# Experimental Study of a Moored Floating Oscillating Water Column Wave-Energy Converter and of a Moored Cubic Box

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

#### 2.1. Description of the Models

**G’**as reference, which is the projection point of the center of gravity on the side surface shown in Figure 1b. To simulate the air turbine PTO damping, an orifice of a diameter of 5.0 cm is made on the top surface of the OWC WEC model, which equals to approximately 6.1% of the top surface area. Table 2 lists the geometric properties of OWC WEC model.

#### 2.2. Wave Flume Setup and Instrumentation

#### 2.3. Experimental Program

#### 2.4. Uncertainty Sources

## 3. BOX model Experimental Results

## 4. OWC WEC Model Experimental Results

#### 4.1. OWC WEC Motion Response

#### 4.2. Water Surface Elevation Variation Inside the OWC WEC Vhamber

#### 4.3. Mooring-Line Tensions

#### 4.4. Effect of Unequal Mooring-Line Lengths

#### 4.5. Effect of the Orifice Diameter at the Top of the OWC WEC Chamber

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

BBDB | Backward Bend Duck Buoy |

BOX | cubic floating box model |

CFD | Computational Fluid Dynamics |

DOF | Degree of Freedom |

EMEC | The European Marine Energy Center |

EPS | Expanded Polystyrene |

ITTC | The International Towing Tank Conference |

OWC | Oscillating Water Column |

PTO | power-take-off |

SPH | Smoothed Particle Hydrodynamics |

WEC | Wave-Energy Converter |

WG | wave gauge |

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**Figure 3.**Moored models in the wave flume: (

**a**) front view of the OWC WEC model with rope mooring; (

**b**) side and back view of the OWC WEC model with chain mooring (this image of the model “broken” into two pieces is a result of light refraction); (

**c**) back view of the BOX model with chain mooring.

**Figure 4.**Applied wave conditions plotted in the adapted Le méhauté diagram [32]. All cases in Test group 1 to 5 are plotted. [Adapted with from Le méhauté, B. An Introduction to Hydrodynamics and Water Waves]

**Figure 5.**Synchronized data of validation test with BOX model in regular waves of $T=1.6$ s and $H=12.0$ cm (target values): (

**a**) wave surface elevation; (

**b**) surge motion; (

**c**) heave motion; (

**d**) pitch motion; (

**e**) mooring-line tensions measured by Loadcell A and B; (

**f**) mooring-line tensions measured by Loadcell C and D.

**Figure 6.**Synchronized data of validation test with BOX model in regular waves of $T=1.8$ s and $H=15.0$ cm (target values): (

**a**) wave surface elevation; (

**b**) surge motion; (

**c**) heave motion; (

**d**) pitch motion; (

**e**) mooring-line tensions measured by Loadcell A and B; (

**f**) mooring-line tensions measured by Loadcell C and D.

**Figure 7.**OWC WEC surge motion response for different mooring-line materials: (

**a**) wave height $H=4.0$ cm and $H=8.0$ cm; (

**b**) wave height $H=11.0$ cm and $H=14.0$ cm; (

**c**) using only iron chain, $H=4.0$ cm to $H=14.0$ cm; (

**d**) using only nylon rope $H=4.0$ cm to $H=14.0$ cm. (All wave conditions are target values).

**Figure 8.**OWC WEC heave motion response for different mooring-line materials: (

**a**) wave height $H=4.0$ cm and $H=8.0$ cm; (

**b**) wave height $H=11.0$ cm and $H=14.0$ cm; (

**c**) using only iron chain, $H=4.0$ cm to $H=14.0$ cm; (

**d**) using only nylon rope $H=4.0$ cm to $H=14.0$ cm. (All wave conditions are target values).

**Figure 9.**OWC WEC model motions in regular waves of $T=1.9$ s: (

**a**) surge, $H=8.0$ cm; (

**b**) surge, $H=14.0$ cm; (

**c**) heave, $H=8.0$ cm; (

**d**) heave, $H=14.0$ cm; (

**e**) pitch, $H=8.0$ cm; (

**f**) pitch, $H=14.0$ cm. (All wave conditions are target values).

**Figure 10.**Water surface elevation time series: (

**a**) $T=0.9$ s and $H=4.0$ cm; (

**b**) $T=1.0$ s and $H=4.0$ cm; (

**c**) $T=1.7$ s and $H=11.0$ cm; (

**d**) $T=1.7$ s and $H=14.0$ cm. (All wave conditions are target values.

**Figure 11.**Iron chain mooring-line tensions measured by loadcells in regular waves of $T=1.7$ s and $H=14.0$ cm (target values): (

**a**) Loadcells A and B; (

**b**) Loadcells C and D.

**Figure 12.**Nylon rope mooring-line tensions measured by loadcells in regular waves of $T=1.7$ s and $H=14.0$ cm (target values): (

**a**) Loadcells A and B; (

**b**) Loadcells C and D.

**Figure 13.**Mooring-line tensions measured by loadcells in regular waves of $T=1.7$ s and $H=14.0$ cm (target values) for unequal mooring-line lengths: (

**a**) $\delta {L}_{C,1}=$ −$2.4$ cm (−1.65% of ${L}_{C,1}$); (

**b**) $\delta {L}_{C,1}=-0.8$ cm (−0.55 % of ${L}_{C,1}$); (

**c**) $\delta {L}_{C,1}=0.8$ cm (+0.55% of ${L}_{C,1}$); (

**d**) $\delta {L}_{C,1}=2.4$ cm (+1.65% of ${L}_{C,1}$).

**Figure 14.**Comparisons of the OWC WEC motion and water surface elevation inside the chamber between different orifice sizes regular waves of $T=1.7$ s and $H=11.0$ cm (target values): (

