# Performance of a Raft-Type Wave Energy Converter with Diverse Mooring Configurations

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Potential Flow Approach

#### 2.2. Motion Response of a Raft-Type WEC

**A**and the hydrodynamic damping

**c**are frequency-dependent, the equation of motion of such a floating system is expressed in a convolution integral form in time domain calculations [34]:

**m**and

**K**are the $6n\times 6n$ mass and stiffness matrices, respectively.

**U**is the $6n\times 1$ motion response and

**F**is the $6n\times 1$ external force at frequency $\omega $. Furthermore, the acceleration impulse matrix is defined as:

## 3. Physical Model Test and Numerical Validation

#### 3.1. Physical Model Test

#### 3.2. Validation of the Numerical Model

## 4. Numerical Results and Discussions

#### 4.1. Hydrodynamic Characteristics of the Two-Body System

#### 4.2. Effect of PTO Damping

#### 4.3. Effect of Mooring Configuration

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bouckaert, S.; Pales, A.F.; McGlade, C.; Remme, U.; Wanner, B.; Varro, L.; D’Ambrosio, D.; Spencer, T. Net Zero by 2050: A Roadmap for the Global Energy Sector; International Energy Agency: Paris, France, 2021. [Google Scholar]
- Li, X.; Chen, C.; Li, Q.; Xu, L.; Liang, C.; Ngo, K.; Parker, R.G.; Zuo, L. A compact mechanical power take-off for wave energy converters: Design, analysis, and test verification. Appl. Energy
**2020**, 278, 115459. [Google Scholar] [CrossRef] - Guo, B.; Ringwood, J.V. Geometric optimisation of wave energy conversion devices: A survey. Appl. Energy
**2021**, 297, 117100. [Google Scholar] [CrossRef] - Murray, R.; Rastegar, J. Novel two-stage piezoelectric-based ocean wave energy harvesters for moored or unmoored buoys. In Active and Passive Smart Structures and Integrated Systems 2009; Ahmadian, M., Ghasemi-Nejhad, M.N., Eds.; International Society for Optics and Photonics, SPIE: San Diego, CA, USA, 2009; Volume 7288, p. 72880E. [Google Scholar]
- Drew, B.; Plummer, A.R.; Sahinkaya, M.N. A review of wave energy converter technology. Proc. Inst. Mech. Eng. Part A J. Power Energy
**2009**, 223, 887–902. [Google Scholar] [CrossRef] - Agyekum, E.B.; PraveenKumar, S.; Eliseev, A.; Velkin, V.I. Design and construction of a novel simple and low-cost test bench point-absorber wave energy converter emulator system. Inventions
**2021**, 6, 20. [Google Scholar] [CrossRef] - Wang, L.; Kolios, A.; Cui, L.; Sheng, Q. Flexible multibody dynamics modelling of point-absorber wave energy converters. Renew. Energy
**2018**, 127, 790–801. [Google Scholar] [CrossRef] - Noad, I.; Porter, R. Modelling an articulated raft wave energy converter. Renew. Energy
**2017**, 114, 1146–1159. [Google Scholar] [CrossRef] - Melikoglu, M. Current status and future of ocean energy sources: A global review. Ocean Eng.
**2018**, 148, 563–573. [Google Scholar] [CrossRef] - McCormick, M.; Murthagh, J.; McCabe, P. Large-scale experimental study of a hinged-barge wave energy conversion system. In Proceedings of the 3rd European Wave Energy Conference, Patras, Greece, 30 September–2 October 1998; pp. 215–222. [Google Scholar]
- Retzler, C. Measurements of the slow drift dynamics of a model Pelamis wave energy converter. Renew. Energy
**2006**, 31, 257–269. [Google Scholar] [CrossRef] - Giannini, G.; Temiz, I.; Rosa-Santos, P.; Shahroozi, Z.; Ramos, V.; Göteman, M.; Engström, J.; Day, S.; Taveira-Pinto, F. Wave energy converter power take-off system scaling and physical modelling. J. Mar. Sci. Eng.
**2020**, 8, 632. [Google Scholar] [CrossRef] - Paredes, G.M.; Palm, J.; Eskilsson, C.; Bergdahl, L.; Taveira-Pinto, F. Experimental investigation of mooring configurations for wave energy converters. Int. J. Mar. Energy
**2016**, 15, 56–67. [Google Scholar] [CrossRef] - Elhanafi, A.; Macfarlane, G.; Fleming, A.; Leong, Z. Experimental and numerical investigations on the hydrodynamic performance of a floating–moored oscillating water column wave energy converter. Appl. Energy
**2017**, 205, 369–390. [Google Scholar] [CrossRef] - Wu, M.; Stratigaki, V.; Troch, P.; Altomare, C.; Verbrugghe, T.; Crespo, A.; Cappietti, L.; Hall, M.; Gómez-Gesteira, M. Experimental study of a moored floating oscillating water column wave-energy converter and of a moored cubic box. Energies
**2019**, 12, 1834. [Google Scholar] [CrossRef] - Xu, S.; Soares, C.G. Experimental investigation on short-term fatigue damage of slack and hybrid mooring for wave energy converters. Ocean Eng.
