139

ＯＴＥＣ
Vol. 27（2022），139 ～ 149

Structural analysis of a newly proposed hybrid wave
energy convertor using OpenFOAM
Mobin Masoomi*1, kourosh Rezanejad2*1 Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran.

2

Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior Técnico, Universidade de Lisboa, Av.
Rovisco Pais, 1049-001, Lisboa, Portugal

Abstract
Fixed Oscillating Water Column (OWC) and Wavestar Wave Energy Converter (WEC) are two standard converters withdifferent strategies but the same goal, extracting energy from waves. Fixed-OWC is a coastal system that uses pneumaticpressure with a turbine, but Wavestar uses a power take-off (PTO) damping system to extract power and operate in both shore
and offshore areas. The innovation of the present study is using these two systems simultaneously in a shared platform, in thesense that fixed-OWC is used as the base structure for Wavestar convertor. For this purpose, three main designs with variable
distances between the Wavestars' floating object and the fixed-OWCs' front wall, WEC-17.5, WEC-17.8, and WEC-18.1, were
performed for four different wavelengths using the numerical solution. The solver is OverInterDymFoam from the standard
library of the OpenFOAM solvers, considering both dynamic mesh (Overset mesh technique) and wave generation schemes.
Although the idle combination is extracting power from Wavestar besides no efficiency reduction for fixed-OWC, a decreasein efficiency for some cases is inevitable. An overall assessment of the proposed combined system for 12 different case studies
reveals that there is an efficiency reduction in some cases, near 38% for the worst case. Still, the superiority of this method isefficiency increment up to 13% for system design points "the efficient span in which the convertor works." Finally, a structural
analysis was performed to calculate the exerted force on the front wall of fixed-OWC in the new combined platform.
Keywords: Oscillating water column (OWC); Wavestar; hybrid WEC; OpenFOAM; structural forces.

1. Introduction
We are facing an ever-increasing demand for renewable energy research and development. Ocean energy
has proven to be a reliable source of renewable energy and has consequently been subject to various investigations
in recent years. The present paper has been introduced the combination of the two types of WEC in a new hybrid
installation plan. Here a novel configuration is proposed to use the structure of a fixed-OWC as the base structure
for Wavestar1 WEC. There is no need to build a new fixed structure to install the Wavestar by using this layout,which caused lowering the budget and complexity of the wave energy farm at shorelines. Although someresearchers investigated improving the fixed-OWC efficiency, such as using multi-chambers (Shalby et al., 2019)and L-shaped duct (Rezanejad et al., 2019), the purpose of the present study is only to investigate the rate ofchange in OWC efficiency by adding Wavestar in the front of it. If the OWC's efficiency does not change, ourresearch plan is compelling enough, and whatever the efficiency increases, it is considered an optimal state. The
OWC's efficiency is directly related to the free surface motion, chamber pressure, and the phase difference; thus,
adding a floated body will probably cause changes in the converter's efficiency.
To the best of the authors' knowledge, similar research has not been performed in the literature. But among
various WECs, the fixed-OWC and oscillating buoy prototypes such as the Wavestar have received particularattention (see, e.g., (Falcão & Henriques, 2016), (Drew et al., 2009), (Sarlak et al., 2010)). (Maeda et al., 1985)
introduced a simple method to predict the rate of wave energy absorption, a full-scale investigation performed by
Takahashi et al. (1993), to improve wave energy converter performance. In addition to shape and type of
convertor, some researchers like (Rezanejad et al., 2013) researched the step-bottom for a fixed-OWC
numerically; they concluded that adding step-bottom could increase the overall convertors' efficiency. And also,*'DWHRI0DQXVFULSW$FFHSWDQFH
(PDLORIFRUUHVSRQGLQJDXWKRUm.mo.masoomi@gmail.com
http://wavestarenergy.com/projects

