 doi: 10.6052/1000-0992-23-045

Cheng H Y, Ji B, Long X P, Peng X X. Research progresses and prospects of vortex cavitation dynamics. Advances in Mechanics, 2024, 54(1): 86-137 doi: 10.6052/1000-0992-23-045

Citation:

Cheng H Y, Ji B, Long X P, Peng X X. Research progresses and prospects of vortex cavitation dynamics. Advances in Mechanics, 2024, 54(1): 86-137 doi: 10.6052/1000-0992-23-045

PDF( 5167 KB)

Research progresses and prospects of vortex cavitation dynamics

doi: 10.6052/1000-0992-23-045

1.
State Key Laboratory of Water Resources Engineering and Management, Wuhan University,Wuhan 430072, P.R. China
2.
National Key Lab on Ship Vibration and Noise, China Ship Scientific Research Center,Wuxi 214082, P.R. China

More Information

Corresponding author: jibin@whu.edu.cn
Received Date: 2023-11-01
Accepted Date: 2024-01-22

Available Online: 2024-01-27

Publish Date: 2024-03-24

Abstract

Abstract

Vortex cavitation, a cavitation phenomenon that occurs at the vortex center on propeller blades, often appears first on propeller prototypes. Once it occurs, it will seriously affect the acoustic stealth performance of naval vessels (the noise can increase by more than 10 dB), which limits the further increase in the critical speed of naval vessels to a great extent. Therefore, it has long been one of the key and challenging topics in the field of cavitation hydrodynamics. In this paper, the characteristics of vortex cavitating flow compared with other forms of cavitating flow are briefly introduced first, with tip vortex cavitation as the main research object. The evolution behaviors and flow mechanisms of vortex cavitation inception and development are then expounded. At the same time, the influential factors of vortex cavitation inception and development and their mechanisms are discussed in depth from the perspective of cavitation elements. In addition, the relevant research progress on several key issues, including scale effect and flow control in vortex cavitating flow, is reviewed. The internal causes of vortex cavitation scale effect and the controlling methods and ideas for vortex cavitating flow are systematically sorted. Finally, aimed at the key and tricky problems in the current research field of vortex cavitation, the experimental measurement and numerical simulation technologies used in the future research on vortex cavitating flow are summarized and outlooked.
- Cavitation,
- Vortex cavitation,
- Vortex model,
- Scale effect,
- Flow control

FullText(HTML)

References(182)

