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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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