1

140

Mobin MASOOMI and Kourosh REZANEJAD

Ashlin et al. (Ashlin et al., 2016) investigated how the different bottom profile shapes of a nearshore OWC couldchange the system efficiency. Recently using sequential chambers was an exciting subject for the researchers(Ashlin et al., 2018) installed an array of OWC with different distances to evaluate the total efficiency. Besides,
wave frequency is an essential factor in the converter's performance. (Ning et al., 2018) investigated two single
and dual-chamber fixed-OWC; they concluded that dual-chamber OWC was more stable, especially for the highfrequency waves. A complete comparison between single and dual-chamber OWC was performed by (Elhanafi etal., 2018). It shows a significant increase in converters' efficiency, about 40% for dual-chamber.
Further, the fixed-WECs, floating structures are other kinds of WEC used both for nearshore and offshore,with different strategies and a wide range of size, water depth, mooring system. The present study combines thefloating WEC named Wavestar, which is appropriate with our proposed hybrid system. A scaled model of the
Wavestar was investigated by (Jakobsen et al., 2016). After them, (Ransley et al., 2017) analyzed the dynamic
behavior of the floated body in fixed and unrestricted (free movement) modes. (Xu et al., 2019) investigated akind of floating WEC named floating point absorber. They compared the numerical and experimental survival
and operational status results and concluded that the most significant discrepancy belonged to surge and pitch
RAOs in survivability cases. A 1/5 scale model of Wavestar was investigated by (Windt et al., 2020); they
compared the numerical and physical results for all hydrodynamic parameters and related dynamic motions.
Besides, they investigated the Froude and Reynolds scaling factors. Recently, they analyzed a Wavestar inoperational status to assess the scaling effect on the hydrodynamic parameters and WEC response by considering
the numerical solution (Windt et al., 2021). Their conclusion was apart from the mechanical scaling effect,
especially friction, numerical modeling in the Numerical Wave Tank (NWT) could accurately model the WEC
devices with high fidelity.
Some researchers investigate the hybrid floating WEC, mostly involved installing the converters on floating
wind turbine, (Stansby et al., 2022) proposed a wave diffraction radiation model for a floated WEC installed on
the floating wind turbine platform. They concluded that the diffraction effects are less than 5%. (Sakr et al., 2021)
investigate on controlling the floating WEC to maximize the power absorption; their control system was based on
effective stiffness to maintain the natural system frequency near the frequency of the incident wave to haveresonance oscillations. (Moreno & Stansby, 2019) experimentally investigate a six-float WEC system with two
PTOs installed on the floating wind turbine base structures.
This report addressed extending research based on the previous work by (Masoomi et al., 2021) byconsidering the three different installation plans of the proposed hybrid system at various wave frequencies tocheck the comprehensiveness of the investigation. The numerical solution for the new hybrid plan is based on
Reynolds Navier Stokes Equation (RANS) by implementing an adjustable NWT, "length in each case study isrelated to used wave frequency." The OverSetMesh2 technique, one of the functional new dynamic methods, isused as a dynamic approach on the standard OpenFOAM's3 solver, "OverInterDyMFoam."

2. Material and Methods
2.1 Governing Equations
The first step in implementing an NWT for wave generating is that the accuracy of this solution is highly
dependent on the numerical modeling approach. For instance, the solution based on the potential flow is a low
computational cost method appropriate for parametric studies (Penalba et al., 2017; Tanizawa, 2000). Highfidelity but costly methods such as the CFD-based-NWT could accurately track the wave breaking, complex freesurface, and turbulence effects. For the present study, an open-source 𝐶𝐶 ++ The solver "OpenFOAM" uses the
RANS equation. A two-phase problem, Air and Water, forcing us to use the Volume Of Fluid (VOF) technique(Nichols et al., 1981) and related boundary and initial conditions. The wave generation and absorption, an integral
part of each NWT, are added to the standard solver. Air and water inside the NWT are considered incompressible,
and the fluid is Newtonian. The RANS equation, including the continuity and momentum conservation equation(Weller et al., 1998) as described below:
2 https://www.openfoam.com/documentation/guides/latest/doc/guide-overset.html
3 https://www.openfoam.com

141

Structural analysis of a newly proposed hybrid wave energy convertor using OpenFOAM

.u = 0(1)

 (  u)+ .(  uu) = − p + .( u) +  f b
t(2)

where, u is the fluid velocity, p represents the fluid pressure, 𝜌𝜌, ν are the fluid density and the kinematic
viscosity, respectively. f𝑏𝑏 denotes the external forces involved gravity, per unit mass. The partial differential
equations discretize into the algebraic equation by implementing the Finite Volume Method (FVM). Now it istime to solve these Algebraic equations systems with our three choices, pressure-linked equations (SIMPLE), thepressure-implicit split-operator (PISO), and finally, the combination of these two methods known as PIMPLE.
PISO and PIMPLE could be used for transient case studies, whereas the SIMPLE implemented for steady-state
problems. The PIMPLE algorithm is considered as an appropriate approach for high-fidelity pressure and velocity
coupling. The two-phase flow capturing with the complex free surface is implemented using the VOF technique(Weller et al., 1998).
+ .(u  ) + .[u r  (1 −  )] = 0(3)t,  water + (1 −  ) air=  water + (1 −  ) air=(4)

u r = min[cr u , max( u )](5)

