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Hybrid wave/current energy harvesting with a flexible piezoelectric plate

Published online by Cambridge University Press:  08 August 2023

Kourosh Shoele Open the ORCID record for Kourosh Shoele [Opens in a new window]
Kourosh Shoele*
Affiliation:
Department of Mechanical Engineering, Joint College of Engineering, Florida A&M University-Florida State University, Tallahassee, FL 32310, USA
*
†Email address for correspondence: kshoele@fsu.edu
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Abstract

We investigate the dynamics and energy production capability of a flexible piezoelectric plate submerged close to the free surface and exposed to incident head gravity waves and current. A theoretical model is derived in which the flag and its wake are represented with a vortex line while the body of the fluid is considered to be inviscid. The model is employed to describe the hydrodynamic interactions between a flexible plate, its wake, gravity incident waves and the current. The model reveals two distinct vibration states of a piezoelectric device corresponding to almost similar optimal energy production levels. The first is associated with the cantilever fluttering mode of the plate, with limited dependency on the plate's flexibility across different Froude numbers and incoming wave frequencies. The other resembles the flow-induced flapping mode in more flexible plates, with the energy output showing a higher dependency on plate flexibility. The concurrent existence of these two energetic modes allows adjustment of the plate length to consistently achieve the maximum energy production level across different flow conditions. The role of the Froude number of the system's responses is explored and correlated to the appearance of gravity wave groups on the surface, each propagating with a different wavenumber. It is shown that a submergence depth of less than half of the body length is required to reach a high energetic condition in subcritical and critical flows. Finally, the optimal inductive and resistive values are related to proper matching between flow, mechanical and electrical time scales.

