# Hydraulic Performance of an Innovative Breakwater for Overtopping Wave Energy Conversion

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## Abstract

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## 1. Introduction

- (1)
- the device shows a similar or even reduced reflection coefficient with respect to traditional rubble mound breakwater;
- (2)
- overtopping at the rear side of the structure is reduced by adopting appropriate precautions, e.g., the realization of a parapet at the crest of the OBREC crown wall;
- (3)
- new design methods have been proposed for the estimation of the reflection coefficient, overtopping at the rear side of the structure and overtopping volume in the front reservoir.

## 2. Experimental Procedure and Setup

#### 2.1. Wave Flume

#### 2.2. Tested Configurations

#### 2.3. Wave Characteristics

#### 2.4. Instruments

## 3. Results

#### 3.1. Overtopping Discharge in the Front Reservoir

#### 3.2. Reflection

#### 3.3. Wave Overtopping at the Rear Side of the Structure

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

${B}_{r}$ (m) | reservoir width |

${B}_{s}$ (m) | emerged sloping plate width |

${d}_{d}$ (m) | height of the submerged sloping plate |

${D}_{n50}$ (m) | equivalent cube side length exceed by 50% of the stones |

${d}_{w}$ (m) | height of sloping plate |

g ($m\xb7{s}^{-2}$) | gravity acceleration |

h (m) | depth at the toe of the structure |

${h}_{box}$ (m) | depth in the accumulation box |

${H}_{m0,r}$ (m) | reflected significant wave height at the toe of the structure |

${H}_{m0}$ (m) | incident significant wave height at the toe of the structure |

${h}_{r}$ (m) | depth in the front reservoir |

${K}_{r}$ (-) | $\frac{{H}_{m0,r}}{{H}_{m0}}$ reflection coefficient |

${L}_{m-1,0}$ (m) | deep water wavelength referenced to ${T}_{m-1,0}$ |

${m}_{0}$ (${m}^{2}$) | spectral moment of order 0 |

${m}_{-1}$ (${m}^{2}\xb7s$) | spectral moment of order −1 |

${q}_{rear}^{*}$ (-) | non-dimensional overtopping discharge towards the rear of the traditional rubble mound breakwater crown wall or towards the rear OBREC crown wall |

${q}_{reservoir}^{*}$ (-) | non-dimensional overtopping discharge into the reservoir |

${q}_{rear}$ (${m}^{3}\xb7{m}^{-1}\xb7{s}^{-1}$) | average overtopping discharge towards the rear of the traditional rubble mound breakwater crown wall or towards the rear of the OBREC crown wall |

${q}_{reservoir}$ [${m}^{3}\xb7{m}^{-1}\xb7{s}^{-1}$] | average overtopping discharge into the reservoir |

R [m] | crest free-board of the structure |

${R}_{c}^{*}=\frac{{R}_{c}}{{H}_{m0}}$ [-] | relative crest free-board of crown wall |

${R}_{r}^{*}=\frac{{R}_{r}}{{H}_{m0}}$ [-] | relative crest free-board of front reservoir |

${R}_{c}$ [m] | crest free-board of crown wall, i.e., the vertical distance between the crest of the vertical walland the still water level |

${R}_{r}$ [m] | crest free-board of front reservoir, i.e., the vertical distance between the crest of the sloping plate and the still water level |

$rmse$ [-] | root mean square error |

${s}_{m-1,0}=\frac{2\pi {H}_{m0}}{g{T}_{m-1,0}^{2}}$ [-] | wave steepness at the toe of the structure |

${s}_{Rr}$ [-] | non-dimensional wave-structure steepness |

${T}_{m-1,0}=\frac{{m}_{-1}}{{m}_{0}}$ [s] | spectral incident energy wave period at the toe of the structure |

