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Dynamics and surface stability of a cylindrical cavitation bubble in a rectilinear vortex

Published online by Cambridge University Press:  01 March 2019

Yunqiao Liu Open the ORCID record for Yunqiao Liu [Opens in a new window]  and
Benlong Wang Open the ORCID record for Benlong Wang [Opens in a new window]
Yunqiao Liu
Affiliation:
Key Laboratory of Hydrodynamics (Ministry of Education), School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Benlong Wang*
Affiliation:
Key Laboratory of Hydrodynamics (Ministry of Education), School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
*
†Email address for correspondence: benlongwang@sjtu.edu.cn
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Abstract

In this paper, we formulate the dynamic equations of radial and surface modes for a cylindrical cavitation bubble subject to a prescribed uniform rectilinear vortex flow. The potential flow in the bulk volume of the external flow is modelled using the general mode decomposition approach. The stability of surface modes is investigated under linear analysis. The effects of confinement due to a limited flow domain in a water tunnel and viscosity at the bubble surface are evaluated, which can be fairly neglected for the cylindrical cavitation bubbles discussed. Our model is capable of predicting the developments of surface modes, which agrees well with experimental observations reported in the literature. We derive the Mathieu structure in the dynamic equation of the surface oscillation and the associated instability condition of the surface mode oscillations. The numerical results confirm that the Mathieu-type instability controls the stability diagrams and the emergence of surface modes under specific radial oscillation.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Cavitation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 963 - 992
Copyright
© 2019 Cambridge University Press 

