Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Advertisement

Scientific Reports
  • View all journals
  • Search
  • My Account Login
  • Content Explore content
  • About the journal
  • Publish with us
  • Sign up for alerts
  • RSS feed
  1. nature
  2. scientific reports
  3. articles
  4. article
Computational investigation on the hydrodynamic performance of a vertically submerged plate-type wave energy converter under variable relative openings
Download PDF
Download PDF
  • Article
  • Open access
  • Published: 24 March 2026

Computational investigation on the hydrodynamic performance of a vertically submerged plate-type wave energy converter under variable relative openings

  • Surendra Singh Yadav1,
  • Sujit Roy2 &
  • Pushpendra Kumar Singh Rathore3 

Scientific Reports , Article number:  (2026) Cite this article

  • 619 Accesses

  • Metrics details

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Engineering
  • Mathematics and computing
  • Ocean sciences
  • Physics

Abstract

This study aspires to analyze a wave energy converter (WEC) through its hydrodynamic efficiency featuring a stationary submerged thin vertical plate (STVP) situated at free surface level (z = 0 m). The investigation incorporates arrangements with both flat and uneven seabed profiles, and also various wave steepness conditions. To perform the computational work, a numerical wave tank (NWT) is developed utilizing the ANSYS Fluent 2024 R2 software, and the fluid interface tracking is done employing the volume of fluid (VOF) approach. Stokes waves of second-order are produced at NWT entrance using the inflow velocity approach, and the wave reflection is minimized at the end by using numerical damping. The effect of four distinct relative opening (α) and wave height (H), with uneven bottom, is evaluated and subsequently compared to the hydrodynamic efficiency over a flat sea bed. The study is conducted for four distinct wave time periods (T) in the range of 1.16–2 s. The axial flow velocity under the stationary plate is computed for various conditions, such as (a) thin plate only, (b) thin plate and a trapezoidal structure of distinct altitude below it. This research study illustrates that optimal efficiency occurs at α2 = 50%. Additionally, axial flow velocity (vx) exhibits elevated values at T = 1.87s for increased wave steepness. The findings indicate noticeably improved hydrodynamic efficiency with higher wave steepness.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

d :

Depth of water

g :

Gravitational acceleration

H :

Incoming wave height

a :

Wave amplitude

T :

Time period

P flow :

Water flow power

αq :

Volume fraction function

ρ :

Density

φ :

Velocity potential

α :

Relative opening

ω :

Angular frequency

L :

Wavelength

k :

Wavenumber

p :

Pressure

V :

Velocity

t :

Time

P wave :

Wave power

x :

 Distance from the inlet boundary in x-direction

µ :

Viscosity

η :

Surface elevation

h :

Height of opening

b :

Width of opening area beneath the plate

BC:

Boundary Condition

CFD :

Computational Fluid Dynamics

GE:

Governing Equation

NWT :

Numerical Wave Tank

OWC :

Oscillating Water Column

SD :

Submergence Depth

STVP:

Submerged Thin Vertical Plate

VOF :

Volume of Fluid

WEC :

Wave Energy Converter

References

  1. Drew, B., Plummer, A. R. & Sahinkaya, M. N. A Review of Wave Energy Converter Technology (Sage Publications Sage UK, 2009).

  2. He, F., Lin, Y., Pan, J. & Wei, M. Experimental investigation of vortex evolution around oscillating water column wave energy converter using particle image velocimetry. Physics of Fluids, 35(1), 015151 (2023).

  3. Senol, K. & Raessi, M. Enhancing power extraction in bottom-hinged flap-type wave energy converters through advanced power take-off techniques. Ocean Eng. 182, 248–258 (2019).

    Google Scholar 

  4. Xu, Q. et al. Parametric analysis of a two-body floating-point absorber wave energy converter. Physics of Fluids, 35(9), p.097115 (2023).

  5. Fernandes, A. M. & Fonseca, N. Finite depth effects on the wave energy resource and the energy captured by a point absorber. Ocean Eng. 67, 13–26 (2013).

    Google Scholar 

  6. Soleimani, K., Ketabdari, M. J. & Gharechae, A. Smoothed particle hydrodynamics study of a heaving point absorber in various waves using wave tank and calm-water models. Physics of Fluids, 35(3), p.033116 (2023).

