CFD design-load analysis of a two-body wave energy converter

  • Ryan G. CoeEmail author
  • Brian J. Rosenberg
  • Eliot W. Quon
  • Chris C. Chartrand
  • Yi-Hsiang Yu
  • Jennifer van Rij
  • Tim R. Mundon
Research Article


Wave energy converters (WECs) must survive in a wide variety of conditions while minimizing structural costs, so as to deliver power at cost-competitive rates. Although engineering design and analysis tools used for other ocean systems, such as offshore structures and ships, can be applied, the unique nature and limited historical experience of WEC design necessitates assessment of the effectiveness of these methods for this specific application. This paper details a study to predict extreme loading in a two-body WEC using a combination of mid-fidelity and high-fidelity numerical modeling tools. Here, the mid-fidelity approach is a time-domain model based on linearized potential flow hydrodynamics and the high-fidelity modeling tool is an unsteady Reynolds-averaged Navier–Stokes model. In both models, the dynamics of the WEC power take-off and mooring system have been included. For the high-fidelity model, two design wave approaches (an equivalent regular wave and a focused wave) are used to estimate the worst case wave forcing within a realistic irregular sea state. These simplified design wave approaches aim to capture the extreme response of the WEC within a feasible amount of computational effort. When compared to the mid-fidelity model results in a long-duration irregular sea, the short-duration design waves simulated in CFD produce upper percentile load responses, hinting at the suitability of these two approaches.


Wave energy converter (WEC) Extreme Survival Design load CFD 



This material is based upon work supported by the U.S. Department of Energy under Award Number DE-EE0007346. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This work was authored [in part] by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract no. DE-AC36-08GO28308. Funding provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.


