65

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Vol. 26（2021），65 ～ 74

Development of a novel multi-level hybrid methodology for a
new concept of Wave Energy Converter (WEC)
Saghy Saeidtehrani
Faculty of Civil Engineering and Geosciences, Delft University of Technology (TU Delft)
Stevinweg 1, 2628 CN Delft, Netherlands

Abstract
Successful WEC design and development needs massive experimental and in-field studies to cover different
aspects of hydro-servo-elastic-geo interaction. Consequently, the lack of fairly accurate modeling methodology
has inevitable effects on developing cost-effective harnessing technologies. Through this paper, a novel multilevel methodology combining experimental and numerical simulation is presented for a new WEC concept whichsignificantly decreases the time-consuming process of concept validation. The methodology is comprised ofmulti-level numerical and experimental studies that are developed for reliable while the fast representation of a
WEC device. The methodology can be easily tailored and adapted for different phases of analysis and design ofany type of hybrid concept or single WEC devices. The proposed modelling methodology is hybrid multi-level
experimental numerical simulations and is developed based on lessons learned and the expected challenges in
representing a device. The proposed methodology has the advantage of easily being adapted for the fast-paced
industry environment. The case study WEC device is also a new concept inspired by nature and in its first levelsof concept validation. This concept is expected to operate efficiently even in areas with less energetic waves.
The primary shape of the moving part of the device is inspired by nature to overcome resistance forces andincrease the penetration and motion in water. The shape is also further improved considering manufacturing
possibilities and the required symmetry for the device operation in the real sea. The corresponding numericalresults are also presented along with a novel systematic modeling methodology to show the efficiency of themethodology in the development process of WEC.
Key words : WEC design and development, Numerical simulation, Experimental tests, Hydrodynamic
optimization, Multi-level hybrid methodology

1. Introduction
There is a lot of untapped energy in waves that could contribute to the overall energy picture; however, wave energy
converters are still at initial development phases [1] and the process to refine new technologies is ongoing. One of theimportant challenges in the way of commercialization is finding the optimum design for a specific device in a particularsite e.g. [2]. Among different concepts introduced in recent years, wave-activated bodies are recognized with higherhydrodynamic power efficiency in comparison to other WEC types [3].
This paper deals with the development of a novel concept of WEC devices by using a new multi-level hybrid
methodology. The WEC concept is inspired by nature to increase the penetration of the oscillatory part and decrease theresistant forces [4]. Drag and viscous effects could reduce the available power [5]; therefore, it is expected that bydecreasing the drag effect, the power performance is enhanced. For the primary shape and dimension ratio of theoscillating body, the dimensions of taxidermy specimen swordfish are used. Swordfish is known as a specimen that isgone through several evolutionary processes to be drag efficient [6], further explanation regarding the concept
development is provided in Section 2.
Received date: 2021.11.30
Email of corresponding author: S.Saeidtehrani@tudelft.nl

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Saghy Saeidtehrani

A new methodology comprising multi-level theoretical, experimental, and numerical is proposed for WEC analyses
and design (see Section 3). The concept of this methodology is to overcome the difficulty in simulating the whole hydroservo-elastic-geo interaction of any kind of WEC device. In this methodology, the required level of sophistication will
be used based on the engineering judgment, and whenever possible the most simple while fairly accurate models areused.
The wave-structure interaction is one of the important aspects of WEC device. Some parameters representing theinteraction are difficult or impossible to be estimated by an analytical formula such as darg effects. It also applies to othersources of damping [7] such as mechanical damping. For this study, the results of the previous studies for hinge base
WECs as non-dimensional mechanical damping are used [8]. The drag and the fluid flow around the body are also
investigated by using multi-level Micro modeling.
The model is gradually developed with different levels of complexity to provide a thorough understanding of thefluid flow and the simplifications that can be applied without missing important effects. By reaching enough accuracy in
2D model, an optimization algorithm is combined with Navier- stokes equation to study and optimize the streamlined
body. The most advanced model is used to prove that the drag can be negligible in the simulation. Since then, a Macromodel is developed to consider the general behavior of the structure to incoming waves and with the presence of PTO.
The Macro model for the fluid-structure interaction consists of the partial differential equation for simulating fluid andordinary differential equation for the ideal dynamic representation of the WEC floating body. The optimized mass, centerof rotation, and PTO coefficients are found by Macro modeling. The study will be continued based on the developed
methodology for further development of the Sword WEC.

