Author Information

Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow G4 0LZ, UK

Department of Civil, Maritime and Environmental Engineering, University of Southampton, Southampton SO16 7QF, UK

*

Authors to whom correspondence should be addressed.

Received: 24 August 2024 Accepted: 20 September 2024 Published: 27 September 2024

© 2024 The authors. This is an open access article under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).

ABSTRACT:
This study presents a
numerical investigation of a point absorber wave energy converter (WEC) with a
focus on improving its performance through the utilization of a vertical wall
and latching control in the power take-off (PTO) system. Prior to numerical
evaluations, experimental data incorporating PTO considerations and numerical
simulation results were examined to validate the accuracy of the numerical
methodology employed in this research. This
study introduces a numerical PTO model and latching control for a further
investigation. Comparative analyses were carried out on the displacement,
velocity, and force of the PTO, absorbed power, and capture width ratio (CWR),
considering the incorporation of a vertical wall and latching control. The
results confirm that the introduction of both vertical wall and latching
control significantly improves the CWR of the WEC, showing the effectiveness of
incorporating a vertical wall and latching control in enhancing power
extraction.

Keywords:
Wave energy
converter; Vertical wall; Power take-off; Latching control; Computational fluid dynamics

Harnessing the power from the ocean, wave energy converters (WECs) have an important role to play in energy generation. Due to a rapid changing climate, the quest for sustainable and clean energy sources is crucial. In the academic and industrial fields of WECs, numerous methodologies have been suggested for harnessing wave energy, and considerable endeavours are underway to reach its commercialisation.
Efforts to enhance the efficiency of Wave Energy Converters (WECs) have been made by numerous researchers, and one approach involves integrating WECs with other marine structures. According to Mustapa et al. [1], coupling WECs with coastal structures can yield notable advantages. Firstly, it can lead to cost savings in construction, installation, and maintenance. Secondly, this integration allows for the establishment of energy production facilities while simultaneously providing infrastructure for coastal protection.
According to Zhao et al. [2], various studies on the combination of hybrid floating breakwaters and Wave Energy Converters (WECs) were examined. The primary objective of these studies was to enhance synergy by combining the wave-damping effects achievable from floating breakwaters with the energy production obtained from WECs. Strategies for increasing the efficiency of WECs through the integration of breakwaters included altering the natural frequency of WECs using Power Take-Off (PTO) mechanisms and using stationary effect induced by reflection waves of incident waves from breakwater. Several papers have reported the phenomenon of increased motion in WECs due to stationary waves. According to the findings of some studies based on the linear potential flow theory [3], an increase in WEC motion was observed at specific periods, and substantial performance improvements were achieved when optimal PTO damping was applied. Coiro et al. [4] discussed the establishment of a stationary wave effect in front of a breakwater wall, resulting from the interaction between the incident wave and the wave reflected from the wall. They anticipated that this stationary wave system would be highly sensitive to the incident wavelength, influencing the power output performance. In a related study, Reabroy et al. [5] examined the impact of the distance between the Wave Energy Converter (WEC) and the breakwater wall within a specific wave period. Their findings indicated that the breakwater effect, especially in the case of a point absorber-type WEC, could enhance the hydrodynamic performance, particularly the heave motion of the WEC. However, it is worth noting that the distance range explored in their study to determine the optimal distance was relatively shorter than the wavelength. This limitation suggests that the motion amplification of the WEC due to the stationary wave may not have been fully realized within the tested distance range. Yang et al. [6] assessed the hydrodynamic performance of WEC in intermediate water depth using Computational Fluid Dynamics (CFD). The study investigated how the performance of the WEC varied with changes in the distance between the breakwater and WEC over a wide range. Through this analysis, it was confirmed that the performance of the WEC can be improved by leveraging the effects of stationary waves, which are influenced by the presence of the breakwater.
Another approach to improve the efficiency of WEC is to choose the control of the PTO force. The latching control used in WEC was proposed by Budal and Falnes [7]. It involves fixing the oscillating body when its velocity reaches zero, then releasing the body after a specific delay time when the motion of a WEC and the wave force are in a favourable phase. This control strategy aims to maximise the movement of the WEC. There are many control systems such as Declutching control and Latching control suggested by Babarit et al. [8]. Research on latching control has commonly been conducted by analytical methods based on linear potential flow theory. The study by Ringwood and Butler [9] proposed an optimised latching duration for regular and monochromatic waves, establishing a foundation for a constant latching duration without prediction of future incoming waves. This approach is particularly useful in investigations where wave predictions over time are not necessary, as in the case of regular wave studies. In a study by Giorgi and Ringwood [10], the research delved into latching control strategies using OpenFOAM software (version 2.3) based on computational fluid dynamics. The outcome of this study facilitated the analysis of the nonlinear motion of WEC and the interpretation of WEC movements under the influence of latching control. The results revealed a pronounced manifestation of nonlinear effects, especially at the natural period of the WEC.
This study aims to devise a method to maximise power extraction from a WEC by leveraging latching control to enhance the motion of the system and capitalizing on the stationary wave effects generated from a vertical wall. Using CFD techniques, the research validates the proposed methodology through a verification process based on experimental results [11] that include an existing Power Take-Off (PTO) system. The investigation involves CFD simulations to assess how the presence of a vertical wall, variations in the damping coefficient of the PTO, and the implementation of latching control influence the performance of the WEC. By systematically analysing these factors, the study aims to provide insights into how the power extraction efficiency can be maximized under different conditions. This research contributes to the understanding of WEC dynamics and lays the groundwork for optimizing the design and operation of wave energy conversion systems.

```latex\frac{\partial(\rho\overline{u_l})}{\partial x_i}=0```

where $$\bar{\tau}_{ij}$$ represent the components of the mean viscous stress tensor, as indicated in Equation (2)

