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Hydrodynamics of large wave energy converter arrays with random configuration variations

Published online by Cambridge University Press:  21 July 2021

Grgur Tokić Open the ORCID record for Grgur Tokić [Opens in a new window]  and
Dick K.P. Yue Open the ORCID record for Dick K.P. Yue [Opens in a new window]
Grgur Tokić*
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: gtokic@mit.edu
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Abstract

We study the effect of random perturbations of body positions in large uniformly spaced arrays of axisymmetric wave energy converters (WECs). We perform systematic computational simulations of ensembles of randomized array configurations that are obtained by introducing zero-mean position perturbations (characterized by randomness parameter $\varepsilon$) to line arrays of uniform spacing $d$. Of special interest are the conditions under which these randomized arrays can extract more energy than the underlying uniform arrays. We find that random WEC arrays achieve substantial energy extraction gains over the same number of isolated bodies in monochromatic and irregular incident seas. Introducing $\varepsilon >0$ acts to smooth out the uneven performance of uniformly spaced arrays over varying incident wavenumber. In the low-scattering regime, the standard deviation of array gain grows with the square of wavenumber, for which we provide a theoretical explanation. We show that the uniform line array with spacing optimized for a given incident spectrum generally outperforms randomized arrays of any mean $d$ and $\varepsilon$ in that spectrum, and we offer a heuristic explanation. This holds for a wide range of incident spectra.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , R1
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Archer, A.J., Wolgamot, H.A., Orszaghova, J., Bennetts, L.G., Peter, M.A. & Craster, R.V. 2020 Experimental realization of broadband control of water-wave-energy amplification in chirped arrays. Phys. Rev. Fluids 5 (6), 062801.CrossRefGoogle Scholar
Bennetts, L.G., Peter, M.A. & Craster, R.V. 2018 Graded resonator arrays for spatial frequency separation and amplification of water waves. J. Fluid Mech. 854, R4.CrossRefGoogle Scholar
Bennetts, L.G., Peter, M.A. & Craster, R.V. 2019 Low-frequency wave-energy amplification in graded two-dimensional resonator arrays. Phil. Trans. R. Soc. A 377 (2156), 20190104.CrossRefGoogle ScholarPubMed
Bennetts, L.G., Peter, M.A. & Montiel, F. 2017 Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders. J. Fluid Mech. 813, 508–527.CrossRefGoogle Scholar
Benzaouia, M., Tokić, G., Miller, O.D., Yue, D.K.P. & Johnson, S.G. 2019 From solar cells to ocean buoys: wide-bandwidth limits to absorption by metaparticle arrays. Phys. Rev. Appl. 11 (3), 034033.CrossRefGoogle Scholar
De Ponti, J.M., Colombi, A., Riva, E., Ardito, R., Braghin, F., Corigliano, A. & Craster, R.V. 2020 Experimental investigation of amplification, via a mechanical delay-line, in a rainbow-based metamaterial for energy harvesting. Appl. Phys. Lett. 117 (14), 143902.CrossRefGoogle Scholar
Duclos, G. & Clément, A.H. 2004 Wave propagation through arrays of unevenly spaced vertical piles. Ocean Engng 31 (13), 1655–1668.CrossRefGoogle Scholar
Falnes, J. & Budal, K. 1982 Wave-power absorption by parallel rows of interacting oscillating bodies. Appl. Ocean Res. 4 (4), 194–207.CrossRefGoogle Scholar
Göteman, M., Engström, J., Eriksson, M. & Isberg, J. 2015 Optimizing wave energy parks with over 1000 interacting point-absorbers using an approximate analytical method. Intl J. Mar. Energy 10, 113–126.CrossRefGoogle Scholar
Kagemoto, H. & Yue, D.K.P. 1986 Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 166, 189–209.CrossRefGoogle Scholar
Linton, C.M. & McIver, P. 2001 Handbook of Mathematical Techniques of Wave/Structure Interactions. Chapman & Hall.CrossRefGoogle Scholar
Mei, C.C., Stiassnie, M.S. & Yue, D.K.P. 2005 Theory and Applications of Ocean Surface Waves. 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
Oehlert, G.W. 1992 A note on the delta method. Am. Stat. 46 (1), 27.Google Scholar
Sarkar, D., Contal, E., Vayatis, N. & Dias, F. 2016 Prediction and optimization of wave energy converter arrays using a machine learning approach. Renew. Energy 97, 504–517.CrossRefGoogle Scholar
Tokić, G. & Yue, D.K.P. 2019 a A fast method for optimization of large wave energy converter arrays. In Proceedings 34th International Workshop on Water Waves and Floating Bodies.CrossRefGoogle Scholar
Tokić, G. & Yue, D.K.P. 2019 b Hydrodynamics of periodic wave energy converter arrays. J. Fluid Mech. 862, 34–74.CrossRefGoogle Scholar
Wolgamot, H., Meylan, M. & Reid, C. 2017 Multiply heaving bodies in the time-domain: symmetry and complex resonances. J. Fluids Struct. 69, 232–251.CrossRefGoogle Scholar
Yablonovitch, E. 1982 Statistical ray optics. J. Opt. Soc. Am. 72 (7), 899–907.CrossRefGoogle Scholar