References

[1]	Abdel-Maksoud M, Hänel D, Lantermann U. 2010. Modeling and computation of cavitation in vortical flow. International Journal of Heat and Fluid Flow, 31(6): 1065-1074. doi: 10.1016/j.ijheatfluidflow.2010.05.010
[2]	Amini A, Reclari M, Sano T, Iino M, et al. 2019a. On the physical mechanism of tip vortex cavitation hysteresis. Experiments in Fluids, 60(7): 118. doi: 10.1007/s00348-019-2762-x
[3]	Amini A, Reclari M, Sano T, et al. 2019b. Suppressing tip vortex cavitation by winglets. Experiments in Fluids, 60(11): 1-15.
[4]	Amini A, Seo J, Rhee S H, et al. 2019c. Mitigating tip vortex cavitation by a flexible trailing thread. Physics of Fluids, 31(12): 127103. doi: 10.1063/1.5126376
[5]	Anderson E A, Lawton T A. 2003. Correlation between vortex strength and axial velocity in a trailing vortex. Journal of Aircraft, 40(4): 699-704. doi: 10.2514/2.3148
[6]	Arndt R. 2006. From wageningen to minnesota and back: Perspectives on cavitation research//6th International Symposium on Cavitation, Wageningen, Netherlands.
[7]	Arndt R E A. 2002. Cavitation in vortical flows. Annual Review of Fluid Mechanics, 34(1): 143-175. doi: 10.1146/annurev.fluid.34.082301.114957
[8]	Arndt R E A, Keller A P. 1992. Water quality effects on cavitation inception in a trailing vortex. Journal of Fluids Engineering, 114(3): 430-438. doi: 10.1115/1.2910049
[9]	Arroyo M P, Hinsch K D. 2008. Recent developments of PIV towards 3D measurements, in: Schroeder, A., Willert, C. E. (Eds.), Particle Image Velocimetry: New Developments and Recent Applications, pp. 127-154.
[10]	Asnaghi A, Svennberg U, Gustafsson R, et al. 2019. Propeller tip vortex cavitation mitigation using roughness// MARINE 2019: VIII Computational methods in marine engineering, Göteborg, Sweden.
[11]	Asnaghi A, Svennberg U, Gustafsson R, et al. 2020. Investigations of tip vortex mitigation by using roughness. Physics of Fluids, 32(6): 065111. doi: 10.1063/5.0009622
[12]	Aurelia V. 2013. Simulations of cavitation-from the large vapour structures to the small bubble dynamics, Faculty of Engineering. Lund University.
[13]	Bai X R, Cheng H Y, Ji B. 2022. LES Investigation of the noise characteristics of sheet and tip leakage vortex cavitating flow. International Journal of Multiphase Flow, 146: 103880. doi: 10.1016/j.ijmultiphaseflow.2021.103880
[14]	Batchelor G K. 2006. Axial flow in trailing line vortices. Journal of Fluid Mechanics, 20(4): 645-658.
[15]	Beresh S J. 2021. Time-resolved particle image velocimetry. Measurement Science and Technology, 32(10): 102003. doi: 10.1088/1361-6501/ac08c5
[16]	Betge A, Hochbaum A C, Weitendorf E A. 2021. Measurement of nuclei content by digital holography in a free surface cavitation tunnel. Ship Technology Research, 68(2): 63-69. doi: 10.1080/09377255.2020.1808759
[17]	Billet M L, Holl J W. 1981. Scale effects on various types of limited cavitation. Journal of Fluids Engineering-Transactions of the Asme, 103(3): 405-414. doi: 10.1115/1.3240800
[18]	Billet M L, Weir D S. 1975. The effect of gas diffusion on the flow coefficient for a ventilated cavity. Journal of Fluids Engineering, 97(4): 501-505. doi: 10.1115/1.3448090
[19]	Birch D, Lee T, Mokhtarian F, et al. 2003. Rollup and Near-Field Behavior of a Tip Vortex. Journal of Aircraft, 40(3): 603-607. doi: 10.2514/2.3137
[20]	Bohren C F, Huffman D R. 1998. Absorption and scattering of light by small particles. Wiley, Hoboken.
[21]	Bosschers J. 2018a. An analytical and semi-empirical model for the viscous flow around a vortex cavity. International Journal of Multiphase Flow, 105 : 122-133.
[22]	Bosschers J. 2018b. Propeller tip-vortex cavitation and its broadband noise. University of Twente, Enschede.
[23]	Boulon O, Callenaere M, Franc J P, et al. 1999. An experimental insight into the effect of confinement on tip vortex cavitation of an elliptical hydrofoil. Journal of Fluid Mechanics, 390: 1-23. doi: 10.1017/S002211209900525X
[24]	Brennen C E. 2013. Cavitating Flows. Cambridge University Press, Cambridge.
[25]	Brennen C E. 2014. Cavitation and Bubble Dynamics. Cambridge University Press.
[26]	Cellini F, Peterson S D, Porfiri M. 2017. Highly compressible fluorescent particles for pressure sensing in liquids. Applied Physics Letters, 110(22): 221904. doi: 10.1063/1.4984223
[27]	Chahine G L, Frederick G F, Bateman R D. 1993. Propeller Tip Vortex Cavitation Suppression Using Selective Polymer Injection. Journal of Fluids Engineering, 115(3): 497-503. doi: 10.1115/1.2910166
[28]	Chahine G L, Kalumuck K M. 2003. Development of a Near Real-Time Instrument for Nuclei Measurement: The ABS Acoustic Bubble Spectrometer//4th ASME JSME Joint Fluids Engineering Conference, Honolulu, Hawaii, USA, July 6-10, 2003
[29]	Chang N, Ganesh H, Yakushiji R, et al. 2011. Tip Vortex Cavitation Suppression by Active Mass Injection. Journal of Fluids Engineering, 133(11): 111301. doi: 10.1115/1.4005138
[30]	Charonko J J, King C V, Smith B L, et al. 2010. Assessment of pressure field calculations from particle image velocimetry measurements. Measurement Science and Technology, 21(10): 105401. doi: 10.1088/0957-0233/21/10/105401
[31]	Chen L Y, Zhang L X, Peng X X, et al. 2019. Influence of water quality on the tip vortex cavitation inception. Physics of Fluids, 31(2): 023303. doi: 10.1063/1.5053930