${T}_{p}$ [s] | incident peak wave period |

α [°] | slope angle of the structure |

γ [-] | peak-enhancement factor |

${\gamma}_{\beta}$ [-] | reduction factor for oblique wave attack |

${\gamma}_{b}$ [-] | reduction factor for berm |

${\gamma}_{f}$ [-] | reduction factor for slope roughness |

${\gamma}_{v}$ [-] | reduction factor for the storm wall |

${\gamma}_{par}$ [-] | reduction factor for the parapet |

${\gamma}_{prom}$ [-] | reduction factor for the promenade |

ρ [$kg\xb7{m}^{-3}$] | water density |

${\xi}_{m-1,0}=\frac{tan\alpha}{{s}_{m-1,0}^{0.5}}$ [-] | breaker parameter referenced to ${T}_{m-1,0}$ |

$\Delta {B}_{rs}={B}_{r}-{B}_{s}$ [m] | horizontal distance between the crown wall and the crest of the ramp |

$\Delta {R}_{c}={R}_{c}-{R}_{r}$ [m] | vertical distance between the crown wall and the crest of the ramp |

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**Figure 1.**OBREC prototype at Naples Harbor: (

**a**) prototype photo; (

**b**) prototype structural components; (

**c**) working principle (where SWL indicates the still water level).

**Figure 2.**Plant and cross-section of the wave flume. OBREC, Overtopping BReakwater for Energy Conversion.

**Figure 3.**Cross-section of the analyzed configuration: (

**a**) flat configuration (α equal to 34°); (

**b**) curved configuration (α varies linearly between 52° and 17°).

**Figure 4.**OBREC configuration in the AAU12 tests after Vicinanza et al. [8].

**Figure 7.**Non-dimensional average wave overtopping as function of ${R}_{r}^{*}$. The point data refer to tests with ${R}_{r}$ = 0.125 m.

**Figure 9.**Comparison between the dimensionless measurement overtopping discharge and the one estimated by Equation (7) using ${\gamma}_{f}$ = 1.

**Figure 10.**Overtopping discharge in the front reservoir: (

**a**) comparison between ${\gamma}_{f}$ estimated on the basis of the AAU14 tests and predicted values by Equation (10); (

**b**) comparison between the ${q}_{reservoir}$ observed and ${q}_{reservoir}$ estimated with Equation (6) by using the ${\gamma}_{f}$ computed from Equation 10. In (

**b**) the red line indicates the perfect matching between the two quantities.

**Figure 11.**Overtopping into the front reservoir: ${q}_{reservoir}^{*}/{R}_{r}^{*}$ observed in the presence of the flat configuration versus ${q}_{reservoir}^{*}/{R}_{r}^{*}$ observed in the presence of the curved configuration.

**Figure 12.**Comparison between the measured ${K}_{r}$ in the AUU14 test and those estimated by Equation (12).

**Figure 15.**Comparison between the observed overtopping discharge and Equation (18).

**Figure 16.**Comparison between the observed values and Equation (19) (${\gamma}_{v}$ = 0.78 ; ${\gamma}_{par}$ = 0.72): (

**a**) the case of the structure without a parapet; (

**b**) the case of the structure with a parapet.

**Figure 17.**Comparison between Equation (24) and the data observed in the AAU14 tests with a flat ramp and the AAU12 tests.

**Figure 18.**Overtopping at the rear of the structure: comparison between Equation (26) and the observed values during the AAU14 tests (flat and curved configurations).

**Table 1.**Geometrical characteristics of the different configuration tested. The values refer to the Aalborg University 2014 (AAU14) and AAU12 tests.

AAU14 | AAU12 | ||
---|---|---|---|

Flat Configuration | Curved Configuration | Flat Configuration | |

${h}_{r}$ (m) | 0.090 | 0.094 | 0.100 |

${B}_{s}$ (m) | 0.119 | 0.160 | 0.534 |

$\Delta {B}_{rs}$ (m) | 0.100, 0.200, 0.300 | 0.100, 0.200, 0.300 | 0.415, 0.488 |

${d}_{w}$ (m) | 0.192 | 0.192 | 0.075, 0.125 |

${R}_{r}$ (m) | 0.045 ($R1$), 0.095 ($R2$), 0.125 ($R3$) | 0.049 ($R1$), 0.099 ($R2$), 0.129 ($R3$) | 0.035–0.155 |