JFM classification

Aerodynamics: Flow-structure interactions Vortex Flows: Vortex dynamics Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 968 , 10 August 2023 , A31
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Aderinto, T. & Li, H. 2018 Ocean wave energy converters: status and challenges. Energies 11 (5), 1250.CrossRefGoogle Scholar
Alam, M.-R. 2012 Nonlinear analysis of an actuated seafloor-mounted carpet for a high-performance wave energy extraction. Proc. R. Soc. A 468 (2146), 3153–3171.CrossRefGoogle Scholar
Alben, S. 2008 a The flapping-flag instability as a nonlinear eigenvalue problem. Phys. Fluids 20 (10), 104106.CrossRefGoogle Scholar
Alben, S. 2008 b Optimal flexibility of a flapping appendage in an inviscid fluid. J. Fluid Mech. 614, 355–380.CrossRefGoogle Scholar
Babarit, A. 2017 Ocean Wave Energy Conversion: Resource, Technologies and Performance. Elsevier.Google Scholar
Babarit, A., Gendron, B., Singh, J., Mélis, C. & Jean, P. 2013 Hydro-elastic modelling of an electro-active wave energy converter. In International Conference on Offshore Mechanics and Arctic Engineering, vol. 55430, V009T12A033. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Belibassakis, K.A. & Politis, G.K. 2013 Hydrodynamic performance of flapping wings for augmenting ship propulsion in waves. Ocean Engng 72, 227–240.CrossRefGoogle Scholar
Collins, I., Hossain, M., Dettmer, W. & Masters, I. 2021 Flexible membrane structures for wave energy harvesting: a review of the developments, materials and computational modelling approaches. Renew. Sustain. Energy Rev. 151, 111478.CrossRefGoogle Scholar
Crimi, P. & Statler, I.H. 1964 Forces and moments on an oscillating hydrofoil. In Fourth Symposium Naval Hydrodynamics, Office of Naval Research (ed. B.L. Silverstein), ACR-92, pp. 477–494. Office of Naval Research.Google Scholar
Doaré, O. & Michelin, S. 2011 Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency. J. Fluids Struct. 27 (8), 1357–1375.CrossRefGoogle Scholar
Drew, B., Plummer, A.R. & Sahinkaya, M.N. 2009 A review of wave energy converter technology. In Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy. 223 (8), 887–902.Google Scholar
Erturk, A. & Inman, D.J. 2011 Piezoelectric Energy Harvesting. John Wiley & Sons.CrossRefGoogle Scholar
Falnes, J. & Kurniawan, A. 2020 Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction, vol. 8. Cambridge University Press.CrossRefGoogle Scholar
Fish, F.E. & Rohr, J.J. 1999 Review of dolphin hydrodynamics and swimming performance. Space Nav. Warf. Syst. Cent. Tech. Rep. 1801.CrossRefGoogle Scholar
Grue, J., Mo, A. & Palm, E. 1988 Propulsion of a foil moving in water waves. J. Fluid Mech. 186, 393–417.CrossRefGoogle Scholar
Grue, J. & Palm, E. 1985 Wave radiation and wave diffraction from a submerged body in a uniform current. J. Fluid Mech. 151, 257–278.CrossRefGoogle Scholar
Haskind, M.D. 1954 On wave motion of a heavy fluid. Prikl. Mat. Mekh. 18, 15–26.Google Scholar
Jbaily, A. & Yeung, R.W. 2015 Piezoelectric devices for ocean energy: a brief survey. J. Ocean Engng Mar. Energy 1 (1), 101–118.CrossRefGoogle Scholar
Koola, P.M. & Ibragimov, A. 2003 The dynamics of wave carpet – a novel deep water wave energy design. In Oceans 2003. Celebrating the Past … Teaming Toward the Future (IEEE Cat. No. 03CH37492), vol. 4, pp. 2288–2293. IEEE.CrossRefGoogle Scholar
Michele, S., Buriani, F., Renzi, E., van Rooij, M., Jayawardhana, B. & Vakis, A.I. 2020 Wave energy extraction by flexible floaters. Energies 13 (23), 6167.CrossRefGoogle Scholar
Michele, S., Zheng, S. & Greaves, D. 2022 Wave energy extraction from a floating flexible circular plate. Ocean Engng 245, 110275.CrossRefGoogle Scholar
Michelin, S. & Doaré, O. 2013 Energy harvesting efficiency of piezoelectric flags in axial flows. J. Fluid Mech. 714, 489–504.CrossRefGoogle Scholar
Mougel, J. & Michelin, S. 2020 Flutter and resonances of a flag near a free surface. J. Fluids Struct. 96, 103046.CrossRefGoogle Scholar
Mutsuda, H., Tanaka, Y., Doi, Y. & Moriyama, Y. 2019 Application of a flexible device coating with piezoelectric paint for harvesting wave energy. Ocean Engng 172, 170–182.CrossRefGoogle Scholar
Mutsuda, H., Watanabe, R., Azuma, S., Tanaka, Y. & Doi, Y. 2013 Ocean power generator using flexible piezoelectric device. In International Conference on Offshore Mechanics and Arctic Engineering, vol. 55423, V008T09A002. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Newman, J.N. 2018 Marine Hydrodynamics. The MIT Press.Google Scholar