[32]	Cheng H Y, Long X P, Ji B, et al. 2021. A new Euler-Lagrangian cavitation model for tip-vortex cavitation with the effect of non-condensable gas. International Journal of Multiphase Flow, 134: 103441. doi: 10.1016/j.ijmultiphaseflow.2020.103441
[33]	Cheon J H, Lee S W. 2015. Tip leakage aerodynamics over the cavity squealer tip equipped with full coverage winglets in a turbine cascade. International Journal of Heat and Fluid Flow, 56: 60-70. doi: 10.1016/j.ijheatfluidflow.2015.07.003
[34]	Choi J, Ceccio S L. 2007. Dynamics and noise emission of vortex cavitation bubbles. Journal of Fluid Mechanics, 575: 1-26. doi: 10.1017/S0022112006003776
[35]	Choi J, Hsiao C T, Chahine G, et al. 2009. Growth, oscillation and collapse of vortex cavitation bubbles. Journal of Fluid Mechanics, 624: 255-279. doi: 10.1017/S0022112008005430
[36]	Chow J S, Zilliac G G, Bradshaw P. 1997. Mean and turbulence measurements in the near field of a wingtip vortex. Aiaa Journal, 35(10): 1561-1567. doi: 10.2514/2.1
[37]	Dai C, Fraser J S. 1995. Hydrodynamic simulation of a passive blade control for tip vortex cavitation control//PROPCAV ‘95 Conference on Propeller Cavitation, Newcastle upon Tyne, UK.
[38]	del Pino C, Parras L, Felli M, et al. 2011. Structure of trailing vortices: Comparison between particle image velocimetry measurements and theoretical models. Physics of Fluids, 23(1): 013602. doi: 10.1063/1.3537791
[39]	Devenport W J, Rife M C, Liapis S I, et al. 1996. The structure and development of a wing-tip vortex. Journal of Fluid Mechanics, 312: 67-106. doi: 10.1017/S0022112096001929
[40]	Dey D, Camci C. 2001. Aerodynamic tip desensitization of an axial turbine rotor using tip platform extensions//ASME Turbo Expo 2001: Power for Land, Sea, and Air, New Orleans, Louisiana, USA.
[41]	Dreyer M. 2015. Mind The Gap: Tip leakage vortex dynamics and cavitation in axial turbines. École polytechnique fédérale de Lausanne, Lausanne, Switzerland.
[42]	Dreyer M, Decaix J, Munch-Alligne C, et al. 2014. Mind the gap: a new insight into the tip leakage vortex using stereo-PIV. Experiments in Fluids, 55(11): 1-13.
[43]	Duncan P B, Needham D. 2004. Test of the Epstein-Plesset Model for gas microparticle dissolution in aqueous media: effect of surface tension and gas undersaturation in solution. Langmuir, 20(7): 2567-2578. doi: 10.1021/la034930i
[44]	Ebert E, Kroger W, Damaschke N, Iop. 2015. Hydrodynamic Nuclei Concentration Technique in Cavitation Research and Comparison to Phase-Doppler Measurements//9th International Symposium on Cavitation, Lausanne, Switzerland.
[45]	Epstein P S, Plesset M S. 1950. On the stability of gas bubbles in liquid-gas solutions. The Journal of Chemical Physics, 18(11): 1505-1509. doi: 10.1063/1.1747520
[46]	Fabre D, Jacquin L. 2004. Short-wave cooperative instabilities in representative aircraft vortices. Physics of Fluids, 16(5): 1366-1378. doi: 10.1063/1.1686951
[47]	Fabry E P. 1998. 3D holographic PIV with a forward-scattering laser sheet and stereoscopic analysis. Experiments in Fluids, 24(1): 39-46. doi: 10.1007/s003480050148
[48]	Foeth E J, van Doorne C W H, van Terwisga T, et al. 2006. Time resolved PIV and flow visualization of 3D sheet cavitation. Experiments in Fluids, 40(4): 503-513. doi: 10.1007/s00348-005-0082-9
[49]	Franc J P, Michel J M. 2005. Fundamentals of Cavitation. Springer Netherlands.
[50]	Fruman D H, Aflalo S S. 1989. Tip Vortex Cavitation Inhibition by Drag-Reducing Polymer Solutions. Journal of Fluids Engineering, 111(2): 211-216. doi: 10.1115/1.3243625
[51]	Fruman D H, Cerrutti P, Pichon T, et al. 1995a. Effect of Hydrofoil Planform on Tip Vortex Roll-Up and Cavitation. Journal of Fluids Engineering, 117(1): 162-169. doi: 10.1115/1.2816806
[52]	Fruman D H, Pichon T, Cerrutti P. 1995b. Effect of a drag-reducing polymer solution ejection on tip vortex cavitation. Journal of Marine Science and Technology, 1(1): 13-23. doi: 10.1007/BF01240009
[53]	Fyrillas M M, Szeri A J. 1994. Dissolution or growth of soluble spherical oscillating bubbles. Journal of Fluid Mechanics, 277: 381-407. doi: 10.1017/S0022112094002806
[54]	Gaggero S, Tani G, Viviani M, et al. 2014. A study on the numerical prediction of propellers cavitating tip vortex. Ocean Engineering, 92: 137-161. doi: 10.1016/j.oceaneng.2014.09.042
[55]	Gao H T, Zhu W C, Liu Y T, et al. 2019. Effect of various winglets on the performance of marine propeller. Applied Ocean Research, 86: 246-256. doi: 10.1016/j.apor.2019.03.006
[56]	Gao Q, Wang H P, Shen G X. 2013. Review on development of volumetric particle image velocimetry. Chinese Science Bulletin, 58(36): 4541-4556. doi: 10.1007/s11434-013-6081-y
[57]	Gates E M. 1977. The influence of free-stream turbulence free-stream nuclei populations and a drag-reducing polymer on cavitation inception on two axisymmetric bodies. California Institute of Technology, California, USA.
[58]	Gates E M, Bacon J. 1978. A Note on the Determination of Cavitation Nuclei Distributions by Holography. Journal of Ship Research, 22(01): 29-31. doi: 10.5957/jsr.1978.22.1.29
[59]	Ghahramani E, Arabnejad M H, Bensow R E. 2018. Realizability improvements to a hybrid mixture-bubble model for simulation of cavitating flows. Computers & Fluids, 174: 135-143.
[60]	Ghahramani E, Ström H, Bensow R E. 2021. Numerical simulation and analysis of multi-scale cavitating flows. Journal of Fluid Mechanics, 922: A22. doi: 10.1017/jfm.2021.424
