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旋涡空化水动力学特性研究进展与展望

程怀玉 季斌 龙新平 彭晓星

程怀玉, 季斌, 龙新平, 彭晓星. 旋涡空化水动力学特性研究进展与展望. 力学进展, 2024, 54(1): 86-137 doi: 10.6052/1000-0992-23-045
引用本文: 程怀玉, 季斌, 龙新平, 彭晓星. 旋涡空化水动力学特性研究进展与展望. 力学进展, 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

旋涡空化水动力学特性研究进展与展望

doi: 10.6052/1000-0992-23-045
基金项目: 衷心感谢北京理工大学王国玉教授、清华大学罗先武教授、瑞士洛桑联邦理工学院(EPFL) Mohamed Farhat教授在本论文研究和撰写过程中给予的指导和帮助. 国家重点研发计划(2022YFB3303501)和国家自然科学基金(52176041, 12102308, 11332009, 11772305)资助项目.
详细信息
    作者简介:

    季斌, 武汉大学教授、博士生导师, 主要从事水力机械/船舶海洋装备空化水动力学应用基础研究. 主持国家自然科学基金5项, 出版学术专著2部, 发表SCI论文105篇(第一/通讯作者65篇), 谷歌学术引用5828次, SCI他引3912次, 8篇论文入选ESI高被引论文, 1篇论文获评中国百篇最具影响国际学术论文, 1篇论文入选《国际多相流杂志》近10年被引次数最多的论文, 获省部级科研奖励4项, 入选爱思唯尔“中国高被引学者榜单” 、全球前2%顶尖科学家“年度影响力榜单”和“生涯影响力榜单” 、湖北省“楚天学者计划”. 现任《J Hydrodyn》等4个杂志编委, 湖北省力学学会理事等. 曾获国家优秀青年基金项目、湖北省杰出青年基金项目、周培源水动力学奖等

    通讯作者:

    jibin@whu.edu.cn

  • 中图分类号: O352

Research progresses and prospects of vortex cavitation dynamics

More Information
  • 摘要: 涡空化作为一种在推进器叶顶涡心处产生的空化现象, 在推进器原型上往往最早出现, 其一旦发生将会严重影响舰艇的声隐身性能(噪声增加10 dB以上), 在很大程度上限制了舰艇临界航速的进一步提升, 因而长期以来一直是空化水动力学领域研究的重点与难点课题之一. 本文首先简要介绍了旋涡空化流动相较于其他形式空化流动的特点, 并以梢涡空化为主要对象, 系统阐述了旋涡空化初生、发展的演变行为与流动机理研究, 从空化三要素的角度深入讨论了其影响因素与作用机制. 在此基础上, 本文分别对旋涡空化流动中尺度效应、流动控制等关键问题的相关研究进展进行了回顾, 较为系统地梳理了旋涡空化尺度效应的内在原因以及旋涡空化流动控制方法与控制思路. 最后, 本文针对目前旋涡空化研究领域关注的重点与难点问题, 对旋涡空化流动研究中采用的实验测量及数值模拟技术进行了总结与展望.

     

  • 图  1  典型的绕舰船推进器及水翼旋涡空化流动. (a) 螺旋桨梢涡空化(Bosschers 2018b), (b) 椭圆翼梢涡空化(Dreyer 2015)

    图  2  典型的旋涡空化初生过程. (a) 一个游离气核在梢涡作用下的运动与生长过程(多时刻叠加), (b) 0.5 ms后的梢涡形态

    图  3  不同涡模型预报的切向速度分布与实验结果(Dreyer 2015)对比

    图  4  涡丝卷吸理论及基于水翼升力的旋涡环量预报结果. (a) 涡丝卷吸理论Franc和Michel (2005), (b) 基于水翼升力的旋涡环量预报结果对比(Xu et al. 2023)

    图  5  旋涡半径关系式预测得到的旋涡半径变化与实验、模拟值的对比(季斌等 2022)

    图  6  理想涡流场中游离气核的分布和运动(Chen et al. 2019). (a) 不同初始尺寸气核的初始分布, (b) 不同初始尺寸气核的运动轨迹和生长

    图  7  旋涡涡心处的轴向速度分布(Dreyer 2015)

    图  8  不同条件下旋涡空化的发展形态(Amini et al. 2019a). (a) 不同空化数下旋涡空化形态, (b) 不同雷诺数下旋涡空化形态, (c) 不同攻角下旋涡空化形态, (d) 不同含气率下旋涡空化形态

    图  9  不同空化涡模型切向速度分布与实验值(Dreyer 2015)的对比

    图  10  Amini等(2019a)建立的旋涡空化溶解气体扩散模型

    图  11  溶解气体扩散诱发的梢涡空化失稳现象(Nanda et al. 2022)

    图  12  绕椭圆翼的梢涡空化及其尺度效应 (Keller 2001)

    图  13  几种典型的梢涡空化抑制方法. (a) 涡心注质法(Chang et al. 2011), (b) 叶梢卸载法(辛公正 2014), (c) 异性叶梢法(Amini et al. 2019b), (d) 表面加粗法(Asnaghi et al. 2020), (e) 细绳干扰法(Lee et al. 2017b)

