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

^{1}

^{2}

^{o}11, 1

^{o}, 1400-119 Lisboa, Portugal

^{3}

^{*}

## Abstract

**:**

## 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

- Falcão, A.F.; Henriques, J.C. Oscillating-water-column wave energy converters and air turbines: A review. Renew. Energy
**2016**, 85, 1391–1424. [Google Scholar] [CrossRef] - Lopes, B.S.; Gato, L.M.; Falcão, A.F.; Henriques, J.C. Test results of a novel twin-rotor radial inflow self-rectifying air turbine for OWC wave energy converters. Energy
**2018**. [Google Scholar] [CrossRef] - Lopes, B. Construction and Testing of a Double Rotor Self-Rectifying Air Turbine Model for Wave Energy Recovery Systems. Language of Reference: Portuguese. Master’s Thesis, Tecnico Lisboa, Lisboa, Portugal, 2017. [Google Scholar]
- Falcão, A.F.; Henriques, J.C.; Gato, L.M. Self-rectifying air turbines for wave energy conversion: A comparative analysis. Renew. Sustain. Energy Rev.
**2018**, 91, 1231–1241. [Google Scholar] [CrossRef] - Vicente, M.; Benreguig, P.; Crowley, S.; Murphy, J. Tupperwave-preliminary numerical modelling of a floating OWC equipped with a unidirectional turbine. In Proceedings of the 12th European Wave and Tidal Energy Conference (EWTEC), Cork, Ireland, 27 August–1 September 2017. [Google Scholar]
- Sheng, W.; Alcorn, R.; Lewis, A. Assessment of primary energy conversions of oscillating water columns. I. Hydrodynamic analysis. J. Renew. Sustain. Energy
**2014**, 6, 053113. [Google Scholar] [CrossRef][Green Version] - Giorgi, G.; Ringwood, J.V. Consistency of viscous drag identification tests for wave energy applications. In Proceedings of the 12th European Wave and Tidal Energy Conference (EWTEC), Cork, Ireland, 27 August–1 September 2017. [Google Scholar]
- Lee, C.H.; Newman, J.N. WAMIT User Manual. WAMIT, Inc.: Chestnut Hill, MA, USA, 2006. [Google Scholar]
- Sheng, W.; Alcorn, R.; Lewis, A. A new method for radiation forces for floating platforms in waves. Ocean Eng.
**2015**, 105, 43–53. [Google Scholar] [CrossRef] - Benreguig, P.; Vicente, M.; Murphy, J. Anisentropic study of the Tupperwave device. Energy
**2018**. submitted. [Google Scholar] - Finnegan, W.; Goggins, J. Numerical simulation of linear water waves and wave–structure interaction. Ocean Eng.
**2012**, 43, 23–31. [Google Scholar] [CrossRef][Green Version] - Silva, M.; Vitola, M.D.A.; Pinto, W.; Levi, C. Numerical simulation of monochromatic wave generated in laboratory: Validation of a cfd code. In Proceedings of the 23 Congresso Nacional De Transporte Aquaviário, Construção Naval e Offshore, Rio de Janeiro, Brazil, 25–29 October 2010; pp. 25–29. [Google Scholar]
- Benreguig, P.; Kelly, J.F.; Murphy, J. Wave-to-Wire model development and validation for two OWC type wave energy converters, part II: From pneumatic to electrical energy. Energy
**2018**. submitted. [Google Scholar] - Falcão, A.F.; Henriques, J.C. Model-prototype similarity of oscillating-water-column wave energy converters. Int. J. Mar. Energy
**2014**, 6, 18–34. [Google Scholar] [CrossRef] - Tennekes, H.; Lumley, J.L.; Lumley, J. A First Course in Turbulence; MIT Press: Cambridge, MA, USA, 1972. [Google Scholar]
- Benreguig, P.; Murphy, J.; Sheng, W. Model scale testing of the Tupperwave device with comparison to a conventional OWC. In Proceedings of the ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering OMAE2018, Madrid, Spain, 17–22 June 2018. [Google Scholar]
- Benreguig, P.; Murphy, J. Wave-to-Wire model development and validation for two OWC type wave energy converters, part I: From wave to pneumatic energy. Energy
**2018**. submitted. [Google Scholar]

**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.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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