# Enhancements of Wave Power Absorption with Arrays and a Vertical Breakwater

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Time Domain Equation of Motion of WECs Arrays

#### 2.2. Mean and Instantaneous Wave Power

#### 2.3. Constructive and Destructive Effects with Mean Interaction Factor

#### 2.4. Transient Boundary Integral Equation for WECs Arrays

## 3. Results

#### 3.1. Validation of ITU-WAVE Numerical Results

#### 3.1.1. Added Mass and Damping Coefficients

#### 3.1.2. Exciting Force Amplitude

#### 3.1.3. Mean Interaction Factor

#### 3.2. Exciting and Radiation Force IRFs

#### 3.2.1. Exciting Force IRFs

#### 3.2.2. Radiation Force IRFs

#### 3.3. Response of Each WEC in an Array System—RAOs

#### 3.4. Wave Power Absorption with 2 × 3 Arrays

#### 3.5. Effects of a Vertical Wall on Mean Interaction Factors

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Positions of WECs in 2 × 5 arrays with a vertical wall (breakwater) and a coordinate system in xy-plane.

**Figure 2.**Nondimensional interaction sway radiation force coefficients between WEC1 and WEC4 [10]; (

**a**) ${A}_{22}^{14}$; (

**b**) ${B}_{22}^{14}$.

**Figure 3.**Nondimensional interaction sway radiation force coefficients between WEC1 and WEC5 [10]; (

**a**) ${A}_{22}^{15}$; (

**b**) ${B}_{22}^{15}$.

**Figure 4.**Nondimensional amplitudes of exciting forces in surge mode [3]; (

**a**) ${F}_{1E}^{1,2}$; (

**b**) ${F}_{1E}^{3,4}$.

**Figure 5.**Mean interaction factor ${\mathrm{q}}_{{\mathrm{mean}}_{3}}$ of rectangle 2 × 5 arrays [28].

**Figure 6.**Nondimensional heave IRF of exciting force for 5th row of 5 × 5 arrays with and without a vertical wall effect.

**Figure 7.**Nondimensional IRFs of exciting force in heave mode at the centre of each row of 3 × 5 arrays; (

**a**) without a vertical breakwater; (

**b**) with a vertical breakwater.

**Figure 8.**Nondimensional heave radiation interaction IRFs of 3 × 5 arrays; (

**a**) without a vertical wall; (

**b**) with a vertical wall.

**Figure 9.**Effects of a vertical wall on each WEC’s RAO for 1 × 3 arrays of sphere; (

**a**) sway; (

**b**) heave.

**Figure 10.**Effects of a vertical wall on each WEC’s RAO for 2 × 3 arrays of sphere; (

**a**) 1st row sway; (

**b**) 2nd row sway; (

**c**) 1st row heave; (

**d**) 2nd row heave.

**Figure 11.**Heave and sway modes of isolated sphere; (

**a**) ${x}_{2}$, ${x}_{3}$; (

**b**) ${P}_{2},{P}_{3}$.

**Figure 12.**Effects of a vertical wall with 2 × 3 arrays on wave power absorption; (

**a**) ${P}_{2}$ (

**b**) ${P}_{3}$.

**Figure 13.**Heave mean interaction factors of each row without a vertical wall effect; (

**a**) 2 × 3; (

**b**) 3 × 3 arrays.

**Figure 14.**Effects of a vertical wall on heave mean interaction factors of each row; (

**a**) 2 × 3 arrays; (

**b**) 3 × 3 arrays.

**Figure 15.**Heave mean interaction factors in a range of row numbers; (

**a**) without a vertical wall; (

**b**) with a vertical wall.

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**MDPI and ACS Style**

Kara, F.
Enhancements of Wave Power Absorption with Arrays and a Vertical Breakwater. *J. Mar. Sci. Eng.* **2024**, *12*, 1523.
https://doi.org/10.3390/jmse12091523

**AMA Style**

Kara F.
Enhancements of Wave Power Absorption with Arrays and a Vertical Breakwater. *Journal of Marine Science and Engineering*. 2024; 12(9):1523.
https://doi.org/10.3390/jmse12091523

**Chicago/Turabian Style**

Kara, Fuat.
2024. "Enhancements of Wave Power Absorption with Arrays and a Vertical Breakwater" *Journal of Marine Science and Engineering* 12, no. 9: 1523.
https://doi.org/10.3390/jmse12091523