# Investigation on Performance of a Modified Breakwater-Integrated OWC Wave Energy Converter

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Configuration of the Modified OWC

## 3. 3D CFD Modelling

_{i}and x

_{j}represent Cartesian coordinates, u

_{i}and u

_{j}are the ensemble-averaged velocity components in subscript direction, t is the time, p is the ensemble-averaged pressure intensity, ρ is the fluid density, g

_{i}is the gravitational acceleration, μ is the absolute viscosity, V

_{F}is the fractional volume open to the flow, A is the fraction area for the subscript direction, and $\rho \langle {{u}^{\prime}}_{i}{{u}^{\prime}}_{j}\rangle $ is the Reynolds stresses term. The above equations are identical to Reynolds-averaged Navier-Stokes (RANS) equations as V

_{F}and A are equal to 1. In the current numerical simulation, the Renormalization Group method (RNG turbulent model) is implemented to model the Reynolds stresses term. The RNG model was originally derived by Yokhot and Orszag [45] based on k-ε turbulent model and improved by Yakhot et al. [46] with scale expansions for the Reynolds stress and production of dissipation terms. Speziale and Thangam [47] indicated that the RNG model can be a useful turbulence model for scientific calculations and practical engineering. The reliability of RNG model has been demonstrated for a wider class of wave-structure interaction problems [48,49].

## 4. OWC Hydrodynamic Efficiency

_{E}is the instantaneous pneumatic power, T is the wave period, and w is the width of the OWC chamber.

_{w}is the time-average energy flux of the incident wave per unit width, that is, wave power, which is defined as the product of the wave energy density and the group velocity.

_{o}is the area of the orifice, $V(t)$ is the air velocity profile at the orifice, ${V}_{c}(t)$ is the air velocity at the center of the orifice, and C

_{c}is a constant.

_{c}has to be determined prior. The numerical results of the representative velocity distribution across the orifice is shown in Figure 4 using the experimental condition (shown in Table 2) of incident wave height H

_{i}= 0.0345 m, wave period T = 0.875 s and water depth h = 0.21 m. As indicated in this figure, the computed velocity profile of the air flow in the orifice is in good correlation with the empirical power-law representation for a typical turbulent flow [51] by using

_{c}= 0.82 is obtained. Figure 5 depicts that the numerical result is in good agreement with the experimental result of the flowrate through the orifice, which is obtained using $q(t)={C}_{c}{V}_{c}(t){A}_{o}$ for experimental measurement and using $q(t)={\displaystyle {\int}_{{A}_{o}}V(t)dA}$ for numerical simulation. The positive and negative values of the flowrate mean the quantities of air exhalation and inhalation through the orifice, respectively.

## 5. Experiments and Validations

#### 5.1. Experiments

^{®}(Ahlborn GmbH, Holzkirchen, Germany) measuring connector and data acquisition system to read the instantaneous air dynamic pressure with resolution of 0.1 Pa. The air velocity was then obtained directly by means of the ALMEMO

^{®}View software which includes programming for automatic atmospheric pressure compensation. The data records of all measurements were taken with eight wave periods and implemented before the incoming wave was affected by the undesired wave reflection from the assigned structure.

_{o}= 0.21 m (kh

_{o}= 1.28, k is the wave number), that is, the foundation was not placed below the OWC device. The experimental conditions are listed in Table 2.

#### 5.2. Validations

#### 5.2.1. Hydrodynamic Performance Parameters

_{E}). Figure 7 shows that the numerical results are in good agreement with the experimental measurements of the time series of all performance parameters for both OWC devices. Noting that the wave condition conducted in the experiment for both OWC devices is the same, the only difference in the geometry is that the present OWC device has a perforated front wall but the typical device does not have it. The results demonstrate that the present OWC device has better performance than the typical OWC device under the same wave condition.

_{o}= 1.285, h

_{b}/h = 0.43, ε = 1% and λ = 25%.

#### 5.2.2. Flow Patterns

## 6. Effects of Chamber Geometry on Hydrodynamic Efficiency

#### 6.1. Effect of the Chamber Breadth

_{b}/h = 0.5, ε = 1% and λ = 25% are used, where h

_{b}/h is the relative opening height of the front submerged wall, λ is the porosity of the perforated front wall, and ε is the orifice opening ratio defined by ε = A

_{o}/A (A

_{o}is the orifice area and A is the cross-sectional area of the air chamber). The results show that the breadth of OWC chamber (B) has a significant influence on the hydrodynamic efficiency of the present OWC device. It can be seen that the hydrodynamic efficiency increases with the increase of the breadth of B in the low frequency region (i.e., smaller kh

_{o}, k is the wave number), but follows an opposite tendency in the high frequency region. The maximum hydrodynamic efficiency occurs at kh

_{o}= 1.44 for b:B = 1:1.5, at kh

_{o}= 1.58 for b:B = 1:1, and at kh

_{o}= 1.94 for b:B = 1.5:1, corresponding to the maximum value of 82%, 80% and 72%, respectively. It indicates that the resonant frequency decreases with the increase of the breadth (B) of the OWC chamber. Ning et al. [39] indicated that the reason is due to the fact that the inertia of the OWC water column increases with the chamber breadth. Figure 10 illustrates the variations of incident wave power P

_{w}and pneumatic power P

_{air}against the relative water depth kh

_{o}, which shows that the values of P

_{w}and P

_{air}are the closest at the resonant frequency of kh

_{o}= 1.44, 1.5 and 1.94 for b:B = 1:1.5, 1:1 and 1.5:1, respectively.