Where α is the phase fraction, 0 < 𝛼𝛼 < 1, α= 0 denotes water and α= 1 is water. 𝜌𝜌, 𝜇𝜇 are the density andviscosity respectively, and ur is the compression velocity. Cr is the factor that controls the interface compression.

2.2 Model Geometry and boundary condition

The first step is devoting an appropriate Numerical Wave Tank (NWT) depending on the type anddimensions of the wave besides considering the solver types, dynamic or static. In this section, the fixed OWC
must be validated with the experimental results; the convertors' overall dimensions are included in Table 1. Thiscase is compatible with (Kamath et al., 2015) study; the length of an NWT is usually considered five times the
wavelength. The overall domain height is not related to incident wave characteristics and is considered h = 2 mconstantly for all cases. The boundary condition is a critical factor that must be following the requirements of eachproblem. For the wave generating cases, the inlet patch must generate the wave, and the outlet patch is such thatthe water particles exit without backward current and the atmosphere is total pressure-inlet/outlet; for WEC hull,a no-slip boundary condition is dedicated.
Table.1 The numerical wave tank and the fixed-OWC related dimentions
Dimensions [m]SymbolModel

OWC- heightOWC thickness
Chamber breadth
Chamber lip height
Orifice width
Water depth

H
C
B
a
dB
d

1.275
0.05
0.64
0.15
0.005
0.92

Fig. 1 The schematic view of the main fixed-OWC dimensions

142

Mobin MASOOMI and Kourosh REZANEJAD

Needless to say that the first and the main section of this research is producing waves in NWT to test the
WECs'. There were some different approaches used before to handle this issue in OpenFOAM. Some extensions
could be added to standard solvers such as IHFoam (Higuera et al., 2013a, 2013b, 2014), OlaFoam (Lee et al.,2016; Lee et al., 2017), Wave2Foam (Jacobsen et al., 2015; Lin et al., 2017); furthermore, the waves could
generate the same as real wave tanks by using oscillating flaps. For the latest versions of OpenFOAM (version
5.0 onwards), wave generation could be easily accessible with the standard solver "InterFoam." A "waveDict"folder involving the wave parameters was added to the "constant" folder. This solver uses the control volume
method to discretize the transport equations, besides the free surface generation, by considering the Volume Of
Fluid (VOF) method. Another important factor for wave generation in the NWTs' is the boundary condition, whichshould be defined as one Inlet and one Outlet. The generated wave from the Inlet boundary condition should exitfrom the outlet without any back-flow into the domain; (Sommerfeld, 1964) first proposed this kind of boundary
condition. In experimental tests, physical beaches, obstacles, friction mechanisms, or sponge layers are usedinstead.

3. Introducing the Hybrid WEC
The overall objective of this research plan included using a Wavestar energy convertor in front of a fixedOWC; the only reason for this plan is to use the fixed structure of the OWC as a base structure for the Wavestar
device without losing efficiency. The Wavestar was installed in the front of OWC at three different points, as
shown in Figure 2, to evaluate the OWC efficiency. The efficiency of the Wavestar is only related to the stroke ofthe floated body; thus, it is almost constant. In fact, the efficiency of the OWC is complex and related to manyfactors such as free surface velocity and pressure within the chamber and, more importantly, the phase difference
between them. The idle result for this research plan is the efficiency increase; although it could be a plus award,
constant efficiency is also considered optimal for the design purpose. But the decrease in efficiency is a drawbackof the project. Three different layouts are introduced with the same mechanism; the difference is the distance
between the floated-body relative to the front wall of fixed-OWC. Three cases are WEC-17.5, 17.8, 18.1 with the
distance of Lx = 0.8, 0.5, 0.2 m from the floated-body center to the front wall of the fixed-OWC.

