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A ring-source/integral-equation method for the calculation of hydrodynamic forces exerted on floating bodies of revolution

Published online by Cambridge University Press:  20 April 2006

Andrew Hulme
Andrew Hulme
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL
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Abstract

The wave forces exerted on a floating 3-dimensional body can be found by expressing the velocity potential of the surrounding fluid as the field of a distribution of point wave sources over the wetted part of the body surface. The problem then reduces to one of finding the solution to a 2-dimensional Fredholm integral equation of the second kind, to give the (unknown) surface source density. A simplification is possible for bodies that have a vertical axis of symmetry: for this type of body we can distribute ‘rings of sources’ over the body surface, and the problem then reduces to the solution of 1-dimensional Fredholm equations of the second kind. This approach has been adopted before, but earlier work has made use of expressions for the fundamental ring-source potentials which are not always suitable for numerical computation. It is possible to derive many alternative expressions for the ring-source potentials, but it appears that no single expression is computationally convenient in every situation; the present paper discusses the computational merits of three different types of expression, the aim being to provide a comprehensive scheme for the evaluation of the ring-source potentials. The ring-source/integral-equation method will be used to calculate the wave forces exerted on certain specific bodies of revolution and results are presented here. A brief discussion of the problem of ‘irregular values’ is also given: these only occur when the body intersects the free surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 128 , March 1983 , pp. 387 - 412
Copyright
© 1983 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions, 9th edn. Dover. (Also available as National Bureau of Standards, Applied Mathematics Series, no. 55, 1964.)
Baker, C. T. H. 1977 Numerical Solution of Integral Equations. Clarendon.
Black, J. L. 1975 Wave forces on vertical axisymmetrical bodies J. Fluid Mech. 67, 369–376.Google Scholar
Budal, K. et al. 1981 Model experiment with a phase controlled point absorber. In Proc. 2nd Int. Symp. on Wave and Tidal Energy, pp. 191–206. BHRA Fluid Engineering.
Count, B. M. & Knott, G. 1980 An experimental investigation of point absorber arrays. Central Electricity Generating Board Res. Rep. RM/M/N1144.Google Scholar
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Higher Transcendental Functions, vol. 1. McGraw-Hill.
Evans, D. V. 1981 Power from water waves Ann. Rev. Fluid Mech. 13, 157–187.Google Scholar
Fenton, J. D. 1978 Wave forces on vertical bodies of revolution J. Fluid Mech. 85, 241–255.Google Scholar
Garabedian, P. R. 1964 Partial Differential Equations. Wiley, New York.
Garrison, C. J. & Chow, P. Y. 1972 Wave forces on submerged bodies J. Waterways Harbours Div. A.S.C.E. 98, 375–392.Google Scholar
Havelock, T. 1955 Waves due to a floating hemisphere making periodic heaving oscillations. Proc. R. Soc. Lond A 231, 1–7.Google Scholar
Hogben, N. & Standing, R. G. 1974 Wave loads on large bodies. In Proc. Int. Symp. Dyn. Marine Vehicles and Structures in Waves, University College, London, pp. 273–292.
Hulme, A. 1981a The potential of a horizontal ring of wave forces in a fluid with a free surface. Proc. R. Soc. Lond A 375, 295–305.Google Scholar
Hulme, A. 1981b A ring-source/integral equation method for the calculation of wave forces acting on bodies of revolution. Ph.D. thesis, University of Manchester.
Hulme, A. 1982 The wave forces acting on a floating hemisphere undergoing forced periodic oscillations J. Fluid Mech. 121, 443–463.Google Scholar
John, F. 1950 On the motion of floating bodies, II Communs Pure Appl. Math. 3, 45–101.Google Scholar
Kim, W. D. 1965 Oscillations of a rigid body on a free surface J. Fluid Mech. 21, 427–451.Google Scholar
Mei, C. C. 1978 Numerical methods in water wave diffraction and radiation Ann. Rev. Fluid Mech. 10, 393–416.Google Scholar
Milgram, H. & Halkyard, J. E. 1971 Wave forces on large objects in the sea J. Ship Res. 15, 115–124.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, vol. II. McGraw-Hill.
Motora, S. & Kayama, T. 1966 Wave excitationless ship forms. In Proc. 6th Symp. on Naval Hydrodynamics, Washington D.C., pp. 383–403.
Newman, J. N. 1962 The exciting forces on fixed bodies in waves J. Ship Res. 6, 10–17.Google Scholar
Sayer, P. 1977 The virtual mass of heaving cylinders on water of finite depth. Ph.D. thesis, University of Manchester.
Stroud, A. H. & Secrest, D. 1966 Gaussian Quadrature Formulas. Prentice-Hall.
Ursell, F. 1953 Short surface waves due to an oscillating immersed body. Proc. R. Soc. Lond A 220, 90–103.Google Scholar
Ursell, F. 1974 Short surface waves in a canal: dependence of frequency on curvature. J. Fluid Mech. 63, 177–181.Google Scholar
Ursell, F. 1981 Irregular frequencies and the motion of floating bodies J. Fluid Mech. 105, 143–156.Google Scholar
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions. Cambridge University Press.