[61]	Gindroz B, Billet M L. 1998. Influence of the Nuclei on the Cavitation Inception for Different Types of Cavitation on Ship Propellers. Journal of Fluids Engineering, 120(1): 171-178. doi: 10.1115/1.2819643
[62]	Goyal R, Gandhi B K, Cervantes M J. 2018. PIV measurements in Francis turbine – A review and application to transient operations. Renewable and Sustainable Energy Reviews, 81: 2976-2991. doi: 10.1016/j.rser.2017.06.108
[63]	Graßmann A, Peters F. 2004. Size measurement of very small spherical particles by mie scattering imaging (MSI). Particle & Particle Systems Characterization, 21(5): 379-389.
[64]	Green S I, Acosta A J. 1991. Unsteady flow in trailing vortices. Journal of Fluid Mechanics, 227: 107-134. doi: 10.1017/S0022112091000058
[65]	Guo Q, Zhou L J, Wang Z W, et al. 2018. Numerical simulation for the tip leakage vortex cavitation. Ocean Engineering, 151: 71-81. doi: 10.1016/j.oceaneng.2017.12.057
[66]	H. V G, V K, C. M W. 1991. A simpler model for concentrated vortices. Experiments in Fluids, 11: 73-76. doi: 10.1007/BF00198434
[67]	Holl J W, Arndt R E A, Billet M L. 1972. Limited cavitation and the related scale effects problem//2nd international symposium on fluid mechanics and fluidics, JSME, Tokyo, Japan.
[68]	Holl J W, Treaster A L. 1966. Cavitation hysteresis. Journal of Basic Engineering, 88(1): 199-211. doi: 10.1115/1.3645802
[69]	Hsiao C T, Chahine G. 2004. Prediction of tip vortex cavitation inception using coupled spherical and nonspherical bubble models and Navier-Stokes computations. Journal of Marine Science and Technology, 8(3): 99-108. doi: 10.1007/s00773-003-0162-6
[70]	Hsiao C T, Chahine G L. 2001. Numerical simulation of bubble dynamics in a vortex flow using Navier-Stokes computations and moving chimera grid scheme//4th International Symposium on Cavitation, Pasadena, USA.
[71]	Hsiao C T, Chahine G L. 2005. Scaling of tip vortex cavitation inception noise with a bubble dynamics model accounting for nuclei size distribution. Journal of Fluids Engineering, 127(1): 55-65. doi: 10.1115/1.1852476
[72]	Hsiao C T, Chahine G L, Liu H L. 2003. Scaling effect on prediction of cavitation inception in a line vortex flow. Journal of Fluids Engineering-Transactions of the Asme, 125(1): 53-60. doi: 10.1115/1.1521956
[73]	Hsiao C T, Pauley L L. 1999. Study of tip vortex cavitation inception using Navier-Stokes computation and bubble dynamics model. Journal of Fluids Engineering-Transactions of the Asme, 121(1): 198-204. doi: 10.1115/1.2822002
[74]	Hsu C C. 1991. Studies of scaling of tip vortex cavitation inception on marine lifting surfaces. Journal of Fluids Engineering, 113(3): 504-508. doi: 10.1115/1.2909525
[75]	Iliescu M S, Ciocan G D, F A. 2008. Analysis of the cavitating draft tube vortex in a Francis turbine using particle image velocimetry measurements in two-phase flow. J Fluids Eng, 130(2): 021105. doi: 10.1115/1.2813052
[76]	Inoue M, Kuroumaru M, Fukuhara M. 1986. Behavior of tip leakage flow behind an axial compressor rotor. Journal of Engineering for Gas Turbines and Power-Transactions of the Asme, 108(1): 7-14. doi: 10.1115/1.3239889
[77]	ITTC. 1975. Cavitation Committee Report of the 14th ITTC, Ottawa, p. Appendix 1.
[78]	Jeong S J, Hong S Y, Song J H, et al. 2021. Establishment of cavitation inception speed judgment criteria by cavitation noise analysis for underwater vehicles. Proceedings of the Institution of Mechanical Engineers. Part M:Journal of Engineering for the Maritime Environment, 235(2): 546-557.
[79]	Keller A P. 2001. Cavitation scale effects-empirically found relations and the correlation of cavitation number and hydrodynamic coefficients//4th International Symposium on Cavitation, Pasadena, USA.
[80]	Khoo M T, Venning J A, Pearce B W, et al. 2020a. Statistical aspects of tip vortex cavitation inception and desinence in a nuclei deplete flow. Experiments in Fluids, 61(6): 145. doi: 10.1007/s00348-020-02967-x
[81]	Khoo M T, Venning J A, Pearce B W, et al. 2020b. Natural nuclei population dynamics in cavitation tunnels. Experiments in Fluids, 61(2): 34. doi: 10.1007/s00348-019-2843-x
[82]	Kimura F, McCann J, Khalil G E, et al. 2010. Simultaneous velocity and pressure measurements using luminescent microspheres. Review of Scientific Instruments, 81(6): 064101. doi: 10.1063/1.3422324
[83]	Klein C, Engler R H, Henne U, et al. 2005. Application of pressure-sensitive paint for determination of the pressure field and calculation of the forces and moments of models in a wind tunnel. Experiments in Fluids, 39(2): 475-483. doi: 10.1007/s00348-005-1010-8
[84]	Kravtsova A Y, Markovich D M, Pervunin K S, et al. 2014. High-speed visualization and PIV measurements of cavitating flows around a semi-circular leading-edge flat plate and NACA0015 hydrofoil. International Journal of Multiphase Flow, 60 : 119-134.
[85]	Kuiper G. 2001. New developments around sheet and tip vortex cavitation on ships propellers//4th International Symposium on Cavitation, Pasadena, USA.
[86]	Kumar S S, Hong J. 2018. Digital fresnel reflection holography for high-resolution 3D near-wall flow measurement. Optics Express, 26(10): 12779-12789. doi: 10.1364/OE.26.012779
[87]	Kumar S S, Karn A, Arndt R E A, et al. 2017. Internal flow measurements of drop impacting a solid surface. Experiments in Fluids, 58(3): 12. doi: 10.1007/s00348-016-2293-7
[88]	Lamb H. 1993. Hydrodynamics. Cambridge University Press.