WEC-17.5

WEC-17.8

WEC-18.1

Fig. 2 Three different layouts for hybrid system (Wavestar and fixed-OWC combination).

The optimum situation for the new combined system is extracting the same power for OWC with Wavestar
rather than the solitary fixed-OWC. However, increasing the power range of the OWC could be impressive; only
the same power as before could be enough to prove the efficiency of the new hybrid system. In fact, the purposeof designing this system is not to increase the fixed-OWC efficiency; it is only involved a newly installed Wavestar
within the fixed-OWC for further power extraction besides maintaining the former fixed-OWC efficiency. As

143

Structural analysis of a newly proposed hybrid wave energy convertor using OpenFOAM

mentioned, three main parameters influenced the rate of the output power of OWC, chamber pressure, free surface
velocity within the chamber, and the phase difference between pressure and free surface velocity.

3.1 dynamic motions of floating-body
Although the power absorbed by the Wavestar is not considered in the present study, the analysis of thefloated semi-hemisphere could be helpful for better understanding and inference. Figure 3 helps us capture theinduced motion from generated waves and the water reflection from the fixed-OWC, besides understanding theeffect of floated-body distance (x = 17.5, 17.8, 18.1) on the oscillating motions. The standard theoretical motionof the body should be between z = 0.86 and z = 0.98 (initial free surface level: z = 0.92 meter, wave height h =0.06 meter). As predicted, the reflected waves from fixed-OWC disrupt the floated-body oscillation in both
harmony and value such that the worst condition is related to WEC-17.5, the reflected waves combined with theincident wave and decrease the wave efficiency, the situation for WEC-17.8 is better. The idle condition belongs
to WEC-18.1, in which the reflected waves could not influence the floated body. Even in the case kd = 0.52
(maximum wave frequency) due to water rise-up on the front wall of the OWC, the top point of the floated-bodyreaches z = 1.03, which is higher than the theoretical value (z = 0.98). In fact, the lower the wave frequency, themore regular the oscillation of the body and nearer to theoretical values.

Kd = 0.52

Kd = 1.26

Kd = 1.8

Kd = 2.5

Fig. 3 The heave amplitude of the floated semi-hemisphere for each wavelength

3.2 Total Efficiency Evaluation of the fixed-OWC merged with Wavestar
The efficiency of the WECs with PTO is highly related to the rate of energy flux converted by the device,
the inlet energy (Pin), Eqs. (6) is the energy of water particles extracted by the fixed-OWC device (Pout), Eqs. (7).
The share of energy extraction relative to primary energy is called efficiency (ⴄ); all these values computes withthe following formula:
𝑃𝑃𝑖𝑖𝑖𝑖 =𝜌𝜌𝑤𝑤 ⋅ 𝑔𝑔 ⋅ ℎ2 ⋅ 𝜆𝜆4𝜋𝜋𝜋𝜋/𝜆𝜆
[1 +
]
16𝑇𝑇
𝑠𝑠𝑠𝑠𝑠𝑠ℎ(4𝜋𝜋𝜋𝜋/𝜆𝜆)(6)where h and λ are the wave height and length and d water depth (depth in the OWC chamber),𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜 =1 𝑇𝑇
1∫ 𝑃𝑃𝑐𝑐 (𝑡𝑡) ⋅ 𝑞𝑞(𝑡𝑡)𝑑𝑑𝑑𝑑 = |𝑃𝑃𝑐𝑐 | ⋅ |𝑉𝑉𝑤𝑤𝑤𝑤𝑤𝑤 |𝑏𝑏 ⋅ 𝑙𝑙 𝑐𝑐𝑐𝑐𝑐𝑐(𝜃𝜃)
𝑇𝑇 0
2

𝜂𝜂 =

𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜
𝑃𝑃𝑖𝑖𝑖𝑖

(7)

(8)

144

Mobin MASOOMI and Kourosh REZANEJAD

where q(t), (𝑉𝑉𝑤𝑤𝑤𝑤𝑤𝑤 ), (𝑃𝑃𝑐𝑐 ), and (θ) are the volume flow rate, free surface velocity, air pressure, and the phasedifference between “(𝑃𝑃𝑐𝑐 ),(𝑉𝑉𝑤𝑤𝑤𝑤𝑤𝑤 ),” respectively. As previously mentioned, three parameters affect the fixed-OWC
efficiency, chamber pressure (p), free surface velocity (wfs) in the middle of the chamber, and the phase difference
between "p" and "wfs." Although these parameters were entirely analyzed in the last sections, a further comparison
needs to better understand how these parameters changed when a Wavestar was added to fixed-OWC. A simple
way to allocate the percentage value for each parameter is using the disparity symbol, which demonstrates thedifference between each new system development rather than standard fixed-OWC.
𝑝𝑝amended − 𝑝𝑝standard= disparity%
𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑒𝑒amended − 𝑒𝑒standard= disparity%𝑒𝑒standard(9)

