Wave Energy System Combined by a Heaving Box and a Perforated Flexible Membrane Wall

Abstract

An analytical model of a floating heaving box integrated with a vertical flexible porous membrane placed right next to the box applications to wave energy extraction and breakwater systems is developed under the reduced wave equation. The theoretical solutions for the heave radiating potential to the assigned physical model in the corresponding zones are attained by using the separation of variables approach along with the Fourier expansion. Applying the matching eigenfunction expansion technique and orthogonal conditions, the unknown coefficients that are involved in the radiated potentials are determined. The attained radiation potential allows the computation of hydrodynamic coefficients of the heaving buoy, Power Take-Off damping, and wave quantities. The accuracy of the analytical solution for the hydrodynamic coefficients is demonstrated for different oblique angles with varying numbers of terms in the series solution. The current analytical analysis findings are confirmed by existing published numerical boundary element method simulations. Several numerical results of the hydrodynamic coefficients, power capture, power take-off optimal damping, and transmission coefficients for numerous structural and physical aspects are conducted. It has been noted that the ideal power take-off damping increases as the angle of incidence rises, and the analysis suggests that the ability to capture waves is more effective in shallower waters compared to deeper ones.

Keywords

Analytical model / Heaving buoy / Flexible membrane perforated wall / Boundary element method code / Power take-off / Power capture

References

[1] Amouzadrad P, Mohapatra SC, Guedes Soares C. Review of recent developments on the hydroelastic response and gap resonance of multi-body floating structures. Ocean Engineering, 2024, 313: 119398

[2] Bhattacharjee J, Guedes Soares C. Oblique wave interaction with a floating structure near a wall with stepped bottom. Ocean Engineering, 2011, 38: 1528-1544

[3] Chen Q, Zang J, Birchall, Ning DZ, Zhao XL, Gao JL. On the hydrodynamic performance of a vertical pile-restrained WEC-type floating breakwater. Renewable Energy, 2020, 146: 414-425

[4] Cheng Y, Du W, Dai S, Yuan Z, Incecik A. Wave energy conversion by an array of oscillating water columns deployed along a long-flexible floating breakwater. Renewable and Sustainable Energy Reviews, 2024, 192: 114206

[5] Elchahal G, Younes R, Lafon P. The effects of reflection coefficient of the harbour sidewall on the performance of floating breakwaters. Ocean Engineering, 2008, 35: 1102-1112

[6] Guo YC, Mohapatra SC, Guedes Soares C. Submerged breakwater of a flexible porous membrane with a vertical flexible porous wall over variable bottom topography. Ocean Engineering, 2022, 243: 109989

[7] Hallak TS, Guedes Soares C. Overview of the recent developments in hybrid floating wind-wave platforms. Journal of Marine Science and Application, 2025, 24: 98-119

[8] Han X, Dong S. Experimental study of wave force on breakwater head under oblique waves. Proceedings of Institution of Mechanical Engineers Part M: Journal of Engineering for the Maritime Environment, 2021, 236(3): 553-568

[9] Hsu HH, Wu YC. The hydrodynamic coefficients for an oscillating rectangular structure on a free surface with sidewall. Ocean Engineering, 1997, 24(2): 177-199

[10] Islam H, Mohapatra SC, Gadelho J, Guedes Soares C. OpenFOAM analysis of the wave radiation by a box-type floating structure. Ocean Engineering, 2019, 193: 106532

[11] Islam H, Mohapatra SC, Guedes Soares C. Guedes Soares C, Santos TA. Comparison of CFD, experimental and analytical simulations of a heaving box-type floating structure. Progress in Maritime Technology and Engineering, 2018, London, Taylor & Francis Group633-639

[12] Ji Q, Xu C, Jiao C. Numerical investigation on the hydrodynamic performance of a vertical pile-restrained reversed L-type floating breakwater integrated with WEC. Ocean Engineering, 2021, 238: 109635