  7. Wang, L., Xie, C., Deng, Y., Wu, Y. & Deng, Z. Numerical and experimental study on the hydrodynamic performance of an offshore-stationary dual-chamber OWC wave energy converter with a horizontal bottom-plate. Ocean Engineering, 310, p.118793. (2024).

  8. Ko, C. H. & Tsai, C. P. Hydrodynamic performance of an OWC wave energy converter combined with a perforated wall. Ocean Eng. 327, 120955 (2025).

    Google Scholar 

  9. Lin, Y. et al. Enhancing the efficiency of oscillating water column wave energy converters with sawtooth-shaped front walls: An experimental investigation. Energy (article in press) (2025).

  10. Gaspar, L. A., Teixeira, P. R. & Didier, E. Numerical analysis of the performance of two onshore oscillating water column wave energy converters at different chamber wall slopes. Ocean Eng. 201, 107119 (2020).

    Google Scholar 

  11. Qu, M., Yu, D., Xu, Z. & Gao, Z. The effect of the elliptical front wall on energy conversion performance of the offshore OWC chamber: A numerical study. Energy 255, 124428 (2022).

    Google Scholar 

  12. Mandev, M. B. & Altunkaynak, A. Cylindrical frontwall entrance geometry optimization of an oscillating water column for utmost hydrodynamic performance. Energy 280, 128147 (2023).

    Google Scholar 

  13. Fan, Y., Li, J., Liu, S. & Zhang, H. Experimental and numerical analysis of wave forces on a vertical truncated cylinder with different depths of submergence under focused waves. Ocean Eng. 309, 118523 (2024).

    Google Scholar 

  14. Anbarsooz, M., Passandideh-Fard, M. & Moghiman, M. Fully nonlinear viscous wave generation in numerical wave tanks. Ocean Eng. 59, 73–85 (2013).

    Google Scholar 

  15. Wang, R. Q., Ning, D. Z., Zhang, C. W., Zou, Q. P. & Liu, Z. Nonlinear and viscous effects on the hydrodynamic performance of a fixed OWC wave energy converter. Coast. Eng. 131, 42–50 (2018).

    Google Scholar 

  16. Martin, D. et al. Numerical analysis and wave tank validation on the optimal design of a two-body wave energy converter. Renew. Energy. 145, 632–641 (2020).

    Google Scholar 

  17. Malavasi, S. & Guadagnini, A. Interactions between a rectangular cylinder and a free-surface flow. J. Fluids Struct. 23 (8), 1137–1148 (2007).

    Google Scholar 

  18. Yadav, S. S. & Roy, P. D. Generation of stable linear waves in shallow water in a numerical wave tank. J. Appl. Fluid Mech. 15 (2), 537–549 (2022).

    Google Scholar 

  19. Arslan, T., Malavasi, S., Pettersen, B. & Andersson, H. I. Turbulent flow around a semi-submerged rectangular cylinder. J. Offshore Mech. Arct. Eng. 135 (4), 041801 (2013).

    Google Scholar 

  20. Roy, P. D. & Ghosh, S. Wave force on vertically submerged circular thin plate in shallow water. Ocean Eng. 33 (14–15), 1935–1953 (2006).

    Google Scholar 

  21. Morison, J. R., Johnson, J. W. & Schaaf, S. A. The force exerted by surface waves on piles. J. Petrol. Technol. 2 (05), 149–154 (1950).

    Google Scholar 

  22. Rajagopalan, K. & Nihous, G. Study of the force coefficients on plates using an open source numerical wave tank. Ocean Eng. 118, 187–203 (2016).

    Google Scholar 

  23. Fernando, J. N. & Rival, D. E. Reynolds-number scaling of vortex pinch-off on low-aspect-ratio propulsors. J. Fluid Mech. 799, R3 (2016).

    Google Scholar 

  24. Satheesh, S. & Huera-Huarte, F. J. Effect of free surface on a flat plate translating normal to the flow. Ocean Eng. 171, 458–468 (2019).

