Skip to main content

Advertisement

SpringerLink
Log in

Constructal Design on full-scale numerical model of a submerged horizontal plate-type wave energy converter

  • Original Paper
  • Published:
Marine Systems & Ocean Technology Aims and scope Submit manuscript

Abstract

Considering the growing worldwide energy demand, the available energy in ocean waves is an important resource in the field of renewable energy. In this paper, a numerical assessment of the design of the Submerged Horizontal Plate device in full scale was performed aiming to improve its performance. In this sense, the Constructal Design method was applied to define the constraints, performance parameter and degree of freedom. The two-dimensional numerical wave channel on a model scale performed in previous work was full scaled according to Froude similitude criteria. The hydrodynamic performance and similarity among the results of both model and full scale are analyzed. The degree of freedom relative plate height (X) was performed from 20.00% up to 90.00%. Conservation equations of mass and momentum were solved using Computational Fluid Dynamics software based on the Finite Volume Method, adopting the multiphase model Volume of Fluid. The similarity between model and full scale was achieved with a mean difference of 1.15% among the device efficiency results. The analysis results showed an improvement in device performance of up to 35.61% between the worst and the best-studied geometries. The optimal geometry was achieved at X = 90.00% resulting in a device efficiency of 37.15%.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

Data sets generated during the current study are available from the corresponding author under request.

References

  1. L. Margheritini, A.M. Hansen, P. Frigaard, A method for EIA scoping of wave energy converters—based on classification of the used technology. Environ. Impact Assess. Rev. 32(1), 33–44 (2012). https://doi.org/10.1016/j.eiar.2011.02.003

    Article  Google Scholar 

  2. A.F.O. Falcão, Wave energy utilization: a review of the Technologies. Renew. Sustain. Energy Rev. 14(3), 899–918 (2010). https://doi.org/10.1016/j.rser.2009.11.003

    Article  Google Scholar 

  3. A. Uihlein, D. Magagna, Wave and tidal current energy—a review of the current state of research beyond technology. Renew. Sustain. Energy Rev. 58, 1070–1081 (2016). https://doi.org/10.1016/j.rser.2015.12.284

    Article  Google Scholar 

  4. P. Contestabile, V. Ferrante, D. Vicinanza, Wave energy resource along the coast of Santa Catarina (Brazil). Energies 8(12), 14219–14243 (2015). https://doi.org/10.3390/en81212423

    Article  Google Scholar 

  5. R.C. Guimarães, P.H. Oleinik, E.P. Kirinus, B.V. Lopes, T.B. Trombetta, W.C. Marques, An overview of the Brazilian continental shelf wave energy potential. Reg Stud. Mar. Sci. 25, 100446 (2019). https://doi.org/10.1016/j.rsma.2018.100446

    Article  Google Scholar 

  6. R.C. Lisboa, P.R.F. Teixeira, C.J. Fortes, Numerical evaluation of wave energy potential in the south of Brazil. Energy 121, 176–184 (2017). https://doi.org/10.1016/j.energy.2017.01.001

    Article  Google Scholar 

  7. P.H. Oleinik, W.C. Marques, E.P. Kirinus, Evaluation of the seasonal pattern of wind-driven waves on the south-southeastern Brazilian shelf. Defect Diffus. Forum 370, 141–151 (2017). https://doi.org/10.4028/www.scientific.net/DDF.370.141

    Article  Google Scholar 

  8. P.M. Singh, Z. Chen, Y.-D. Choi, Numerical analysis for a proposed hybrid system with single HAWT, double HATCT and vertical oscillating wave energy converters on a single tower. J. Mech. Sci. Technol. 30(10), 4609–4619 (2016). https://doi.org/10.1007/s12206-016-0932-9

    Article  Google Scholar 

  9. S. Astariz, G. Iglesias, Co-located wind and wave energy farms: Uniformly distributed arrays. Energy 113, 497–508 (2016). https://doi.org/10.1016/j.energy.2016.07.069

    Article  Google Scholar 

  10. D. Ning, Q. Li, H. Lin, B. Teng, Numerical investigation of nonlinear wave scattering by a horizontal submerged plate. Proc. Eng. 116, 237–244 (2015). https://doi.org/10.1016/j.proeng.2015.08.286

    Article  Google Scholar 

  11. R.W. Carter, Wave energy converters and a submerged horizontal plate. (MSc. thesis, University of Hawai’i, USA, 2005).