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139–161.CrossRefGoogle Scholar
Palm, E. & Grue, J. 1999 On the wave field due to a moving body performing oscillations in the vicinity of the critical frequency. J. Engng Maths 35 (1), 219–232.CrossRefGoogle Scholar
Pecher, A. & Kofoed, J.P. 2017 Handbook of Ocean Wave Energy. Springer Nature.CrossRefGoogle Scholar
Peng, H.H., Qiu, W., Meng, W., Chen, M., Lundrigan, B. & Gardiner, T. 2020 Experimental studies and time-domain simulation of a hinged-type wave energy converter in regular waves. Mar. Syst. Ocean Technol. 15 (1), 1–15.CrossRefGoogle Scholar
Pullin, D.I. & Wang, Z.J. 2004 Unsteady forces on an accelerating plate and application to hovering insect flight. J. Fluid Mech. 509, 1–21.CrossRefGoogle Scholar
Reece, J.W. 1963 Motion of a flexible hydrofoil near a free surface. PhD thesis, University of Florida.Google Scholar
Reece, J.W. & Siekmann, J. 1964 Swimming of a flexible hydrofoil near a free surface. Z. Angew. Math. Mech. 44 (12), 559–571.CrossRefGoogle Scholar
Renzi, E. 2016 Hydroelectromechanical modelling of a piezoelectric wave energy converter. Proc. R. Soc. A 472 (2195), 20160715.CrossRefGoogle Scholar
Renzi, E., Michele, S., Zheng, S., Jin, S. & Greaves, D. 2021 Niche applications and flexible devices for wave energy conversion: a review. Energies 14 (20), 6537.CrossRefGoogle Scholar
Ringwood, J.V. 2020 Wave energy control: status and perspectives 2020. IFAC-PapersOnLine 53 (2), 12271–12282.CrossRefGoogle Scholar
Rozhdestvensky, K.V. & Ryzhov, V.A. 2003 Aerohydrodynamics of flapping-wing propulsors. Prog. Aerosp. Sci. 39 (8), 585–633.CrossRefGoogle Scholar
Saffman, P.G. 1995 Vortex Dynamics. Cambridge University Press.Google Scholar
Selvan, S.A. & Behera, H. 2020 Wave energy dissipation by a floating circular flexible porous membrane in single and two-layer fluids. Ocean Engng 206, 107374.CrossRefGoogle Scholar
Shoele, K. & Mittal, R. 2016 Energy harvesting by flow-induced flutter in a simple model of an inverted piezoelectric flag. J. Fluid Mech. 790, 582–606.CrossRefGoogle Scholar
Shoele, K. & Zhu, Q. 2015 Drafting mechanisms between a dolphin mother and calf. J. Theor. Biol. 382, 363–377.CrossRefGoogle ScholarPubMed
Stansby, P., Moreno, E.C. & Stallard, T. 2015 Capture width of the three-float multi-mode multi-resonance broadband wave energy line absorber M4 from laboratory studies with irregular waves of different spectral shape and directional spread. J. Ocean Engng Mar. Energy 1 (3), 287–298.CrossRefGoogle Scholar
Tan, H.S. 1955 On source and vortex of fluctuating strength travelling beneath a free surface. Q. Appl. Maths 13 (3), 314–317.CrossRefGoogle Scholar
Tan, H.S. 1957 Waves produced by a pulsating source travelling beneath a free surface. Q. Appl. Maths 15 (3), 249–255.CrossRefGoogle Scholar
Thomas, O., Deü, J.-F. & Ducarne, J. 2009 Vibrations of an elastic structure with shunted piezoelectric patches: efficient finite element formulation and electromechanical coupling coefficients. Intl J. Numer. Meth. Engng 80 (2), 235–268.CrossRefGoogle Scholar
Thwaites, B. & Meyer, R.E. 1960 Incompressible aerodynamics. J. Appl. Mech. 27 (4), 760.CrossRefGoogle Scholar
Vahab, M., Sussman, M. & Shoele, K. 2021 Fluid-structure interaction of thin flexible bodies in multi-material multi-phase systems. J. Comput. Phys. 429, 110008.CrossRefGoogle Scholar
Viet, N.V., Wu, N. & Wang, Q. 2017 A review on energy harvesting from ocean waves by piezoelectric technology. J. Model. Mech. Mater. 1 (2), 20160161.Google Scholar
Xia, Y., Michelin, S. & Doaré, O. 2015 Fluid-solid-electric lock-in of energy-harvesting piezoelectric flags. Phys. Rev. Appl. 3 (1), 014009.CrossRefGoogle Scholar
Zheng, S., Meylan, M.H., Fan, L., Greaves, D. & Iglesias, G. 2020 Wave scattering by a floating porous elastic plate of arbitrary shape: a semi-analytical study. J. Fluids Struct. 92, 102827.CrossRefGoogle Scholar
Zheng, S., Meylan, M., Zhang, X., Iglesias, G. & Greaves, D. 2021 Performance of a plate-wave energy converter integrated in a floating breakwater. IET Renew. Power Gen. 15 (14), 3206–3219.CrossRefGoogle Scholar
Zhu, Q., Liu, Y. & Yue, D.K.P. 2006 Dynamics of a three-dimensional oscillating foil near the free surface. AIAA J. 44 (12), 2997–3009.CrossRefGoogle Scholar
Zhu, Q. & Peng, Z. 2009 Mode coupling and flow energy harvesting by a flapping foil. Phys. Fluids 21 (3), 033601.CrossRefGoogle Scholar