**2020**, 195, 106618. [Google Scholar] [CrossRef] - Sirigu, S.A.; Bonfanti, M.; Begovic, E.; Bertorello, C.; Dafnakis, P.; Giorgi, G.; Bracco, G.; Mattiazzo, G. Experimental investigation of the mooring system of a wave energy converter in operating and extreme wave conditions. J. Mar. Sci. Eng.
**2020**, 8, 180. [Google Scholar] [CrossRef] - Davidson, J.; Ringwood, J.V. Mathematical modelling of mooring systems for wave energy converters—A review. Energies
**2017**, 10, 666. [Google Scholar] [CrossRef] - Jiang, C.; el Moctar, O.; Paredes, G.M.; Schellin, T.E. Validation of a dynamic mooring model coupled with a RANS solver. Mar. Struct.
**2020**, 72, 102783. [Google Scholar] [CrossRef] - Jiang, C. Mathematical Modelling of Wave Induced Motions and Loads on Moored Offshore Structures. Ph.D. Thesis, University of Duisburg-Essen, Essen, Germany, 2021. [Google Scholar]
- Cerveira, F.; Fonseca, N.; Pascoal, R. Mooring system influence on the efficiency of wave energy converters. Int. J. Mar. Energy
**2013**, 3, 65–81. [Google Scholar] [CrossRef] - Luo, L.; Sun, K.; Ge, W.; Yuan, Z.; Huang, H.; Leng, J. Research on hydrodynamic performance of modular offshore wave energy platform. In Proceedings of the OCEANS 2016-Shanghai, Shanghai, China, 10–13 April 2016; pp. 1–5. [Google Scholar]
- Huang, S.; Sheng, S.; You, Y.; Gerthoffert, A.; Wang, W.; Wang, Z. Numerical study of a novel flex mooring system of the floating wave energy converter in ultra-shallow water and experimental validation. Ocean Eng.
**2018**, 151, 342–354. [Google Scholar] [CrossRef] - Chen, W.; Zhang, Y.; Yang, J.; Yu, H.; Liang, S. Experiments and CFD modeling of a dual-raft wave energy dissipator. Ocean Eng.
**2021**, 237, 109648. [Google Scholar] [CrossRef] - Jin, S.; Wang, D.; Hann, M.; Collins, K.; Conley, D.; Greaves, D. A designed two-body hinged raft wave energy converter: From experimental study to annual power prediction for the EMEC site using WEC-Sim. Ocean Eng.
**2023**, 267, 113286. [Google Scholar] [CrossRef] - Jiang, C.; el Moctar, O.; Schellin, T.E. Capability of a potential-flow solver to analyze articulated multibody offshore modules. Ocean Eng.
**2022**, 266, 112754. [Google Scholar] [CrossRef] - Palm, J.; Eskilsson, C.; Paredes, G.M.; Bergdahl, L. CFD simulation of a moored floating wave energy converter. In Proceedings of the 10th European Wave and Tidal Energy Conference, Aalborg, Denmark, 2–5 September 2013; Volume 25. [Google Scholar]
- Palm, J.; Eskilsson, C.; Paredes, G.M.; Bergdahl, L. Coupled mooring analysis for floating wave energy converters using CFD: Formulation and validation. Int. J. Mar. Energy
**2016**, 16, 83–99. [Google Scholar] [CrossRef] - Palm, J.; Eskilsson, C. Influence of bending stiffness on snap loads in marine cables: A study using a high-order discontinuous galerkin method. J. Mar. Sci. Eng.
**2020**, 8, 795. [Google Scholar] [CrossRef] - Jiang, C.; el Moctar, O.; Schellin, T.E. Prediction of hydrodynamic damping of moored offshore structures using cfd. In Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, Glasgow, UK, 9–14 June 2019; Volume 58776, p. V002T08A047. [Google Scholar]
- Jiang, C.; el Moctar, O.; Schellin, T.E. Mooring-configurations induced decay motions of a buoy. J. Mar. Sci. Eng.
**2021**, 9, 350. [Google Scholar] [CrossRef] - Jiang, C.; el Moctar, O. Extension of a coupled mooring–viscous flow solver to account for mooring–joint–multibody interaction in waves. J. Ocean Eng. Mar. Energy
**2023**, 9, 93–111. [Google Scholar] [CrossRef] - ANSYS, A. AQWA User’s Manual Release 17.0; ANSYS Inc.: Canonsburg, PA, USA, 2016. [Google Scholar]
- Cummins, W. The Impulse Response Function and Ship Motions; Technical report; David Taylor Model Basin: Washington, DC, USA, 1962. [Google Scholar]
- Coulling, A.J.; Goupee, A.J.; Robertson, A.N.; Jonkman, J.M.; Dagher, H.J. Validation of a FAST semi-submersible floating wind turbine numerical model with DeepCwind test data. J. Renew. Sustain. Energy
**2013**, 5, 023116. [Google Scholar] [CrossRef] - Robertson, A.N.; Wendt, F.; Jonkman, J.M.; Popko, W.; Dagher, H.; Gueydon, S.; Qvist, J.; Vittori, F.; Azcona, J.; Uzunoglu, E. OC5 project phase II: Validation of global loads of the DeepCwind floating semisubmersible wind turbine. Energy Procedia
**2017**, 137, 38–57. [Google Scholar] [CrossRef]

