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Water entry of an expanding wedge/plate with flow detachment

Published online by Cambridge University Press:  23 May 2016

Yuriy A. Semenov  and
Guo Xiong Wu
Yuriy A. Semenov
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK Institute of Hydromechanics, Academy of Sciences of Ukraine, Kiev 03680, Zhelyabova 8/4, Ukraine
Guo Xiong Wu*
Affiliation:
Department of Mechanical Engineering, University College London, London WC1E 6BT, UK
*
†Email address for correspondence: [email protected]
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Abstract

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

JFM classification

Mathematical Foundations: General fluid mechanics Interfacial Flows (free surface): Interfacial Flows (free surface) Mathematical Foundations: Mathematical Foundations
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 322 - 344
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Copyright
© 2016 Cambridge University Press 

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References

Armand, J. L. & Cointe, R. 1987 Hydrodynamic impact analysis of a cylinder. J. Offshore Mech. Arctic Engng 9, 237–243.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Cumberbatch, E. 1960 The impact of a water wedge on the wall. J. Fluid Mech. 7, 353–374.Google Scholar
Dobrovol’skaya, Z. N. 1969 Some problems of similarity flow of fluid with a free surface. J. Fluid Mech. 36, 805–829.Google Scholar
Faltinsen, O. M. 2005 Hydrodynamics of High-speed Marine Vehicles. p. 454. Cambridge University Press.Google Scholar
Faltinsen, O. M. & Semenov, Y. A. 2008 Nonlinear problem of flat plate entry into an incompressible liquid. J. Fluid Mech. 611, 151–173.CrossRefGoogle Scholar
Fraenkel, L. E. & Keady, G. 2004 On the entry of a wedge into water: the thin wedge and an all-purpose boundary-layer equation. J. Engng Maths 48, 219–252.Google Scholar
Fraenkel, L. E. & McLeod, J. B. 1997 Some results for the entry of a blunt wedge into water. Phil. Trans. R. Soc. Lond. A 355, 523–535.Google Scholar
Garabedian, P. R. 1953 Oblique water entry of a wedge. Commun. Pure Appl. Maths 6 (2), 157–165.Google Scholar
Garabedian, P. R. 1965 Asymptotic description of a free boundary at the point of separation. In Proceedings of Symposia in Applied Mathematics (ed. Finn, R.), vol. 17, p. 111. American Mathematical Society.Google Scholar
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1 (06), 625–643.Google Scholar
Greenhow, M. 1987 Wedge entry into initially calm water. Appl Ocean Res. 9, 259–275.CrossRefGoogle Scholar
Gurevich, M. I. 1965 Theory of Jets in Ideal Fluids. p. 585. Academic.Google Scholar
Howison, S. D., Ockendon, J. R. & Oliver, J. M. 2002 Deep- and shallow-water slamming at small and zero deadrise angles. J. Engng Maths 42, 373–388.Google Scholar
Howison, S. D., Ockendon, J. R. & Oliver, J. M. 2004 Oblique slamming, planing and skimming. J. Engng Maths 48, 321–337.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. & Battistin, D. 2003 Hydrodynamics of water entry in presence of flow separation from chines. In The 8th International Conference on Numerical Ship Hydrodynamics, 22–25 September, Busan, Korea.Google Scholar
Iafrati, A. & Korobkin, A. A. 2004 Initial stage of flat plate impact onto liquid free surface. Phys. Fluids 16, 2214–2227.Google Scholar
von Karman, T. 1929 The impact of seaplane floats during landing. NACA Tech. Note 321. Washington, DC.Google Scholar
Keller, J. B. & Miksis, M. J. 1983 Surface tension driven flows. SIAM J. Appl. Maths 43, 268–277.CrossRefGoogle Scholar
Korobkin, A. A. 2004 Analytical models of water impact. Eur. J. Appl. Maths 15, 821–838.Google Scholar
Longuet-Higgins, M. S. 1976 Self-similar, time-dependent flows with a free surface. J. Fluid Mech. 73 (04), 603–620.Google Scholar
Mackie, A. G. 1962 A linearized theory of the water entry problem. Q. J. Mech. Appl. Maths 15, 137–151.Google Scholar
Mackie, A. G. 1963 Initial value problems in water wave theory. J. Austral. Math. Soc. 3, 340–350.CrossRefGoogle Scholar
Maki, K. J., Lee, D., Troesch, A. W. & Vlahopoulos, N. 2011 Hydroelastic impact of a wedge-shaped body. Ocean Engng 38, 621–629.Google Scholar
Mei, X., Lui, Y. & Yue, D. K. P. 1999 On the water impact of general two-dimensional sections. Appl. Ocean Res. 21, 1–15.Google Scholar
Moore, M. R., Ockendon, H., Ockendon, J. R. & Oliver, J. M. 2015 Capillary and viscous perturbations to Helmholtz flows. J. Fluid Mech. 742, R1.Google Scholar
Polyan, A.D. & Manzhirov, A. V. 2008 Handbook of Integral Equations. Chapman and Hall/CRC.Google Scholar
Pullin, D. I. 1978 The large-scale structure of unsteady self-similar rolled-up vortex sheets. J. Fluid Mech. 88 (03), 401–430.Google Scholar
Pullin, D. I. & Perry, A. E. 1980 Some flow visualization experiments on the starting vortex. J. Fluid Mech. 97 (02), 239–255.Google Scholar
Semenov, Y. A. & Cummings, L. J. 2006 Free boundary Darcy flows with surface tension: analytical and numerical study. Eur. J. Appl. Maths 17, 607–631.Google Scholar
Semenov, Y. A. & Iafrati, A. 2006 On the nonlinear water entry problem of asymmetric wedges. J. Fluid Mech. 547, 231–256.Google Scholar
Semenov, Y. A., Wu, G. X. & Korobkin, A. A 2015 Impact of liquids with different densities. J. Fluid Mech. 766, 5–27.Google Scholar
Semenov, Y. A., Wu, G. X. & Oliver, J. M 2013 Splash jet caused by collision of two liquid wedges. J. Fluid Mech. 737, 132–145.Google Scholar
Shakeri, M., Tavakolinejad, M. & Duncan, J. H. 2009 An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave marker technique. J. Fluid Mech. 634, 217–243.Google Scholar
Sun, S. L. & Wu, G. X. 2014 Self-similar solution for oblique impact of a water column with sharp front on a wall and its zero inner angle steady limit. Phys. Fluids 26, 082106.Google Scholar
Tassin, A., Korobkin, A. A. & Cooker, M. J. 2014 On analytical models of vertical water entry of a symmetric body with separation and cavity initiation. Appl. Ocean Res. 48, 33–41.Google Scholar
Vella, D. & Li, J. 2010 The impulsive motion of a small cylinder at an interface. Phys. Fluids 22, 052104.Google Scholar
Wagner, H. 1932 Über Stoßund Gleitvorgänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech. 12, 192–215.Google Scholar
Wu, G. X. & Sun, S. L. 2014 Similarity solution for oblique water entry of an expanding paraboloid. J. Fluid Mech. 745, 398–408.Google Scholar
Zeff, B. W., Kleber, B., Fineberg, J. & Lathrop, D. P. 2000 Singularity dynamics in curvature collapse and jet eruption on a fluid surface. Nature 403, 401–404.Google Scholar
Zhao, R. & Faltinsen, O. 1993 Water-entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612.Google Scholar
Zhao, R., Faltinsen, O. & Aarsnes, J. 1997 Water entry of arbitrary two-dimensional sections with and without flow separation. In 21st Symposium on Naval Hydrodynamics, Trondheim, Norway.Google Scholar