[89]	Lee C S, Ahn B K, Han J M, et al. 2017a. Propeller tip vortex cavitation control and induced noise suppression by water injection. Journal of Marine Science and Technology, 23(3): 453-463.
[90]	Lee S J, Shin J W, Arndt R E A, et al. 2017b. Attenuation of the tip vortex flow using a flexible thread. Experiments in Fluids, 59(1): 1-12.
[91]	Lee T, Pereira J. 2010. Nature of wakelike and jetlike axial tip vortex flows. Journal of Aircraft, 47(6): 1946-1954. doi: 10.2514/1.C000225
[92]	Li C, Panday R, Gao X, et al. 2021. Measuring particle dynamics in a fluidized bed using digital in-line holography. Chemical Engineering Journal, 405: 126824. doi: 10.1016/j.cej.2020.126824
[93]	Li G N, Chen Q R, Liu Y. 2020a. Experimental study on dynamic structure of propeller tip vortex. Polish Maritime Research, 27(2): 11-18. doi: 10.2478/pomr-2020-0022
[94]	Li L M, Li X J, Zhu Z C, et al. 2020b. Numerical modeling of multiphase flow in gas stirred ladles: From a multiscale point of view. Powder Technology, 373: 14-25. doi: 10.1016/j.powtec.2020.06.028
[95]	Lidtke A K, Turnock S R, Humphrey V F. 2016. Multi-scale modelling of cavitation-induced pressure around the delft twist 11 hydrofoil//31st Symposium on Naval Hydrodynamics, Monterey, USA.
[96]	Liu T J. 2002. An effective signal processing method for resistivity probe measurements in a two-phase bubbly flow. Measurement Science and Technology, 13(2): 206. doi: 10.1088/0957-0233/13/2/311
[97]	Liu X F, Katz J. 2006. Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Experiments in Fluids, 41(2): 227-240. doi: 10.1007/s00348-006-0152-7
[98]	Liu X F, Katz J. 2008. Cavitation phenomena occurring due to interaction of shear layer vortices with the trailing corner of a two-dimensional open cavity. Physics of Fluids, 20(4): 041702. doi: 10.1063/1.2897320
[99]	Liu Z H, Brennen C E. 1998. Cavitation nuclei population and event rates. Journal of Fluids Engineering-Transactions of the Asme, 120(4): 728-737. doi: 10.1115/1.2820730
[100]	Ma J S, Hsiao C T, Chahine G L. 2015. Euler-lagrange simulations of bubble cloud dynamics near a wall. Journal of Fluids Engineering, 137(4): 041301. doi: 10.1115/1.4028853
[101]	Magintyre F. 1986. On reconciling optical and acoustical bubble spectra in the mixed layer//Monahan E C, Niocaill G M. Oceanic Whitecaps. Oceanographic Sciences Library, vol 2. Springer, Dordrecht.
[102]	Maines B H, Arndt R E A. 1997. Tip vortex formation and cavitation. Journal of Fluids Engineering, 119(2): 413-419. doi: 10.1115/1.2819149
[103]	McCormick B W Jr. 1962. On cavitation produced by a vortex trailing from a lifting surface. Journal of Basic Engineering, 84(3): 369-378. doi: 10.1115/1.3657328
[104]	Muñoz-Cobo J L, Chiva S, Méndez S, et al. 2017. Development of conductivity sensors for multi-phase flow local measurements at the Polytechnic University of Valencia (UPV) and University Jaume I of Castellon (UJI). Sensors, 17(5): 1077. doi: 10.3390/s17051077
[105]	Muthanna C, Devenport W J. 2004. Wake of a compressor cascade with tip gap, Part 1: Mean flow and turbulence structure. Aiaa Journal, 42(11): 2320-2331. doi: 10.2514/1.5270
[106]	Nanda S, Westerweel J, van Terwisga T, et al. 2022. Mechanisms for diffusion-driven growth of cavitating wing-tip vortices. International Journal of Multiphase Flow, 156: 104146. doi: 10.1016/j.ijmultiphaseflow.2022.104146
[107]	Oweis G F, van der Hout I E, Iyer C, et al. 2005. Capture and inception of bubbles near line vortices. Physics of Fluids, 17(2): 022105. doi: 10.1063/1.1834916
[108]	Park I, Kim J, Paik B, et al. 2021. Numerical study on tip vortex cavitation inception on a foil. Applied Sciences, 11(16): 7332. doi: 10.3390/app11167332
[109]	Park S L L, Lee S J, You G S, et al. 2014. An experimental study on tip vortex cavitation suppression in a marine propeller. Journal of Ship Research, 58(3): 157-167. doi: 10.5957/jsr.2014.58.3.157
[110]	Parkin B, Ravindra K. 1991. Convective gaseous diffusion in steady axisymetric cavity flows. J. Fluids Eng, 113(2): 285-289. doi: 10.1115/1.2909493
[111]	Pascal R W, Yelland M J, Srokosz M A, et al. 2011. A spar buoy for high-frequency wave measurements and detection of wave breaking in the open ocean. Journal of Atmospheric and Oceanic Technology, 28(4): 590-605. doi: 10.1175/2010JTECHO764.1
[112]	Peng X X, Wang B L, Li H Y, et al. 2017a. Generation of abnormal acoustic noise: Singing of a cavitating tip vortex. Physical Review Fluids, 2(5): 053602. doi: 10.1103/PhysRevFluids.2.053602
[113]	Peng X X, Xu L H, Liu Y W, et al. 2017b. Experimental measurement of tip vortex flow field with/without cavitation in an elliptic hydrofoil. Journal of Hydrodynamics, 29(6): 939-953. doi: 10.1016/S1001-6058(16)60808-9
[114]	Pennings P C, Westerweel J, van Terwisga T J C. 2015. Flow field measurement around vortex cavitation. Experiments in Fluids, 56(11): 1-13.
[115]	Proctor F. 1998. The NASA-Langley wake vortex modelling effort in support of an operational aircraft spacing system//36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada.
[116]	Rivetti A, Angulo M, Lucino C, et al. 2014. Mitigation of tip vortex cavitation by means of air injection on a Kaplan turbine scale model//27th Iahr Symposium on Hydraulic Machinery and Systems, Montreal, Canada.
[117]	Russell P, Barbaca L, Venning J, et al. 2022. The influence of nucleation on cavitation inception in tip-leakage flows. Physics of Fluids, 35: 013341.
