# Assessment of Primary Energy Conversion of a Closed-Circuit OWC Wave Energy Converter

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## Abstract

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## 1. Introduction

## 2. Numerical Models From Wave to Pneumatic Power

#### 2.1. Hydrodynamics

#### 2.2. Thermodynamics

#### 2.2.1. General Equations

#### 2.2.2. Conventional OWC Thermodynamics

#### 2.2.3. Tupperwave Device Thermodynamics

#### 2.3. Numerical Solution

## 3. Physical Modelling in the Wave Tank

#### 3.1. Physical Models Design and Fabrication

#### 3.1.1. Scaling

#### 3.1.2. Turbines

#### 3.1.3. Valves

#### 3.2. Experimental Setup and Test Plan

## 4. Results and Numerical Model Validation

#### 4.1. Correction in the Tupperwave Numerical Model

#### 4.2. Numerical Model Validation

#### 4.3. Power Performance Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Prony’s Method

## References

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**Figure 1.**Schematic diagram of the conventional Oscillating-Water-Column (OWC) and Tupperwave device concepts.

**Figure 2.**2D schematic of the full-scale conventional OWC and Tupperwave devices. HP, High-Pressure; LP, Low-Pressure.

**Figure 7.**MiniHab HypAirBalance from Capricorn used in the Tupperwave small-scale model [37].

**Figure 9.**Schematic of a mooring line. The device was moored by 3 mooring lines with 120 degrees between any two mooring lines.

**Figure 11.**Pressure drop time series across Orifice 3 of the Tupperwave device obtained by the physical model, the initial numerical model, and the corrected model in the regular waves of a 9-s period and heights of $2\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ and $4\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$.

**Figure 12.**Pressure drop time series across Orifice 3 of the Tupperwave device obtained by the physical model, the initial numerical model, and the corrected model in the irregular sea state {${H}_{s}=3$ m; ${T}_{p}=8.5$ s}.

**Figure 13.**Pressure drop time series across Orifice 3 of the Tupperwave device obtained by the physical model and the corrected model in the irregular sea state {${H}_{s}=3$ m; ${T}_{p}=8.5$ s} with different chamber stiffness values.

**Figure 14.**Response Amplitude Operator (RAO) of the buoy and water column relative motion and their phase difference for the conventional OWC and Tupperwave device in regular waves ($H=2$ m).

**Figure 15.**Average pressure drop and volumetric flow rate across the orifice for the conventional OWC and the Tupperwave device in two-meter high regular waves.

**Figure 16.**Average pneumatic power normalized by the significant wave height squared for the conventional OWC and the Tupperwave device in irregular sea states.

**Figure 17.**Pneumatic power time series for the conventional OWC and the Tupperwave device in the irregular sea state {${H}_{s}=3$ m; ${T}_{p}=7.1$ s}.

**Figure 18.**Average power absorbed from the waves ${P}_{abs}$ and pneumatic power available to the turbine ${P}_{avail}$ by the conventional OWC and the Tupperwave device in 2 and 4 m-high regular waves.

Model Scale | Full Scale | |
---|---|---|

Total mass (kg) | 58.4 | $817\times {10}^{3}$ |

Distance device bottom, COG(m) | 0.892 | 21.49 |

Distance device bottom, COB(m) | 0.961 | 23.16 |

Ixx ($\mathbf{kg}\xb7{\mathbf{m}}^{\mathbf{2}}$) | 23 | $1.87\times {10}^{8}$ |

Iyy ($\mathbf{kg}\xb7{\mathbf{m}}^{\mathbf{2}}$) | 23.5 | $1.91\times {10}^{8}$ |

Izz ($\mathbf{kg}\xb7{\mathbf{m}}^{\mathbf{2}}$) | 2 | $1.62\times {10}^{7}$ |

Model Scale | Full Scale | ||||
---|---|---|---|---|---|

Orifice | Diameter (mm) | ${\mathbf{k}}_{\mathbf{t}}$ ($\mathbf{Pa}\xb7{\mathbf{s}}^{\mathbf{2}}\xb7{\mathbf{m}}^{-\mathbf{6}}$) | $\alpha \mathbf{A}$ (${\mathbf{m}}^{\mathbf{2}}$) | ${\mathbf{k}}_{\mathbf{t}}$ ($\mathbf{Pa}\xb7{\mathbf{s}}^{\mathbf{2}}\xb7{\mathbf{m}}^{-\mathbf{6}}$) | $\alpha \mathbf{A}$ (${\mathbf{m}}^{\mathbf{2}}$) |

OWC1 | 22.6 | $7.10\times {10}^{6}$ | $2.94\times {10}^{-4}$ | 21.1 | $1.71\times {10}^{-1}$ |

OWC2 | 20.6 | $10.4\times {10}^{6}$ | $2.42\times {10}^{-4}$ | 30.9 | $1.41\times {10}^{-1}$ |

OWC3 | 17.5 | $19.6\times {10}^{6}$ | $1.77\times {10}^{-4}$ | 58.3 | $1.03\times {10}^{-1}$ |

T1 | 11.5 | $0.70\times {10}^{8}$ | $9.33\times {10}^{-5}$ | 209 | $5.42\times {10}^{-2}$ |

T2 | 9.2 | $1.86\times {10}^{8}$ | $5.74\times {10}^{-5}$ | 552 | $3.33\times {10}^{-2}$ |

T3 | 7 | $4.85\times {10}^{8}$ | $3.55\times {10}^{-5}$ | 1439 | $2.06\times {10}^{-2}$ |

**Table 3.**Pearson correlation coefficient between $\Delta {P}_{t}$ time series obtained physically and numerically for the various irregular sea states.

Sea State | Pearson Correlation Coefficient (-) | ||
---|---|---|---|

${\mathit{H}}_{\mathit{s}}$ (m) | ${\mathit{T}}_{\mathit{p}}$ (s) | Initial Model | Corrected Model $\mathit{C}=\mathbf{8}.\mathbf{3}\times {\mathbf{10}}^{-\mathbf{5}}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{3}\xb7{\mathrm{Pa}}^{-1}$ |

2 | 5.7 | 0.72 | 0.85 |

3 | 7.1 | 0.68 | 0.93 |

3 | 8.5 | 0.69 | 0.93 |

5 | 8.5 | 0.65 | 0.94 |

3 | 10.6 | 0.70 | 0.94 |

5 | 10.6 | 0.65 | 0.93 |

5 | 12.7 | 0.62 | 0.93 |

3 | 14.1 | 0.70 | 0.86 |

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**MDPI and ACS Style**

Benreguig, P.; Pakrashi, V.; Murphy, J. Assessment of Primary Energy Conversion of a Closed-Circuit OWC Wave Energy Converter. *Energies* **2019**, *12*, 1962.
https://doi.org/10.3390/en12101962

**AMA Style**

Benreguig P, Pakrashi V, Murphy J. Assessment of Primary Energy Conversion of a Closed-Circuit OWC Wave Energy Converter. *Energies*. 2019; 12(10):1962.
https://doi.org/10.3390/en12101962

**Chicago/Turabian Style**

Benreguig, Pierre, Vikram Pakrashi, and Jimmy Murphy. 2019. "Assessment of Primary Energy Conversion of a Closed-Circuit OWC Wave Energy Converter" *Energies* 12, no. 10: 1962.
https://doi.org/10.3390/en12101962