On Wave-Induced Elastic Deformations of a Submerged Wave Energy Device

Abstract

Structural integrity has remained a challenge for design and analysis of wave energy devices. A difficulty in assessment of the structural integrity is often laid in the accurate determination of the wave-induced loads on the wave energy devices and the repones of the structure. Decoupled hydroelastic response of a submerged, oscillating wave energy device to extreme nonlinear wave loads is studied here. The submerged wave energy device consists of an oscillating horizontal disc attached to a direct-drive power take-off system. The structural frame of the wave energy device is fixed on the seafloor in shallow water. Several extreme wave conditions are considered in this study. The nonlinear wave loads on members of the submerged structure are obtained by use of the level I Green-Naghdi equations and Morison’s equation for cylindrical members. Distribution of Von Mises stresses and the elastic response of the structure to the extreme wave loads are determined by use of a finite element method. The decoupled hydroelastic analysis of the structure is carried out for devices built by four different materials, namely stainless steel, concrete, aluminium alloy, and titanium alloy. The elastic response of these devices is studied and results are compared with each other. Points of maximum stress and deformations are determined and the structural integrity under the extreme conditions is assessed. It is shown that the proposed approaches provide invaluable information about the structural integrity of wave energy devices.

Keywords

Renewable energy / Wave energy converter / Wave loads / Hydroelasticity / Green-Naghdi equations

References

[1] ANSYS Inc (2016) ANSYS^® Academic Research, Release 16.2, help system. engineering data sources

[2] Antonio FO. Wave energy utilization: a review of the technologies. Renew Sustain Energ Rev, 2010, 14(3): 899-918

[3] Carter RW, Ertekin RC. Focusing of wave-induced flow through a submerged disk with a tubular opening. Appl Ocean Res, 2014, 47: 110-124

[4] Clément A, McCullen P, Falcão A, Fiorentino A, Gardner F, Hammarlund K, Lemonis G, Lewis T, Nielsen K, Petroncini S, Pontes MT, Schild P, Sjöström BO, HC Sørensen, Thorpe T. Wave energy in europe: current status and perspectives. Renew Sustain Energ Rev, 2002, 6(5): 405-431

[5] Cruz J. Ocean wave energy: current status and future prespectives, 2007, United Kingdom: Springer Science & Business Media

[6] Daniel TL. Flexible wings and fins: Bending by inertial or fluid-dynamic forces? Integr Comp Biol, 2002, 42(5): 1044-1049

[7] Drew B, Plummer AR, Sahinkaya MN (2009) A review of wave energy converter technology, vol 223, pp 887–902, DOI https://doi.org/10.1243/09576509JPE782

[8] Duffett J, Beck RF, Zhang X, Maki KJ, Newman JN (2016) Experimental and numerical study of waves amplified by a submerged plate. In: Proceedings of the 31st Int. workshop on water waves and floating bodies (IWWWFB), 3-6 April, Plymouth, MI, USA, pp 37–40

[9] Ertekin RC (1984) Soliton generation by moving disturbances in shallow water: Theory, computation and experiment. PhD thesis, University of California at Berkeley, May, v + 352 pp

[10] Ertekin RC (1988) Nonlinear shallow water waves: the Green-Naghdi equations. In: Pacific congress on marine science and technology, PACON, vol 88, pp 42–52

[11] Ertekin RC, Becker JM. Nonlinear diffraction of waves by a submerged shelf in shallow water. J Offshore Mechan Arctic Eng, 1998, 120(4): 212-220

[12] Ertekin RC, Webster WC, Wehausen JV. Waves caused by a moving disturbance in a shallow channel of finite width. J Fluid Mechan, 1986, 169: 275-292

[13] Ertekin RC, Hayatdavoodi M, Kim JW. On some solitary and cnoidal wave diffraction solutions of the green–naghdi equations. Appl Ocean Res, 2014, 47: 125-137

[14] Filippas E, Gerostathis T, Belibassakis K. Semi-activated oscillating hydrofoil as a nearshore biomimetic energy system in waves and currents. Ocean Eng, 2018, 154: 396-415

[15] Graw K (1996) About the development of wave energy breakwaters

[16] Green AE, Naghdi PM. Directed fluid sheets. Proceedings of the royal society of london a mathematical and physical sciences, 1976, 347(1651): 447-473

[17] Green AE, Naghdi PM. A derivation of equations for wave propagation in water of variable depth. J Fluid Mech, 1976, 78: 237-246

[18] Green AE, Naghdi PM, Wainwright WL. A general theory of a Cosserat surface. Arch Ration Mech Anal, 1965, 20(4): 287-308

[19] Hayatdavoodi M (2013) Nonlinear wave loads on decks of coastal structures. PhD thesis, University of Hawaii at Manoa, xiv+ 186