    表  1  各类针对旋涡空化修正的空化数对比

    代表性的空化数 优点 缺点
    第一类 $ {\sigma _{\text{0}}}{\text{ = }}\dfrac{{{p_\infty } - {p_v}}}{{0.5{\rho _l}U_\infty ^2}} $ 在片空化、云空化流动中应用十分广泛,
    得到了广泛的检验与认可
    无法反映旋涡旋转运动引起的压降
    以及气核的影响
    第二类 $ {\sigma _i} = {\text{ }}{k_{{\mathrm{s}}1}}{\left( {\dfrac{\varGamma }{{{r_{\mathrm{c}}}{U_\infty }}}} \right)^2} $ 反映了旋涡旋转运动引起的压降 没有反映水体中气核的影响
    第三类 $ {\sigma _i} = - {C_{{p_{\mathrm{s}}}}} + \dfrac{{{p_{\mathrm{g}}}}}{{1/2\rho U_\infty ^2}} $ 同时反映了旋涡旋转运动引起的压降
    以及气核的影响
    需要额外给出气核要素的定量评估方法
    下载: 导出CSV

    表  2  原始Zwart模型与几个典型的旋涡空化修正模型对比

    序号 模型名称 相间质量输运速率 与原模型的主要区别
    1 原始Zwart模型 $ \left. \begin{gathered} {{\dot m}^ + } = {C_{{\text{p0}}}}\frac{{3\left( {1 - {\alpha _{{v}}}} \right){\alpha _{{\text{nuc}}}}{\rho _{{v}}}}}{R}\sqrt {\frac{2}{3}\frac{{\left( {{p_v} - p} \right)}}{{{\rho _{\text{l}}}}}} ,p < {p_{{v}}} \\ {{\dot m}^ - } = {C_{{\text{d0}}}}\frac{{3{\alpha _{{v}}}{\rho _{{v}}}}}{R}\sqrt {\frac{2}{3}\frac{{\left( {p - {p_{{v}}}} \right)}}{{{\rho _{\text{l}}}}}} ,p > {p_{{v}}} \\ \end{gathered} \right\} $ /
    2 考虑旋涡环量的修正模型(Zhao et al. 2016) $ \left. \begin{gathered} {{\dot m}^ + } = {C_{\text{p}}}\frac{{2\pi }}{{\left| \varGamma \right|}}\frac{{(1 - {\alpha _v}){\rho _{{v}}}}}{{{\rho _l}}}\left| {p - {p_v}} \right|,p < {p_{{v}}} \\ {{\dot m}^ - } = {C_{\text{d}}}\frac{{2\pi }}{{\left| \varGamma \right|}} \cdot \frac{{{\alpha _v}{\rho _v}\left| {p - {p_v}} \right|}}{{{\rho _{\mathrm{l}}}}},p > {p_{{v}}} \\ \end{gathered} \right\} $ 考虑了旋涡对空化泡半径的影响, 并将其引入相间质量输运速率的计算
    3 基于涡识别的修正模型(Guo et al. 2018) $ \left. \begin{gathered} {{\dot m}^ + } = {C_{{\text{p0}}}}\frac{{3\left( {1 - {\alpha _{{v}}}} \right){\alpha _{{\text{nuc}}}}{\rho _{{v}}}}}{R}\sqrt {\frac{2}{3}\frac{{\left( {{p_v} - p} \right)}}{{{\rho _{\text{l}}}}}} ,p < {p_{{v}}} \\ {{\dot m}^ - } = {F_{\rm d}}{C_{{\text{d0}}}}\frac{{3{\alpha _{{v}}}{\rho _{\text{v}}}}}{R}\sqrt {\frac{2}{3}\frac{{\left( {p - {p_{{v}}}} \right)}}{{{\rho _{\text{l}}}}}} ,p > {p_{{v}}} \\ \end{gathered} \right\} $ 利用旋转因子对旋涡区域进行识别, 并对当地的凝结过程系数进行了针对性修正
    4 考虑气核效应的修正模型(Cheng et al. 2021) $ \left. \begin{gathered} {{\dot m}^ + } = {C_{{\text{p0}}}}\frac{{3\left( {1 - {\alpha _{{v}}}} \right){\alpha _{{\text{nuc}}}}{\rho _{{v}}}}}{R}\sqrt {\frac{2}{3}\frac{{\left( {{p_v} + {p_{\text{g}}} - p} \right)}}{{{\rho _{\text{l}}}}}} ,p < {p_{\rm b}} \\ {{\dot m}^ - } = {C_{{\text{d0}}}}\frac{{3{\alpha _{{v}}}{\rho _{{v}}}}}{R}\sqrt {\frac{2}{3}\frac{{\left( {p - {p_v} - {p_{\text{g}}}} \right)}}{{{\rho _{\text{l}}}}}} ,p > {p_{\rm b}} \\ \end{gathered} \right\} $ 考虑了气核不可凝结气体分压对当地空化的贡献, 其中气核的空间分布由DPM模块提供
    下载: 导出CSV
  • [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.
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出版历程
  • 收稿日期:  2023-11-01
  • 录用日期:  2024-01-22
  • 网络出版日期:  2024-01-27
  • 刊出日期:  2024-03-24

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