LiU Electronic Press

# Konferensartikel

## The Wave Excitation Forces on a Floating Vertical Cylinder in Water of Infinite Depth

William Finnegan
College of Engineering and Informatics, National University of Ireland, Galway, Ireland

Martin Meere
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Jamie Goggins
Ryan Institute for Environmental, Marine and Energy Research, National University of Ireland, Galway, Ireland

Linköping Electronic Conference Proceedings 57:5, s. 2175-2182

Visa mer +

ISBN: 978-91-7393-070-3

ISSN: 1650-3686 (tryckt), 1650-3740 (online)

### Abstract

When carrying out any numerical modeling it is vital to have an analytical approximation to insure that realistic results are obtained. The numerical modeling of wave energy converters is an efficient and inexpensive method of undertaking initial optimisation and experimentation. Therefore; the main objective of this paper is to determine an analytical solution for the heave; surge and pitch wave excitation forces on a floating cylinder in water of infinite depth. The boundary value problem technique; using the method of separation of variables; is employed to derive the velocity potentials throughout the fluid domain. A Fourier transform is used to represent infinite depth. Additionally; Havelock’s expansion theorem is used to invert the complicated combined Fourier sine/cosine transform. An asymptotic approximation is taken for low frequency incident waves in order to create an analytical solution to the problem. Graphical representations of the wave excitation forces with respect to incident wave frequencies for various draft to radius ratios are presented; which can easily be used in the design of wave energy converters.

### Nyckelord

Infinite depth; Wave energy; Wave structure interaction; Wave water problem

### Referenser

[1] F. Ursell; On The Heaving Motion of a Circular Cylinder on the Surface of a Fluid; The Quarterly Journal of Mechanics and Applied Mathematics; 2(2); 1949; pp. 218-231. doi: 10.1093/qjmam/2.2.218.

[2] T. Havelock; Waves due to a Floating Sphere Making Periodic Heaving Oscillations. Proceedings of the Royal Society of London; Series A; Mathematical and Physical Sciences; 231(1184); 1955; pp. 1-7. doi: 10.1098/rspa.1955.0152.

[3] C.J.R. Garrett; Wave forces on a circular dock; Journal of Fluid Mechanics; 46(01); 1971; pp. 129-139. doi: 10.1017/S0022112071000430.

[4] J.L. Black; Wave forces on vertical axisymmetric bodies; Journal of Fluid Mechanics; 67(02); 1975; pp. 369-376. doi: 10.1017/S0022112075000353.

[5] R.W. Yeung; Added mass and damping of a vertical cylinder in finite-depth waters; Applied Ocean Research; 3(3); 1981; pp. 119-133. doi: 10.1016/0141-1187(81)90101-2.

[6] D.D. Bhatta and M. Rahman; On scattering and radiation problem for a cylinder in water of finite depth; International Journal of Engineering Science; 41(9); 2003; pp. 931-967. doi: 10.1016/S0020-7225(02)00381-6.

[7] C.M. Linton and P.McIver; Handbook of Mathematical Techniques for Wave/Structure Interactions; Chapman & Hall/CRC; 2001. doi: 10.1201/9781420036060.

[8] C.H. Kim; Nonlinear Waves and Offshore Structures; Advanced Series on Ocean Engineering; World Scientific Publishing Co. Pte. Ltd; 2008.

[9] A. Chakrabarti; On the Solution of the Problem of Scattering of Surface-Water Waves by the Edge of an Ice Cover; Proceedings: Mathematical; Physical and Engineering Sciences; 456(1997); 2000 pp. 1087-1099.