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A linearized model of water exit

Published online by Cambridge University Press:  25 November 2013

Alexander A. Korobkin
Alexander A. Korobkin*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
*
†Email address for correspondence: a.korobkin@uea.ac.uk
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Abstract

A model of hydrodynamic loads acting on a rigid floating body during the lifting of the body from the liquid surface is presented. The liquid is of infinite depth, inviscid and incompressible. Initially the liquid is at rest. The body suddenly starts to move upwards from the liquid at a constant acceleration. Boundary conditions on the liquid surface are linearized and imposed on the equilibrium position of the liquid surface. The resulting boundary problem is solved by the methods of analytical functions. Negative pressures are allowed and the pressure is assumed continuous at the periphery of the wetted area. The unknown size of the wetted area is determined by the condition that the speed of the contact points is proportional to the local velocity of the flow. This condition provides a nonlinear Abel-type integral equation which is solved explicitly. Both two-dimensional and axisymmetric configurations are considered. Predicted hydrodynamic forces are compared with the computational fluid dynamics results by Piro & Maki (11th International Conference on Fast Sea Transport. Honolulu, Hawaii, USA, 2011) for both a rigid wedge and circular cylinder, which initially enter the water and then exit from it.

JFM classification

Aerodynamics: Aerodynamics Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 368 - 386
Copyright
©2013 Cambridge University Press 