```latex\bar{\tau}_{ij} = \mu(\frac{\partial\bar{u}_i}{\partial x_j}+\frac{\partial\bar{u}_j}{\partial x_i})```

```latexf_1=\pi\omega ```

```latex\tau_{PTO}=B_{PTO}\omega_{WEC}+K_{PTO}\Theta_{WEC} ```

```latexF_{PTO}(t)=-B_{num}\cdot V_{PTO}(t)-K_{num}\cdot S_c(t) ```

```latexK_{num}=184B_{PTO}-4700 ```

```latexB_{num}=70B_{PTO}```

```latex\omega_{WEC}=\frac{V_\perp}r```

```latexV_B=\overline{AB}\omega_{WEC}```

```latex\beta(t) = \cos^{-1}\left(\frac{S_c^2(t)+c^2-b^2}{2cS_c(t)}\right)```

```latexV_{PTO}(t)=V_B(t)\cos\left(\frac\pi2-\beta(t)\right)=V_B(t)\mathrm{sin}\beta(t)```

In this study, an ideal PTO model is used, which does not account for losses such as friction, heat dissipation, or the dynamic system of the PTO. As a result, the absorbed power (

```latexP_{abs}(t)=-V_{PTO}(t)F_{PTO}(t)```

```latexP_{wave}=\frac18\rho gH^2c_g```

```latexCWR=\frac{P_{abs}}{P_{wave}\cdot width_{active}}```

```latexT_L = \frac{t_5-t_1}{2}-(t_5-t_4) = \frac{T_W}{2}-\frac{T_n}{2}```

This study focused on the analysis of a pivoted point absorber-type WEC using numerical simulations with CFD to assess its performance. It examined the WEC’s performance under various conditions, particularly the presence of a vertical wall and the application of latching control across different wave periods and PTO damping forces. Building on previous research that explored the hydrodynamic performance of WECs based on the distance between the vertical wall and WEC, this study introduced a numerical PTO design to validate the WEC’s performance.
Star-CCM+ was utilized as the CFD software, and a wave-forcing scheme was implemented to ensure stable numerical results, optimizing computation time. In order to apply the numerical PTO model in Star-CCM+, modifications were made to the 1-D linear spring-damping system, and the latching control algorithm was adapted. Verification and validation processes were conducted to confirm the accuracy of the computational domain. Comparison with experimental measurements and other numerical simulations revealed minimal discrepancies, confirming the reliability of the numerical model.
The results indicated that for shorter wave periods of 2 s and 2.2 s, the WEC achieved a high Capture Width Ratio (CWR) regardless of the PTO damping force. For longer wave periods (2.5 s and above), the presence of the vertical wall had minimal impact on the CWR, resulting in lower values. The study also demonstrated that latching control significantly enhanced the WEC’s performance, particularly in the long-wave period range. The application of latching control led to consistently improved CWR, especially in conditions where the wave period exceeded the natural period of the WEC. This indicates the effectiveness of latching control for optimizing WEC performance in these conditions. Additionally, the analysis of the effects of the vertical wall during latching control revealed that the highest CWR was achieved at a wave period of 2.2 s, highlighting a synergistic interaction between the vertical wall and latching control. This combination showed the greatest performance enhancement for shorter wave periods. However, as the wave period increased, the influence of the vertical wall became negligible.
In summary, this study has demonstrated that the combination of a vertical wall and latching control can significantly enhance WEC performance, particularly for short to moderate wave periods, while the influence of the vertical wall diminishes at longer wave periods.

Results were obtained using the ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk) based at the University of Strathclyde.

Conceptualization, I.Y.; Methodology, I.Y.; Software, I.Y.; Validation, I.Y., and A.I.; Formal Analysis, I.Y.; Investigation, I.Y. and A.I.; Resources, I.Y. and A.I.; Data Curation, I.Y.; Writing—Original Draft Preparation, I.Y.; Writing—Review & Editing, I.Y., M.T., T.T. and A.I.; Visualization, I.Y.; Supervision, M.T., T.T. and A.I.; Project Administration, I.Y., M.T., T.T. and A.I.; Funding Acquisition, T.T. and A.I.

Not applicable.

Not applicable.

This research received no external funding.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Yang I, Terziev M, Tezdogan T, Incecik A. Numerical Investigation of a Point Absorber Wave Energy Converter Integrated with Vertical Wall and Latching Control for Enhanced Power Extraction. *Marine Energy Research*. 2024; 1(1):10004. https://doi.org/10.70322/mer.2024.10004

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