## 1. Introduction

In Taiwan, more than 80% of electricity comes from thermal power generation, and fossil fuels are dependent on imports. The authorities are now actively promoting energy-policy in order to mitigate greenhouse gas emissions. On the other hand, Taiwan is surrounded by the sea where the ocean power generation, including wave power, tidal power and ocean-current power, is a natural and worthwhile development for renewable energy options. Of these, strong seasonal winds create considerable wave power potential that may contribute significantly to electrical energy if they are extensively exploited.

A large number of techniques of wave energy converter (WEC) have been proposed, in which the Oscillating Water Column (OWC) device has been the most studied and implemented. The OWC device basically consists of a chamber with submerged open wall and an air-duct connecting the air chamber to a turbine. The incident wave motion through the submerged open can cause water column oscillation in the confined chamber, and then the OWC exhales and inhales air to drive a self-rectifying turbine coupled to a power generator. So far, the prototypes for OWC wave energy converters have largely been deployed into the sea [

1]. Among the various types of OWC device, Falcão and Henriques [

1] pointed out that the integration of an OWC device into a breakwater (known as a breakwater-integrated OWC) has several advantages, such as access for construction, and the fact that operation and maintenance of the wave energy plant has become much easier. The breakwater-integrated OWC has been constructed successfully in Sakata harbor in Japan [

2,

3], Mutriku port in Spain [

4], and Civitavecchia harbor in Italy [

5], among other locations. In recent, by means of large-scale experiments under random waves, Viviano et al. [

6] showed that the OWC wave energy converter can be integrated into vertical wall breakwaters to serve as a wave absorber for reducing wave reflection. Naty et al. [

7] demonstrated that the OWC system integrated into coastal structures is an economic feasible proposal for the Mediterranean port. There are other WEC devices integrated with the breakwaters proposed for overtopping wave energy conversion [

8,

9,

10]. Nevertheless, there are about three to four typhoons in average a year attacking Taiwan’s coast, and the typical OWC device without any protective equipment may suffer large wave force when the storm waves impact on it. An improvement of a breakwater-integrated OWC device involving a non-conventional perforated front wall is thus proposed in this paper. Compared with the impermeable structure, wave force acting on the porous structures is relatively reduced [

11,

12,

13]. Therefore, the present modified OWC device is anticipated to work for not only promoting the efficiency of the WEC in general, but also enduring the large wave force impact on the structure during storms.

The hydrodynamic performance of OWC devices has been examined analytically in a number of studies since the 1970s. Evans [

14] presented an approximate analytical solution based on a potential theory for the efficiency of an OWC device consisting of two submerged plates. Evans and Porter [

15] then investigated the typical OWC device in finite depth water using the linear wave theory. Large circular OWC devices installed at the tip of a breakwater [

16], along a straight coast [

17], and at a coastal corner [

18] were investigated analytically by the linearized theories of wave radiation and diffraction.

As a result of the significant development of computational fluid dynamics (CFD), numerous works have successfully implemented numerical simulations for the hydrodynamics of OWC devices. Zhang et al. [

19] presented a numerical model based on a level-set immersed boundary method to simulate the hydrodynamic performance of the OWC device with different drafts of the front wall of the chamber. Based on Fluent CFD software, Liu et al. [

20] investigated the nozzle effects of the chamber-duct system on relative amplitudes of the free water surface in the chamber and air flow rate in the duct. Also, by using Fluent code, EI Marhani et al. [

21] simulated the flow characteristics in the components of an OWC system. Iturrioz et al. [

22] developed a simplified time-domain model to investigate the hydrodynamic appearances and efficiency of a fixed detached OWC with different aperture sizes. López et al. [

23] studied the optimum turbine-chamber coupling for a given OWC employing STAR-CCM+ code based on RANS equations. Ning et al. [

24,

25] investigated the hydrodynamic performance of OWC devices based on a time-domain higher-order boundary element method. Iturrioz et al. [

26] employed OpenFOAM for the three-dimensional simulation of an OWC, which was validated by the laboratory measurements. Based on Fluinco model, Torres et al. [

27] studied the turbine power output of an OWC device by using a hydrodynamic-aerodynamic coupled model. Elhanafi et al. [

28] also applied STAR-CCM+ code to investigate the impacts of scaling and air compressibility on the OWC performance. Kuo et al. [

29] employed FLOW-3D to simulate the interaction behavior between air and water for an OWC caisson breakwater. Crespo et al. [

30] applied a smoothed particle hydrodynamics (SPH) code for simulating a floating OWC moored to the seabed.