2. Concept development
The oscillating body of the WEC is inspired by one of the fastest animals in the sea, swordfish, with recognized dragefficiency adaptation during the evolutionary processes. Indeed, the goal was to develop an oscillatory shape with rapid
penetration and drag resistancy. Studying the shape of the taxidermy specimen swordfish [10] and regenerating the shapefor practical usage is shown in Fig. 1.

Fig. 1 Concept development

As previously mentioned the oscillatory part will be used for OWEC device application. The absorbing energy
mechanism and how it could be installed on different types of support structures are shown in Fig. 2. The oscillatory
body is supposed to be partially submerged and will slam into the free surface interface during the oscillations and rotation
around the hinge. The oscillatory part and the rod can be mounted on various types of support structures appropriate forthe candidate site. As can be expected for each candidate site, the required tuning of the shape and dynamic characteristics
should be conducted. The focus is to develop a small size WEC due to its benefits for future series-manufactured plants
and development costs [9].

Development of a novel multi-level hybrid methodology for a new concept ofWave Energy Converter (WEC)

67

Fig. 2 Absorbing energy mechanism and support structures

3. Multi-level hybrid methodology
Multi-level Micro-and Macro-modelling composed of experimental and numerical simulation is used to respond to
the need for a representation of the whole device for different phases of analyses and design. While Micro-modelingconsiders all possible details to accurately represent the physical phenomena, Macro model simulates a general
representation and mainly uses the simplified governing equations. Consequently, the unknowns are decreased and theinterpretation of the results can be conducted with less computational and time effort. Although it cannot precisely
represent the local behaviour, it can be used for global analyses or in combination with Micro-modeling and experimental
tests. Fig. 3 shows the flowchart of analyses and the correlation between Macro- and Micro- modelling for different
phases from the primary assessment to various stages of analyses and design procedure.

Fig. 3 Flowchart of hybrid theoretical, experimental, and numerical analyses

Here, the developed methodology is used for the first phases of the concept development and tuning the device
characterization for the specific site of operation. However, as previously mentioned, the proposed methodology can beused for various stages of analyses and design. For example, it would be possible to use mathematical models to represent
some behaviors that are difficult to be captured by mapping sensors. Thus, instead of a complicated numerical model orfully sensored experimental tests, a more simplified while informative Macro model can be used. This model not only
can receive data from the experimental tests but can also be used in connection with various kinds of tests such as

68Saghy Saeidtehrani

accelerated testing of the components. Stated differently as is also shown in Fig.
tests have a bidirectional connection.

3, the Macro model and experimental

3.1 Theoretical study
Theoretical studies can significantly help to make a clear picture of the required tests and numerical simulations
needed to be conducted for a better understanding of the device's behavior. The primary idea was to study the applicationof this WEC for the Iranian sea and to be more accurate for the south of the Caspian Sea, near Ramsar [10] which isreported as one of the highest energy resources[11]. For the feasibility study and tuning of the WEC for the site, anaverage 15 years wave period of 4.40 s and a height of 0.51 m as reported in [11] has been chosen. For calculating fluids'
dynamic viscosity, an average annual air temperature (20O C) above the Caspian Sea in Iranian borders [12,13] has been
considered. Consequently, the corresponding fluid’s dynamic viscosity can be assumed 10−3 𝑁𝑁𝑁𝑁⁄𝑚𝑚2 [14]. The velocityof the wave for this site is not going beyond 2.5 𝑚𝑚⁄𝑠𝑠. The Reynolds number is calculated for the proposed shape and it
will be around 2 × 105 for the maximum velocity equal to 2.5 𝑚𝑚⁄𝑠𝑠. Reynolds number provides a better understandingof fluid behavior. This number suggests that the flow around the device would enter the turbulent behavior which means
shaping bubbles, growing in size, and finally bursting[15]. However, it should also be considered that the calculated
Reynolds came from an equation of 𝜌𝜌𝜌𝜌𝜌𝜌⁄𝜇𝜇; ρ is the fluid density; 𝑣𝑣 is the velocity; 𝑙𝑙 is the characteristic length (in thiscase, the distance from the leading edge); and 𝜇𝜇 is the fluid’s dynamic viscosity. As can be seen in this equation, only
the characteristic length of the shape is coming into account. Therefore, the prediction for fluid flow can be useful but
needs further studies and examination.