    Google Scholar 

  25. Prasad, D. D., Ahmed, M. R., Lee, Y. H. & Sharma, R. N. Validation of a piston type wave-maker using numerical wave tank. Ocean Eng. 131, 57–67 (2017).

    Google Scholar 

  26. Wong, V. H., Thompson, C. P. & Avery, P. A computational and experimental study of flows in a distribution chamber: validation of a numerical model. Proc. Institution Mech. Eng. Part. E: J. Process. Mech. Eng. 213 (4), 217–230 (1999).

    Google Scholar 

  27. Patten, T. Future trends in offshore engineering. Proc. Institution Mech. Eng. Part. E: J. Process. Mech. Eng. 208 (2), 97–106 (1994).

    Google Scholar 

  28. Lyons, G. J. Offshore technology—advances at the dawn of the new millennium reviewed from a UK perspective. Proc. Institution Mech. Eng. Part. E: J. Process. Mech. Eng. 214 (1), 1–21 (2000).

    Google Scholar 

  29. Falcão, A. F. D. O. Wave energy utilization: A review of the technologies. Renew. Sustain. Energy Rev. 14 (3), 899–918 (2010).

    Google Scholar 

  30. Wang, C. & Zhang, Y. Hydrodynamic performance of an offshore Oscillating Water Column device mounted over an immersed horizontal plate: A numerical study. Energy 222, 119964 (2021).

    Google Scholar 

  31. Elhanafi, A., Fleming, A., Macfarlane, G. & Leong, Z. Numerical hydrodynamic analysis of an offshore stationary–floating oscillating water column–wave energy converter using CFD. Int. J. Naval Archit. Ocean. Eng. 9 (1), 77–99 (2017).

    Google Scholar 

  32. Luo, Y., Nader, J. R., Cooper, P. & Zhu, S. P. Nonlinear 2D analysis of the efficiency of fixed oscillating water column wave energy converters. Renew. Energy. 64, 255–265 (2014).

    Google Scholar 

  33. Ning, D. Z., Shi, J., Zou, Q. P. & Teng, B. Investigation of hydrodynamic performance of an OWC (oscillating water column) wave energy device using a fully nonlinear HOBEM (higher-order boundary element method). Energy 83, 177–188 (2015).

    Google Scholar 

  34. Ning, D. Z., Wang, R. Q., Zou, Q. P. & Teng, B. An experimental investigation of hydrodynamics of a fixed OWC wave energy converter. Appl. Energy. 168, 636–648 (2016).

    Google Scholar 

  35. Dong, J., Xue, L., Cheng, K., Shi, J. & Zhang, C. An experimental investigation of wave forces on a submerged horizontal plate over a simple slope. J. Mar. Sci. Eng. 8 (7), 507 (2020).

    Google Scholar 

  36. Dong, J., Wang, B., Zhao, X. & Liu, H. Wave forces exerted on a submerged horizontal plate over an uneven bottom. J. Eng. Mech. 144 (6), 04018030 (2018).

    Google Scholar 

  37. Qiao, D. et al. Numerical simulation and experimental analysis of wave interaction with a porous plate. Ocean Eng. 218, 108106 (2020).

    Google Scholar 

  38. Orer, G. & Ozdamar, A. An experimental study on the efficiency of the submerged plate wave energy converter. Renew. Energy. 32 (8), 1317–1327 (2007).

    Google Scholar 

  39. Sangtarash, A. & Roohi, E. Numerical investigation of wave interactions in an experimental wave-energy converter using OpenFOAM. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 235(5), 1205–1224 (2021).

  40. Chappelear, J. E. Direct numerical calculation of nonlinear ocean waves. J. Phys. Res. 66, 501–508 (1961).

    Google Scholar 

  41. Dean, R. G. Stream function representation of nonlinear ocean waves. J. Phys. Res. 70 (18), 4561–4572 (1965).

    Google Scholar 

  42. Fluent, I. & ANSYS FLUENT 14. : Theory Guide Fluent Inc, Canonsburg, PA, USA; (2012).

  43. Hirt, C. W. & Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225 (1981).

    Google Scholar 

  44. Hedges, T. S. & Ursell Regions of validity of analytical wave theories. Proceedings of the Institution of Civil Engineers-Water Maritime and Energy, 112(2), 111–114. (1995).