**Figure 5.**Experimental setup for the raft-type WEC during model tests in head waves in the towing tank at Zhejiang Ocean University.

**Figure 6.**Comparative analysis of numerical simulations and experimental measurements for three regular waves with periods of $T=1.42$ s, $T=1.67$ s, and $T=2.00$ s.

**Figure 7.**Relative pitch motions and corresponding energy capture coefficients for various wavelengths.

**Figure 9.**Relative pitch motions, corresponding energy capture coefficients, and generated power for various wavelengths with different damping coefficients.

**Figure 10.**Diagrams of the considered four mooring configurations: a right-double-left-no mooring configuration (left); a right-double-left-single mooring configuration (middle left); a right-left-double mooring configuration (middle right); a right-double-left-single mooring configuration (right).

**Figure 11.**Relative pitch motions, corresponding energy capture coefficients, and the capture power for various mooring configurations with a damping of 100 Nms/rad.

**Figure 12.**Horizontal and vertical force components acting in the hinged connection for the four mooring configurations with a wavelength of $\lambda /L=2.7$.

**Figure 13.**Tensions acting in the mooring lines for the considered four mooring configurations with a wavelength of $\lambda /L=2.7$.

Property | Length (m) | Width (m) | Height (m) | Draft (m) | Weight (kg) |
---|---|---|---|---|---|

Value | 1.6 | 0.8 | 0.4 | 0.126 | 143 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Chen, X.; Xu, P.; Zhao, X.; el Moctar, O.; Jiang, C.
Performance of a Raft-Type Wave Energy Converter with Diverse Mooring Configurations. *J. Mar. Sci. Eng.* **2023**, *11*, 2352.
https://doi.org/10.3390/jmse11122352

**AMA Style**

Zhang Y, Chen X, Xu P, Zhao X, el Moctar O, Jiang C.
Performance of a Raft-Type Wave Energy Converter with Diverse Mooring Configurations. *Journal of Marine Science and Engineering*. 2023; 11(12):2352.
https://doi.org/10.3390/jmse11122352

**Chicago/Turabian Style**

Zhang, Yuan, Xuanyu Chen, Peng Xu, Xizeng Zhao, Ould el Moctar, and Changqing Jiang.
2023. "Performance of a Raft-Type Wave Energy Converter with Diverse Mooring Configurations" *Journal of Marine Science and Engineering* 11, no. 12: 2352.
https://doi.org/10.3390/jmse11122352