Fig. 4 Wave-body interaction parameters

Fig. 4 summarizes the wave-body interaction parameters calculated from the theoretical formula. 𝐾𝐾𝐾𝐾 show the
scattered waves and spreading of the energy in other directions of the incoming wave by the presence of the body [16].
As it can be seen this parameter is less than one. As parameter 𝑑𝑑⁄𝐿𝐿 suggested the shallow water condition is governed
the wave propagation which means that the wave characteristics are related to the depth [17]. As the device operation isconsidered nearshore, the possibility of wave breaking and dissipating of energy should also be considered [18].
As is shown in Fig. 4, the ratio of wave height to wavelength passes the maximum ratio suggested by Micheequation [17]. On the other hand, this ratio is still less than the criteria by Longuet-Higgins and Fenton, one of the accurate
values for breaking wave index [18].
The theoretical studies provide us with a better understanding of the wave-structure interaction. According to thispreliminary study, a sophisticated model of wave-body interaction seems necessary to provide a deeper knowledge offlow regimes and the spreading of energy around. From the theoretical studies, it would be possible to anticipate therequired level of sophistication for the simulation. The first level of numerical analyses will represent the Micro-modelingof fluid around flow and is used for shape optimization.

3.2 Numerical analyses- Micromodeling
The part related to wave-structure interaction is an essential part in defining the WEC behavior and needs to beinvestigated thoroughly. Due to the uncertainties involved in the wave-structure interaction, several experimental andnumerical simulations need to be conducted to verify the hypothesis. CFD simulation can play an important role andprovide a picture of the fluid flow passing the device. For this part of the analysis, Navier- stokes equations for describing
the fluid flows by the conservation of mass, momentum, and energy are used [18–20]:
(1)
(2)

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Development of a novel multi-level hybrid methodology for a new concept ofWave Energy Converter (WEC)(3)
In these equations, ρ is the density [𝑘𝑘𝑘𝑘⁄m3]; u is the velocity vector [m⁄𝑠𝑠]; p is pressure [𝑃𝑃𝑃𝑃]; τ is the viscousstress tensor [𝑃𝑃𝑃𝑃]; F is the volume force vector [𝑁𝑁⁄𝑚𝑚3]; Cp is the specific heat capacity at constant pressure [𝐽𝐽⁄𝑘𝑘𝑘𝑘. 𝐾𝐾];
T is the absolute temperature [𝐾𝐾]; q is the heat flux vector [𝑊𝑊⁄𝑚𝑚2]; Q contains the heat sources [𝑊𝑊⁄𝑚𝑚3]; S is thestrain-rate tensor:(4)