[118]	Russell P S, Barbaca L, Venning J A, et al. 2020. Measurement of nuclei seeding in hydrodynamic test facilities. Experiments in Fluids, 61(3): 79. doi: 10.1007/s00348-020-2911-2
[119]	Russell P S, Venning J A, Brandner P A, et al. 2018. Microbubble disperse flow about a lifting surface//32nd Symposium on Naval Hydrodynamics, Hamburg, Germany.
[120]	Scarano F. 2013. Tomographic PIV: Principles and practice. Measurement Science and Technology, 24(1): 012001. doi: 10.1088/0957-0233/24/1/012001
[121]	Sezen S, Uzun D, Turan O, et al. 2021. Influence of roughness on propeller performance with a view to mitigating tip vortex cavitation. Ocean Engineering, 239: 109703. doi: 10.1016/j.oceaneng.2021.109703
[122]	Shekarriz A, Fu T C, Katz J, et al. 1993. Near-field behavior of a tip vortex. Aiaa Journal, 31(1): 112-118. doi: 10.2514/3.11326
[123]	Shen Y, Chahine G, Hsiao C T, et al. 2001. Effects of model size and free stream nuclei on tip vortex cavitation inception scaling//4th International Symposium on Cavitation, Pasadena, USA.
[124]	Shi X, Tan C, Dong F, et al. 2021. Conductance sensors for multiphase flow measurement: A Review. IEEE Sensors Journal, 21(11): 12913-12925. doi: 10.1109/JSEN.2020.3042206
[125]	Song M T, Xu L H, Peng X X, et al. 2017. An acoustic approach to determine tip vortex cavitation inception for an elliptical hydrofoil considering nuclei-seeding. International Journal of Multiphase Flow, 90: 79-87. doi: 10.1016/j.ijmultiphaseflow.2016.12.008
[126]	Souders W G, Platzer G P, David W T N S R, Development C. 1981. Tip vortex cavitation characteristics and delay of inception on a three-dimensional hydrofoil. David W. Taylor Naval Ship Research and Development Center, Bethesda, Md.
[127]	Stinebring D R, Farrell K J, Billet M L. 1991. The structure of a three-dimensional tip vortex at high reynolds numbers. Journal of Fluids Engineering, 113(3): 496-503. doi: 10.1115/1.2909524
[128]	Storer J A, Cumpsty N A. 1991. Tip leakage flow in axial compressors. Journal of Turbomachinery, 113(2): 252-259. doi: 10.1115/1.2929095
[129]	Svennberg U, Asnaghi A, Gustafsson R, et al. 2020. Experimental analysis of tip vortex cavitation mitigation by controlled surface roughness. Journal of Hydrodynamics, 32(6): 1059-1070. doi: 10.1007/s42241-020-0073-6
[130]	Szantyr J A. 2006. Scale effects in cavitation experiments with marine propeller models. Polish Maritime Research, 4: 3-10.
[131]	Tanger H, Weitendorf E A. 1992. Applicability tests for the phase doppler anemometer for cavitation nuclei measurements. Journal of Fluids Engineering-Transactions of the Asme, 114(3): 443-449. doi: 10.1115/1.2910051
[132]	Tomar G, Fuster D, Zaleski S, et al. 2010. Multiscale simulations of primary atomization. Computers & Fluids, 39(10): 1864-1874.
[133]	Trieling R R, Fuentes O U V, Heijst G J F v. 2005. Interaction of two unequal corotating vortices. Physics of Fluids, 17(8): 087103. doi: 10.1063/1.1993887
[134]	Tropea C. 2011. Optical particle characterization in flows. Annual Review of Fluid Mechanics 43 (1): 399-426.
[135]	Tyvand P A. 2022. Viscous Rankine vortices. Physics of Fluids, 34(7): 073603. doi: 10.1063/5.0090143
[136]	Venning J A, Pearce B W, Brandner P A. 2022. Nucleation effects on cloud cavitation about a hydrofoil. Journal of Fluid Mechanics, 947: A1. doi: 10.1017/jfm.2022.535
[137]	Viitanen V, Siikonen T, Sanchez-Caja A. 2020. Cavitation on model-and full-scale marine propellers: Steady and transient viscous flow simulations at different reynolds numbers. Journal of Marine Science and Engineering, 8(2): 141. doi: 10.3390/jmse8020141
[138]	Wang H L, Wang Y. 2005. Micro-piv: A new development of particle image velocimetry. Advances in Mechanics, 35(1): 77-90.
[139]	Wang L, Wu Y, Wu X, et al. 2021a. Measurement of dynamics of laser-induced cavitation around nanoparticle with high-speed digital holographic microscopy. Experimental Thermal and Fluid Science, 121: 110266. doi: 10.1016/j.expthermflusci.2020.110266
[140]	Wang Z Y, Cheng H Y, Ji B. 2021b. Euler-Lagrange study of cavitating turbulent flow around a hydrofoil. Physics of Fluids, 33(11): 112108. doi: 10.1063/5.0070312
[141]	Wang Z Y, Cheng H Y, Ji B. 2022. Numerical prediction of cavitation erosion risk in an axisymmetric nozzle using a multi-scale approach. Physics of Fluids, 34: 062112. doi: 10.1063/5.0095833
[142]	Wu X J, Wendel M, Chahine G, Riemer B. 2014. Gas bubble size measurements in liquid mercury using an acoustic spectrometer. Journal of Fluids Engineering, 136(3): 031303. doi: 10.1115/1.4026440
[143]	Wu Y, Liu Y, Shao S Y, et al. 2019. On the internal flow of a ventilated supercavity. Journal of Fluid Mechanics, 862: 1135-1165. doi: 10.1017/jfm.2018.1006
[144]	Xie C M, Liu J Y, Jiang J W, et al. 2021. Numerical study on wetted and cavitating tip-vortical flows around an elliptical hydrofoil: Interplay of cavitation, vortices, and turbulence. Physics of Fluids, 33(9): 093316. doi: 10.1063/5.0064717
[145]	Xu C, Huang J, Wang Y W, et al. 2018. Supercavitating flow around high-speed underwater projectile near free surface induced by air entrainment. AIP Advances, 8(3): 035016. doi: 10.1063/1.5017182
[146]	Xu M, Cheng H, Ji B, et al. 2023. Prediction method of tip vortex circulation based on hydrofoil load. Ocean Engineering, 288: 116176. doi: 10.1016/j.oceaneng.2023.116176
