# Numerical Investigation of Multi-Floater Truss-Type Wave Energy Convertor Platform

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation

#### 2.1. Calculation of Platform and Floaters

#### 2.2. Calculation of the Truss Structure

#### 2.3. Motion Response

## 3. Model Validation

## 4. Results and Discussions

#### 4.1. The Influence of Floater Number on the Motion Response

#### 4.2. The Selection of Floater Arrangement

## 5. Calculation of Energy Utilization Efficiency of WEC Platform

#### 5.1. Theory of Capture Efficiency

#### 5.2. Capture Efficiency of WEC Platform

## 6. Conclusions

- Since the platform is composed of a truss structure, the floaters’ motion responses under wave action in all directions are very close, and each floater has good wave-following performance. The motion response of the up-wave floater is slightly greater than that of the back-wave floater, and the motion response of the side floaters is slightly greater than that of the middle floater.
- With an increase in the number of floaters arranged at one side, the average RAO of the floats is smaller, but the overall difference is small. Multiple floaters as a whole show very good wave-following performance. Therefore, if conditions permit, arranging as many floats as possible can effectively improve the power generation efficiency of the platform.
- The power and efficiency of a single float first increase and then decrease with the increase of linear damping under the regular wave action. When the damping is 30,000 N/(m/s), the power generation efficiency is the highest, and the capture efficiency of the whole platform is 9.7%

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 4.**Wave forces of barges in the surge direction: (

**a**) up-wave barge; (

**b**) back-wave barge [26].

**Figure 5.**Displacement of barges in the surge direction: (

**a**) up-wave barge; (

**b**) back-wave barge [26].

**Figure 12.**Velocity time histories of the floater when linear damping coefficient C is 3000 N/(m/s).

**Figure 13.**Velocity time histories of the floater when linear damping coefficient C is 20,000 N/(m/s).

**Figure 14.**Velocity time histories of the floater when linear damping coefficient C is 30,000 N/(m/s).

**Figure 15.**Velocity time histories of the floater when linear damping coefficient C is 70,000 N/(m/s).

**Figure 16.**Generation power and capture efficiency of the floater to capture wave energy under different linear PTO damping coefficients.

Symbol | Meaning | Value |
---|---|---|

L | Length (m) | 30 |

B | Width (m) | 22 |

T | Draft (m) | 1.5 |

d | Water depth (m) | 15 |

W | Distance of twin-boxes (m) | 8 |

${R}_{x}$ | Rotation radius around x-axis (m) | 9.0 |

${R}_{y}$ | Rotation radius around y-axis (m) | 6.6 |

${R}_{z}$ | Rotation radius around z-axis (m) | 10.8 |

Meaning | Value |
---|---|

Size of platform | 20 m |

Mass of platform | $1.025\times {10}^{5}$ kg |

Mass center of platform | (0.0, 0.0, 0.0) |

Rotation center of platform | (0.0, 0.0, 0.0) |

Platform moment of inertia ${I}_{xx}$ | $6.56\times {10}^{6}$ kg·m${}^{2}$ |

Platform moment of inertia ${I}_{yy}$ | $6.56\times {10}^{6}$ kg·m${}^{2}$ |

Platform moment of inertia ${I}_{zz}$ | $9.72\times {10}^{6}$ kg·m${}^{2}$ |

Distance between floater and platform edge | 5 m |

Distance between adjacent floater edge | 1 m |

Truss diameter | $0.06$ m |

Truss number in one side | 6 |

Meaning | Value |
---|---|

Diameter of floater | 3 m |

Mass of floater | 3000 kg |

Draft of floater | 1 m |

Mass of floating arm | 300 kg |

Length of floating arm | 7 m |

Displacement | 7.07 m${}^{3}$ |

Floater moment of inertia ${I}_{xx}$ | 2687 kg·m${}^{2}$ |

Floater moment of inertia ${I}_{yy}$ | 2687 kg·m${}^{2}$ |

Floater moment of inertia ${I}_{zz}$ | 3375 kg·m${}^{2}$ |

Damping Box 1 | Damping Box 2 | Damping Box 3 | Damping Box 4 | Damping Box 5 |
---|---|---|---|---|

(8.35, 8.35) | (8.35, −8.35) | (−8.35, −8.35) | (−8.35, 8.35) | (0.0, 0.0) |

Floater number | ${f}_{l1}$ | ${f}_{l2}$ | ${f}_{l3}$ | ${f}_{l4}$ |

${\eta}_{f}\left(\%\right)$ | 5.38 | 4.07 | 4.07 | 5.38 |

Floater number | ${f}_{r1}$ | ${f}_{r2}$ | ${f}_{r3}$ | ${f}_{r4}$ |

${\eta}_{f}\left(\%\right)$ | 15.55 | 13.80 | 13.80 | 15.55 |

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**MDPI and ACS Style**

Jin, R.; Wang, J.; Chen, H.; Geng, B.; Liu, Z.
Numerical Investigation of Multi-Floater Truss-Type Wave Energy Convertor Platform. *Energies* **2022**, *15*, 5675.
https://doi.org/10.3390/en15155675

**AMA Style**

Jin R, Wang J, Chen H, Geng B, Liu Z.
Numerical Investigation of Multi-Floater Truss-Type Wave Energy Convertor Platform. *Energies*. 2022; 15(15):5675.
https://doi.org/10.3390/en15155675

**Chicago/Turabian Style**

Jin, Ruijia, Jiawei Wang, Hanbao Chen, Baolei Geng, and Zhen Liu.
2022. "Numerical Investigation of Multi-Floater Truss-Type Wave Energy Convertor Platform" *Energies* 15, no. 15: 5675.
https://doi.org/10.3390/en15155675