Interaction of Hydrodynamic Forces in Wave Energy
Converter
Kotaro MORI*, and Yasutaka IMAI***Faculty of Science and Engineering, Saga University
1 Honjo, Saga 840-8502, Japan
E-mail: 21728017@edu.cc.saga-u.ac.jp**Institute of Ocean Energy, Saga University
1 Honjo, Saga 840-8502, Japan

Abstract
As one of the power generation methods using wave energy, the movable-type wave power generator has been
attracting attention around the world and has been the subject of various studies. (Karayaka et al., 2020, Vincent S et al.,2014, M. Lawson et al., 2015). This device generates electricity by converting the vertical motion of waves into rotationalmotion using a power converter inside the device. This wave power generator can be classified into two types according
to the shape of the movable body and the way it is subjected to waves: the translational type and the flexural type. The
translational type is the subject of this research, in which the part of the movable body in contact with the sea surface iscircular and can receive waves from any direction in 360°. There are various methods for converting wave energy, suchas hydraulic, gyro, and direct drive systems using linear generators. Movable animal-type wave energy generators havebecome the mainstream of equipment installed offshore. In this study, we investigate the energy conversion of theseanimal-driven wave power generators using numerical simulations. The device is roughly divided into three parts: a float,a spar, and a rocker. The effects of the presence or absence of the damping plate on the hydrodynamic coefficients ofadded mass, wave damping, and wave forcing, and the hydrodynamic coefficients when the float and spar are combinedare obtained, and the hydrodynamic interference of the device is clarified.
Keywords : Power buoy, Reference Model 3 (RM3), Translational-motion type, Wave damping, Coefficient ofhydrodynamic force, Wave Point Absorber

1. Introduction
In recent years, global temperatures have been gradually increasing due to global warming, which has begun to affectclimate and sea surface temperatures. In the seas around Japan, sea surface temperatures have risen by about 0.7 to 1.6
degrees Celsius. As a result, fish that were originally caught in certain areas have moved to other areas, making fishingdifficult. The occurrence of red tides has also had a significant impact on the fishing industry. Red tides caused by toxic
plankton can kill fish and shellfish. However, it is not possible to obtain this information without actually visiting the sea
area. In recent years, the aging of the fishing industry and the shortage of labor have placed a heavy burden on fishermen,
and the cost of fuel has also become a problem. Therefore, we thought that the use of IoT technology to remotely monitor
images and water temperature in the field would reduce the burden on fishermen by eliminating the need to go all theway to the field. To achieve this, an independent power source to generate electricity for IoT use offshore is necessary.
Therefore, we decided to use a small, movable wave power generator as an independent power source. In order to improvethe efficiency of the device, we investigate the fluid force interference that affects the motion by numerical simulation.

2. Research method
2.1 Device model
Figure 1 shows the shape, dimensions, and mass of the initial model of the wave power buoy developed in this study.
The buoy consists of three parts: a doughnut-shaped float in the center, a longitudinal cylindrical spar, and a damping
plate at the bottom of the spar. The moment of inertia of each is shown in Table 1.

Table 1 Inertia moment
Part6kg

Fig.1 Model shapes and dimensions

Spar
Damping plate
Float top surface
Float side
Float bottom
Total

Ix (Roll)

Iy (Pitch)

Iy (Yaw)

22[kg ∙ m2 ]0.06180.37240.362
0.36870.12242.9244[kg ∙ m ][kg ∙ m ]0.4656
0.34750.3374
0.32020.18783.26890.4656
0.34750.33738
0.320220.18777
3.2667