[147]	Xu M, Cheng H Y, Ji B, et al. 2020. LES of tip-leakage cavitating flow with special emphasis on different tip clearance sizes by a new Euler-Lagrangian cavitation model. Ocean Engineering, 213: 107661. doi: 10.1016/j.oceaneng.2020.107661
[148]	Yakubov S, Cankurt B, Abdel-Maksoud M, et al. 2013. Hybrid MPI/OpenMP parallelization of an Euler–Lagrange approach to cavitation modelling. Computers & Fluids, 80: 365-371.
[149]	Yakushiji R Z. 2009. Mechanism of Tip Vortex Cavitation Suppression by Polymer and Water Injection. University of Michigan, Michigan.
[150]	Yao X L, Li Z P, Sun L Q, et al. 2020. A study on bubble nuclei population dynamics under reduced pressure. Physics of Fluids, 32(11): 112019. doi: 10.1063/5.0026361
[151]	Zhang H, Liu Y, Wang B L, et al. 2022. Phase-resolved characteristics of bubbles in cloud cavitation shedding cycles. Ocean Engineering, 256: 111529. doi: 10.1016/j.oceaneng.2022.111529
[152]	Zhang L X, Chen L Y, Peng X X, et al. 2017. The effect of water quality on tip vortex cavitation inception. Journal of Hydrodynamics, Ser. B 29 (6) : 954-961.
[153]	Zhang L X, Zhang N, Peng X X, et al. 2015. A review of studies of mechanism and prediction of tip vortex cavitation inception. Journal of Hydrodynamics, 27(4): 488-495. doi: 10.1016/S1001-6058(15)60508-X
[154]	Zhang X S, Wang J H, Wan D C. 2019. Euler-Lagrangian study of bubble drag reduction in turbulent channel flow and boundary layer flow. Physics of Fluids, 32: 027101.
[155]	Zhang Y C, Chen L S, Yan L, et al. 2010a. Investigation and application of pressure sensitive paint technique in wind tunnel test. Journal of Experiments in Fluid Mechanics, 24(1): 74-78,94.
[156]	Zhang Y Y, Sun X J, Huang D G. 2010b. A numerical study on cavitation suppression using local cooling. International Journal of Fluid Machinery & Systems, 3(4): 292-300.
[157]	Zhao Y, Wang G Y, Jiang Y T, et al. 2016. Numerical analysis of developed tip leakage cavitating flows using a new transport-based model. International Communications in Heat and Mass Transfer, 78: 39-47. doi: 10.1016/j.icheatmasstransfer.2016.08.007
[158]	Zhou Z, S S K, Mallery K, et al. 2020. Holographic astigmatic particle tracking velocimetry (HAPTV). Measurement Science and Technology, 31(6): 065202. doi: 10.1088/1361-6501/ab7281
[159]	Zhu W C, Gao H T. 2019. A numerical investigation of a Winglet-Propeller using an LES model. Journal of Marine Science and Engineering, 7(10): 1-18.
[160]	陈瑛, 鲁传敬, 郭建红, 等. 2011. 大攻角水下航行体侧面空化特性的数值分析. 弹道学报, 23(1): 45-49 (Chen Y, Lu C J, Guo J H, et al. 2011. Numerical analysis on the characteristics of side cavitation around submerged vehicle with large attack angle. Journal of ballistics, 23(1): 45-49). Chen Y, Lu C J, Guo J H, et al. 2011. Numerical analysis on the characteristics of side cavitation around submerged vehicle with large attack angle. Journal of ballistics, 23(1): 45-49.
[161]	戴军涛, 刘莉, 刘帅, 等. 2022. 基于丝网探针的螺旋管内气液两相流气泡行为研究. 化工学报, 73(10): 4377-4388 (Dai J T, Liu L, Liu S, et al. 2022. Investigation of bubble behaviors in gas-liguid two-phase flow in helically coiled tube based on wire mesh sensor. CIESC Journal, 73(10): 4377-4388). Dai J T, Liu L, Liu S, et al. 2022. Investigation of bubble behaviors in gas-liguid two-phase flow in helically coiled tube based on wire mesh sensor. CIESC Journal, 73(10): 4377-4388.
[162]	韩正英, 于佳, 王金城, 等. 2010. 基于数字全息术的水中气泡场获取方法的研究. 光学技术, 36(4): 617-621 (Han Z Y, Yu J, Wang J C, et al. 2010. The research of under water bubble field on digital holography. Optical Technique, 36(4): 617-621). Han Z Y, Yu J, Wang J C, et al. 2010. The research of under water bubble field on digital holography. Optical Technique, 36(4): 617-621.
[163]	季斌, 程怀玉, 黄彪, 等. 2019. 空化水动力学非定常特性研究进展及展望. 力学进展, 49: 428-479 (Ji B, Cheng H Y, Huang B, et al. 2019. Research progresses and prospects of unsteady hydrodynamics characteristics for cavitation. Advances in Mechanics, 49: 428-479). doi: 10.6052/1000-0992-17-012 Ji B, Cheng H Y, Huang B, et al. 2019. Research progresses and prospects of unsteady hydrodynamics characteristics for cavitation. Advances in Mechanics, 49: 428-479. doi: 10.6052/1000-0992-17-012
[164]	季斌, 程怀玉, 徐顺, 等. 2022. 推进泵叶顶间隙空化水动力学. 科学出版社, 北京.
[165]	刘亢, 曹留帅, 万德成. 2023. 基于主动射流方法的椭圆水翼梢涡空化抑制研究. 中国舰船研究, 18(4): 175-185 (Liu K, Cao L S, Wan D C. 2023. Suppression of tip vortex cavitation of elliptical hydrofoil based on active water injection methods. Chinese Journal of Ship Research, 18(4): 175-185). Liu K, Cao L S, Wan D C. 2023. Suppression of tip vortex cavitation of elliptical hydrofoil based on active water injection methods. Chinese Journal of Ship Research, 18(4): 175-185.
[166]	刘玉文, 徐良浩, 宋明太, 等. 2020. 水翼叶梢涡空化实验研究进展. 实验流体力学, 34(5): 1-11 (Liu Y W, Xv L H, Song M T, et al. 2020. Experimental research progress of hydrofoil tip vortex cavitation. Journal of Experiments in Fluid Mechanics, 34(5): 1-11). doi: 10.11729/syltlx20190083 Liu Y W, Xv L H, Song M T, et al. 2020. Experimental research progress of hydrofoil tip vortex cavitation. Journal of Experiments in Fluid Mechanics, 34(5): 1-11. doi: 10.11729/syltlx20190083
[167]	陆芳, 张万军. 2023. 实船空泡性能试验研究进展综述. 船舶力学, 27(5): 763-773 (Lu F, Zhang W J. 2023. Progress of cavitation research on full scale ships. Journal of Ship Mechanics, 27(5): 763-773). doi: 10.3969/j.issn.1007-7294.2023.05.015 Lu F, Zhang W J. 2023. Progress of cavitation research on full scale ships. Journal of Ship Mechanics, 27(5): 763-773. doi: 10.3969/j.issn.1007-7294.2023.05.015