For practical engineering usage, these equations can be further simplified as the Reynolds-averaged Navier-Stokes(RANS) equation:(5)
Then two-equation models of 𝑘𝑘 − 𝜀𝜀 (Turbulent kinetic energy k- Turbulent dissipation rate 𝜀𝜀) for the calculationof the drag forces are used [21,22]. By using the Multi-level modeling, analyses are started from 2D simulation and arefurther progressed to 3D. Multi-level modeling provides the opportunity to step by step increase the complexity of the
problem and figure out which parameters are important to be studied in detail. Moreover, in the process of developing a
numerical model that is very sensitive to various factors such as time-stepping algorithm, mesh, and the solver selection;
the 2D can help to find out the optimized setup of the model to tackle a 3D representation. Besides, for this specific
WEC that its expected rotation is aligned with the wave direction, 2D model can be effectively used for the shape
optimization in wave direction.
Consequently, a hybrid optimization algorithm and CFD solver are used for the shape optimization of the oscillatory
part of the WEC. Fig. 5 shows the general dimensions and the points selected for the shape optimization. Flow aroundthe shape and drag forces calculated for each generated shape are also shown in this figure.
Since it is not clear if the tail of the sword can also help for the drag adapting of the shape, the effect of the tail andits length are also studied. However, these studies show that the shape without a tail can provide a more streamlined
body [23]. Formation of bubbles and hollow voids around the tail (could be observed in Fig. 5) b. ) suggests thepresence of resistance forces against the device movement.

Fig. 5 2D hybrid optimization and CFD simulation; a) general dimension and selected points for the optimization; b and c)
fluid flow around the generated shapes from the optimization; d) Exemplary calculated drag forces for generated shapes

Finding a better understanding of the fluid flow around the shape in 2D, leads to a better set-up for 3D simulation
which confirms the findings of 2D. The generated optimized shape can provide a smooth transition of flow around it.
By finding the optimized shape, it would be possible to go further in the operation of the device and its power
performance. The next level is using the Macro-modeling for the calculation of power and its dynamic behavior.
It can be said that only experimental simulation could be used for determining the drag forces on an object [24],however by using a more accurate numerical model, it is possible to virtually simulate the wave-body interaction. By
developing an optimized and streamlined body it can be safely assumed that the drag force can be neglected andeliminated from the Macro model.

70

Saghy SaeidtehraniFig. 6. Fluid flow around the generated shape from the optimization;

3.3 Numerical analyses- Macro modeling
The goal of this part is to find an accurate while fast representation of the device to estimate its power performanceand it mainly deals with the tuning of the device's dynamic characteristics and PTO coefficients. For this reason, adynamic model of WEC is coupled with potential theory representing the fluid flow around the device. Therefore, thefluid-structure interaction is simplified from the Navier-stokes but still is time-dependent and can catch the change that
happens in each time-step in fluid and the corresponding rotation of the device. As previously mentioned the model isalso simplified in terms of darg forces; as was found that the shape of the body provides a smooth transition of flow by
the Micro modeling.
The pitch motion of the oscillatory part can be modeled by one degree of freedom:(6)
This equation mainly combines the ordinary differential equation (the dynamic representation of the device) withthe solution of the partial differential equation representing the fluid flow. A numerical model with a fluid domain
simulating the part of the selected site is combined with the dynamic equation. Further information regarding thedevelopment of this equation can be found in [8,25–28].
𝐼𝐼𝐼𝐼𝐼 and 𝐾𝐾𝐻𝐻𝜃𝜃 are used to simulate the inertia and hydrostatic moments, the constants of 𝐼𝐼 and 𝐾𝐾𝐻𝐻 are analyticallycalculated [25]. 𝐾𝐾𝑃𝑃 and 𝐶𝐶𝑃𝑃 are representing PTO stiffness and damping paramters. The remaining part to complete thedynamic equation of the device is the damping term. Damping is difficult to be analytichly represented, and shuld be
experimentally estimated. Here, since the device is rotating around a hinge, it can be safely assumed that the main lossof energy would be mechanical damping which is symbolized by 𝐶𝐶𝐹𝐹 in Eq. 6. The nondimensional damping coefficientfrom the previous experimental tests on hinge-connected WEC is used for this model [8,10,27,28].
As was previously explained, the operation site is considered in the south of the Caspian Sea, near Ramsar. Therefore,
the dynamic characteristics of the device are tuned for an average 15 years wave period of 4.40 s and a height of 0.51 m.
For tuning the dynamic characteristics of the device the scale, mass, and the centre of rotation and their effects on the
moment of inertia and hydrostatic stiffness and consequently on the natural period of the device are studied. Like anyother part of the analysis and design procedure, tuning is an iterative process. It should be noted that tunning is theiterative procedure, and due to the interaction of different parts, all parameters should be in balance to make a device act
as was anticipated for the maximum harnessing of the wave energy.
Four different masses (Mass 1 to Mass 4) corresponding with densities equal to 200, 300, 400, 500 𝑘𝑘𝑘𝑘⁄𝑚𝑚3andcoordinate of the centre of rotation as a coefficient of the device height (HD) are used for the simulation. For each mass,Development of a novel multi-level hybrid methodology for a new concept ofWave Energy Converter (WEC)71