The maximum reduction rate of about 40% occurred for kd = 0.52, WEC-17.5, but this value was about 18%
for WEC-18.1. These differences show how the position of the floated body could change the results, Figure 4.
The device's efficiency has no constant formula; everything goes back to the correlation between wave parameterand fixed-OWC dimension, chamber breath, water depth within the chamber, orifice size, front wall size, etc.
Based on all these points, each convertor has its peak efficiency point, kd = 1.26 for the present fixed-OWC. The
output's data for "wfs" are quite different, such that the values increased especially in the range of the design point(kd = 1.26 to kd = 1.8), maximum 25% increase for kd = 1.8, WEC-18.1.
Finally, all these values are substituted in the related equation to calculate the total efficiency; the phasedifference is considered constant based on our findings, section 3.2.3 only "p" and "wfs" used. For the range ofsystem design points, a slight increase, maximum 12% recorded, Figure 4 is idle for the innovative presented plan.
Our optimistic forecast was; no efficiency reduction occurred for the fixed-OWC, and any increment wasconsidered an idle result.

Chamber pressure (p)Free surface velocity (wfs)

Fixed-OWC efficiency

Fig. 4 Disparity Comparison between the standard model and amended OWC for different wavelengths

3.3 Structural Force
The combination of fixed-OWC and Wavestar could have many challenges, including hydrodynamic andstructural issues. The variation of the hydrodynamic efficiency is the most significant issue that should beconsidered for the present research, but the interpretation of structural loads could be considerable since the front
wall of the OWC is the vulnerable part of the convertor which bears the most wave loads on the structure, it isused as a basis for comparison. The durability of a WEC, shore or offshore, is a critical design point that should
be considered carefully to prevent system failure. The coastal structure must be constructed so that it can withstandthe maximum forces from stormy waves or any harsh conditions. Still, in the present study, only force changes
created by adding Wavestar on fixed-OWC will be considered at standard wavelength.

Structural analysis of a newly proposed hybrid wave energy convertor using OpenFOAM

145

Although the force analysis on the structure is fundamental, little research has been done in this area.
(Jayakumar, 1994) investigates induced force on WECs experimentally; (Ashlin et al., 2018; Ashlin et al., 2016)
investigate how wave steepness and chamber depth of a fixed-OWC change the indued forces. Wave height isanother parameter that greatly impacts the forces acting on the structure, studied by (Didier et al., 2016) with the
Smooth Particle Hydrodynamic (SPH) method, especially for the front wall. Further to the standard OWCs, someresearchers pay attention to newly introduced fixed-OWC, the hydrodynamic characteristics of a dual-chamber
fixed-OWC investigated experimentally by (Ning et al., 2019). (Masoomi et al., 2021) introduced a new designthat included adding blades inside the chamber; besides evaluating the hydrodynamic efficiency, a further analysis
was performed for the structural force variation due to vertical blades.
In OpenFoam, there are two ways to obtain the forces acting on the structure, first using additional code andlibrary added in controlDict "functionObjectLibs-libforces.so." These are simulation-based solvers; they must be
solved simultaneously with the primary simulation in each time step. The second choice is to use the postprocessing tool ParaView to capture the point by point pressure, surface, and surface normals and calculate theresulting forces, finally integrating the new defined variable "force" to extract the diagrams. For the case in-handa normal pressure 𝐹𝐹𝑝𝑝 is considered the basis of comparison, Eqs. (10) calculates any force on the desired section,
wave-induced force, hydrostatic force, and air force.
(10)=
F p   i.S f ,i( p i − p ref )Where 𝜔𝜔𝑖𝑖 is the density, 𝑆𝑆𝑓𝑓,𝑖𝑖 the face area vector, p the pressure. The initial impression is that the shorter the
wavelength, the greater the forces acting on the front wall; Figure 5 maximum pressure P = 12 [N], for kd = 0.52
and P = 32 [N] for kd = 2.5. The force variations are the same as the pressure changes, with no constant trend;
thus, the force changes are different for kd = 1.26 rather than kd = 2.5. Because for “kd = 1.26, WEC-18.1” force
decreased, but for “kd = 2.5, WEC-18.1” the exerted force increased by about 30%, albeit for “kd = 1.26, WEC17.5” the force reduced to approximately 18%. As we concluded in the last section, WEC-17.5, the pneumaticpressure decreases within the chamber apart from the wave frequency. The condition is also applied for force
evaluation such that, for WEC-17.5, the force decreases for all wavelengths.