  12. K.-U. Graw, Shore protection and electricity by submerged plate wave energy converter. In: European Wave Energy Symposium (1993), pp. 379–384.

  13. G. Wang, B. Ren, Y. Wang, Experimental study on hydrodynamic performance of arc plate breakwater. Ocean Eng. 111, 593–601 (2016). https://doi.org/10.1016/j.oceaneng.2015.11.016

    Article  Google Scholar 

  14. G. Orer, A. Ozdamar, An experimental study on the efficiency of the submerged plate wave energy converter. Renew. Energy 32(8), 1317–1327 (2007). https://doi.org/10.1016/j.renene.2006.06.008

    Article  Google Scholar 

  15. F.M. Seibt, E.C. Couto, E.D. Dos Santos, L.A. Isoldi, L.A.O. Rocha, P.R.F. Teixeira, Numerical study on the effect of submerged depth on the horizontal plate wave energy converter. China Ocean Eng. 28(5), 687–700 (2014). https://doi.org/10.1007/s13344-014-0056-x

    Article  Google Scholar 

  16. F.M. Seibt, E.C. Couto, P.R.F. Teixeira, E.D. Dos Santos, L.A.O. Rocha, L.A. Isoldi, Numerical analysis of the fluid-dynamic behavior of a submerged plate wave energy converter. Comput. Therm. Sci.: Int. J. 6(6), 525–534 (2014). https://doi.org/10.1615/ComputThermalScien.2014010456

    Article  Google Scholar 

  17. M.N. Gomes, M.F.E. Lara, S.L.P. Iahnke, B.N. Machado, M.N. Goulart, F.M. Seibt, E.D. Dos Santos, L.A. Isoldi, L.A.O. Rocha, Numerical approach of the main physical operational principle of several wave energy converters: oscillating water column, overtopping and submerged plate. Defect Diffus. Forum 362, 115–171 (2015). https://doi.org/10.4028/www.scientific.net/DDF.362.115

    Article  Google Scholar 

  18. C. Windt, J. Tchoufag, M.-R. Alam, Numerical investigation of threedimensional effects on wave excitation forces on a submerged rigid board. In: 2nd International Conference on Offshore Renewable Energy (CORE2016), (2016), pp. 1–9.

  19. M. Kharati-Koopaee, M. Kiali-Kooshkghazi, Assessment of plate-length effect on the performance of the horizontal plate wave energy converter. J. Waterw. Port Coast. Ocean Eng. 145(1), 04018037 (2019). https://doi.org/10.1061/(ASCE)WW.1943-5460.0000498

    Article  Google Scholar 

  20. R. Carmigniani, A. Leroy, D. Violeau, A simple SPH model of a free surface water wave pump: waves above a submerged plate. Coast. Eng. J. 61(1), 96–108 (2019). https://doi.org/10.1080/21664250.2018.1560923

    Article  Google Scholar 

  21. F.M. Seibt, F.V. De Camargo, E.D. Dos Santos, M.N. Gomes, L.A.O. Rocha, L.A. Isoldi, C. Fragassa, Numerical evaluation on the efficiency of the submerged horizontal plate type wave energy converter. FME Trans. 47(3), 543–551 (2019). https://doi.org/10.5937/fmet1903543S