different locations for the hinge connection (centre of rotation) are considered. For each set, inertia and hydrostatic
coefficients are calculated; an exemplary graph showing the change in these coefficients for Mass 1 is presented in Fig.
7. Evidently, with the increment of centre of rotation, both inertia and hydrostatic stiffness are growing. Although thedimensions of these coefficients are different, they are presented in the same graph, to emphasize the growth rate of eachwith the place of centre of rotation.

Fig. 7 Inertia and hydrostatic coefficients

The natural period (T) is calculated for each mass and centre of rotation. The classic formula T = 2π√m⁄𝑘𝑘 [29] isused which can be re-symbolized for the current study as 2π√I⁄KH. Apart from the analytical estimation of the inertia
and hydrostatic stiffness, and consequently the natural period; numerical simulations have also been conducted for each
set of mass and centre of rotation to understand the effect of these parameters on the amplitude of rotation.
Studying time-series responses of a dynamic device like this WEC and concluding about the behavior is not astraightforward procedure. As can be seen, by changing the centre of rotation and mass, the dynamic characteristics arealtered. Although, these changes can be in direction of making resonance in the system; increasing the stiffness is notalways in our favor and can limit the device motion. Therefore, the results should be studied in terms of not only theperiod of the structure but also the amplitude of the response to the incoming waves.

Fig. 8 Micro-modleing numerical results: a) Constant depth for different mass; b) Constant mass with various depth

Form the first set of tuning, the primary scale, mass, and centre of rotation are determined. The next step is
optimizing the hydrodynamic performance by adding the PTO model to the system. It should be emphasized that thepresence of PTO could also change the dynamic characteristics and consequently the response and power. Although thepresence of damping would increase the natural period; the stiffness decreases it. Both stiffness and damping could

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Saghy Saeidtehrani

restrain the amplitude. Therefore the hydrodynamic optimization is an iterative procedure that should include theeffective parameters (see Fig. 3).
For the optimization of PTO coefficients, some parameter bounds should be defined. First of all, it is expected thatthe device oscillates as an underdamped system [30]; therefore, the maximum implied damping should not extend thecritical damping [10,27].Two parameters of 𝜉𝜉 = 𝐶𝐶𝑃𝑃⁄𝐶𝐶𝑐𝑐𝑐𝑐 and 𝜅𝜅 = 𝐾𝐾𝑃𝑃⁄𝐾𝐾𝐻𝐻 are introduced which connect the PTO
damping and stiffness to the critical damping and hydrostatic stiffness, respectively. It is generally accepted that byincreasing the complexity of a problem, the interpretation of the results become difficult. Therefore, for each parameter,a separate parametric study have been conducted. Fig. 9 shows the variation of natural period of the device due to thechange in the Mass, centre of rotation, and PTO stiffness.
CWR presented in this graph is the ratio of the absorbed power (watt) to the available power (watt⁄𝑚𝑚) multipliedby the active width (𝑚𝑚), 𝐶𝐶𝐶𝐶𝐶𝐶 = 𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎 ⁄(𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 ∗ 𝑃𝑃𝑤𝑤) [31,32]. As can be seen, tunning a WEC device should bedone from a multistate point of view. As was explained Mass and COR can significantly change the dynamic
characteristics which in turn could change the natural period of the device and the amplitude of rotation. On the other
hand, the implied energy to the system by PTO can also alter dynamic characteristics. In different control schemes, bychanging the implied PTO force, which here is simulated by damping and stiffness terms, the device is set to respond inresonance. On the contrary, these parameters can reduce the amplitude of oscillation. Therefore, it is essential to consider
the effects of various parameters separately and then study their effects in the big picture. This method helps to exactly
figure out and study the trend of a device's behavior under the change of one parameter.