Kd = 0.52

Kd = 1.26

Kd = 1.8

Kd = 2.5

Fig. 5 Horizontal force values acting on a standard OWC for different kd.

To better understand why WEC-18.1 increases the wave exerted forces? The answer is represented by acontour-based figure designated for three different combination layouts for kd = 2.5; the reason for using kd = 2.5
is; it had changed a lot. It is all about cumulative pressure beneath the floated body and the front wall of the fixed-

146

Mobin MASOOMI and Kourosh REZANEJAD

OWC. As the floated body is installed closer to the front wall, the entrapped water gains more energy; this extra
energy increases the pressure, resulting in the structural force. This could easily be inferred based on the pressure
contour in Fiure 6. The pressure is shown between p = 8000 [pa] and p = 11000 [pa]; the cumulative pressure isquite obvious for WEC-17.8 and WEC-18.1. These regional pressures only influenced the structural forces, andthere were not many obvious differences observed for the chamber's pressure.

OWC-standard

WEC-17.5

WEC-17.8

WEC-18.1

Fig. 6 Pressure contour for the different hybrid plan, WEC-17.5, 17.8, 18.1 versus standard fixed-OWC for kd= 2.5.

4. Conclusions
Increasing demand for green energy induces the need for a more efficient renewable energy source withlower complexity, and structural cost spread rapidly worldwide. In the present study, we proposed a simple but
efficient way to decrease the structural costs by combining two different wave energy convertors, fixed-OWC,
and Wavestar, in a shared platform. The hybrid WEC system was designed based on the different installed
positions of floated-body in the front of fixed-OWC, WEC-17.5, 17.8, 18.1. Since each convertor has its systemdesign point and related efficiency, Due to incident wavelength and the converters' dimension, especially chamber
breath, the proposed hybrid WEC, investigated with the most important work condition (system design point, kd= 1.26 for the present fixed-OWC). The simulated wave number for the three case studies was kd = 0.52, 1.26,
1.8, 2.5. The structural loads were investigated based on the hydrodynamic pressures. The obtained results wererelated to only the front wall; WEC-18.1 increased the structural load, near 30% for the worst condition and WEC17.5 decreased these exerted loads, about 18% for the best condition, the opposite of the efficiency results. Albeit
these are logical, due to cumulative pressure between the floated-body and the front wall of the fixed-OWC. Less
distance caused less cumulative pressure and consequently less structural force; therefore, WEC-18.1 with dx =0.2 meters applied more loads than WEC-17.5 with dx = 0.8-meter distance.
Nomenclature Latin letters
a
B
C
d
E
e
EL
g
F
b
H

Chamber lip height [m]Chamber breadth [m]OWC thickness [m]Water depth [m]error [%]
efficiency value [%]Free surfce elevation
Acceleration of gravity [m.s-2]
Force [N]Sub-chamber width [m]OWC height [m]λWave length [m]Fluid kinematic viscosity

wfs
kd
dB
X
T
𝑈𝑈
h
k
Z

Free surface velocity [m.s-1]
Wavenumber [-]Orifice width [m]Position vector [m]Wave period [s]Velocity vector [m.s-1]
Wave height [m]Angular Wavenumber [m-1]
Height of plates [m]Greek lettersεω

Kinetic energy dissapation rate
Angular frequency

Structural analysis of a newly proposed hybrid wave energy convertor using OpenFOAM

References𝜏𝜏𝑖𝑖𝑖𝑖κ𝜌𝜌

Reynolds Stress term
Turbulent Kinetic energy
Density [kg.m-3]