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References

Arndt, R. E. A. 2002 Cavitation in vortical flows. Annu. Rev. Fluid Mech. 34 (1), 143–175.10.1146/annurev.fluid.34.082301.114957Google Scholar
Arndt, R. E. A., Arakeri, V. H. & Higuchi, H. 1991 Some observations of tip-vortex cavitation. J. Fluid Mech. 229, 269–289.10.1017/S0022112091003026Google Scholar
Bark, G. 1985 Prediction of propeller cavitation noise from model tests and its comparison with full scale data. Trans. ASME J. Fluids Engng 107 (1), 112–119.10.1115/1.3242424Google Scholar
Bender, C. M. & Orszag, S. A. 1999 Advanced Mathematical Methods for Scientists and Engineers. Springer.10.1007/978-1-4757-3069-2Google Scholar
Blake, W. K., Wolpert, M. J. & Geib, F. E. 1977 Cavitation noise and inception as influenced by boundary-layer development on a hydrofoil. J. Fluid Mech. 80 (4), 617–640.10.1017/S0022112077002390Google Scholar
Chahine, G. L. 1995 Bubble interactions with vortices. In Fluid Vortices. pp. 783–828. Springer.10.1007/978-94-011-0249-0_18Google Scholar
Chang, N. A. & Ceccio, S. L. 2011 The acoustic emissions of cavitation bubbles in stretched vortices. J. Acoust. Soc. Am. 130 (5), 3209–3219.10.1121/1.3626121Google Scholar
Chapman, R. B. & Plesset, M. S. 1971 Thermal effects in the free oscillation of gas bubbles. Trans. ASME J. Basic Engng 93, 373–376.10.1115/1.3425258Google Scholar
Choi, J. & Ceccio, S. L. 2007 Dynamics and noise emission of vortex cavitation bubbles. J. Fluid Mech. 575, 1–26.10.1017/S0022112006003776Google Scholar
Choi, J., Hsiao, C. T., Chahine, G. & Ceccio, S. 2009 Growth, oscillation and collapse of vortex cavitation bubbles. J. Fluid Mech. 624, 255–279.10.1017/S0022112008005430Google Scholar
Fabre, D., Sipp, D. & Jacquin, L. 2006 Kelvin waves and the singular modes of the Lamb–Oseen vortex. J. Fluid Mech. 551, 235–274.10.1017/S0022112005008463Google Scholar
Feng, Z. C. & Leal, L. G. 1993 On energy transfer in resonant bubble oscillations. Phy. Fluids A 5 (4), 826–836.10.1063/1.858630Google Scholar
Feng, Z. C. & Leal, L. G. 1997 Nonlinear bubble dynamics. Annu. Rev. Fluid Mech. 29 (1), 201–243.10.1146/annurev.fluid.29.1.201Google Scholar
Fitzpatrick, R. 2012 Oscillations and Waves: an Introduction. CRC Press.Google Scholar
Franc, J. P. & Michel, J. M. 2010 Fundamentals of Cavitation, chap. 10. Kluwer Academic.Google Scholar
Hildebrand, J. A. 2009 Anthropogenic and natural sources of ambient noise in the ocean. Mar. Ecol. Prog. Ser. 395, 5–20.10.3354/meps08353Google Scholar
Hilgenfeldt, S., Lohse, D. & Brenner, M. P. 1996 Phase diagrams for sonoluminescing bubbles. Phys. Fluids 8 (11), 2808–2826.10.1063/1.869131Google Scholar
Ilinskii, Y. A., Zabolotskaya, E. A., Hay, T. A. & Hamilton, M. F. 2012 Models of cylindrical bubble pulsation. J. Acoust. Soc. Am. 132 (3), 1346–1357.10.1121/1.4730888Google Scholar
Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, chap. 4. Cambridge University Press.10.1017/CBO9780511800245Google Scholar
Levkovskii, V. L. 1968 Modeling of cavitation noise. Sov. Phys. Acoust. 13 (1), 337–339.Google Scholar
Maines, B. & Arndt, R. E. A. 1997 The case of the singing vortex. Trans. ASME J. Fluids Engng 119 (2), 271–276.10.1115/1.2819130Google Scholar
McCormick, B. W. 1962 On cavitation produced by a vortex trailing from a lifting surface. Trans. ASME J. Basic Engng 83, 369–379.10.1115/1.3657328Google Scholar
Oshima, A. A. 1990 Study on correlation of vortex cavitation noise of propeller mesured in model experiments and full scale. J. Soc. Nav. Archit. Japan 168, 89–96.10.2534/jjasnaoe1968.1990.168_89Google Scholar
Park, J. & Seong, W. 2017 Novel scaling law for estimating propeller tip vortex cavitation noise from model experiment. J. Hydrodyn. 29 (6), 962–971.10.1016/S1001-6058(16)60810-7Google Scholar
Peng, X., Wang, B., Li, H., Xu, L. & Song, M. 2017 Generation of abnormal acoustic noise: singing of a cavitating tip vortex. Phys. Rev. Fluids 2 (5), 053602.10.1103/PhysRevFluids.2.053602Google Scholar
Pennings, P. C., Bosschers, J., Westerweel, J. & van Terwisga, T. J. C. 2015 Dynamics of isolated vortex cavitation. J. Fluid Mech. 778, 288–313.10.1017/jfm.2015.379Google Scholar
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9 (1), 145–185.10.1146/annurev.fl.09.010177.001045Google Scholar
Quinto-Su, P. A. & Ohl, C. D. 2009 Interaction between two laser-induced cavitation bubbles in a quasi-two-dimensional geometry. J. Fluid Mech. 633, 425–435.10.1017/S0022112009008064Google Scholar
Roberts, P. H. 2003 On vortex waves in compressible fluids. I. The hollow-core vortex. Proc. R. Soc. Lond. A 459, 331–352.10.1098/rspa.2002.1034Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Shen, Y. T., Gowing, S. & Jessup, S. 2009 Tip vortex cavitation inception scaling for high Reynolds number application. Trans. ASME J. Fluids Engng 131 (7), 1301–1306.Google Scholar
Thomson, S. W. 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.10.1080/14786448008626912Google Scholar
Vadivukkarasan, M. & Panchagnula, M. V. 2017 Combined Rayleigh–Taylor and Kelvin–Helmholtz instabilities on an annular liquid sheet. J. Fluid Mech. 812, 152–177.10.1017/jfm.2016.784Google Scholar
Williams, J. E. & O’Sher, S. 1970 Sound generation by hydrodynamic sources near a cavitated line vortex. J. Fluid Mech. 43 (4), 675–688.10.1017/S0022112070002665Google Scholar
Yang, S. M., Feng, Z. C. & Leal, L. G. 1993 Nonlinear effects in the dynamics of shape and volume oscillations for a gas bubble in an external flow. J. Fluid Mech. 247, 417–454.10.1017/S0022112093000515Google Scholar