    Article  Google Scholar 

  22. M. He, X. Gao, W. Xu, B. Ren, H. Wang, Potential application of submerged horizontal plate as a wave energy breakwater: a 2D study using the WCSPH method. Ocean Eng. 185, 27–46 (2019). https://doi.org/10.1016/j.oceaneng.2019.05.034

    Article  Google Scholar 

  23. A. Bejan, S. Lorente, Design with constructal theory (Wiley, Hobken, 2008)

    Book  Google Scholar 

  24. L.A.O. Rocha, S. Lorente, A. Bejan, Constructal theory in heat transfer, in Handbook of Thermal Science and Engineering. ed. by F.A. Kulacki (Springer, Cham, 2017). https://doi.org/10.1007/978-3-319-32003-8_66-1

    Chapter  Google Scholar 

  25. E.D. Dos Santos, B.N. Machado, M.M. Zanella, M.N. Gomes, J.A. Souza, L.A. Isoldi, L.A.O. Rocha, Numerical study of the effect of the relative depth on the overtopping wave energy converters according to constructal design. Defect Diffus. Forum 348, 232–244 (2014). https://doi.org/10.4028/www.scientific.net/DDF.348.232

    Article  Google Scholar 

  26. M.M. Goulart, J.C. Martins, I.C.A. Junior, M.N. Gomes, J.A. Souza, L.A.O. Rocha, L.A. Isoldi, E.D. Dos Santos, Constructal design of an onshore overtopping device in real scale for two different depths. Mar. Syst. Ocean Technol. 10(2), 120–129 (2015). https://doi.org/10.1007/s40868-015-0010-7

    Article  Google Scholar 

  27. J.C. Martins, C. Fragassa, M.M. Goulart, E.D. Dos Santos, L.A. Isoldi, M.N. Gomes, L.A.O. Rocha, Constructal design of an overtopping wave energy converter incorporated in a breakwater. J. Mar. Sci. Eng. 10(4), 471 (2022). https://doi.org/10.3390/jmse10040471

    Article  Google Scholar 

  28. J.C. Martins, M.M. Goulart, E.D. Dos Santos, L.A. Isoldi, M.N. Gomes, L.A.O. Rocha, Constructal design of a two ramps overtopping wave energy converter integrated into a breakwater: effect of the vertical distance between the ramps over its performance. Defect Diffus. Forum 420, 242–258 (2022). https://doi.org/10.4028/p-408n90

    Article  Google Scholar 

  29. J.C. Martins, M.M. Goulart, M.N. Gomes, J.A. Souza, L.A.O. Rocha, L.A. Isoldi, E.D. Dos Santos, Geometric evaluation of the main operational principle of an overtopping wave energy converter by means of constructal design. Renew. Energy 118, 727–741 (2018). https://doi.org/10.1016/j.renene.2017.11.061

    Article  Google Scholar 

  30. E.D. Dos Santos, B.N. Machado, N. Lopes, J.A. Souza, P.R.F. Teixeira, M.N. Gomes, L.A. Isoldi, L.A.O. Rocha (2013) Constructal design of wave energy converters, in constructal law and the unifying principle of design. In: L.A.O. Rocha, S. Lorente, A. Bejan (eds.) Understanding Complex Systems, Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5049-8_16

  31. M.N. Gomes, G. Lorenzini, L.A.O. Rocha, E.D. Dos Santos, L.A. Isoldi, Constructal design applied to the geometric evaluation of an oscillating water column wave energy converter considering different real scale wave periods. J. Eng. Thermophys. 27(2), 173–190 (2018). https://doi.org/10.1134/S1810232818020042

    Article  Google Scholar 

  32. M. Letzow, G. Lorenzini, D.V.E. Barbosa, R.G. Hübner, L.A.O. Rocha, M.N. Gomes, L.A. Isoldi, E.D. Dos Santos, Numerical analysis of the influence of geometry on a large scale onshore oscillating water column device with associated seabed ramp. Int. J. Des. Nat. Ecodyn. 15(6), 873–884 (2020). https://doi.org/10.18280/ijdne.150613