θηξ

Phase difference
efficiency symbol
Wave steepness [-]Ashlin, S. J., Sannasiraj, S., & Sundar, V. (2018). Performance of an array of oscillating water column devices
integrated with an offshore detached breakwater. Ocean Engineering, 163, 518-532.
Ashlin, S. J., Sundar, V., & Sannasiraj, S. (2016). Effects of bottom profile of an oscillating water column device on
its hydrodynamic characteristics. Renewable energy, 96, 341-353.
Didier, E., Neves, D. R., Teixeira, P. R., Dias, J., & Neves, M. G. (2016). Smoothed particle hydrodynamics
numerical model for modeling an oscillating water chamber. Ocean Engineering, 123, 397-410.
Elhanafi, A., Macfarlane, G., & Ning, D. (2018). Hydrodynamic performance of single–chamber and dual–chamber offshore–stationary Oscillating Water Column devices using CFD. Applied Energy, 228, 82-96.
Falcão, A. F., & Henriques, J. C. (2016). Oscillating-water-column wave energy converters and air turbines: A
review. Renewable energy, 85, 1391-1424.
Higuera, P., Lara, J. L., & Losada, I. J. (2013a). Realistic wave generation and active wave absorption for Navier–Stokes models: Application to OpenFOAM®. Coastal Engineering, 71, 102-118.
Higuera, P., Lara, J. L., & Losada, I. J. (2013b). Simulating coastal engineering processes with OpenFOAM®.
Coastal Engineering, 71, 119-134.
Higuera, P., Lara, J. L., & Losada, I. J. (2014). Three-dimensional interaction of waves and porous coastal
structures using OpenFOAM®. Part II: Application. Coastal Engineering, 83, 259-270.
Jacobsen, N. G., van Gent, M. R., & Wolters, G. (2015). Numerical analysis of the interaction of irregular waves
with two dimensional permeable coastal structures. Coastal Engineering, 102, 13-29.
Jakobsen, M. M., Beatty, S., Iglesias, G., & Kramer, M. M. (2016). Characterization of loads on a hemisphericalpoint absorber wave energy converter. International Journal of Marine Energy, 13, 1-15.
Jayakumar, V. (1994). Wave force on oscillating water column type wave energy caisson: an experiment study Ph. D.
thesis, Dept. of Ocean Engineering, Indian Institute of Technology].
Kamath, A., Bihs, H., & Arntsen, Ø. A. (2015). Numerical investigations of the hydrodynamics of an oscillatingwater column device. Ocean Engineering, 102, 40-50.
Lee, K.-H., Bae, J.-H., An, S.-W., Kim, D.-S., & Bae, K. S. (2016). Numerical analysis on wave characteristics
around submerged breakwater in wave and current coexisting field by OLAFOAM. Journal of Korean
Society of Coastal and Ocean Engineers, 28(6), 332-349.
Lee, K.-H., Bae, J.-H., Kim, S.-G., & Kim, D.-S. (2017). Three-dimensional simulation of wave reflection andpressure acting on circular perforated caisson breakwater by OLAFOAM. Journal of Korean Society of
Coastal and Ocean Engineers, 29(6), 286-304.
Lin, Z., Pokrajac, D., Guo, Y., Jeng, D.-s., Tang, T., Rey, N., Zheng, J., & Zhang, J. (2017). Investigation of
nonlinear wave-induced seabed response around mono-pile foundation. Coastal Engineering, 121, 197211.
Lopez Mejia, O. D., Mejia, O. E., Escorcia, K. M., Suarez, F., & Laín, S. (2021). Comparison of Sliding and Overset
Mesh Techniques in the Simulation of a Vertical Axis Turbine for Hydrokinetic Applications. Processes,
9(11), 1933.

