HYDRODYNAMICS AND ACOUSTICS

2019 ◊ Volume 1 (91) ◊ Issue 4 ◊ p. 449-468

Yu. N. Savchenko^*, Yu. A. Semenov^*, O. I. Naumova^*

^* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine

Water impact of an expanding cylindrical body

Gidrodin. akust. 2019, 1(4):449-468

TEXT LANGUAGE:English

ABSTRACT

A self-similar flow with the splash jet generated by water entry of an expanding two-dimensional arbitrarily shaped body is studied theoretically based on the incompressible velocity potential theory. The flow is assumed to be irrotational, the liquid to be ideal, and gravity and surface tension are ignored. The solution is obtained in the form of integral equations using the integral hodograph method. It is shown the solution with the detached splash jet exists in all ranges of expansion speeds from zero to infinity. Detailed results in terms of pressure distribution, free surface shape and streamlines, and contact angle of the splash jet are presented.

KEY WORDS

water entry, free surface flow, splash jet

REFERENCES

[1] T. Karman, "The impact of seaplane floats during landing," National Advisory Committee for Aeronautics, Washington, Tech. Rep., 1932.

[2] H. Wagner, "Uber Stoß- und Gleitvorgange an der Oberflache von Fl¨ussigkeiten," Zeitschrift f¨ur Angewandte Mathematik und Mechanik, vol. 12, pp. 193-215, 1932.
https://doi.org/10.1002/zamm.19320120402

[3] A. Mackie, "A linearized theory of the water entry problem," Quarterly Journal of Mechanics and Applied Mathematics, vol. 15, pp. 137-151.
https://doi.org/10.1093/qjmam/15.2.137

[4] P. R. Garabedian, "Oblique water entry of a wedge," Communications on Pure and Applied Mathematics, vol. 6, no. 2, pp. 157-165, 1953.
https://doi.org/10.1002/cpa.3160060201

[5] P. R. Garabedian, "Asymptotic description of a free boundary at the point of separation," in Applications of nonlinear partial differential equations in mathematical physics, ser. Proceedings of Symposia in Applied Mathematics, R. Finn, Ed., vol. XVII. Providence, RI: AMS, 1965, p. 111.
https://doi.org/10.1090/psapm/017/0182231

[6] R. Cointe and J. L. Armand, "Hydrodynamic impact analysis of a cylinder," Journal of Offshore Mechanics and Arctic Engineering, vol. 109, pp. 237-243, 1987.
https://doi.org/10.1115/1.3257015

[7] S. D. Howison, J. R. Ockendon, and J. M. Oliver, "Oblique slamming, planing and skimming," Journal of Engineering Mathematics, vol. 48, pp. 321-337, 2004.
https://doi.org/10.1023/B:engi.0000018156.40420.50

[8] A. A. Korobkin, "Analytical models of water impact," European Journal of Applied Mathematics, vol. 15, pp. 821-838, 2004.
https://doi.org/10.1017/S0956792504005765

[9] M. Greenhow, "Wedge entry into initially calm water," Applied Ocean Research, vol. 9, pp. 214-223, 1987.
https://doi.org/10.1016/0141-1187(87)90003-4

[10] X. Mei, Y. Lui, and D. K. P. Yue, "On the water impact of general two-dimensional sections," Applied Ocean Research, vol. 21, pp. 1-15, 1999.
https://doi.org/10.1016/S0141-1187(98)00034-0

[11] E. Cumberbatch, "The impact of a water wedge on the wall," Journal of Fluid Mechanics, vol. 7, pp. 353-374, 1960.
https://doi.org/10.1017/S002211206000013X

[12] Z. N. Dobrovol'skaya, "Some problems of similarity flow of fluid with a free surface," Journal of Fluid Mechanics, vol. 36, pp. 805-829, 1969.
https://doi.org/10.1017/S0022112069001996

[13] R. Zhao and O. Faltinsen, "Water-entry of two-dimensional bodies," Journal of Fluid Mechanics, vol. 246, pp. 593-612, 1993.
https://doi.org/10.1017/S002211209300028X

[14] Y. A. Semenov and A. Iafrati, "On the nonlinear water entry problem of asymmetric wedges," Journal of Fluid Mechanics, vol. 547, pp. 231-256, 2006.
https://doi.org/10.1017/S0022112005007329

[15] Y. A. Semenov, G. X. Wu, and J. M. Oliver, "Splash jet caused by collision of two liquid wedges," Journal of Fluid Mechanics, vol. 737, pp. 132-145, 2013.
https://doi.org/10.1017/jfm.2013.529

[16] A. Iafrati and A. A. Korobkin, "Initial stage of flat plate impact onto liquid free surface," Physics of Fluids, vol. 16, pp. 2214-2227, 2004.
https://doi.org/10.1063/1.1714667

[17] O. M. Faltinsen, Hydrodynamics of high-speed marine vehicles. Cambridge University Press, 2005.
https://doi.org/10.1017/CBO9780511546068

[18] M. Shakeri, M. Tavakolinejad, and J. H. Duncan, "An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave marker technique," Journal of Fluid Mechanics, vol. 634, pp. 217-243, 2009.
https://doi.org/10.1017/S0022112009007216

[19] H. Climent, L. Benitez, F. Rueda, and N. Toso-Pentecote, "Aircraft ditching numerical simulation," in ICAS 2006, 2006.

[20] Y. A. Semenov and L. J. Cummings, "Free boundary Darcy flows with surface tension: Analytical and numerical study," European Journal of Applied Mathematics, vol. 17, pp. 607-631, 2006.
https://doi.org/10.1017/S0956792506006759

[21] N. E. Joukovskii, Modification of Kirchhof's method for determination of a fluid motion in two directions at a fixed velocity given on the unknown streamline, ser. Mathematical Transactions. Moscow: Moscow Mathematical Society, 1890, vol. XV. [Online]. Available: http://books.e-heritage.ru/book/10070428

[22] J. H. Michell, "On the theory of free stream lines," Philosophical Transactions of the Royal Society A, vol. 181, pp. 389-431, 1890.
https://doi.org/10.1098/rsta.1890.0006

[23] M. I. Gurevich, Theory of jets in ideal fluids. New York: Academic Press, 1965.

[24] M. Brillouin, "Les surfaces de glissement de Helmholtz et la resistance des fluids," Annales de Chimie et de Physique, vol. 23, pp. 145-230, 1911.

[25] H. Villat, "Sur la validite des solutions de certains problemes d'Hydrodynamique," Journal de Mathematiques Pures et Appliquees, vol. 10, pp. 231-290, 1914.

[26] Y. A. Semenov and G. X. Wu, "Water entry of an expanding wedge/plate with flow detachment," Journal of Fluid Mechanics, vol. 797, pp. 322-344.
https://doi.org/10.1017/jfm.2016.291

[27] J. M. Oliver, "Second-order Wagner theory for two-dimensional water-entry problems at small deadrise angles," Journal of Fluid Mechanics, vol. 572, pp. 59-85, 2007.
https://doi.org/10.1017/S002211200600276X