As for the physical models of OWC, Sarmento [

31] performed experiments to validate the oscillating surface pressure theory of Sarmento and Falcão [

32]. Tseng et al. [

33] conducted model tests to investigate the energy-conversion efficiency of a shoreline wave-power system. Boccotti et al. [

34] performed a small-scale field experiment on a breakwater embodying an OWC chamber with a small opening. Morris-Thomas et al. [

35] experimentally studied the wave interaction with the OWC chamber and the power take-off efficiency. He et al. [

36] carried out experiments on the hydrodynamic performance of a floating breakwater with OWC chambers. López et al. [

37] experimentally investigated the flow fields in an OWC by means of particle imaging velocimetry. Several studies of physical tests were carried out as well to validate numerical or theoretical solutions [

28,

29,

38,

39].

The objective of this study is to propose a modified breakwater-integrated OWC and to investigate the hydrodynamic performance by using experiments and numerical simulations. The configuration of the present modified OWC is illustrated in

Section 2. The 3D CFD modeling and the definition of the hydrodynamic efficiency are presented in

Section 3 and

Section 4, respectively.

Section 5 illustrates the experiments and validations of the numerical simulations. Then the effects of the geometry of the OWC device on the hydrodynamic efficiency are discussed in

Section 6. The comparisons of the hydrodynamic efficiency between the present and typical OWC devices are demonstrated in

Section 7. Finally, the main conclusions of this study are presented in

Section 8.

## 3. 3D CFD Modelling

Elhanafi et al. [

28] indicated that the air must be modelled as a compressible fluid in a full-scale OWC device but the air compressibility can be ignored for a small model scale. To simulate this two-fluid problem including air and water behaviors inside the OWC chamber considering the fluid compressibility, the 3D CFD model FLOW-3D [

42] is applied in the present study. FLOW-3D provides exclusively the FAVOR (fractional area/volumes obstacle representation) technique [

43] to efficiently represent the complex obstacle and uses the true Volume of Fluid (VOF) method [

44] to track the fluid interfaces. The three-dimensional mass continuity equation and the momentum equation are represented by

where the subscripts of

i and

j = 1, 2, 3 represent

x-,

y- and

z-directions,

x_{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].

The internal energy equation has to be included when the air flow inside the chamber is considered as a compressible flow. It is expressed as

where

I is the macroscopic mixture internal energy.

In the numerical simulations, the incident wave conditions were generated at the inlet boundary based on the nonlinear waves by using Fenton’s Fourier approximation method [

50]. No-slip boundary conditions are imposed on all solid surfaces of the assigned structure. The outflow boundary is treated by the continuative boundary, in which the boundary condition consists of zero normal derivatives at the boundary for all quantities. Tangential stresses at free surfaces are zero because of vanishing velocity derivatives across the surface. Regarding to the turbulence condition at wall boundaries, FLOW-3D specified values of turbulent kinetic energy and turbulent dissipation at mesh locations adjacent to wall boundaries based on a log-law-of-the-wall velocity profile. FLOW-3D used the finite difference approximation for discretizing each equations and executed numerical computations by associating with FAVOR technique and true volume of fluid method. More detailed information on the numerical schemes associated with FAVOR technique can be found in the FLOW-3D manual [

42].

The computational meshes are performed using the mesh generator in FLOW-3D which is capable of generating intricate meshes. After appropriate numerical convergence tests, seven mesh blocks and six mesh blocks are respectively performed for the present and typical OWC devices, as shown in

Figure 3 and

Table 1, in which the mesh at the zones of free surface and OWC devices are refined. The fluid domain before the assigned structure has a length of 20

L (

L is the considered wavelength) to sufficiently collect the data length with eight wave periods without getting undesired data due to the wave reflection affecting the incoming wave.

## 4. OWC Hydrodynamic Efficiency

The average pneumatic power extracted by an OWC device per unit width during one wave period can be calculated by

where Δ

p(

t) is the instantaneous air pressure inside the chamber,

q(

t) is the instantaneous flowrate through the orifice,

P_{E} is the instantaneous pneumatic power,

T is the wave period, and

w is the width of the OWC chamber.

The hydrodynamic efficiency, or conversion efficiency, is generally defined by the ratio of average pneumatic power and the average incident wave power [

23,

24,

25,

26,

27,

28,

29,

35,

38], given using

where

P_{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.

Considering the velocity profile over the flow cross-sectional area is non-uniform distribution, the flowrate in Equation (4) can be defined by

where

A_{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.

