Design, optimization and numerical modelling of a novel floating pendulum wave energy converter with tide adaptation

A novel floating pendulum wave energy converter (WEC) with the ability of tide adaptation is designed and presented in this paper. Aiming to a high efficiency, the buoy’s hydrodynamic shape is optimized by enumeration and comparison. Furthermore, in order to keep the buoy’s well-designed leading edge always facing the incoming wave straightly, a novel transmission mechanism is then adopted, which is called the tidal adaptation mechanism in this paper. Time domain numerical models of a floating pendulum WEC with or without tide adaptation mechanism are built to compare their performance on various water levels. When comparing these two WECs in terms of their average output based on the linear passive control strategy, the output power of WEC with the tide adaptation mechanism is much steadier with the change of the water level and always larger than that without the tide adaptation mechanism.


Introduction
Ocean wave energy is regarded as one of the most promising sustainable sources. Its practical worldwide potential is projected to be 93-100 trillion kilowatt hours per year (Arman and Yuksel, 2013). The World Energy Council estimates that about 10% of the worldwide electricity demand could be met by harvesting ocean energy (World Energy Council, 1993). With global attention now being drawn to climate change and greenhouse effect, wave energy exploitation is becoming an increasing concern. A considerable number of large-scale exploitations of wave energy have been deployed until now. Devices like Pelamis, Archimedes Wave Swing (AWS) have already started to deliver offshore wave power to a national electricity grid (Henderson, 2006;Valério et al., 2008). Although problems like high cost and low efficiency still exist, wave energy is believed to be more competitive with the technology development and market promotion.
According to the deployment location, WECs can be classified into three types: shoreline devices, near-shore devices and offshore devices (Drew et al., 2009). Shoreline devices, by contrast, have the advantage of being close to the utility network, and easy to maintain. However, waves will be attenuated as they run and break in shallow water. Tidal range also has effect on efficiency of shoreline devices. A typical example of shoreline device is the Limpet oscillating water column (OWC) device. It is installed on the island of Islay, Scotland, and produces power for the national grid (Boake et al., 2002). The device consists of a chamber with an opening to the sea below the water line. With the variation of the water level, air passes in and out the chamber that drives a turbine to generate electricity. Theoretically, the mass of water inside the chamber determines the water column resonance, which can be coupled to the predominant period of the incoming waves. Thus, the water level changes caused by tides may influence its efficiency dramatically.
Another typical shoreline device is SDE wave power device, a shoreline device of the floating type, developed by S.D.E. Ltd in Israel. The incoming wave drives the floating buoy to rotate around the axis that is fixed on the shore. The device takes advantages of both kinetic and potential energy of wave, the upper bound of its efficiency is theoretically higher (Clément et al., 2002). However, it also suffers the tidal range problem. As the water level changes, the gesture of the floating buoy will change as well, leading to an efficiency decline, as shown in Fig. 1. Until now, they have not given out a good solution. This type of WEC is now being further developed by Eco Wave Power (EWP) and several power plants have been deployed.
There are examples of shoreline devices that take account of the water level changes. Wavestar extracts energy by directly converting the waves into an oscillating mechanical motion by using a float with a smaller extension than the average wave length (Gaspar et al., 2016;Hansen and Kramer, 2011;Zurkinden et al., 2014). In their design, the base can move up and down along a set of piers to follow the tide. Another example is the Drakoo wave energy device, developed by Hann-Ocean Energy in Singapore. This modularized shoreline device transforms waves into a continuous water flow that drives a hydro turbine generator. The contact section between Drakoo and the dock is designed as an unsmooth rubbery rail. Only the net buoyancy change could push it to move up and down. Thus, it achieved the tide adaptation easily without imposing a burden under normal working condition. This paper introduces an innovative floating pendulum WEC with the consideration of tidal range. Firstly, the buoy's hydrodynamic shape is optimized in order to achieve a higher wave energy absorbing efficiency. Secondly, in order to keep this buoy always working under its optimum working condition no matter what the water level is, a unique rotating mechanism is designed, which is the socalled tide adaptation mechanism. Furthermore, the numerical models are built, aiming to evaluate the design effects. The remainder of this paper is then organized as follows: Section 2 gives the description of the novel WEC. Section 3 introduces the optimization process of the buoy's hydrodynamic shape. Both the novel WEC and ordinary floating pendulum WEC are analyzed numerically in Section 4 in order to contrast effects taken by the tide adaptation mechanism. The results of simulation and comparison are exhibited and discussed in Section 5.