Fig.

9 Parametric study of PTO stiffness, mass, and center of rotation.

From these analyses, a primary set of Mass, COR, PTO stiffness, and damping were found, and then another set ofanalyses for optimizing the PTO coefficients have been conducted. The goal is to decrease the implemented energy andincrease the hydrodynamic efficiency; accordingly, the design goal is to tune the device that it needs minimum stiffness
to apply and produce the maximum power. The findings confirm that for the selected site, the combination of Mass 3 andCOR around 2HD can tune the device to make resonance with the average wave characteristics and the tunned systemdoes not need any implemented energy in terms of PTO stiffness. While for the non-tunned system in terms of mass andcentre of rotation, 40 % of hydrostatic stiffness should be applied to reach almost the same CWR. These findings show
the importance of tuning the dynamic characteristics of a device for a specific site of operation.

4. Conclusion
The hydro-servo-elastic-geo interaction of any kind of WEC device made the simulation complicated and timeconsuming, which in turn makes the engineering judgment and providing a reasonable solution to improve the behavior
difficult and with lots of uncertainty.
Through this paper, a novel methodology comprised of theoretical, experimental, and numerical studies for theDevelopment of a novel multi-level hybrid methodology for a new concept ofWave Energy Converter (WEC)73

analyses and design of WECs is proposed. The methodology is further described by implying it to a novel WEC device
in its early stage of development. However, the methodology itself can be used for any stage of analysis and design. The
goal of this method is to speed up the process of understanding the device behavior with multi-level modeling techniques.
It allows to be tailored based on the information required to be obtained. The results confirm that the methodology
is successful in improving the drag resistancy of the device with advanced Micro modeling and improving its
hydrodynamic efficiency with Macro-modeling. It was shown that the tuned system doesn't need to imply the PTO
stiffness, while untuned system needs almost 40% of the hydrostatic stiffness to reach the same efficiency. The proposed
methodology will be used for the future development of this WEC with the combination of more advanced experimental
tests.