    Article  Google Scholar 

  33. Y.T.B. Lima, M.N. Gomes, L.A. Isoldi, E.D. Dos Santos, G. Lorenzini, L.A.O. Rocha, Geometric analysis through the constructal design of a sea wave energy converter with several coupled hydropneumatic chambers considering the oscillating water column operating principle. Appl. Sci. 11(18), 8630 (2021). https://doi.org/10.3390/app11188630

    Article  Google Scholar 

  34. M.R. Oliveira, E.D. Dos Santos, L.A. Isoldi, L.A.O. Rocha, M.N. Gomes, Numerical and geometrical analysis of the onshore oscillating water column wave energy with a ramp. Defect Diffus. Forum 412, 11–26 (2021). https://doi.org/10.4028/www.scientific.net/DDF.412.11

    Article  Google Scholar 

  35. F.M. Seibt, L.A. Isoldi, E.D. Dos Santos, L.A.O. Rocha, Study of the effect of the relative height on the efficiency of a submerged horizontal plate type wave energy converter applying constructal design. In: XXXVIII Ibero-Latin American Congress on Computational Methods in Engineering (CILAMCE), November (2017), pp. 1–17. https://doi.org/10.20906/CPS/CILAMCE2017-0862

  36. S.A. Hughes, Physical models and laboratory techniques in coastal engineering, in Advanced Series on Ocean Engineering, vol. 7, ed. by P. Liu (World Scientific Publishing Co Pte Ltd, Singapore, 1993)

    Google Scholar 

  37. A. Viviano, S. Naty, E. Foti, Scale effects in physical modelling of a generalized OWC. Ocean Eng. 162, 248–258 (2018). https://doi.org/10.1016/j.oceaneng.2018.05.019

    Article  Google Scholar 

  38. W. Sheng, R. Alcorn, T. Lewis, Physical modelling of wave energy converters. Ocean Eng. 84, 29–36 (2014). https://doi.org/10.1016/j.oceaneng.2014.03.019

    Article  Google Scholar 

  39. A. Bejan, Constructal-theory network of conducting paths for cooling a heat generating volume. Int. J. Heat Mass Transf. 40(4), 799–816 (1997). https://doi.org/10.1016/0017-9310(96)00175-5

    Article  Google Scholar 

  40. A. Bejan, Evolution in thermodynamics. Appl. Phys. Rev. 4(1), 011305 (2017). https://doi.org/10.1063/1.4978611

    Article  Google Scholar 

  41. R.G. Dean, R.A. Dalrymple, Water Wave Mechanics for Engineers and Scientists. (World Scientific Publishing Co. Pte. Ltd., Singapore, 1991).

    Book  Google Scholar 

  42. M.E. McCormick, Ocean Wave Energy Conversion (Dover Publications Inc, New York, 1981)

    Google Scholar 

  43. H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics – The Finite Volume Method. (Pearson, England, 2007)

  44. C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981). https://doi.org/10.1016/0021-9991(81)90145-5

    Article  Google Scholar 

  45. V. Srinivasan, A.J. Salazar, K. Saito, Modeling the disintegration of modulated liquid jets using volume-of-fluid (VOF) methodology. Appl. Math. Model. 35(8), 3710–3730 (2011). https://doi.org/10.1016/j.apm.2011.01.040

    Article  MathSciNet  Google Scholar 

  46. M. Horko, CFD optimisation of an oscillating water column energy converter. (MSc. thesis, University of Western Australia, Australia, 2007).

  47. R.S. Ramalhais, Estudo numérico de um dispositivo de conversão da energia das ondas do tipo coluna de água oscilante (CAO). (MSc. thesis, Universidade Nova de Lisboa, Portugal, 2011).

