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Application of the time-dependent mild-slope equations for the simulation of wake effects in the lee of a farm of Wave Dragon wave energy converters

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  • Beels, Charlotte
  • Troch, Peter
  • De Visch, Kenneth
  • Kofoed, Jens Peter
  • De Backer, Griet

Abstract

Time-dependent mild-slope equations have been extensively used to compute wave transformations near coastal and offshore structures for more than 20 years. Recently the wave absorption characteristics of a Wave Energy Converter (abbreviated as WEC) of the overtopping type have been implemented in a time-dependent mild-slope equation model by using numerical sponge layers. In this paper the developed WEC implementation is applied to a single Wave Dragon WEC and multiple Wave Dragon WECs. The Wave Dragon WEC is a floating offshore converter of the overtopping type. Two wave reflectors focus the incident wave power towards a ramp. The focussed waves run up the ramp and overtop in a water reservoir above mean sea level. The obtained potential energy is converted into electricity when the stored water drains back to the sea through hydro turbines. The wave reflectors and the main body (ramp and reservoir) are simulated as porous structures, exhibiting the same reflection, respectively absorption characteristics as obtained for the prototype Wave Dragon WEC. The wake effects behind a single Wave Dragon WEC are studied in detail for uni- and multidirectional waves. The shadow zone indicating the wake effect is decreasing with increasing directional spreading. The wake in the lee of a farm of five Wave Dragon WECs, installed in a staggered grid (3 WECs in the first row and 2 WECs in the second row), is calculated for three in-between distances of respectively D, 2D and 3D, with D the distance between the tips of the wave reflectors of a single WEC. As a result, a farm of five Wave Dragon WECs installed in a staggered grid with an in-between distance of 2D is preferred, when taking cost and spatial considerations into account.