5. References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]

Bhattacharyya R, McCormick ME. Chapter 11 - Conclusions and Future Prospects. In: Bhattacharyya R,
McCormick MEBT-EOES, editors. Wave Energy Convers., vol. 6, Elsevier; 2003, p. 133–4.
https://doi.org/https://doi.org/10.1016/S1571-9952(03)80062-4.
Czech B, Bauer P. Wave energy converter concepts : Design challenges and classification. IEEE Ind Electron
Mag 2012;6:4–16. https://doi.org/10.1109/MIE.2012.2193290.
Aderinto T, Li H. Review on power performance and efficiency of wave energy converters. Energies 2019;12:1–
24. https://doi.org/10.3390/en12224329.
Saeidtehrani S. A new type of wave energy converter by inspiration from nature. Natl. offshore ideation event,2019.
Todalshaug JH. Hydrodynamics of WECs - Handbook of Ocean Wave Energy. In: Pecher A, Kofoed JP, editors.,
Cham: Springer International Publishing; 2017, p. 139–58. https://doi.org/10.1007/978-3-319-39889-1_6.
Sagong W, Jeon WP, Choi H. Hydrodynamic characteristics of the sailfish (Istiophorus platypterus) and swordfish(Xiphias
gladius)ingliding
posturesattheircruisespeeds.
PLoS
One
2013;8.
https://doi.org/10.1371/journal.pone.0081323.
Adhikari S. Damping Models for Structural Vibration. 2000.
Saeidtehrani S. Physical and numerical modeling of a wave energy converter (PhD Thesis). Roma Tre University,
2016.
Bhattacharyya R, McCormick ME. Chapter 3 - Wave Energy Conversion Systems. In: Bhattacharyya R,
McCormick MEBT-EOES, editors. Wave Energy Convers., vol. 6, Elsevier; 2003, p. 27–35.
https://doi.org/https://doi.org/10.1016/S1571-9952(03)80054-5.
Saeidtehrani S. Study on hydrodynamic characteristics and efficiency of a prototype wave energy converter. In:
Greaves {D}.{M}., editor. Proc. Fourteenth Eur. Wave Tidal Energy Conf., 2021, p. 2065_1--2065_ 8.
Alamian R, Shafaghat R, Hosseini SS, Zainali A. Wave energy potential along the southern coast of the CaspianSea. Int J Mar Energy 2017;19:221–34. https://doi.org/10.1016/j.ijome.2017.08.002.
Molavi-Arabshahi M, Arpe K, Leroy SAG. Precipitation and temperature of the southwest Caspian Sea region
during the last 55 years: Their trends and teleconnections with large-scale atmospheric phenomena. Int J Climatol
2016;36:2156–72. https://doi.org/10.1002/joc.4483.
Climate information 2020;210:10–2. http://www.caspinfo.net/.
Julien PY. River Mechanics. Cambridge University Press; 2018.
Schewe G. Reynolds-number effects in flow around more-or-less bluff bodies. J Wind Eng Ind Aerodyn
2001;89:1267–89. https://doi.org/10.1016/S0167-6105(01)00158-1.
Dean RG, Dalrymple RA. Water wave mechanics for engineers and scientists. 1984.
https://doi.org/10.1029/eo066i024p00490-06.
Sorensen RM. Basic coastal engineering: Third edition. 2006. https://doi.org/10.1007/b101261.
Svendsen IA. Introduction to Nearshore Hydrodynamics. vol. 24. World Scientific; 2006.
Pope SB, Eccles PJ, Pope SB, Press CU. Turbulent Flows. Cambridge University Press; 2000.
Multiphysics C. CFD Module User ’s Guide. COMSOL Multiphysics 2016:598.
Zaïdi H, Fohanno S, Taïar R, Polidori G. Turbulence model choice for the calculation of drag forces when using
the CFD method. J Biomech 2010;43:405–11. https://doi.org/10.1016/j.jbiomech.2009.10.010.
Frei W. Which Turbulence Model Should I Choose for my CFD Application? COMSOL Blog 2013:1–8.
Saeidtehrani S. Development of a novel oscillating wave energy converter: CFD optimization and power
performance. Unpublished 2021.
Durst F. Fluid Mechanics: An Introduction to the Theory of Fluid Flows. Springer Berlin Heidelberg; 2008.
Mei C, Stiassnie M, Yue D. Theory and applications of ocean surface waves. Part I: Linear aspects. World

74

[26]
[27]
[28]
[29]
[30]
[31]
[32]

Saghy Saeidtehrani

Scientific; 2005.
E. Renzi, A. Abdolali GB, Dias F. Mathematical modelling of the oscillating wave surge converter. XXXIII
Convegno Naz. di Idraul. e Costr. Idraul., 2012.
Saeidtehrani S, Karimirad M. Multipurpose breakwater: Hydrodynamic analysis of flap-type wave energy
converter
array
integrated
toabreakwater.
Ocean
Eng
2021;235:109426.
https://doi.org/https://doi.org/10.1016/j.oceaneng.2021.109426.
Saeidtehrani S. Flap-type wave energy converter arrays: nonlinear dynamic analysis. Ocean Eng 2021;236.
Clough RW, Penzien J. Dynamics of Structures. McGraw−Hill; n.d.
Clough RW, Penzien J. Dynamics of Structures. McGraw-Hill; 1993.
Pecher A, Kofoed JP. Introduction. In: Pecher A, Kofoed JP, editors. Handb. Ocean Wave Energy, Cham: Springer
International Publishing; 2017, p. 1–15. https://doi.org/10.1007/978-3-319-39889-1_1.
Babarit A. A database of capture width ratio of wave energy converters. Renew Energy 2015;80:610–28.
https://doi.org/10.1016/j.renene.2015.02.049.