[168]	罗先武, 季斌, 彭晓星, 等. 2020. 空化基础理论及应用. 清华大学出版社, 北京 (Luo X W, Ji B, Peng X X, et al. 2020. Basics of Cavitation and its Applicatlons. Tinghua University Press, Beijing). Luo X W, Ji B, Peng X X, et al. 2020. Basics of Cavitation and its Applicatlons. Tinghua University Press, Beijing.
[169]	吕瑞, 于开平, 魏英杰, 等. 2010. 超空泡航行体的增益自适应变结构控制设计. 兵工学报, 31(3): 303-308 (Lv R, Yu K P, Wei Y J, et al. 2010. Design of gain adaptive variable-structure controller for supercavitating vehicle. Acta Armamentarii, 31(3): 303-308). Lv R, Yu K P, Wei Y J, et al. 2010. Design of gain adaptive variable-structure controller for supercavitating vehicle. Acta Armamentarii, 31(3): 303-308.
[170]	潘森森. 1985. 空化核最新研究评述. 力学进展, 15 (3): 329-332 (Pan S S. Critical review on cavitation nuclei research. Advances in Mechanics, 15 (3): 329-332). Pan S S. Critical review on cavitation nuclei research. Advances in Mechanics, 15 (3): 329-332.
[171]	潘森森, 彭晓星. 2013. 空化机理. 国防工业出版社, 北京 (Pan S S, Peng X X. 2013. Physical mechanism of cavitation. National defense industry press, Beijing). Pan S S, Peng X X. 2013. Physical mechanism of cavitation. National defense industry press, Beijing.
[172]	彭晓星, 王力, 潘森森. 1989. 水中空气含量对旋涡空化的影响. 水动力学研究与进展, 04: 60-68 (Peng X X, Wang L, Pan S S. 1989. Air Content Effect on the Vortex Cavitation. Chinese Journal of Hydrodynamics, 04: 60-68). Peng X X, Wang L, Pan S S. 1989. Air Content Effect on the Vortex Cavitation. Chinese Journal of Hydrodynamics, 04: 60-68.
[173]	蒲汲君, 熊鹰, 王睿. 2017. 三维水翼初始梢涡空泡数的尺度效应. 上海交通大学学报, 51(3): 374-378 (Pu J J, Xiong Y, Wang R. 2017. Scaling effects of hydrofoil tip vortex cavitation inception. Journal of Shanghai Jiaotong University, 51(3): 374-378). Pu J J, Xiong Y, Wang R. 2017. Scaling effects of hydrofoil tip vortex cavitation inception. Journal of Shanghai Jiaotong University, 51(3): 374-378.
[174]	沈熙, 张德胜, 刘安, 等. 2018. 轴流泵叶顶泄漏涡与垂直涡空化特性. 农业工程学报, 34 (12): 87-94 (Shen X, Zhang D S, Liu A, et al. Cavitation characteristics of tip leakage vortex and suction-side-perpendicular vortices in axial flow pump. Transactions of the Chinese Society of Agricultural Engineering, 34 (12): 87-94). Shen X, Zhang D S, Liu A, et al. Cavitation characteristics of tip leakage vortex and suction-side-perpendicular vortices in axial flow pump. Transactions of the Chinese Society of Agricultural Engineering, 34 (12): 87-94.
[175]	万初瑞, 王本龙, 刘桦. 2015. 片空泡内部孔隙率和流速的实验测量//第二十七届全国水动力学研讨会, 中国南京 (Wan C R, Wang B L, Liu H. 2015. Experimental study of internal structure of attached sheet cavitation//27th National Conference on Hydrodynamic, Nanjing, China). Wan C R, Wang B L, Liu H. 2015. Experimental study of internal structure of attached sheet cavitation//27th National Conference on Hydrodynamic, Nanjing, China.
[176]	王文全, 赵雷明, 马开放, 等. 2021. 端板对叶梢负载桨空化性能影响数值分析. 推进技术, 42(9): 2145-2151 (Wang W Q, Zhao L M, Ma K F, et al. 2021. Effects of end plate on cavitation performance of contracted and loaded tip propeller. Journal of Propulsion Technology, 42(9): 2145-2151). Wang W Q, Zhao L M, Ma K F, et al. 2021. Effects of end plate on cavitation performance of contracted and loaded tip propeller. Journal of Propulsion Technology, 42(9): 2145-2151.
[177]	吴迎春. 2014. 数字颗粒全息三维测量技术及其应用 (Wu Y C. 2014. Digital particle holography for 3D measurement and its applications). Wu Y C. 2014. Digital particle holography for 3D measurement and its applications.
[178]	武珅, 曾志波, 徐良浩. 2020. 柔性随边螺旋桨水动力和空泡性能模型实验研究. 水动力学研究与进展(A辑), 35(6): 675-680 (Wu S, Zeng Z B, Xv L H. 2020. Experimental research on hydrodynamic and cavitation performance of model propeller with flexible trailing edge. Chinese Journal of Hydrodynamics, 35(6): 675-680). Wu S, Zeng Z B, Xv L H. 2020. Experimental research on hydrodynamic and cavitation performance of model propeller with flexible trailing edge. Chinese Journal of Hydrodynamics, 35(6): 675-680.
[179]	项乐, 陈晖, 谭永华, 等. 2020. 液体火箭发动机诱导轮空化热力学效应研究. 推进技术, 41(4): 812-819 (Xiang L, Chen H, Tan Y H, et al. 2020. Study of cavitation thermodynamic effect of liquid rocket engine inducer. Journal of Propulsion Technology, 41(4): 812-819). Xiang L, Chen H, Tan Y H, et al. 2020. Study of cavitation thermodynamic effect of liquid rocket engine inducer. Journal of Propulsion Technology, 41(4): 812-819.
[180]	辛公正. 2014. 桨叶几何对梢涡空泡起始影响及其机理研究. 中国舰船研究院 (Xin G Z. 2014. The investigation of the effect of blade geometryon tip vortex cavitation inception and its mechanism. CSIC). Xin G Z. 2014. The investigation of the effect of blade geometryon tip vortex cavitation inception and its mechanism. CSIC.
[181]	熊鹰, 韩宝玉, 时立攀. 2013. 螺旋桨梢涡空泡初生及尺度效应研究. 船舶力学, 17(5): 451-459 (Xiong Y, Han B Y, Shi L P. 2013. Study on prediction of tip-vortex cavitation inception. Journal of Ship Mechanics, 17(5): 451-459). Xiong Y, Han B Y, Shi L P. 2013. Study on prediction of tip-vortex cavitation inception. Journal of Ship Mechanics, 17(5): 451-459.
[182]	徐良浩, 彭晓星, 刘玉文, 等. 2017. 梢涡涡核结构的PIV试验研究. 水动力学研究与进展(A辑), 32(6): 712-718 (Xv L H, Peng X X, Liu Y W, et al. 2017. Experimental research on structure of tip vortex core by PIV. Chinese Journal of Hydrodynamics, 32(6): 712-718). Xv L H, Peng X X, Liu Y W, et al. 2017. Experimental research on structure of tip vortex core by PIV. Chinese Journal of Hydrodynamics, 32(6): 712-718.