# Modelling Approaches of a Closed-Circuit OWC Wave Energy Converter

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## Abstract

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## 1. Introduction

^{th}scale tested in a wave tank. The physical results are compared against the results of Numerical Model 1. The paper does not present results comparing the three models simultaneously. Although Numerical Model 1 is quite flexible, easily adapting its parameters, Numerical Model 2 and the physical model are subject to several constraints, which made it difficult to have a set of numerical simulations and physical tests with comparable parameters and conditions for the three approaches. Nevertheless, the comparisons presented are still of interest and useful to show the viability of the Tupperwave concept, as well as the relevance of the different methods. In Section 5, the influence of valves and turbine damping on the device efficiency in converting the absorbed wave power into useful pneumatic power is studied using both physical observations and numerical simulations.

## 2. Numerical Model 1

#### 2.1. Hydrodynamics

#### 2.2. Thermodynamics

## 3. Numerical Model 2

#### 3.1. Model Setup

- Non-slip conditions prescribed at the wave energy device and the boundaries representing the tank walls;
- Non-slip wall conditions applied to the wave dissipation ramp and the tank bottom;
- Opening condition applied to the top wall. The mass and momentum transported through this boundary were constrained by an opening pressure and direction model, with 0 Pa relative pressure. The volume fraction of the opening for air was set to 1.0 and that of water to 0.0. The temperature was set to 17 °C;

#### 3.2. CFD Results

## 4. Physical Modelling

#### 4.1. Experimental Setup

#### 4.2. Experimental Results

## 5. Device Conversion Efficiency

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

OWC | Oscillating Water Column |

HP | High Pressure |

LP | Low Pressure |

CFD | Computational Fluid Dynamics |

## References

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**Figure 7.**2D picture of the full-scale Tupperwave device in two-meter high regular waves of 8-s periods.

**Figure 8.**Flow rate across the turbine-orifice as a function of the pressure drop with quadratic regression (${R}^{2}$ = 0.9996).

**Figure 9.**Flow rate across the HP valves as a function of the pressure drop with linear regression (${R}^{2}$ = 0.9828).

**Figure 10.**Internal Water Surface (IWS) elevation and excess pressures obtained in OWC, HP and LP chambers obtained by Numerical Models 1 and 2 for 2 m-high and 8 s-period regular waves.

**Figure 15.**Time series of pressures in the chambers and flows across the valves and turbine for a 2 m-high regular wave of a nine-second period (full-scale equivalent) obtained in tank testing.

**Figure 16.**Average absorbed power from the waves and dissipated powers across valves and orifice (full-scale equivalent).

**Figure 17.**Valve efficiency obtained in regular waves compared to the efficiency estimated via Formula (24).

**Figure 18.**Parametric study of the turbine damping coefficient to maximise pneumatic power made available to the turbine.

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**MDPI and ACS Style**

Benreguig, P.; Vicente, M.; Dunne, A.; Murphy, J.
Modelling Approaches of a Closed-Circuit OWC Wave Energy Converter. *J. Mar. Sci. Eng.* **2019**, *7*, 23.
https://doi.org/10.3390/jmse7020023

**AMA Style**

Benreguig P, Vicente M, Dunne A, Murphy J.
Modelling Approaches of a Closed-Circuit OWC Wave Energy Converter. *Journal of Marine Science and Engineering*. 2019; 7(2):23.
https://doi.org/10.3390/jmse7020023

**Chicago/Turabian Style**

Benreguig, Pierre, Miguel Vicente, Adrian Dunne, and Jimmy Murphy.
2019. "Modelling Approaches of a Closed-Circuit OWC Wave Energy Converter" *Journal of Marine Science and Engineering* 7, no. 2: 23.
https://doi.org/10.3390/jmse7020023