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References

Baarholm, R. J. 2001 Theoretical and experimental studies of wave impact underneath decks of offshore platforms. PhD thesis, Department of Marine Hydrodynamics, NTNU, Trondheim.Google Scholar
Baarholm, R. J. & Faltinsen, O. M. 2004 Wave impact underneath horizontal decks. J. Mar. Sci. Technol. Fluid Mech. 9, 1–13.Google Scholar
Bugaenko, B. A. 1973 Determination of added masses of elliptic cylinder lifted from the water surface. Proceedings of the Nikolaev Shipbuilding Institute 78, 91–98.Google Scholar
Chapman, S. J., Gillow, K. A., Howison, S. D. & Ockendon, J. R. 1997 Asymptotics of violent surface motion. Phil. Trans. R. Soc. Lond. A 355, 679–685.CrossRefGoogle Scholar
Faltinsen, O. M., Landrini, M. & Greco, M. 2004 Slamming in marine applications. J. Engng Maths 48, 187–217.CrossRefGoogle Scholar
Gillow, K. A. 1998 Codimension-two free boundary problems. PhD thesis, University of Oxford.Google Scholar
Greenhow, M. 1988 Water-entry and -exit of a horizontal circular cylinder. Appl. Ocean Res. 10 (4), 191–198.Google Scholar
Greenhow, M. & Moyo, S. 1997 Water entry and exit of horizontal circular cylinders. Phil. Trans. R. Soc. A 355, 551–563.Google Scholar
Greenhow, M. & Yanbao, L. 1987 Added masses for circular cylinders near or penetrating fluid boundaries: review, extension and application to water-entry, -exit and slamming. Ocean Engng 14 (4), 325–348.Google Scholar
Hicks, P. D. & Smith, F. T. 2011 Skimming impacts and rebounds on shallow liquid layers. Proc. R. Soc. A 467, 653–674.Google Scholar
Howison, S. D., Ockendon, J. R. & Wilson, S. K. 1991 Incompressible water-entry problems at small deadrise angles. J. Fluid Mech. 222, 215–230.Google Scholar
Iafrati, A. & Korobkin, A. A. 2008 Hydrodynamic loads during early stage of flat plate impact onto water surface. Phys. Fluids 20, 082104.CrossRefGoogle Scholar
Kaplan, P. 1987 Analysis and prediction of flat bottom slamming impact of advanced marine vehicles in waves. Intl Shipbuilding Prog. 34 (391), 44–53.CrossRefGoogle Scholar
Khabakhpasheva, T. I. & Korobkin, A. A. 2013 Oblique impact of a smooth body on a thin layer of inviscid liquid. Proc. R. Soc. A 469 (2151).Google Scholar
Korobkin, A. A. 2003 Cavitation in liquid impact problems. In Fifth International Symposium on Cavitation, Osaka, 1–4 November 2003.Google Scholar
Korobkin, A. A. 2004 Analytical models of water impact. Eur. J. Appl. Maths 15, 821–838.Google Scholar
Korobkin, A. A. & Iafrati, A. 2005 Hydrodynamic loads during initial stage of floating body impact. J. Fluids Struct. 21 (4), 413–427.CrossRefGoogle Scholar
Korobkin, A. A. & Peregrine, D. H. 2000 The energy distribution resulting from an impact on a floating body. J. Fluid Mech. 417, 157–181.Google Scholar
Korobkin, A. A. & Pukhnachov, V. V. 1988 Initial stage of water impact. Annu. Rev. Fluid Mech. 20, 159–185.Google Scholar
Korotkin, A. I. 2009 Added Masses of Ship Structures. Fluid Mechanics and its Applications, vol. 88, Springer.Google Scholar
Moore, M. R., Howison, S. D., Ockendon, J. R. & Oliver, J. M. 2013 A note on oblique water-entry. J. Engng Maths 81, 67–74.CrossRefGoogle Scholar
Moore, M. R., Howison, S. D., Ockendon, J. R. & Oliver, J. M. 2012 Three-dimensional oblique water-entry problems at small deadrise angles. J. Fluid Mech. 711, 259–280.Google Scholar
Norkin, M. & Korobkin, A. A. 2011 The motion of the free-surface separation point during the initial stage of horizontal impulsive displacement of a floating circular cylinder. J. Engng Maths 70, 239–254.Google Scholar
Oliver, J. M. 2002 Water entry and related problems. PhD thesis, University of Oxford.Google Scholar
Piro, D. J. & Maki, K. J. 2011 Hydroelastic wedge entry and exit. In 11th International Conference on Fast Sea Transport. Honolulu, Hawaii, USA.Google Scholar
Piro, D. J. & Maki, K. J. 2012 Water exit of a wedge-shaped body. In Proceedings 27th IWWWFB, Copenhagen, Denmark, pp. 141–144.Google Scholar
Piro, D. J. & Maki, K. J. 2013 Hydroelastic analysis of bodies that enter and exit water. J. Fluids Struct. 37, 134–150.Google Scholar
Reis, P. M., Jung, S., Aristoff, J. M. & Stocker, R. 2010 How cats lap: water uptake by Felis catus . Science 330, 1231–1234.Google Scholar
Reinhard, M., Korobkin, A. A. & Cooker, M. J. 2012 The bounce of a blunt body from a water surface at high horizontal speed. In Proceedings 27th IWWWFB, Copenhagen, Denmark, pp. 153–156.Google Scholar
Scolan, Y.-M. & Korobkin, A. A. 2012 Hydrodynamic impact (Wagner) problem and Galin’s theorem. In Proceedings 27th IWWWFB, Copenhagen, Denmark, pp. 165–168.Google Scholar
Scolan, Y.-M., Remy, F. & Thibault, B. 2006 Impact of three-dimensional standing waves on a flat horizontal plate. In Proceedings 21st IWWWFB, Loughborough, UK, pp. 165–168.Google Scholar
Semenov, Y. A., Wu, G. X. & Yoon, B. S. 2012 A surface-piercing body moving along the free surface. In Proceedings 27th IWWWFB, Copenhagen, Denmark, pp. 169–172.Google Scholar
Semenov, Y. A. & Yoon, B. S. 2009 Onset of flow separation for the oblique water impact of a wedge. Phys. Fluids 21, 112103.Google Scholar
Tassin, A., Korobkin, A. A. & Cooker, M. J. 2012 Modelling of the oblique impact of an elongated body by 2D + t approach. In Proceedings 27th IWWWFB, Copenhagen, Denmark, pp. 189–192.Google Scholar
Tassin, A., Piro, D. J., Korobkin, A. A., Maki, K. J. & Cooker, M. J. 2013 Two-dimensional water entry and exit of a body whose shape varies in time. J. Fluids Struct. 40, 317–336.Google Scholar
Tuck, E. O. & Simakov, S. T. 1999 Splash formation at the nose of a smoothly curved body in a stream. J. Austral. Math. Soc. B 40, 421–426.Google Scholar
Wagner, H. 1932 Über Stoss- und Gleitvergänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech. 12 (4), 193–215.Google Scholar