Design concepts
As shown in Fig. 2, the novel WEC includes four main parts: a floating buoy, a base fixed on the seabed, a hydraulic cylinder and a unique rotating device. The rotating mechanism device consists of a connecting rod, a chain and two chain wheels that are exactly the same but fixed on different components, namely, the buoy and the base. Both ends of the connecting rod are hinged by rotating shafts so that no other components are rigidly connected to it. Under the constraints of the chain, two chain wheels always rotate at the same angle, which means that two chain wheels are always in the same phase. As one of them is fixed on the base, no rotating will occur, and then the other chain wheel could only translate along the circumference that is mapped out by the rotating connecting rod. Therefore, the buoy where the chain wheel is fixed can always keep its well-designed leading edge facing the incoming wave without being affected by the water level.
The base of the novel WEC could be specially constructed, but an existing dock or jetty can also be adopted. In principle, the pivot point should be placed in the middle part of the base's tidal region. The reasons are as follows: (1) The tangential component of the wave force will be improved if the floating pendulum oscillates approximately at the same level with the pivot point.
(2) It can work normally when the water level is above or beneath the pivot point. The ability to adapt the tidal range can be enhanced.
(3) When storm comes, the buoy can be pulled out of the water or can be pushed to be submerged into the water, which plays the protective function.
Hydraulic systems are pervasive in all sorts of WEC systems because of the ability to convert the oscillating mo-  YANG Jing et al. China Ocean Eng., 2017, Vol. 31, No. 5, P. 578-588 579 tion to a relatively stable output. Waves apply large forces at slow speeds and hydraulic systems are suited to absorbing energy under this regime. Moreover, it is a simple matter to achieve short-term energy storage, necessary to achieve the smooth electricity production required for a marketable machine, with the use of cheap and available high-pressure gas accumulators (Henderson, 2006). For the novel WEC, the hydraulic system is always the best choice. However, in this paper, in order to simplify the modeling, the power-take-off (PTO) is replaced by a damping, which is believed to make no considerable difference on contrasting outputs of WECs with or without the tide adaptation mechanism.