147

148

Mobin MASOOMI and Kourosh REZANEJAD

Maeda, H., Kinoshita, T., Masuda, K., & Kato, W. (1985). Fundamental research on oscillating water column wave
power absorbers.
Masoomi, M., & Mosavi, A. (2021). The One-Way FSI Method Based on RANS-FEM for the Open Water Test of a
Marine Propeller at the Different Loading Conditions. Journal of Marine Science and Engineering, 9(4), 351.
Masoomi, M., Yousefifard, M., & Mosavi, A. (2021). Efficiency Assessment of an Amended Oscillating Water
Column Using OpenFOAM. Sustainability, 13(10), 5633.
Moreno, E. C., & Stansby, P. (2019). The 6-float wave energy converter M4: Ocean basin tests giving capture
width, response and energy yield for several sites. Renewable and Sustainable Energy Reviews, 104, 307318.
Nichols, B., Hirt, C., & Hotchkiss, R. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries.
Journal of Computational Physics, 39(1), 201-225.
Ning, D.-z., Wang, R.-q., Chen, L.-f., & Sun, K. (2019). Experimental investigation of a land-based dual-chamber
OWC wave energy converter. Renewable and Sustainable Energy Reviews, 105, 48-60.
Ning, D., Zhou, Y., & Zhang, C. (2018). Hydrodynamic modeling of a novel dual-chamber OWC wave energy
converter. Applied Ocean Research, 78, 180-191.
Nuernberg, M., & Tao, L. (2018). Three dimensional tidal turbine array simulations using OpenFOAM withdynamic mesh. Ocean Engineering, 147, 629-646.
Penalba, M., Giorgi, G., & Ringwood, J. V. (2017). Mathematical modelling of wave energy converters: A review
of nonlinear approaches. Renewable and Sustainable Energy Reviews, 78, 1188-1207.
Ransley, E., Greaves, D., Raby, A., Simmonds, D., Jakobsen, M. M., & Kramer, M. (2017). Rans-vof modelling of
the wavestar point absorber. Renewable energy, 109, 49-65.
Rezanejad, K., Bhattacharjee, J., & Soares, C. G. (2013). Stepped sea bottom effects on the efficiency of nearshore
oscillating water column device. Ocean engineering, 70, 25-38.
Rezanejad, K., Souto-Iglesias, A., & Soares, C. G. (2019). Experimental investigation on the hydrodynamic
performance of an L-shaped duct oscillating water column wave energy converter. Ocean Engineering,
173, 388-398.
Sakr, A. H., Metwalli, S. M., & Anis, Y. H. (2021). Dynamics of Heaving Buoy Wave Energy Converters with a
Stiffness Reactive Controller. Energies, 14(1), 44.
Sarlak, H., Seif, M. S., & Abbaspour, M. (2010). Experimental investigation of offshore wave buoy performance.
Journal of Marine Engineering, 6(11), 0-0.
Shalby, M., Elhanafi, A., Walker, P., & Dorrell, D. G. (2019). CFD modelling of a small–scale fixed multi–chamber
OWC device. Applied Ocean Research, 88, 37-47.
Sommerfeld, A. (1964). Thermodynamics and statistical mechanics (Vol. 5). CUP Archive.
Stansby, P., Moreno, E. C., Draycott, S., & Stallard, T. (2022). Total wave power absorption by a multi-float wave
energy converter and a semi-submersible wind platform with a fast far field model for arrays. Journal of
Ocean Engineering and Marine Energy, 8(1), 43-63.
Takahashi, S., Nakada, H., Ohneda, H., & Shikamori, M. (1993). Wave power conversion by a prototype wave
power extracting caisson in Sakata port. In Coastal Engineering 1992 (pp. 3440-3453).
Tanizawa, K. (2000). The state of the art on numerical wave tank. Proceedings of 4th Osaka Colloquium on
Seakeeping Performance of Ships 2000,

Structural analysis of a newly proposed hybrid wave energy convertor using OpenFOAM

Weller, H. G., Tabor, G., Jasak, H., & Fureby, C. (1998). A tensorial approach to computational continuum
mechanics using object-oriented techniques. Computers in physics, 12(6), 620-631.
Windt, C., Davidson, J., Ransley, E. J., Greaves, D., Jakobsen, M., Kramer, M., & Ringwood, J. V. (2020).
Validation of a CFD-based numerical wave tank model for the power production assessment of the
wavestar ocean wave energy converter. Renewable Energy, 146, 2499-2516.
Windt, C., Davidson, J., & Ringwood, J. V. (2021). Numerical analysis of the hydrodynamic scaling effects for the
Wavestar wave energy converter. Journal of Fluids and Structures, 105, 103328.
Xu, Q., Li, Y., Yu, Y.-H., Ding, B., Jiang, Z., Lin, Z., & Cazzolato, B. (2019). Experimental and numericalinvestigations of a two-body floating-point absorber wave energy converter in regular waves. Journal of
Fluids and Structures, 91, 102613.

149