**a**) surge; (

**b**) heave; (

**c**) pitch; (

**d**) in-chamber water surface elevation.

Symbol | Description | Unit | Value |
---|---|---|---|

B${}_{BOX}$ | Width of BOX model | cm | 20.0 |

L${}_{BOX}$ | Length of BOX model | cm | 20.0 |

H${}_{BOX}$ | Height of BOX model | cm | 13.2 |

T${}_{BOX}$ | Draft of BOX model | cm | 7.9 |

M${}_{BOX}$ | Mass of BOX model | g | 3148.0 |

h${}_{k1}$ | Mooring-line fairlead height | cm | 0.5 |

I${}_{XX,BOX}$ | Moment of inertia around X axis | g·${\mathrm{cm}}^{2}$ | 1.5 × 10${}^{5}$ |

I${}_{YY,BOX}$ | Moment of inertia around Y axis | g·${\mathrm{cm}}^{2}$ | 1.5 × 10${}^{5}$ |

I${}_{ZZ,BOX}$ | Moment of inertia around Z axis | g·${\mathrm{cm}}^{2}$ | 2.1 × 10${}^{5}$ |

Symbol | Description | Unit | Value |
---|---|---|---|

B${}_{OWC}$ | Width of OWC model | cm | 20.0 |

L${}_{OWC}$ | Length of OWC model | cm | 20.0 |

H${}_{OWC}$ | Height of OWC model | cm | 44.0 |

T${}_{OWC}$ | Draft of OWC model | cm | 26.0 |

M${}_{OWC}$ | Mass of OWC model | g | 2593.0 |

I${}_{XX,OWC}$ | Moment of inertia around X axis | g·${\mathrm{cm}}^{2}$ | 7.2 × 10${}^{5}$ |

I${}_{YY,OWC}$ | Moment of inertia around Y axis | g·${\mathrm{cm}}^{2}$ | 9.4 × 10${}^{5}$ |

I${}_{ZZ,OWC}$ | Moment of inertia around Z axis | g·${\mathrm{cm}}^{2}$ | 5.6 × 10${}^{5}$ |

h${}_{o}$ | Front opening height | cm | 19.0 |

h${}_{k2}$ | Mooring-line fairlead height | cm | 15.0 |

h${}_{b}$ | EPS foam block height | cm | 8.0 |

s${}_{1}$ | Vertical height of center of gravity | cm | 15.2 |

s${}_{2}$ | Distance from center of gravity to front surface | cm | 9.9 |

∅ | Orifice diameter | cm | 5.0 |

Material | Symbol | Description | Units | Parameter |
---|---|---|---|---|

Iron chain | L${}_{C}$ | Total length of chain mooring line | cm | 145.5 |

k${}_{C}$ | Chain elasticity | N/mm | 19.0 | |

l | Length per chain segment | cm | 0.8 | |

w | Chain weight per centimeter | g/cm | 0.6 | |

v | Chain volume per centimeter | ${\mathrm{cm}}^{3}$/cm | 0.1 | |

Nylon rope | L${}_{R}$ | Total length of rope mooring line | cm | 144.0 |

k${}_{R}$ | Rope elasticity | N/mm | 1.1 |

Test Group | Model | Range of Regular Wave Period, T (s) | Range of Regular Wave Height, H (cm) | Water Depth, d (cm) | Mooring Line Material | Note |
---|---|---|---|---|---|---|

1 | BOX | 1.6–2.0 | 12.0–15.0 | 50.0 | Chain | Benchmark test |

2 | OWC | 0.7– 2.1 | 4.0–8.0 | 60.0 | Chain | Small wave amplitude |

3 | OWC | 1.5– 2.0 | 11.0–14.0 | 60.0 | Chain | Large wave amplitude |

4 | OWC | 0.7–2.1 | 4.0–8.0 | 60.0 | Rope | Small wave amplitude |

5 | OWC | 1.5–2.0 | 11.0–14.0 | 60.0 | Rope | Large wave amplitude |

6 | OWC | 1.7 | 14.0 | 60.0 | Chain | Unbalanced mooring |

7 | OWC | 1.5–2.0 | 11.0 | 60.0 | Chain | ∅ = 1.0 cm |

© 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**

Wu, M.; Stratigaki, V.; Troch, P.; Altomare, C.; Verbrugghe, T.; Crespo, A.; Cappietti, L.; Hall, M.; Gómez-Gesteira, M.
Experimental Study of a Moored Floating Oscillating Water Column Wave-Energy Converter and of a Moored Cubic Box. *Energies* **2019**, *12*, 1834.
https://doi.org/10.3390/en12101834

**AMA Style**

Wu M, Stratigaki V, Troch P, Altomare C, Verbrugghe T, Crespo A, Cappietti L, Hall M, Gómez-Gesteira M.
Experimental Study of a Moored Floating Oscillating Water Column Wave-Energy Converter and of a Moored Cubic Box. *Energies*. 2019; 12(10):1834.
https://doi.org/10.3390/en12101834

**Chicago/Turabian Style**

Wu, Minghao, Vasiliki Stratigaki, Peter Troch, Corrado Altomare, Tim Verbrugghe, Alejandro Crespo, Lorenzo Cappietti, Matthew Hall, and Moncho Gómez-Gesteira.
2019. "Experimental Study of a Moored Floating Oscillating Water Column Wave-Energy Converter and of a Moored Cubic Box" *Energies* 12, no. 10: 1834.
https://doi.org/10.3390/en12101834