Optimization of the buoy's hydrodynamic shape
Hydrodynamic characteristics are one of the crucial factors that affect novel WEC's energy conversion efficiency. Even a little change, for example introducing a rounded corner, will result in completely different hydrodynamic quality (Taylor et al., 2016;Zhang et al., 2015). For the floating buoy adopted in this paper, the outline can be divided into three parts: leading edge, trailing edge and upper edge. Since the upper edge has no contact with the water, it can be designed to be flat or, taking into account aesthetics, fan-shaped. The trailing edge plays a secondary role on deciding the buoy's hydrodynamic performance. The incoming wave has already been attenuated after it goes through the leading edge. Therefore, we just design the trailing edge nearly orthogonal to the connecting rod in order to reduce the energy loss by radiation during the buoy's oscillation. The leading edge has a dominant influence on the buoy's hydrodynamic performance. In this paper, the exhaustion method is adopted. By using a computational fluid dynamics (CFD) software and comparing each one's oscillating performance, it becomes possible to optimize the leading shape. However, it should be noticed that such an optimization strategy is not optimal but rather sub-optimal.
Firstly, five basic shapes are sketched and shown in Fig. 3. All of these five basic buoys are designed with the same rotational inertia and fluid-solid contact area in undisturbed water, which gives them the same hydrostatic stiffness. Thus, without considering the incoming wave, there is no other factor that effects the buoy's hydrodynamic performance but the shape. The following job is to establish models of these five buoys and run a time-domain simulation in the CFD software-FLOW3D that is a RANSE (Reynolds Averaged Navier Stokes Equations) solver. The adopted improved volume of fluid technique (truVOF) has great convenience for tracking and locating the free surface of fluid, meanwhile, the FAVOR TM technique that is based on the concept of the area fraction and volume fraction of the rectangular structured mesh is very helpful for the meshing of a rigid body (Flow Science Inc., 2008). In addition, settings of the wave maker are very considerate. This software has long been widely applied to the interaction between wave and floating bodies (Bhinder et al., 2015).
As FLOW3D is a time-domain CFD solver, selecting proper input wave parameters is an important precondition for gaining helpful simulation results. It is important to specify here that the optimization of the buoy's shape is not for academic purpose only, and in the future, the designed novel WEC is desired to be built and run on Zhoushan, China. Thus, a typical wave condition ( ) in Zhoushan is chosen as a set of input wave parameters (Wang et al., 2011;Zhang et al., 2009). In consideration of the wave's effects on the buoy's hydrodynamic performance, other two wave conditions ( ) are also added into the simulation. It should be pointed out that the wave tank depth is set as 10 m in order to match the shoreline water depth, and no PTO mechanism is introduced in these simulations. The user defined input parameters are presented in Table 1. The buoy's mass is set to be distributed evenly. One constraint is added to ensure that only the rotation around the pivot point will occur.
Before the simulation, getting a good mesh profile has an important effect on increasing the calculation accuracy. On the other side, excessive small girds will spend much more calculation time. For the mesh in this example, grids in focus area are subdivided (see Fig. 4a), which increase   Fig. 4b), are obtained after simulations. As the rotational angle is proportional to the maximum potential energy that the floating buoy can harness under wave's driving, it is finally selected to evaluate buoys' hydrodynamic performance. The comparison results of all five kinds of buoys under three wave conditions are presented in Fig. 5. The figure of Type C seems to have the biggest rotational angle under three typical wave conditions, which means that the leading edge should be designed outward-inclined.
However, whether the slope should be designed flat or uneven is still unknown. Thus, further optimizations are still needed to further refine the slanted plane. In this step, the slope is divided into two parts (Theoretically, dividing into more parts will bring better optimization quality. However, on the other hand, it will sacrifice more simulation time. Dividing into two parts is a trade off between simulation efficiency and optimization quality). Different points are chosen as the turning point of the curved surface: the midpoint or the lower quarter point (as shown in Fig. 6). Curve on one side is designed to be tangential to the curve on the other side. Under these preconditions, two styles are avail-able: convex first and then cuppy (S-shaped) or cuppy first and then convex (Reverse S-shaped). Our analysis indicates that the sharp corner in the bottom of the S-shape buoy will lead to significant vortex shedding, which will affect the energy conversion efficiency dramatically. Thus, we finally choose the reverse S-shape as the basis of our further optimization. Depend on different turning points and tangency angles, six types of buoys are exhibited in Fig. 6. Three types in the first column take the midpoint as the turning point of two curves, while other three take the lower quarter point as the turning point. Each row in this figure has the same tangency angle, varying from 45° to 75°. T 1 = 3 s, H 1 = 0.8 m; T 2 = 5 s, H 2 = 0.8 m; T 3 = 7 s, H 3 = 0.8 m Three sets of wave parameters ( ) are adopted in the simulations in this link. The comparison results are shown in Fig. 7. It can be seen that when the incoming wave period is small, Type 5 has the largest rotational angle, while Type 3 has the largest rotational angle as the wave period increases. In conclusion, if the wave period in the testing site is smaller than 4.3 s, the buoy of Type 3 has better performance, while if the wave period is larger than 4.3 s, the buoy of Type 5 has better performance. Until now, the    YANG Jing et al. China Ocean Eng., 2017, Vol. 31, No. 5, P. 578-588 581 design of the leading edge has been finished, and as a result, two best curves (Type 5 for high frequency waves, while Type 3 for small frequency waves) are recommended after comparisons. As the testing site of our wave tank could only make wave with periods smaller than 5 s, Type 3 is finally chosen as the basis of our design. The vertical face in front of the buoy is covered with an arc to streamline the leading edge. Our ultimate shape that fits small periodic wave is exhibited in Fig. 8, in which the part painted light green is Type 5 in Fig. 6 and the light blue part is the newly introduced arc.