If the flowrate is represented by using the velocity

${V}_{c}(t)$ at the center of the orifice, the value of constant

C_{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

in which

n = 7, that is the well-known one-seventh power law, where

R is the radius of the circular orifice and

r is the radial coordinate. As a result, the constant

C_{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.

## 7. Comparisons of Present and Typical OWC Devices

Finally, we compare the hydrodynamic performance between the present and typical OWC devices under the same incident wave conditions shown in

Table 3. Both the OWC devices use the same breadth of OWC chamber, orifice area and submerged opening height using

B = 10.5 m,

ε = 1%, and

h_{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.

Figure 17 illustrates the snapshots of flow field in the vicinity of the entrance of the submerged open wall of both OWC devices with four frames including in-flow stage (phases A and B) and out-flow stage (phases C and D). Like

Figure 8, the flow fields show that the U-type flow pattern forms by the oscillating water column in the present OWC device, thus causing larger flow intensity through the submerged open wall. The occurrence of U-type flow is because the water outflow at the descending stage of the water column is partly bounded by the perforated front wall. On the contrary, because the flow energy almost disappears at the outer region when the water flows out the chamber of the typical OWC device, the U-type flow pattern could not be formed. Consequently, the present OWC device has a better performance of the pneumatic power extraction, even though it has larger dissipation of turbulent kinetic energy (as shown in

Figure 18).

Figure 19 shows the comparisons of the synthesized surface elevation probed at antinode in front of the present and typical OWC devices, in which the surface profiles of the incident wave for both devices are reconstructed by using inverse FFT based on the method of Goda and Suzuki [

52]. The wave reflection coefficients from the present and typical OWC devices are obtained by

Kr = 0.23 and 0.58, respectively, which demonstrates that the present OWC device can reduce the wave reflection due to the existence of the perforated front wall.

The net horizontal forces acting on the submerged open wall per unit width of the present and typical OWC devices are compared in

Figure 20. The positive and negative force values represent the net force directing on +

x and −

x direction, respectively. Due to the effect of the perforated front wall, the results demonstrate that the present OWC device has smaller wave force acting on the submerged open wall. The maximum net forces on the wall are obtained by 1.8 × 10

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

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

Based on the above comparisons of the hydrodynamic properties of the OWC devices, the results indicate that the present modified OWC device can not only promote the efficiency of the pneumatic power extraction, but also can reduce the wave force acting on the structure.

## 8. Conclusions

This study proposes an innovative modified breakwater-integrated OWC wave energy converter for the purpose of efficiently extracting the wave power and being capable of reducing the wave force on the structure. The present modified OWC device consists of a composite perforated front wall and a vertical submerged open OWC device, which is connected to a caisson breakwater. Both numerical simulation and experimental investigation are carried out to examine the hydrodynamic performance of both the present and the typical OWC devices, the typical OWC device being the model without the perforated front wall. The 3D numerical model based on RANS equations using FLOW-3D solver and considering the fluid compressibility was adopted to investigate the hydrodynamic performance of the OWC devices. The numerical simulations using model scale of OWC device for the hydrodynamic performance parameters are found in good agreement with the experimental measurements including water surface elevation of OWC, the air pressure inside the chamber, the air flowrate through the orifice, and the instantaneous extracted pneumatic power. The simulated flow patterns in the OWC device also agree well with the experimental observations. The vortex shedding can be found near the lip of the submerged open wall as water flow passes through the submerged open wall due to the water column oscillating in the chamber.

By considering full-scale conditions in the numerical simulations, the effects of geometry of the present OWC device, including the breadth, air orifice scale, opening height of the entrance, and the porosity of the perforated front wall of the OWC chamber, are discussed. The simulated results show that the breadth of OWC chamber (B) has a significant influence on the hydrodynamic efficiency. It is found that the resonant frequency decreases with the increase of the breadth of the OWC chamber. At a resonant frequency condition, like kh_{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.

The comparison of hydrodynamic performance between the present and typical OWC devices under the same incident wave condition is investigated in this paper as well. It is found that the U-type flow pattern forms in the present OWC device lead to better performance for extracting pneumatic power. It is also found that the present OWC device results in less wave force acting on the submerged open wall and less wave reflection from the device when compared to the typical OWC device. This research demonstrates that the present modified OWC device can not only promote the efficiency of the pneumatic power extraction, but can also reduce the wave force acting on the structure.

For guidelines on the structure designs, it is suggested that the wave force on the structure of the OWC device impacted by the storm wave conditions should be implemented in the further study.