  48. T.G. Barreiro, Estudo da interacção de uma onda monocromática com um conversor de energia. (MSc. thesis, Universidade Nova de Lisboa, Portugal, 2009).

  49. K.-U. Graw, Is the submerged plate wave energy converter ready to act as a new coastal protection system? In: XXIV Convegno di Idraulica e Costruzioni Idrauliche (1994), pp. 1–9.

  50. A.F.O. Falcão, J.C.C. Henriques, Model-prototype similarity of oscillating-water-column wave energy converters. Int. J. Mar. Energy 6, 18–34 (2014). https://doi.org/10.1016/j.ijome.2014.05.002

    Article  Google Scholar 

  51. A. Elhanafi, G. Macfarlane, A. Fleming, Z. Leong, Scaling and air compressibility effects on a three-dimensional offshore stationary OWC wave energy converter. Appl. Energy 189, 1–20 (2017). https://doi.org/10.1016/j.apenergy.2016.11.095

    Article  Google Scholar 

  52. C. Windt, J. Davidson, J.V. Ringwood, Numerical analysis of the hydrodynamic scaling effects for the wavestar wave energy converter. J.Fluids Struct. 105, 103328 (2021). https://doi.org/10.1016/j.jfluidstructs.2021.103328

    Article  Google Scholar 

  53. B.N. Machado, P.H. Oleinik, E.P. Kirinus, E.D. Dos Santos, L.A.O. Rocha, M.N. Gomes, J.M.P. Conde, L.A. Isoldi, WaveMIMO methodology: numerical wave generation of a realistic sea state. J. Appl. Comput. Mech. 7(4), 2129–2148 (2021). https://doi.org/10.2055/jacm.2021.37617.3051

    Article  Google Scholar 

Download references

Acknowledgements

F.M. Seibt thanks the Brazilian National Council for Scientific and Technological Development—CNPq (process: 140057/2015-3) by doctorate scholarship. The authors thank Research Support Foundation of the State of Rio Grande do Sul—FAPERGS (Public Call FAPERGS 07/2021, Programa Pesquisador Gaúcho (PqG), process: 21/2551-0002231-0) for the financial support. The authors L.A.O. Rocha, E.D. Dos Santos, and L.A. Isoldi are grant holders of the CNPq (processes: 307791/2019-0, 308396/2021-9, and 309648/2021-1, respectively), being grateful for the financial support.

Funding

This study was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq (Grant Nos. 140057/2015-3, 307791/2019-0, 308396/2021-9, 309648/2021-1) and Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul-FAPERGS (Grant No. 21/2551-0002231-0).

Author information

Authors and Affiliations

  1. Programa de Pós-Graduação em Engenharia Oceânica (PPGEO), Escola de Engenharia, Universidade Federal do Rio Grande (FURG), Rio Grande, RS, Brazil

    Flavio Medeiros Seibt, Elizaldo Domingues dos Santos, Liércio André Isoldi & Luiz Alberto Oliveira Rocha

  2. Programa de Pós-Graduação em Modelagem Computacional (PPGMC), Escola de Engenharia, Universidade Federal do Rio Grande (FURG), Rio Grande, RS, Brazil

    Elizaldo Domingues dos Santos, Liércio André Isoldi & Luiz Alberto Oliveira Rocha

  3. Programa de Pós-Graduação em Engenharia Mecânica (PROMEC), Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brazil

    Luiz Alberto Oliveira Rocha

Authors
  1. Flavio Medeiros Seibt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elizaldo Domingues dos Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liércio André Isoldi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Luiz Alberto Oliveira Rocha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Flavio Medeiros Seibt.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seibt, F.M., dos Santos, E.D., Isoldi, L.A. et al. Constructal Design on full-scale numerical model of a submerged horizontal plate-type wave energy converter. Mar Syst Ocean Technol 18, 1–13 (2023). https://doi.org/10.1007/s40868-023-00124-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40868-023-00124-7

Keywords

Search

Navigation