Modelling
As the novel floating pendulum WEC has a special rotating mechanism (as introduced in Section 2), its mathematical analysis is greatly different from classic floating WEC. In this section, the novel WEC will be analyzed in detail. In order to achieve a more precise simulation, several crucial parameters are going to be further discussed before establishing the MATLAB/Simulink model. In the last subsection, ordinary floating pendulum WEC will be analyzed to help building the reference model.

Coordinate system
The global coordinate of the model and the local coordinate are the coordinates for the oscillating buoy. For each WEC, there exists: where and represent the vectors in different coordinate systems (the upper-left corner mark represents the coordinate system); and are the rotation and translation transformation matrix, respectively. For the novel WEC, only translational motion occurs (as shown in Fig. 9). Therefore, the transformation matrixes can be expressed as: 4.2 Dynamic analysis Analysis in this section aims to build a time domain simulation model of the novel WEC. Considering the displacement and velocity of the buoy under irregular waves may lead to results that are close to the actual working condition. However, it also made the model much more complicated. In this paper, a simulation model under regular wave is sufficient to certify the WEC's tidal adaptability. For a regular wave, the water surface elevation can be illustrated as: where H is the wave height; ω is the wave frequency; λ is the wavelength, and there exists: , in which k is the wave number and it satisfies ; is the initial phase difference.
The wave power can be described as: where T is the wave period, ρ is the water density, and g is the acceleration of gravity.
In order to evaluate the WEC's performance, the term efficiency has been displaced by the capture width, which is a parameter defined as the width of the wave front that contains the same amount of power as that absorbed by the WEC (Price et al., 2009) is the absorbed power by the WEC. The main distinctive feature in the novel WEC that can keep the leading edge of the buoy facing the incoming wave all the time is its special rotating mechanism. There is only translation occurs in the floating buoy's oscillating process. Based on the dynamics of the rigid body when the transport motion is translational, the sum of moments on O B has to be zero to ensure that no rotation will occur. Therefore, we have the first equation of the motion: is the excitation moment applied by the incoming wave; is the radiated moment acting on the wetted face of the buoy; is the hydrostatic moment; is the  is the reacting moment of the PTO; is the moment applied by the chain. The added B in the subscript means that they are moments relative to O B .
Then, the floating buoy can be considered as a mass point on the global coordinate system. Based on Newton's second law, we have the second equation of the motion: where J A is the rotational inertia about the pivot point O A , there exists in which m is the mass of the buoy; is the moment applied by the chain acting on O A . Other characters have the same meaning as in Eq. (7). The added A in the subscript means that they are the moments applied on O A .
The PTO system here is modeled as a linear damper. Hence, it can be demonstrated as: where c PTO is the damping coefficient. Then, the absorbed power by WEC can be obtained easily:

Non-linear hydrostatic moment
It is widely acknowledged that the upward buoyant force that is exerted on a body immersed in the fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and it acts in the upward direction at the center of mass of the displaced fluid based on Archimedes' principle. For an irregularly shaped buoy, like the one shown in Fig. 8, nonlinearity of the geometry and the ever-changing moment arm will lead to a highly nonlinear input-output relation. The hydrostatic moment is obtained by integral over the wetted surface S: where p b is the hydrostatic pressure acting on element dS; vector s gives the position of dS, where its unit normal vector is n; Vector p is the normal unit vector of the swinging arm. The hydrostatic pressure p b can be expressed as: where z is the depth of the surrounding water.
Based on Eq. (11) to Eq. (13), we obtained the relationship between the rotational angle and the hydrostatic moments, just as shown in Fig. 11. Point A in the upper curve indicates that when the buoy is completely submerged and the connecting rod is horizontal, the hydrostatic moment reaches the maximum value. After that, although the buoyancy force acting on the buoy holds steady, begins to decrease as the force arm changes. After the abscissa of the buoyant center become positive (Point B in Fig. 11), sees an increase on the positive direction.

B M bB
As the buoyant center and the buoy's pivot do not coincide in this buoy, the hydrostatic moment tends to increase with the rotating angle (as shown in the lower curve in Fig. 11). At Point C, part of the left side of O B begins to be submerged into the water. And at Point D, all parts have been completely submerged.
Judge from the results of the analysis, simplify the hydrostatic moment as proportional to the rotational angle, like the frequency domain simulation models have done, it will lead to a large calculation error (Gomes et al., 2015). However, a time domain can analyze non-linear force or moments accurately.

Wave and float interaction
The hydrodynamic moment acting on the buoy can be computed from the velocity potential ϕ based on the potential flow theory. If the body is fixed, no radiated wave is generated, and then we have the excitation moment M e in such a case. Excitation moments M e on the element dS in terms of different rotation centers are given respectively as: (14)  YANG Jing et al. China Ocean Eng., 2017, Vol. 31, No. 5, P. 578-588 where p e is the excitation pressure applied on element dS. The excitation pressure p e is calculated as: where is the velocity potential of the incident wave (Falnes, 2002).
where k is the wave number; A is the real-time wave height; z is the depth of the surrounding water and h is the depth of the wave tank. Another case is that when the body is oscillating in the absence of an incident wave, the forces and moments acting on the body which are due to the radiated wave caused by the body's oscillation are called the radiation force (moment). It is also labelled with a subscript of lowercase r. Based on the linear potential theory the radiation force (moment) is represented as a function of the added mass and radiation damping both are 6×6 matrices for a general three dimensional analysis. In order to reduce the difficulty in simulation, just like the analysis of similar structures-Wavestar and M4 wave energy devices do, a simpler approach is adopted: the buoy responds in a vertical plane (Hansen and Kramer, 2011;Taylor et al., 2016). In regular waves, the radiation force in the vertical direction can be expressed as: where the parameter a 33 is referred as the added mass and b 33 is the radiation damping coefficient of heave. They are related to reactive energy transport in the near-field region of the oscillating buoy. For the special buoy geometry here, these two parameters can be obtained by WAMIT, a package that is based on the BEM (boundary element method) and have been widely used for WEC's analysis (Babarit et al., 2012;Li and Yu, 2012). For the special buoy shown in Fig. 8 the parameters obtained by WAMIT are shown in Fig. 12. The optimal strategy to get a precise value of the radiation moment is to integrate over the wetted surface based on the hydrodynamic pressure acted on the buoy. However, this method is so inconvenient that may bring many troubles only with slight calculation accuracy improvement. A compromised method is to figure out an equivalent force arm that can obtain the radiation moment by multiplying the radiation force in Eq. (15). As the submerged geometry of the float here is not axisymmetric about a vertical axis, the equivalent point of application of the radiation moment on the buoy is chosen as the center of the gravity of the immersed part of the buoy. Then, the radiation moments based on two turning points O B and O A can be expressed as: l GA l GB where is the distance between the center of the gravity of the immersed part of the buoy and O A , while is the distance between the center of the gravity of the immersed part of the buoy and O B .

