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Optimisation of the geometry of axisymmetric point-absorber wave energy converters

Published online by Cambridge University Press:  17 December 2021

Emma C. Edwards Open the ORCID record for Emma C. Edwards [Opens in a new window]  and
Dick K.-P. Yue Open the ORCID record for Dick K.-P. Yue [Opens in a new window]
Emma C. Edwards
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Dick K.-P. Yue*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

We propose a scientifically rigorous framework to find realistic optimal geometries of wave energy converters (WECs). For specificity, we assume WECs to be axisymmetric point absorbers in a monochromatic unidirectional incident wave, all within the context of linearised potential theory. We consider separately the problem of a WEC moving and extracting wave energy in heave only and then the more general case of motion and extraction in combined heave, surge and pitch. We describe the axisymmetric geometries using polynomial basis functions, allowing for discontinuities in slope. Our framework involves ensuring maximum power, specifying practical motion constraints and then minimising surface area (as a proxy for cost). The framework is robust and well-posed, and the optimisation produces feasible WEC geometries. Using the proposed framework, we develop a systematic computational and theoretical approach, and we obtain results and insights for the optimal WEC geometries. The optimisation process is sped up significantly by a new theoretical result to obtain roots of the heave resonance equation. For both the heave-only, and the heave-surge-pitch combined problems, we find that geometries which protrude outward below the waterline are generally optimal. These optimal geometries have up to 73 % less surface area and 90 % less volume than the optimal cylinders which extract the same power.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A1
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Al-Shami, E., Zhang, R. & Wang, X. 2019 Point absorber wave energy harvesters: a review of recent developments. Energies 12 (1), 47.CrossRefGoogle Scholar
Babarit, A. 2015 A database of capture width ratio of wave energy converters. Renew. Energy 80, 610–628.CrossRefGoogle Scholar
Budal, K. & Falnes, J. 1975 Power generation from ocean waves using a resonant oscillating system. Mar. Sci. Commun. 1 (3, 4), 269–288.Google Scholar
Chang, G., Jones, C., Roberts, J.D. & Neary, V.S. 2018 A comprehensive evaluation of factors affecting the levelized cost of wave energy conversion projects. Renew. Energy 127, 344–354.CrossRefGoogle Scholar
Dallman, A., Jenne, D.S., Neary, V., Discoll, F., Thresher, R. & Gunawan, B. 2018 Evaluation of performance metrics for the wave energy prize converters tested at 1/20th scale. Renew. Sustain. Energy Rev. 98, 79–91.CrossRefGoogle Scholar
Drew, B., Plummer, A.R. & Sahinkaya, M.N. 2009 A review of wave energy converter technology. Proc. IMechE Part A 223, 887–902.CrossRefGoogle Scholar
Edwards, E.C. 2020 Optimization of the geometry of axisymmetric point-absorber wave energy converters. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Evans, D.V. 1976 A theory for wave-power absorption by oscillating bodies. J. Fluid Mech. 77 (1), 1–25.CrossRefGoogle Scholar
Evans, D.V. 1981 Maximum wave-power absorption under motion constraints. Appl. Ocean Res. 3 (4), 200–203.CrossRefGoogle Scholar
Falnes, J. & Kurniawan, A. 2020 Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction. Cambridge University Press.CrossRefGoogle Scholar
Garrison, C.J. 1975 Hydrodynamics of large objects in the sea part ii: motion of free-floating bodies. J. Hydronaut. 9 (2), 58–63.CrossRefGoogle Scholar
Gunn, K. & Stock-Williams, C. 2012 Quantifying the global wave power resources. Renew. Energy 44, 296–304.CrossRefGoogle Scholar
Kim, M.-H. & Yue, D.K.P. 1989 The complete second-order diffraction solution for an axisymmetric body. Part 1. Monochromatic incident waves. J. Fluid Mech. 200, 235–264.CrossRefGoogle Scholar
Kurniawan, A. 2013 Modelling and geometry optimisation of wave energy converters. PhD thesis, NTNU.Google Scholar
Kurniawan, A. & Moan, T. 2012 Optimal geometries for wave absorbers oscillating about a fixed axis. IEEE J. Oceanic Engng 38 (1), 117–130.CrossRefGoogle Scholar
Lee, C.-H. & Newman, J.N. 2006 Wamit user manual. WAMIT, Inc.Google Scholar
McCabe, A.P. 2013 Constrained optimization of the shape of a wave energy collector by genetic algorithm. Renew. Energy 51, 274–284.CrossRefGoogle Scholar
Mei, C.C. 1976 Power extraction from water waves. J. Ship Res. 20, 63–66.CrossRefGoogle Scholar
Mei, C.C., Stiassnie, M. & Yue, D.K.-P. 2005 Theory and Applications of Ocean Surface Waves. Part 1: Linear Aspects. World Scientific.Google Scholar
Michele, S. & Renzi, E. 2019 A second-order theory for an array of curved wave energy converters in open sea. J. Fluids Struct. 88, 315–330.CrossRefGoogle Scholar
Michele, S., Renzi, E. & Sammarco, P. 2019 Weakly nonlinear theory for a gate-type curved array in waves. J. Fluid Mech. 869, 238–263.CrossRefGoogle Scholar
Newman, J.N. 1976 The interaction of stationary vessels with regular waves. In Proceedings of the 11th Symposium on Naval Hydrodynamics, London, 1976, pp. 491–501. ONR.Google Scholar
Shadman, M., Estefen, S.F., Rodriguez, C.A. & Nogueira, I.C.M. 2018 A geometrical optimization method applied to a heaving point absorber wave energy converter. Renew. Energy 115, 533–546.CrossRefGoogle Scholar
Xu, D., Stuhlmeier, R. & Stiassnie, M. 2018 Assessing the size of a twin-cylinder wave energy converter designed for real sea-states. Ocean Engng 147, 243–255.CrossRefGoogle Scholar
Zhang, W.-C., Liu, H.-X., Zhang, L. & Zhang, X.-W. 2016 Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters. China Ocean Engng 30 (6), 954–966.CrossRefGoogle Scholar
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