  1. Arup, Atcheson C (2016) Structural forces and stresses for wave energy devices. Technical Report ARP-LS2, Wave Energy ScotlandGoogle Scholar
  2. Babarit A, Delhommeau G (2015) Theoretical and numerical aspects of the open source BEM solver NEMOH. In: 11th European wave and tidal energy conference (EWTEC2015)Google Scholar
  3. Choi J, Yoon SB (2009) Numerical simulations using momentum source wave-maker applied to RANS equation model. Coast Eng 56(10):1043–1060CrossRefGoogle Scholar
  4. Coe RG, Michelen C, Eckert-Gallup A, Martin N, Yu YH, van Rij J, Quon EW, Manuel L, Nguyen P, Esterly T, Seng B, Stuart Z, Canning J (2018a) WEC design response toolbox (WDRT).
  5. Coe RG, Yu YH, van Rij J (2018b) A survey of WEC reliability, survival and design practices. Energies 11(1):4.,
  6. Courant R, Friedrichs K, Lewy H (1928) Über die partiellen differenzengleichungen der mathematischen physik. Mathematische annalen 100(1):32–74MathSciNetCrossRefzbMATHGoogle Scholar
  7. Crespo AJ, Domínguez JM, Rogers BD, Gómez-Gesteira M, Longshaw S, Canelas R, Vacondio R, Barreiro A, García-Feal O (2015) Dualsphysics: open-source parallel CFD solver based on smoothed particle hydrodynamics (SPH). Comput Phys Commun 187:204–216CrossRefzbMATHGoogle Scholar
  8. Dallman A, Neary V (2014) Characterization of U.S. wave energy converter (WEC) test sites: a catalogue of met-ocean data. Tech. Rep. Tech. Rep. SAND2014-18206, Sandia National LaboratoriesGoogle Scholar
  9. DNV-RP-C205 (2007) Environmental conditions and environmental loads. Det Norske Veritas (DNV), Høvik, NorwayGoogle Scholar
  10. DNV-RP-F205 (2010) Global performance analysis of deepwater floating structures. Det Norske Veritas (DNV), OsloGoogle Scholar
  11. DNV-OS-J103 (2013) Design of floating wind turbine structures. Det Norske Veritas (DNV), Høvik, NorwayGoogle Scholar
  12. Ferziger JH, Peric M (2012) Computational methods for fluid dynamics. Springer, New YorkzbMATHGoogle Scholar
  13. Hadzic H (2006) Development and application of finite volume method for the computation of flows around moving bodies on unstructured, overlapping grids. PhD thesis, Technische Universität Hamburg, 10.15480/882.231,
  14. Hadzic I, Hennig J, Peric M, Xing-Kaeding Y (2005) Computation of flow-induced motion of floating bodies. Appl Math Model 29(12):1196–1210. CrossRefzbMATHGoogle Scholar
  15. Hérault A, Bilotta G, Dalrymple RA (2010) SPH on GPU with CUDA. J Hydraul Res 48:74–79CrossRefGoogle Scholar
  16. Hu ZZ, Causon DM, Mingham CG, Qian L (2011) Numerical simulation of floating bodies in extreme free surface waves. Nat Hazards Earth Syst Sci 11(2):519–527. CrossRefGoogle Scholar
  17. IEC TS 61400-3-2 (2013) Design requirements for floating offshore wind turbines, edn 2. International Electrotechnical Commission (IEC)Google Scholar
  18. IEC TS 62600-2 (2016) Marine energy—Wave, tidal and other water current converters. Part 2: design requirements for marine energy systems, edn 1. International Electrotechnical Commission (IEC)Google Scholar
  19. ITTC (2011) Practical guidelines for ship CFD applications. Technical Report 75-03-02-03. International Towing Tank Conference (ITTC), Rio de Janeiro, BrazilGoogle Scholar
  20. Iturrioz A, Guanche R, Lara J, Vidal C, Losada I (2015) Validation of OpenFOAM for oscillating water column three-dimensional modeling. Ocean Engineering 107:222–236.,
  21. Madhi F, Yeung RW (2017) On survivability of asymmetric wave-energy converters in extreme waves. Renew Energy 119:891–909 CrossRefGoogle Scholar
  22. Mundon T, Rosenberg B, Vining J (2017a) A hybrid drive train for low-speed, linear WEC applications. In: Proceedings of the 5th Marine Energy Technology Symposium (METS), Washington, D.CGoogle Scholar
  23. Mundon TR, Rosenberg BJ, van Rij J (2017b) Reaction body hydrodynamics for a multi-DOF point-absorbing WEC. In: 12th European wave and tidal energy conference (EWTEC2017)Google Scholar
  24. NORSOK (2007) Actions and action effects (N-003), edn 2. Standards Norway, NorwayGoogle Scholar
  25. Ochi MK (2005) Ocean waves: the stochastic approach, vol 6. Cambridge University Press, CambridgezbMATHGoogle Scholar
  26. Omidvar P, Stansby PK, Rogers BD (2013) SPH for 3D floating bodies using variable mass particle distribution. Int J Numer Methods Fluids 72(4):427–452. MathSciNetCrossRefGoogle Scholar
  27. OrcaFlex (2015) OrcaFlex manual. Orcina Ltd., Daltongate Ulverston Cumbria, UKGoogle Scholar
  28. Palm J, Eskilsson C, Paredes GM, Bergdahl L (2016) Coupled mooring analysis for floating wave energy converters using CFD: formulation and validation. Int J Mar Energy 16:83–99CrossRefGoogle Scholar
  29. Penalba M, Davidson J, Windt C, Ringwood JV (2018) A high-fidelity wave-to-wire simulation platform for wave energy converters: coupled numerical wave tank and power take-off models. Appl Energy 226:655–669CrossRefGoogle Scholar
  30. Quon E, Platt A, Yu YH, Lawson M (2016) Application of most likely extreme response method for wave energy converters. In: ASME 2016 35th international conference on ocean, offshore and arctic engineering (OMAE), ASMEGoogle Scholar
  31. Rafiee A, Wolgamot H, Draper S, Orszaghova J, Fivez J, Sawyer T(2016) Identifying the design wave group for the extreme response of a point absorber wave energy converter. In: Asian wave and TidalEnergy conference (AWTEC), SingaporeGoogle Scholar
  32. Ransley E, Greaves D, Raby A, Simmonds D, Hann M (2017a) Survivability of wave energy converters using CFD. Renew Energy 109:235–247CrossRefGoogle Scholar
  33. Ransley E, Greaves D, Raby A, Simmonds D, Jakobsen MM, Kramer M (2017b) RANS-VOF modelling of the wavestar point absorber. Renew Energy 109:49–65CrossRefGoogle Scholar
  34. Rosenberg B, Mundon T (2016) Numerical and physical modeling of a flexibly-connected two-body wave energy converter. In: Proceedings of the 4th marine energy technology symposium (METS), Washington, D.C.Google Scholar
  35. Schetz J (1993) Boundary layer analysis. Prentice Hall,
  36. Sjökvist L, Göteman M (2017) Peak forces on wave energy linear generators in tsunami and extreme waves. Energies 10(9):1323CrossRefGoogle Scholar
  37. van Rij J, Yu YH, Coe RG (2018) Design load analysis for wave energy converters. In: ASME 2018 37th international conference on ocean, offshore and arctic engineering (OMAE2018), ASME, Madrid, SpainGoogle Scholar
  38. Vinokur M (1983) On one-dimensional stretching functions for finite-difference calculations. J Comput Phys 50(2):215–234MathSciNetCrossRefzbMATHGoogle Scholar
  39. Westphalen J, Greaves D, Williams C, Taylor P, Causon D, Mingham C, Hu Z, Stansby P, Rogers B, Omidvar P (2009) Extreme wave loading on offshore wave energy devices using CFD: a hierarchical team approach. In: Proceedings of the 8\(^{\rm th}\) European wave and tidal energy conference (EWTEC), pp 500–508Google Scholar
  40. Westphalen J, Greaves MD, Raby A, Hu ZZ, Causon DM, Mingham CG, Omidvar P, Stansby PK, Rogers BD (2014) Investigation of wave-structure interaction using state of the art CFD techniques. Open J Fluid Dyn 04(01):18–43. CrossRefGoogle Scholar
  41. Yu YH, Li Y (2013) Reynolds-averaged Navier-Stokes simulation of the heave performance of a two-body floating-point absorber wave energy system. Comput Fluids 73:104–114. CrossRefzbMATHGoogle Scholar

Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  1. 1.Sandia National LabsAlbuquerqueUSA
  2. 2.National Renewable Energy LaboratoryGoldenUSA
  3. 3.Oscilla Power, Inc.SeattleUSA

Personalised recommendations