[20] Hayatdavoodi M, Ertekin RC. Nonlinear wave loads on a submerged deck by the Green-Naghdi equations. J Offshore Mechan Arctic Eng, 2015, 137(1): 011,102:1-9

[21] Hayatdavoodi M, Ertekin RC. Wave forces on a submerged horizontal plate. part i: theory and modelling. J Fluids Struct, 2015, 54(April): 566-579

[22] Hayatdavoodi M, Ertekin RC. Wave forces on a submerged horizontal plate. Part ii: solitary and cnoidal waves. J Fluids Struct, 2015, 54(April): 580-596

[23] Hayatdavoodi M, Ertekin RC, Robertson IN, Riggs HR (2015a) Vulnerability assessment of coastal bridges on Oahu impacted by storm surge and waves. Natural Hazards pp 1–25, https://doi.org/10.1007/s11069-015-1896-2

[24] Hayatdavoodi M, Seiffert B, Ertekin RC. Experiments and calculations of cnoidal wave loads on a flat plate in shallow-water. J of Ocean Eng Marine Energ, 2015, 1(1): 77-99

[25] Hayatdavoodi M, Wagner JJ, Wagner JR, Ertekin RC (2016) Vertical oscillation of a horizontal submerged plate. In: 31St international workshop on water waves and floating bodies (IWWWFB31), plymouth, MI, USA, pp 53–56

[26] Hayatdavoodi M, Ertekin RC, Thies JT (2017a) Conceptual design and analysis of a submerged wave energy device in shallow water. In: ASME 36th international conference on ocean, offshore and arctic engineering, american society of mechanical engineers, OMAE, Trondheim, Norway, p V010T09A033

[27] Hayatdavoodi M, Ertekin RC, Valentine BD. Solitary and cnoidal wave scattering by a submerged horizontal plate in shallow water. AIP Advances, 2017, 7(6): 065-212

[28] Hayatdavoodi M, Neill DR, Ertekin RC. Diffraction of cnoidal waves by vertical cylinders in shallow water. Theor Comput Fluid Dynam, 2018, 32(5): 561-591

[29] Hayatdavoodi M, Treichel K, Ertekin RC. Parametric study of nonlinear wave loads on submerged decks in shallow water. J Fluids Struct, 2019, 86: 266-289

[30] Jeanmonod G, Olivier M. Effects of chordwise flexibility on 2D flapping foils used as an energy extraction device. J Fluids Struct, 2017, 70: 327-345

[31] Johansson TB, Patwardhan AP, Nakićenović N, Gomez-Echeverri L. Global energy assessment: toward a sustainable future, 2012, Cambridge: Cambridge University Press

[32] Kim JW, Bai KJ, Ertekin RC, Webster WC. A derivation of the Green-Naghdi equations for irrotational flows. J Eng Math, 2001, 40: 17-42

[33] Liu J, Hayatdavoodi M, Ertekin RC. On bore dynamics and pressure: RANS, GN, and SV equations. J Offshore Mechan Arctic Eng, 2020, 142(2): 021-902 (1–10), https://doi.org/10.1115/1.4044988

[34] Martin PA, Farina L. Radiation of water waves by a heaving submerged horizontal disc. J Fluid Mechan, 1997, 337: 365-379

[35] Morison JR, O’Brien MP, Johnson JW, Schaaf SA. The force exerted by surface waves on piles. J Pet Technol, 1950, 2(05): 149-154

[36] Newman JN (2015) Amplification of waves by submerged plates. 30th international workshop on water waves and floating bodies (IWWWFB), Bristol, UK

[37] Pelc R, Fujita RM. Renewable energy from the ocean. Mar Policy, 2002, 26(6): 471-479

[38] Polinder H, Scuotto M (2005) Wave energy converters and their impact on power systems. In: The international conference on future power systems, vol 2005. IEEE, Netherlands, pp 1–9

[39] Priovolos AK, Filippas ES, Belibassakis KA. A vortex-based method for improved flexible flapping-foil thruster performance. Eng Anal Boundary Elements, 2018, 95: 69-84

[40] Rossi P, Wu X, Le Maou F, Belloc A. Scale effect on concrete in tension. Mater Struct, 1994, 27(8): 437-444

[41] Thorpe TW (1999) A brief review of wave energy. harwell laboratory energy technology support unit (ETSU), Oxford, UK

[42] Ugural AC. Mechanics of materials, 1991, New York: McGraw-Hill

[43] Vermaak R, Kamper MJ. Design aspects of a novel topology air-cored permanent magnet linear generator for direct drive wave energy converters. IEEE Trans Ind Electron, 2012, 59(5): 2104-2115

[44] World Energy Council (2013) World energy resources 2013 Survey. world energy council, London

[45] Xiao Q, Zhu Q. A review on flow energy harvesters based on flapping foils. J Fluids Struct, 2014, 46: 174-191

[46] Zhao BB, Ertekin RC, Duan WY. A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations. J Comput Phys, 2015, 283: 129-147