Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-09T21:54:05.329Z Has data issue: false hasContentIssue false
  • English
  • Français

Resonant behaviour of an oscillating wave energy converter in a channel

Published online by Cambridge University Press:  18 May 2012

Emiliano Renzi  and
F. Dias
Emiliano Renzi*
Affiliation:
UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
F. Dias
Affiliation:
UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland Centre de Mathématiques et de Leurs Applications (CMLA), Ecole Normale Supérieure de Cachan, 94235 Cachan, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A mathematical model is developed to study the behaviour of an oscillating wave energy converter in a channel. During recent laboratory tests in a wave tank, peaks in the hydrodynamic actions on the converter occurred at certain frequencies of the incident waves. This resonant mechanism is known to be generated by the transverse sloshing modes of the channel. Here the influence of the channel sloshing modes on the performance of the device is further investigated. Within the framework of a linear inviscid potential-flow theory, application of Green’s theorem yields a hypersingular integral equation for the velocity potential in the fluid domain. The solution is found in terms of a fast-converging series of Chebyshev polynomials of the second kind. The physical behaviour of the system is then analysed, showing sensitivity of the resonant sloshing modes to the geometry of the device, which concurs in increasing the maximum efficiency. Analytical results are validated with available numerical and experimental data.

JFM classification

Mathematical Foundations: General fluid mechanics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 701 , 25 June 2012 , pp. 482 - 510
Copyright
Copyright © Cambridge University Press 2012