2.2 Numeric calculation
The equation of motion for linear motion of an object moving in a regular wave is expressed by Eq.1. The equationof motion for rotational motion is expressed by Eq.2.
𝑀𝑥̈ + 𝑁𝑥̇ + 𝐶𝑥 = 𝐹(1)𝐼𝜃̈ + 𝑁𝜃̇ + 𝐶𝜃 = 𝑀(2)Assuming that the displacement of the floating body is 𝑥𝑗 (j=1,...,6) from Equations (1) and (2), The equation ofmotion of a floating body in regular waves can be expressed as Eq.3.
∑6𝑗=1 [(𝑀𝑖𝑗 + 𝑚𝑖𝑗 (𝜔)) 𝑥̈𝑗 (𝑡) + 𝑁𝑖𝑗 (𝜔) ∙ 𝑥̇𝑗 (𝑡) + 𝐶𝑖𝑗 (𝜔)𝑥𝑗 (𝑡)] = 𝐹𝜔𝑖 ∙ 𝑒 𝑖𝜔𝑡(3)where 𝜔: wave frequency, 𝑀𝑖𝑗 : mass of floating body, 𝑚𝑖𝑗 (𝜔): added mass, 𝑥: displacement of floating body, 𝑥̇ :velocity, 𝑥̈ : acceleration, 𝑁𝑖𝑗 (𝜔): wave-making attenuation coefficient, 𝐾: restoring force, 𝐹𝜔𝑖 : wave-forcing force.
From Equation (3), the added mass 𝑚𝑖𝑗 (𝜔) and the wave damping 𝐶𝑖𝑗 (𝜔) are obtained by the Nemoh software. The
obtained hydrodynamic force coefficients are non-dimensionalized as in (4), (5) and (6).
𝑚̅ 𝑖𝑗 =
̅ =𝐶𝑖𝑗𝑚𝑖𝑗(4)𝜌𝐿𝑘𝐶𝑖𝑗(5)𝜌𝐿𝑘 𝜔𝐹𝐹̅𝜔𝑖 = 𝜔𝑖𝑘(6)𝜌𝐿 𝑔where 𝜌 : density of water, L: device length, 𝑔 : gravitational acceleration. Also, 𝑘 =3 for 𝑖, 𝑗 =1,2,3, 𝑘 =4 for
𝑖=1,2,3, 𝑗=4,5,6 or 𝑖=4,5,6, 𝑗=1,2,3 and 𝑘=5 for 𝑖, 𝑗=4,5,6.

3. Calculation Results
Figure 2 shows the effects of the plate on the added mass 𝑚𝑖𝑗 (𝜔), the wave damping 𝐶𝑖𝑗 (𝜔), and the wave forcing
𝐹𝜔𝑖 , with and without the plate. The effects on the added mass 𝑚𝑖𝑗 (𝜔), the wave damping 𝐶𝑖𝑗 (𝜔), and the exciting force𝐹𝜔𝑖 are shown in Figure 3, comparing the case with a single float, the case with a float and a spar, and the case with afloat, a spar, and a damping plate.

𝐹̅𝜔3𝐶̅̅ 33
𝑚Change in coefficient of hydrodynamic force with and without damping plate

𝐹̅𝜔3

̅
𝐶33

̅ 33
𝑚

Fig. 2

Fig. 3

Variation of hydrodynamic force coefficients in floats and spars

4. Conclusion
From Figure 2, it was found that the effect of the plate on the hydrodynamic force is larger when the rocker isattached, thus proving the effectiveness of the plate. Figure 3 shows that the interference of hydrodynamic forces between
the float and the spar is clearly observed.
We have clarified the hydrodynamic interaction of the wave energy converter with a movable body in this study, wewould like to obtain the motion of the device under various conditions and investigate the shape of the device to increase
the energy conversion.

References
Karayaka, H. Bora, Yi-Hsiang Yu, Nathan Tom, and Eduard Muljadi.: Investigating the Impact of Power-Take-Off System
Parameters and Control Law on a Rotational Wave Energy Converter's Peak-To-Average Power Ratio Reduction(2020).
Vincent S. Neary, Mirko Previsic, Richard A. Jepsen1, Michael J. Lawson, Yi-Hsiang Yu, Andrea E. Copping, Arnold A.
Fontaine, Kathleen C. Hallett, Dianne K. Murray: Methodology for Design and Economic Analysis of Marine Energy
Conversion (MEC) Technologies(2014), pp.137-178.
Y.-H. Yu, M. Lawson, and Y. Li, M. Previsic and J. Epler, J. Lou: Experimental Wave Tank Test for Reference Model 3
Floating-Point Absorber Wave Energy Converter Project(2015).