_{E}) at kh

_{o}= 1.58 for b:B = 1:1.5, 1:1 and 1.5:1. It can be seen that they have the same characteristics of variations but the significant numeric deviation occurs at the peaks of the time variation of pneumatic power.

#### 6.2. Effect of Opening Height of Submerged Wall

_{b}/h) of the front submerged wall of OWC chamber is demonstrated in Figure 12 for kh

_{o}= 1.58 using b:B = 1:1, ε = 1%, and λ = 25%. The results show that the hydrodynamic efficiency can be larger than 80% if h

_{b}/h ranges between 0.5 and 0.7. It can be seen that the smaller and larger entrances of the submerged open wall could not produce higher pneumatic power. Referring to Delauré and Lewis [38], narrower open of the front submerged wall increases hydrodynamic damping due to vortex shedding by the flow contraction thus reduces the hydrodynamic efficiency. On the other hand, the opening of the submerge wall should not too large to decrease the mass of water column in the chamber that also reduces the pneumatic power.

#### 6.3. Effect of Orifice Scale

_{o}/A, in which A

_{o}is the orifice area and A is the cross-sectional area of the air chamber. Five opening area ratios varied from 0.5% to 1.5% (i.e., the diameters of the circular orifice are varied from 0.82 m to 1.41 m) are simulated for kh

_{o}= 1.58 using b:B = 1:1, h

_{b}/h = 0.5, and λ = 25%. The result show that the hydrodynamic efficiency first increases to the maximum value then decreases with the increase of the opening ratio; this tendency is similar to the experimental results obtained by Ning et al. [39]. Figure 13 depicts that the hydrodynamic efficiency can reach 83% and 80% as ε = 0.7% and 1.0%, respectively.

#### 6.4. Effect of Porosity of Perforated Front Wall

_{o}= 1.58 using b:B = 1:1, h

_{b}/h = 0.5, and ε = 1%. The simulated results show that the hydrodynamic efficiency ξ almost linearly increases from 59% to 80 % as the porosity λ varies from 15% to 25%, then ξ slightly increases to a maximum value of 84% as λ increases to 60% and hereafter ξ decreases to 78% as λ increases to 80%.

_{o}= 1.58.

## 7. Comparisons of Present and Typical OWC Devices

_{b}/h = 0.5. The perforated front wall of the present OWC device employs b = 10.5 m and λ = 25%. Figure 15 shows the variation of hydrodynamic efficiency against the relative water depth, which demonstrates that the resonant frequency occurs at kh

_{o}= 1.58 for both OWC devices. It can be seen that the present OWC device has better hydrodynamic performance than the typical OWC device. The maximum values of the hydrodynamic efficiency are obtained by 80% and 59% of the present and typical OWC devices respectively. The time variations of the performance parameters are shown in Figure 16, which shows that the present OWC device has larger quantities than the typical device.

^{5}N/m of the present OWC device and 3.5 × 10

^{5}N/m of the typical OWC device.

## 8. Conclusions

_{o}= 1.58, the hydrodynamic efficiency of the extracted pneumatic power can be larger than 80% using appropriate opening height of the submerged entrance. The smaller and larger entrances of the submerged open wall could not produce higher pneumatic power. The effect of the air orifice area ratio is also discussed, from which the hydrodynamic efficiency can reach 83% as air orifice area ratio is 0.7%. Regarding to the effect of the porosity of the perforated front wall, it is found that the hydrodynamic efficiency can be larger than 80% as the porosity of the perforated front wall is in range of 25–70%. The present results also demonstrates that the variation of the hydrodynamic efficiency is inversely related to the wave reflection coefficient and the overall dissipation of turbulent kinetic energy.

## 9. Patents

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Correlation of air velocity profile across the orifice between empirical formula and computed result using the experimental conditions shown in Table 2.

**Figure 5.**Comparison between the numerical and experimental results of the flowrate through the orifice.

**Figure 7.**Comparisons of hydrodynamic performance parameters between numerical results and experimental measurements for (

**a**) present OWC device (

**b**) typical OWC device.

**Figure 8.**Flow fields in the vicinity of the entrance of the present OWC chamber during the exhalation and inhalation stages, (

**A**) t/T = 0; (

**B**) t/T = 0.25; (

**C**) t/T = 0.5; (

**D**) t/T = 0.75. Left column: numerical simulations; right column: experimental observations.

**Figure 9.**Hydrodynamic efficiency versus relative water depth kh

_{o}for different chamber breadths.