[13] Mohapatra SC, Bispo IB, Guo YC, Guedes Soares C. Analysis of wave-induced forces on a floating rectangular box with analytical and numerical approaches. Journal of Marine Science and Application, 2024, 23(1): 113-126

[14] Mohapatra SC, Guedes Soares C, Belibassakis K. Current loads on a horizontal flexible membrane in a 3D channel. Journal of Marine Science and Engineering, 2024, 12(91583

[15] Mohapatra SC, Guo YC, Guedes Soares C. Guedes Soares C. Analytical and experimental study on wave interaction with a horizontal floating flexible membrane supporting by linear springs. Trends in Renewable Energies Offshore, 2023, London, Taylor and Francis257-266

[16] Mustapa MA, Yaakob OB, Ahmed YM, Rheem C, Koh KK, Adnan FA. Wave energy device and breakwater integration: A review. Renewable and Sustainable Energy Reviews, 2017, 77: 43-58

[17] Ning DZ, Zhao XL, Zhao M, Hann M, Kang HG. Analytical investigation of hydrodynamic performance of a dual pontoon WEC-type breakwater. Applied Ocean Research, 2017, 65: 102-111

[18] Rezanejad K, Guedes Soares C. Enhancing the primary efficiency of an oscillating water column wave energy converter based on a dual-mass system analogy. Renewable Energy, 2018, 123: 730-747

[19] Rezanejad K, Guedes Soares C. Hydrodynamic investigation of a novel concept of Oscillating Water Column type wave energy converter device. Journal of Offshore Mechanics and Arctic Engineering, 2021, 143: 042003

[20] Schay J, Bhattacharjee J, Guedes Soares C. Numerical modelling of a heaving point absorber in front of a vertical wall. 32nd International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2013), Nantes, OMAE2013-11491, 2013

[21] Shen YM, Zheng YH, You YG. On the radiation and diffraction of linear water waves by a rectangular structure over a sill. Part I. Infinite domain of finite water depth. Ocean Engineering, 2005, 32: 1073-1097

[22] Vicinanza D, Lauro E, Contestabile P, Gisonni C, Lara JL, Losada IJ. Review of innovative harbor breakwaters for wave-energy conversion. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2019, 145(403119001

[23] Wang D, Dong S, Fang K. Breaking wave impact on perforated caisson breakwaters: A numerical investigation. Ocean Engineering, 2022, 249: 110919

[24] Wang Y, Dong S. Theoretical investigation on integrating a torus oscillating body with a concentric perforated cylindrical system. Ocean Engineering, 2021, 242: 110122

[25] Wang Y, Dong S. Theoretical investigation on integrating a heaving WEC in the semicircle opening of a vertical breakwater. Journal of Fluids and Structures, 2023, 120: 103911

[26] Wang Y, Wang D, Dong S. A theoretical model for an integrated wave energy extraction system consisting of a heaving buoy and a perforated wall. Renewable Energy, 2022, 189: 1086-1101

[27] Xu R, Wang H, Xi Z, Wang W, Xu M. Recent progress on wave energy marine buoys. Journal of Marine Science and Engineering, 2022, 10(5566

[28] Xu S, Wang S, Guedes Soares C. Review of mooring design for floating wave energy converters. Renewable and Sustainable Energy Reviews, 2019, 111: 595-621

[29] Zhang H, Zhou B, Vogel C, Willden R, Zang J, Geng J. Hydrodynamic performance of a dual-floater hybrid system combining a floating breakwater and an oscillating-buoy type wave energy converter. Applied Energy, 2020, 259: 114212

[30] Zhao XL, Ning DZ, Zou QP, Qiao D, Cai SQ. Hybrid floating breakwater WEC system: a review. Ocean Engineering, 2019, 186: 106126

[31] Zheng YH, Shen YM, You YG, Wu BJ, Jie DS. Wave radiation by a floating rectangular structure in oblique seas. Ocean Engineering, 2006, 33: 59-81

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