Representation of drag coefficient
Generally, the viscous damping effect that follows the drag term in Morison's equation (Morison et al., 1950) can be expressed as: where C D is the drag coefficient, whose value depends on the body geometry, the Reynolds number and the Keulegan-Carpenter number (Li and Yu, 2012); A c is the characteristic area; u is the velocity of the water particle while u b is the velocity of the buoy. Both these two velocities can be decomposed into the horizontal and vertical components: where x is the horizontal ordinate of the water particle. The horizontal and vertical components can be easily calculated based on the buoy's angular velocity and its shape function. Overall drag moment can be obtained by an integral over the wetted surface: where l′ is the distance between the element dS and the pivot point. The rotational angle of the novel WEC with various drag coefficients are plotted in Fig. 13. It is consistent well with a recent research carried out by Babarit (2012). They changed the drag coefficients from one quarter to twice their nominal values, and finally found that the uncertainty associated with drag effects can be negligible when the heaving buoy is fixed on a platform. In this paper, we adopted a drag coefficient suggested by Flow3D. However, an effective drag coefficient dependent on wave height and possibly period is needed for calibration by conducting additional wave tank tests (Stansby et al., 2015;Yeung et al., 1998).

Modelling of an ordinary floating pendulum WEC
Owing to the ordinary motion mechanism, all elements of the ordinary floating WEC rotate around the turning point O A , which makes it much easier to build the numerical model of ordinary floating WEC. Although, the coordinate system in classic floating WEC (just as shown in Fig. 14) is much different from the novel WEC, the coordinate transformation formula Eq. (1) also works here. However, matrixes and should take diverse values: where p b is the hydrostatic pressure acting on element dS; vector n is the normal unit vector of dS; vector q is the position vector of element dS against O A .
In addition, Eq. (10) still works here. Therefore, the hydrostatic moment can be figured out, just as shown in Fig. 16. Before the buoy is completely submerged, the absolute value of the hydrostatic moment increases non-linearly because of the buoy's special profile. Then it begins to decrease as the force arm changes. Until the abscissa of the buoyant center becomes positive, begins to increase on the positive direction. What has to be explained is that Fig. 16 only presents the hydrostatic moment change when the deployment depth h 0 is 0, 0.2 and -0.2 m. If the deployment depth is changed to other values, the absolute values and turning points may change as well. However, the variation trends will not change significantly.

Time-domain simulations
Dynamic simulation models of both two WECs have been built in MATLAB/Simulink in order to compare these two WECs, which can also guide the later wave tank experiment. Key parameters in simulations are exhibited in Table 2. The length a and height d of the buoy are shown in Fig. 8, while the width b is the thickness of the buoy in Fig. 8. These simulations aim to investigate how the output would change with the water levels. Therefore, various sets of displacement depths are adopted to present the water level change, while the water depth is set as a constant in order to ensure the wave force to be held steady in different water levels.
A basic control strategy called classic linear passive control strategy is adopted in the numerical models. The damping coefficient of the PTO is constant during operation process. For a damping PTO, the power of output can be computed based on Eq. (10). Therefore, for each displacement depth, various PTO reacting moments may lead to different output power and efficiencies. The PTO mechanism should be optimized firstly to guarantee the satisfied damping coefficient c PTO (shown in Eq. (10)) is adopted when there is no advanced control strategy involved.
As shown in Fig. 17, the figure of the average output of novel WEC increases steadily in the beginning, and the highest value appears when the damping coefficient c PTO =1500, after that it begins to decrease. It means that when the damping coefficient is not large enough, the kinetic energy cannot be absorbed completely, but once it is set too large, the rotational angle will be effected dramatically, which will lead to a relatively lower power output. The damping coefficient corresponding to the pole can be considered as the optimal damping coefficient (ODC) at a certain deployment depth.
In Fig. 18a various deployment depths are adopted. The bar chart shows the ODC for each deployment depth while the line chart compares the average output with ODC under a wave condition with T=5 s, H=0.5 m. The deployment depth is the distance between O A and still water level. When it is positive, it means O A is under water, and vice versa. The figure shows that the average output of ordinary floating pendulum WEC varies from 191 W to 244 W, fluctuat-ing as much as 27.7%. The output reaches its peak when the deployment depth is -0.5 m and the damping coefficient is 1500. Correspondingly, simulation results of the novel WEC are exhibited in Fig. 18b. In the deployment depth ranging from -0.5 m to 0.2 m, the average output with ODC varies from 238 W to 255 W, fluctuating only 7.1%. The figure reaches the peak output when the deployment depth is 0.1 m and the damping coefficient is 1300.
Comparison results of these two WECs in terms of different wave conditions are presented in Fig. 19. It is clear that by adopting tidal adaptation mechanism, the ability to adapt varying water levels has been enhanced largely. It   seems that the difference made by tidal adaptation mechanism will be larger as if the wave frequency is getting closer to the buoy's natural frequency which is estimated to be 0.625 Hz. It is interesting that when compared with the ordinary floating WEC, the novel WEC always has a higher efficiency at all deployment depths. One possible reason for this is that the buoy's gesture is holding horizontal all the time even in the wave range. The chain drive system might be another cause. When the pivot in the buoy is located in the front part, M chain figured out from Eq. (7) will have positive contribution to the buoy's rotational acceleration. However, it is just an inference now, evidences that we obtained from simulation results are still not enough to prove this hypothesis. If it is confirmed by additional model or experiments this would clearly be beneficial. Some of our wave conditions are not linear enough due to their large wave height and wavelength ratio. Adopting linear wave theory will lead to larger calculation errors. Zurkinden et al. (2014) have compared the simulation results of linear numerical model and non-linear numerical model with experimental results under similar wave conditions. The results indicate that the advantage of non-linear wave theory (Stokes, higher order) over linear wave theory in calculation accuracy is not significant. Thus, it is reasonable to consider that the calculation errors taking by adopting linear wave theory are acceptable here.

