Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T14:13:44.387Z Has data issue: false hasContentIssue false

Impulsive impact of a submerged body

Published online by Cambridge University Press:  25 May 2021

Y.A. Semenov*
Affiliation:
National Academy of Sciences of Ukraine, Institute of Hydromechanics, 8/4 Marii Kapnist Street, Kyiv03057, Ukraine
Y.N. Savchenko
Affiliation:
National Academy of Sciences of Ukraine, Institute of Hydromechanics, 8/4 Marii Kapnist Street, Kyiv03057, Ukraine
G.Y. Savchenko
Affiliation:
National Academy of Sciences of Ukraine, Institute of Hydromechanics, 8/4 Marii Kapnist Street, Kyiv03057, Ukraine
*
Email address for correspondence: [email protected]

Abstract

An analytical solution of the impulsive impact of a cylindrical body submerged below a calm water surface is obtained by solving a free boundary problem. The shape of the cross-section of the body is arbitrary. The integral hodograph method is applied to derive the complex velocity potential defined in a parameter plane. The boundary-value problem is reduced to a Fredholm integral equation of the first kind in the velocity magnitude on the free surface. The velocity field, the impulsive pressure on the body surface and the added mass are determined in a wide range of depths of submergence for various cross-sectional shapes, such as a flat plate, a circular cylinder and a rectangle.

Type
JFM Rapids
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Cooker, M.J. & Peregrine, D.H. 1995 Pressure-impulse theory for liquid impact problems. J. Fluid Mech. 297, 193214.CrossRefGoogle Scholar
Darwin, C. 1953 Note on hydrodynamics. Math. Proc. Camb. Phil. Soc. 49 (2), 342354.CrossRefGoogle Scholar
Eames, I., Belcher, S.E. & Hunt, J.C.R. 1994 Drift, partial drift and Darwin's proposition. J. Fluid Mech. 275, 201223.CrossRefGoogle Scholar
Faltinsen, O.M. 2005 Hydrodynamics of High-speed Marine Vehicles. Cambridge University Press.Google Scholar
Greenhow, M. 1983 Nonlinear free surface effects: experiments and theory. Tech. Rep. 83-19. MIT, Department of Ocean Engineering.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), 325348.CrossRefGoogle Scholar
Havelock, T.H. 1949 a The wave resistance of a cylinder started from rest. Q. J. Mech. Appl. Maths 2, 325334.CrossRefGoogle Scholar
Havelock, T.H. 1949 b The resistance of a submerged cylinder in accelerated motion. Q. J. Mech. Appl. Maths 2, 419427.CrossRefGoogle Scholar
Hjelmervik, K.B. & Tyvand, P.A. 2017 Incompressible impulsive wall impact of liquid cylinders. J. Engng Maths 103, 159171.CrossRefGoogle Scholar
Iafrati, A. & Korobkin, A.A. 2005 Starting flow generated by the impulsive start of a floating wedge. J Engng Maths 51, 99125.CrossRefGoogle Scholar
Joukowskii, N.E. 1884 On impact of two spheres, one of which floats in liquid. Mat. Otd. Novorossiiskogo Obshchestva Estestvoispytatelej 5, 4348.Google Scholar
Joukovskii, N.E. 1890 Modification of Kirchhoff's method for determination of a fluid motion in two directions at a fixed velocity given on the unknown streamline. Math. Sbornik. 15 (1), 121278.Google Scholar
von Kármán, T. 1929 The impact of seaplane floats during landing. NACA Tech. Note 321.Google Scholar
King, A. & Needham, D. 1994 The initial development of a jet caused by fluid, body and free-surface interaction. Part 1. A uniformly accelerating plate. J. Fluid Mech. 268, 89101.CrossRefGoogle Scholar
Korobkin, A. & Yilmaz, O. 2009 The initial stage of dam-break flow. J. Engng Maths 63, 293308.CrossRefGoogle Scholar
Korobkin, A.A. & Scolan, Y.-M. 2006 Three-dimensional theory of water impact. Part 2. Linearized Wagner problem. J. Fluid Mech. 549, 343373.CrossRefGoogle Scholar
Lagrange, J.-L. 1783 Memoire sur la theorie du mouvement des fluides. Nouv. Mem. Acad. Sci. Berlin 12, 151188.Google Scholar
Michell, J.H. 1890 On the theory of free stream lines. Phil. Trans. R. Soc. Lond. A 181, 389431.Google Scholar
Needham, D., Billingham, J. & King, A. 2007 The initial development of a jet caused by fluid, body and free-surface interaction. Part 2. An impulsively moved plate. J. Fluid Mech. 578, 6784.CrossRefGoogle Scholar
Newman, J.N. 1977 Marine Hydrodynamics. The MIT Press.CrossRefGoogle Scholar
Peters, I.R., Madonia, M., Lohse, D. & van der Meer, D. 2016 Volume entrained in the wake of a disk intruding into an oil-water interface. Phys. Rev. Fluids 1, 033901.CrossRefGoogle Scholar
Polyanin, A.D. & Manzhirov, A.V. 1998 Hand Book of Integral Equations. CRC.CrossRefGoogle Scholar
Semenov, Y.A. & Yoon, B-S. 2009 Onset of flow separation for the oblique water impact of a wedge. Phys. Fluids 21, 112103.CrossRefGoogle Scholar
Tyvand, P.A. & Miloh, T. 1995 Free-surface flow due to impulsive motion of a submerged circular cylinder. J. Fluid Mech. 286, 67101.CrossRefGoogle Scholar
Tyvand, P.A. & Miloh, T. 2012 Incompressible impulsive sloshing. J. Fluid Mech. 708, 279302.CrossRefGoogle Scholar
Venkatesan, S.K. 1985 Added mass of two cylinders. J. Ship Res. 29 (4), 234240.CrossRefGoogle Scholar
Wagner, H. 1932 Über Stoß und Gleitvorgänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech. 12, 192215.CrossRefGoogle Scholar