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

1. Achenbach, J. D. & Li, Z. L. 1986 Reflection and transmission of scalar waves by a periodic array of screens. Wave Motion 8, 225–234.CrossRefGoogle Scholar
2. Chen, X. 1994 On the sidewall effects upon bodies of arbitrary geometry in wave tanks. Appl. Ocean Res. 16, 337–345.CrossRefGoogle Scholar
3. Cruz, J.  (Ed.) 2008 Ocean Wave Energy. Springer.CrossRefGoogle Scholar
4. Dean, R. G. & Dalrymple, R. A. 1991 Water Wave Mechanics for Engineers and Scientists. World Scientific.CrossRefGoogle Scholar
5. Eatock Taylor, R. & Hung, S. M. 1985 Mean drift forces on an articulated column oscillating in a wave tank. Appl. Ocean Res. 7 (2), 66–78.CrossRefGoogle Scholar
6. Evans, D. V. & Porter, R. 1996 Hydrodynamic characteristics of a thin rolling plate in finite depth of water. Appl. Ocean Res. 18, 215–228.CrossRefGoogle Scholar
7. Evans, D. V. & Porter, R. 1997 Efficient calculation of hydrodynamic properties of OWC-type devices. J. Offshore Mech. Arctic Engng 119 (4), 210–218.CrossRefGoogle Scholar
8. Falnes, J. 2002 Ocean Waves and Oscillating Systems. Cambridge University Press.CrossRefGoogle Scholar
9. Folley, M., Whittaker, T. & Henry, A. 2005 The performance of a wave energy converter in shallow water. In 6th European Wave and Tidal Energy Conference, Glasgow, UK.Google Scholar
10. Folley, M., Whittaker, T. & van’t Hoff, J. 2007 The design of small seabed-mounted bottom-hinged wave energy converters. In 7th European Wave and Tidal Energy Conference, Porto, Portugal.Google Scholar
11. Gradshteyn, I. S. & Ryzhik, I. M. 2007 Tables of Integrals Series and Products. Academic.Google Scholar
12. Henry, A. 2008 The hydrodynamics of small seabed mounted bottom hinged wave energy converters in shallow water. PhD thesis, Queen’s University Belfast.Google Scholar
13. Henry, A., Doherty, K., Cameron, L., Whittaker, T. & Doherty, R. 2010 Advances in the design of the Oyster wave energy converter. In RINA Marine and Offshore Renewable Energy, London, UK.CrossRefGoogle Scholar
14. van’t Hoff, J. 2009 Hydrodynamic modelling of the oscillating wave surge converter. PhD thesis, Queen’s University Belfast.Google Scholar
15. Linton, C. M. 1998 The Green’s function for the two-dimensional Helmholtz equation in periodic domains. J. Engng Math. 33, 377–402.CrossRefGoogle Scholar
16. Linton, C. M. & Evans, D. V. 1992 The radiation and scattering of surface waves by a vertical circular cylinder in a channel. Phil. Trans. R. Soc. Lond. A 338, 325–357.CrossRefGoogle Scholar
17. Linton, C. M. & McIver, P. 2001 Mathematical Techniques for Wave/Structure Interactions. Chapman & Hall/CRC.CrossRefGoogle Scholar
18. Lovas, S., Mei, C. C. & Liu, Y. 2010 Oscillating water column at a coastal corner for wave power extraction. Appl. Ocean Res. 32, 267–283.CrossRefGoogle Scholar
19. Martin, P. A. & Farina, L. 1997 Radiation of water waves by a heaving submerged horizontal disc. J. Fluid Mech. 337, 365–379.CrossRefGoogle Scholar
20. Martin, P. A. & Rizzo, F. J. 1989 On boundary integral equations for crack problems. Proc. R. Soc. Lond. A 421, 341–355.Google Scholar
21. McCormick, M. E. 2007 Ocean Wave Energy Conversion. Dover.Google Scholar
22. Mei, C. C. 1997 Mathematical Analysis in Engineering. Cambridge University Press.Google Scholar
23. Mei, C. C., Sammarco, P., Chan, E. S. & Procaccini, C. 1994 Subharmonic resonance of proposed storm gates for Venice lagoon. Proc. R. Soc. Lond. A 444, 257–265.Google Scholar
24. Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005 Theory and Application of Ocean Surface Waves. World Scientific.Google Scholar
25. Milgram, J. H. 1970 Active water-wave absorbers. J. Fluid Mech. 43 (4), 845–859.CrossRefGoogle Scholar
26. Newman, J. N. 1977 Marine Hydrodynamics. MIT Department of Naval Architecture and Marine Engineering.CrossRefGoogle Scholar
27. Parsons, N. F. & Martin, P. A. 1992 Scattering of water waves by submerged plates using hypersingular integral equations. Appl. Ocean Res. 14, 313–321.CrossRefGoogle Scholar
28. Parsons, N. F. & Martin, P. A. 1994 Scattering of water waves by submerged curved plates and by surface-piercing flat plates. Appl. Ocean Res. 16 (3), 129–139.CrossRefGoogle Scholar
29. Parsons, N. F. & Martin, P. A. 1995 Trapping of water waves by submerged plates using hypersingular integral equations. J. Fluid Mech. 284, 359–375.CrossRefGoogle Scholar
30. Sammarco, P. 1996 Theory of subharmonic resonance of storm gates for Venice lagoon. PhD thesis, Massachusetts Institute of Technology.Google Scholar
31. Sammarco, P., Tran, H. H. & Mei, C. C. 1997 Subharmonic resonance of Venice gates in waves. Part 1. Evolution equation and uniform incident waves. J. Fluid Mech. 349, 295–325.CrossRefGoogle Scholar
32. Schmitt, P., Bourdier, S., Sarkar, D., Renzi, E., Dias, F., Doherty, K., Whittaker, T. & van’t Hoff, J. 2012 Hydrodynamic loading on a bottom hinged oscillating wave surge converter. In 22nd International Ocean and Polar Engineering Conference, Rhodes, Greece.Google Scholar
33. Shemer, L., Kit, E. & Miloh, T. 1987 Measurements of two- and three-dimensional waves in a channel, including the vicinity of cut-off frequencies. Exp. Fluids 5, 66–72.CrossRefGoogle Scholar
34. WAMIT Inc., 2008 WAMIT User Manual. WAMIT, Inc., Chestnut Hill, MA..Google Scholar
35. Whittaker, T., Collier, D., Folley, M., Osterried, M., Henry, A. & Crowley, M. 2007 The development of Oyster: a shallow water surging wave energy converter. In 7th European Wave and Tidal Energy Conference, Porto, Portugal.Google Scholar
36. Yeung, R. W. & Sphaier, S. H. 1989 Wave-interference on a truncated cylinder in a channel. J. Engng Math. 23, 95–117.CrossRefGoogle Scholar