  45. Gao, F. An efficient finite element technique for free surface flow. Doctoral Dissertation, University of Brighton, UK. (2003).

  46. Le Méhauté, B. An Introduction To Hydrodynamics and Water Waves (Springer Science & Business Media, 2013).

  47. Fenton, J. D. Nonlinear wave theories. Sea: Ocean. Eng. Sci. 9 (1), 3–25 (1990).

    Google Scholar 

Download references

Acknowledgements

The authors acknowledge the Computational Laboratory at Chandigarh University, Mohali, Punjab, India for providing the computational resources and support that contributed to the research results reported in this paper.

Funding

Open access funding provided by Manipal University Jaipur.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Guru Nanak Dev University, Amritsar, 143005, Punjab, India

    Surendra Singh Yadav

  2. University Centre for Research and Development, Chandigarh University, Mohali, 140301, Punjab, India

    Sujit Roy

  3. Department of Mechanical Engineering, Manipal University Jaipur, Jaipur, 303007, Rajasthan, India

    Pushpendra Kumar Singh Rathore

Authors
  1. Surendra Singh Yadav
    View author publications

    Search author on:PubMed Google Scholar

  2. Sujit Roy
    View author publications

    Search author on:PubMed Google Scholar

  3. Pushpendra Kumar Singh Rathore
    View author publications

    Search author on:PubMed Google Scholar

Contributions

S.S. Yadav: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Visualization, Writing - original draft preparation S. Roy: Conceptualization, Supervision, Writing -review and editing P.K.S. Rathore: Supervision, Writing -review and editing.

Corresponding author

Correspondence to Pushpendra Kumar Singh Rathore.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

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

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yadav, S.S., Roy, S. & Rathore, P.K.S. Computational investigation on the hydrodynamic performance of a vertically submerged plate-type wave energy converter under variable relative openings. Sci Rep (2026). https://doi.org/10.1038/s41598-026-38433-7

Download citation

  • Received: 01 September 2025

  • Accepted: 29 January 2026

  • Published: 24 March 2026

  • DOI: https://doi.org/10.1038/s41598-026-38433-7

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Hydrodynamic efficiency
  • Submerged vertically thin plate
  • CFD
  • Relative opening variable topology
  • Second-order stokes wave
Download PDF

Advertisement

Explore content

  • Research articles
  • News & Comment
  • Collections
  • Subjects
  • Follow us on Facebook
  • Follow us on X
  • Sign up for alerts
  • RSS feed

About the journal

  • About Scientific Reports
  • Contact
  • Journal policies
  • Guide to referees
  • Calls for Papers
  • Editor's Choice
  • Journal highlights
  • Open Access Fees and Funding

Publish with us

  • For authors
  • Language editing services
  • Open access funding
  • Submit manuscript

Search

Advanced search

Quick links

  • Explore articles by subject
  • Find a job
  • Guide to authors
  • Editorial policies

Scientific Reports (Sci Rep)

ISSN 2045-2322 (online)

nature.com footer links

About Nature Portfolio

  • About us
  • Press releases
  • Press office
  • Contact us

Discover content

  • Journals A-Z
  • Articles by subject
  • protocols.io
  • Nature Index

Publishing policies

  • Nature portfolio policies
  • Open access

Author & Researcher services

  • Reprints & permissions
  • Research data
  • Language editing
  • Scientific editing
  • Nature Masterclasses
  • Research Solutions

Libraries & institutions

  • Librarian service & tools
  • Librarian portal
  • Open research
  • Recommend to library

Advertising & partnerships

  • Advertising
  • Partnerships & Services
  • Media kits
  • Branded content

Professional development

  • Nature Awards
  • Nature Careers
  • Nature Conferences

Regional websites

  • Nature Africa
  • Nature China
  • Nature India
  • Nature Japan
  • Nature Middle East
  • Privacy Policy
  • Use of cookies
  • Legal notice
  • Accessibility statement
  • Terms & Conditions
  • Your US state privacy rights
Springer Nature

© 2026 Springer Nature Limited

Nature Briefing Anthropocene

Sign up for the Nature Briefing: Anthropocene newsletter — what matters in anthropocene research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: Anthropocene