Conclusions
In this paper, we have introduced our novel floating pendulum WEC, comprising the base and the buoy connected by the chain drive system. The aim is to keep the welldesigned incoming edge facing the income wave straightly in various water levels, which is believed to be helpful for improving energy conversion efficiency, regardless of tidal range. In order to guarantee the tidal adaptation mechanism works meaningfully, the buoy's hydrodynamic shape should be optimized firstly. This has been achieved through a CFD software-Flow3D, by enumerating several kinds of typical profiles and comparing their hydrodynamic performances. After a two-stage optimization, suggested results are shown in terms of wave conditions. In order to compare the novel WEC with traditional floating pendulum WEC, numerical models of both devices are built respectively. There are approximations inherent in the analysis, and uncertainties regarding the effects of viscosity on the responses of the buoy. The torque induced by vortex-shedding at body edges is also ignored in this paper. However, when the PTO is taken into consideration, the impacts induced by these uncertainties are found to be negligible.
A basic control strategy, called classic linear passive control is adopted to design the PTO. An optimal damping coefficient is set as an invariant during the operation process. After several sets of simulation, we finally clarify the relationship between the wave devices' outputs and the water levels. The comparisons of the results of modelling for two devices in regular seas lead to the following findings: (1) The scaled wave device designed with tidal adaptation mechanism has a steady output, with a fluctuation of only 10%, when the displacement depth ranges from -0.5 m to 0.2 m. It means that it has the ability to adapt a tidal range of 0.7 m. On the contrary, the output of the wave device without tidal adaptation ability changes with water levels in a wide range.
(2) The wave device designed with tidal adaptation mechanism has a larger output than the one without tidal adaptation mechanism in the tidal range of -0.5 m to 0.2 m. It indicates that either the chain link system or the straight forward leading edge contributes positively to the device's energy conversion efficiency.
The study to date has suggested two kinds of buoy shapes for floating pendulum WEC, and has verified the feasibility of tidal adaptation mechanism in regular waves. A wave device of third to fourth the model's size can work functionally near most coastlines in China. Further investigation would be required to compare the output in irregular waves and find an advanced control strategy to further improve the floating pendulum WEC's energy conversion efficiency.