Suggested Citation

  • Beels, Charlotte & Troch, Peter & De Visch, Kenneth & Kofoed, Jens Peter & De Backer, Griet, 2010. "Application of the time-dependent mild-slope equations for the simulation of wake effects in the lee of a farm of Wave Dragon wave energy converters," Renewable Energy, Elsevier, vol. 35(8), pages 1644-1661.
    • Handle: RePEc:eee:renene:v:35:y:2010:i:8:p:1644-1661
    DOI: 10.1016/j.renene.2009.12.001
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    1. Kofoed, Jens Peter & Frigaard, Peter & Friis-Madsen, Erik & Sørensen, Hans Chr., 2006. "Prototype testing of the wave energy converter wave dragon," Renewable Energy, Elsevier, vol. 31(2), pages 181-189.
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    1. Shi, Hongda & Zhao, Chenyu & Hann, Martyn & Greaves, Deborah & Han, Zhi & Cao, Feifei, 2019. "WHTO: A methodology of calculating the energy extraction of wave energy convertors based on wave height reduction," Energy, Elsevier, vol. 185(C), pages 299-315.
    2. Beels, Charlotte & Troch, Peter & Kofoed, Jens Peter & Frigaard, Peter & Vindahl Kringelum, Jon & Carsten Kromann, Peter & Heyman Donovan, Martin & De Rouck, Julien & De Backer, Griet, 2011. "A methodology for production and cost assessment of a farm of wave energy converters," Renewable Energy, Elsevier, vol. 36(12), pages 3402-3416.
    3. David, Daniel R. & Rijnsdorp, Dirk P. & Hansen, Jeff E. & Lowe, Ryan J. & Buckley, Mark L., 2022. "Predicting coastal impacts by wave farms: A comparison of wave-averaged and wave-resolving models," Renewable Energy, Elsevier, vol. 183(C), pages 764-780.
    4. Carrelhas, A.A.D. & Gato, L.M.C. & Falcão, A.F.O. & Henriques, J.C.C., 2022. "Control law design for the air-turbine-generator set of a fully submerged 1.5 MW mWave prototype. Part 1: Numerical modelling," Renewable Energy, Elsevier, vol. 181(C), pages 1402-1418.
    5. Tim Verbrugghe & Vicky Stratigaki & Peter Troch & Raphael Rabussier & Andreas Kortenhaus, 2017. "A Comparison Study of a Generic Coupling Methodology for Modeling Wake Effects of Wave Energy Converter Arrays," Energies, MDPI, vol. 10(11), pages 1-25, October.
    6. Aristodemo, Francesco & Algieri Ferraro, Danilo, 2018. "Feasibility of WEC installations for domestic and public electrical supplies: A case study off the Calabrian coast," Renewable Energy, Elsevier, vol. 121(C), pages 261-285.
    7. Wang, Yize & Liu, Zhenqing, 2021. "Proposal of novel analytical wake model and GPU-accelerated array optimization method for oscillating wave surge energy converter," Renewable Energy, Elsevier, vol. 179(C), pages 563-583.
    8. Zhang, H.C. & Xu, D.L. & Liu, C.R. & Wu, Y.S., 2016. "Wave energy absorption of a wave farm with an array of buoys and flexible runway," Energy, Elsevier, vol. 109(C), pages 211-223.
    9. Greenwood, Charles & Christie, David & Venugopal, Vengatesan & Morrison, James & Vogler, Arne, 2016. "Modelling performance of a small array of Wave Energy Converters: Comparison of Spectral and Boussinesq models," Energy, Elsevier, vol. 113(C), pages 258-266.
    10. Mustapa, M.A. & Yaakob, O.B. & Ahmed, Yasser M. & Rheem, Chang-Kyu & Koh, K.K. & Adnan, Faizul Amri, 2017. "Wave energy device and breakwater integration: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 77(C), pages 43-58.
    11. Stratigaki, Vasiliki & Troch, Peter & Forehand, David, 2019. "A fundamental coupling methodology for modeling near-field and far-field wave effects of floating structures and wave energy devices," Renewable Energy, Elsevier, vol. 143(C), pages 1608-1627.
    12. Craig Jones & Grace Chang & Kaustubha Raghukumar & Samuel McWilliams & Ann Dallman & Jesse Roberts, 2018. "Spatial Environmental Assessment Tool (SEAT): A Modeling Tool to Evaluate Potential Environmental Risks Associated with Wave Energy Converter Deployments," Energies, MDPI, vol. 11(8), pages 1-19, August.
    13. Bao, Jian & Yu, Dingyong, 2024. "Hydrodynamic performance optimization of a cost-effective WEC-type floating breakwater with half-airfoil bottom," Renewable Energy, Elsevier, vol. 226(C).
    14. Clemente, D. & Rosa-Santos, P. & Ferradosa, T. & Taveira-Pinto, F., 2023. "Wave energy conversion energizing offshore aquaculture: Prospects along the Portuguese coastline," Renewable Energy, Elsevier, vol. 204(C), pages 347-358.
    15. Luczko, Ewelina & Robertson, Bryson & Bailey, Helen & Hiles, Clayton & Buckham, Bradley, 2018. "Representing non-linear wave energy converters in coastal wave models," Renewable Energy, Elsevier, vol. 118(C), pages 376-385.
    16. Cui, Lidong & Sergiienko, Nataliia Y. & Leontini, Justin S. & Cohen, Nadav & Bennetts, Luke G. & Cazzolato, Benjamin & Turner, Ian L. & Flocard, Francois & Westcott, Amy-Rose & Cheng, Fanrui & Manasse, 2024. "Protecting coastlines by offshore wave farms: On optimising array configurations using a corrected far-field approximation," Renewable Energy, Elsevier, vol. 224(C).
    17. Martins, J.C. & Goulart, M.M. & Gomes, M. das N. & Souza, J.A. & Rocha, L.A.O. & Isoldi, L.A. & dos Santos, E.D., 2018. "Geometric evaluation of the main operational principle of an overtopping wave energy converter by means of Constructal Design," Renewable Energy, Elsevier, vol. 118(C), pages 727-741.
    18. Vasiliki Stratigaki & Peter Troch & Tim Stallard & David Forehand & Jens Peter Kofoed & Matt Folley & Michel Benoit & Aurélien Babarit & Jens Kirkegaard, 2014. "Wave Basin Experiments with Large Wave Energy Converter Arrays to Study Interactions between the Converters and Effects on Other Users in the Sea and the Coastal Area," Energies, MDPI, vol. 7(2), pages 1-34, February.
    19. Smith, Helen C.M. & Pearce, Charles & Millar, Dean L., 2012. "Further analysis of change in nearshore wave climate due to an offshore wave farm: An enhanced case study for the Wave Hub site," Renewable Energy, Elsevier, vol. 40(1), pages 51-64.
    20. Ozkop, Emre & Altas, Ismail H., 2017. "Control, power and electrical components in wave energy conversion systems: A review of the technologies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 67(C), pages 106-115.
    21. Carballo, R. & Iglesias, G., 2013. "Wave farm impact based on realistic wave-WEC interaction," Energy, Elsevier, vol. 51(C), pages 216-229.
    22. Louise O’Boyle & Björn Elsäßer & Trevor Whittaker, 2017. "Experimental Measurement of Wave Field Variations around Wave Energy Converter Arrays," Sustainability, MDPI, vol. 9(1), pages 1-16, January.
    23. Iglesias, G. & Carballo, R., 2014. "Wave farm impact: The role of farm-to-coast distance," Renewable Energy, Elsevier, vol. 69(C), pages 375-385.

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