${\Delta}_{Rc}$ (m) | 0.102 | 0.098 | 0.045–0.165 |

**Table 2.**Maximum and minimum values of the water level and wave characteristics at the models’ toe evaluated trough the method of Zelt and Skjelbreia [28].

h (m) | ${\mathit{H}}_{\mathit{m}0}$ (m) | ${\mathit{T}}_{\mathit{m}-1,0}$ (s) | ${\mathit{L}}_{\mathit{m}-1,0}$ (m) | |||||
---|---|---|---|---|---|---|---|---|

min | max | min | max | min | max | min | max | |

$\Delta {B}_{rs}$ = 0.1 m | 0.27 | 0.35 | 0.02 | 0.12 | 0.76 | 2.2 | 0.92 | 7.56 |

$\Delta {B}_{rs}$ = 0.2 m | 0.27 | 0.35 | 0.05 | 0.13 | 0.76 | 2.2 | 0.92 | 7.56 |

$\Delta {B}_{rs}$ = 0.3 m | 0.27 | 0.35 | 0.05 | 0.118 | 0.77 | 2.2 | 0.93 | 7.57 |

$\mathbf{\Delta}{\mathit{B}}_{\mathit{rs}}$ = 0.1 m | $\mathbf{\Delta}{\mathit{B}}_{\mathit{rs}}$ = 0.2 m | $\mathbf{\Delta}{\mathit{B}}_{\mathit{rs}}$ = 0.3 m | ||
---|---|---|---|---|

${H}_{m0}$/${L}_{m-1,0}$ | min | 0.016 | 0.015 | 0.015 |

max | 0.031 | 0.033 | 0.031 | |

${H}_{m0}$/h | min | 0.07 | 0.061 | 0.069 |

max | 0.500 | 0.479 | 0.479 | |

${R}_{r}$/${H}_{m0}$ | min | 0.370 | 0.370 | 0.399 |

max | 2.344 | 2.528 | 2.280 | |

${R}_{c}$/${H}_{m0}$ | min | 1.120 | 1.110 | 1.970 |

max | 6.020 | 6.890 | 6.130 | |

${B}_{r}$/${L}_{m-1,0}$ | min | 0.035 | 0.049 | 0.064 |

max | 0.284 | 0.388 | 0.497 | |

h/${L}_{m-1,0}$ | min | 0.037 | 0.039 | 0.037 |

max | 0.382 | 0.377 | 0.378 | |

${\xi}_{m-1,0}$ | min | 3.910 | 3.890 | 3.940 |

max | 5.750 | 5.720 | 5.770 |

Vicinanza et al. [8] | Van Doorslaer et al. [34] | Van Doorslaer et al. [34] | |
---|---|---|---|

Type Structures | OBREC | Promenade-Storm Wall | Promenade-Storm Wall-Parapet |

$\Delta {B}_{rs}=$ 0.10 m | 2.77 | 1.28 | 2.21 |

$\Delta {B}_{rs}=$ 0.20 m | 1.65 | 0.79 | 1.20 |

$\Delta {B}_{rs}=$ 0.30 m | 1.08 | 1.13 | 0.93 |

© 2016 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**

Iuppa, C.; Contestabile, P.; Cavallaro, L.; Foti, E.; Vicinanza, D.
Hydraulic Performance of an Innovative Breakwater for Overtopping Wave Energy Conversion. *Sustainability* **2016**, *8*, 1226.
https://doi.org/10.3390/su8121226

**AMA Style**

Iuppa C, Contestabile P, Cavallaro L, Foti E, Vicinanza D.
Hydraulic Performance of an Innovative Breakwater for Overtopping Wave Energy Conversion. *Sustainability*. 2016; 8(12):1226.
https://doi.org/10.3390/su8121226

**Chicago/Turabian Style**

Iuppa, Claudio, Pasquale Contestabile, Luca Cavallaro, Enrico Foti, and Diego Vicinanza.
2016. "Hydraulic Performance of an Innovative Breakwater for Overtopping Wave Energy Conversion" *Sustainability* 8, no. 12: 1226.
https://doi.org/10.3390/su8121226