**Figure 10.**The incident wave power P

_{w}and pneumatic power P

_{air}against the relative water depth kh

_{o}for b:B = 1:1.

**Figure 11.**Comparisons of the time variation of the performance parameters at kh

_{o}= 1.58 for b:B = 1:1.5, 1:1, and 1.5:1.

**Figure 12.**Hydrodynamic efficiency versus different open heights of front submerged wall of OWC chamber for kh

_{o}= 1.58 using b:B = 1:1, ε = 1%, and λ = 25%.

**Figure 13.**Hydrodynamic efficiency versus different opening sizes of air orifice for kh

_{o}= 1.58 using b:B = 1:1, h

_{b}/h = 0.5, and λ = 25%.

**Figure 14.**(

**a**) Hydrodynamic efficiency; (

**b**) Wave reflection coefficient Kr; (

**c**) Wave amplification coefficient K

_{t}; (

**d**) Dissipation of turbulent kinetic energy versus porosity of perforated front wall for kh

_{o}= 1.58 using b:B = 1:1, h

_{b}/h = 0.5, and ε = 1%.

**Figure 15.**Comparison of hydrodynamic efficiency between present and typical OWC devices versus relative water depth kh

_{o}.

**Figure 16.**Comparison of the time variation of the performance parameters between present and typical OWC devices.

**Figure 17.**Comparisons of flow characteristics at A: t/T = 0; B: t/T = 0.25; C: t/T = 0.5; D: t/T = 0.75. Left column: present OWC device; right column: typical OWC device.

**Figure 19.**Comparisons of the synthesized surface elevation (η) probed at antinode in front of OWC device and the reconstructed profile of incident wave (η

_{i}). Left: present OWC device; right: typical OWC device.

**Figure 20.**Comparison of the horizontal force acting on the submerged open wall of the present and typical OWC devices.

ΔX | ΔY | ΔZ | ΔZ (Water Surface Region) | |
---|---|---|---|---|

zone A | L/56~L/186 | W/10 | H/22 | H/44 |

zone B | L/112~L/372 | W/20 | H/44 | H/88 |

zone C | L/112~L/372 | W/20 | H/66 | H/132 |

zone D | D/10~D/18 | D/10~D/18 | d/5 | - |

zone S | L/168~L/558 | W/20 | H/66 | H/132 |

Parameters | Present OWC Device | Typical OWC Device | |
---|---|---|---|

incident wave | H | 3.45 cm | 3.45 cm |

T | 0.875 s | 0.875 s | |

h | 21.0 cm | 21.0 cm | |

h_{o} | 21.0 cm | 21.0 cm | |

kh_{o} | 1.285 | 1.285 | |

geometry of OWC device | B | 11.5 cm | 11.5 cm |

b | 11.5 cm | - | |

h_{b} | 9.0 cm | 9.0 cm | |

h_{t} | 2.0 cm | - | |

D | 4.0 cm | 4.0 cm | |

d | 1.0 cm | 1.0 cm | |

h_{a} | 9.0 cm | 9.0 cm | |

λ | 25% | - | |

W | 48.0 cm | 48.0 cm |

Parameters | Present OWC Device | Typical OWC Device | |
---|---|---|---|

incident wave | H | 2.2 m | 2.2 m |

T | 6.0–10.0 s | 6.0–10.0 s | |

h | 18.0 m | 18.0 m | |

h_{o} | 26.0 m | 26.0 m | |

kh_{o} | 1.25–2.92 | 1.25–2.92 | |

geometry of OWC device | b + B | 21.0 m | - |

B | 8.4, 10.5, 12.6 m | 10.5 m | |

b | 8.4, 10.5, 12.6 m | - | |

h_{b} | 5.4–14.4 m | 9.0 m | |

h_{t} | 1.5 m | - | |

D | 0.82–1.41m | 1.15 m | |

d | 0.5 m | 0.5 m | |

h_{a} | 8.0 m | 8.0 m | |

λ | 15%–60% | - | |

W | 10.0 m | 10.0 m |

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## Share and Cite

**MDPI and ACS Style**

Tsai, C.-P.; Ko, C.-H.; Chen, Y.-C.
Investigation on Performance of a Modified Breakwater-Integrated OWC Wave Energy Converter. *Sustainability* **2018**, *10*, 643.
https://doi.org/10.3390/su10030643

**AMA Style**

Tsai C-P, Ko C-H, Chen Y-C.
Investigation on Performance of a Modified Breakwater-Integrated OWC Wave Energy Converter. *Sustainability*. 2018; 10(3):643.
https://doi.org/10.3390/su10030643

**Chicago/Turabian Style**

Tsai, Ching-Piao, Chun-Han Ko, and Ying-Chi Chen.
2018. "Investigation on Performance of a Modified Breakwater-Integrated OWC Wave Energy Converter" *Sustainability* 10, no. 3: 643.
https://doi.org/10.3390/su10030643