# An Experimental Study of a Bottom-Hinged Wave Energy Converter with a Reflection Wall in Regular Waves—Focusing on Behavioral Characteristics

^{1}

^{2}

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## Abstract

**:**

_{e}of the flap were investigated, focusing on wave steepness, initial water depth, and distance from the reflection wall. The results show that the condition of the initial water depth being smaller than the flap height is more effective in terms of avoiding unstable rotating of the flap. The maximum k

_{e}appeared slightly far from the node position of the standing waves because the flap shape and the power take-off (PTO) damping induce the phase difference between the reciprocating behavior of the flap and the period of the standing wave. The results imply that the optimum position of a WEC is dependent on WEC shape, PTO damping, and installation water depth.

## 1. Introduction

_{2}emissions have presently reached an all-time high. According to the World Energy Outlook (WEO) 2019 report published by the International Energy Agency (IEA [1]) on 13 November 2019, if countries around the world maintain their current energy policies, the energy demand is expected to increase by 1.3% each year until 2040. To meet the need for reducing CO

_{2}emissions and energy services, it is necessary to accelerate investments in cleaner and more efficient energy technologies (consider issues such as climate change and fossil fuel depletion). The US Energy Information Administration (EIA) has predicted that by 2050, renewable energy will account for approximately 28% of the total global energy consumption, and approximately 49% of the total electricity production [2]. In particular, it has been announced that wind power generation is expected to account for 20% of the power generation capacity by 2021, and solar power generation is expected to grow significantly, accounting for more than 43% of the power generation capacity by 2050.

^{2}respectively, whereas that of wave energy is 2–3 kW/m

^{2}[3]. Additionally, wave energy has a wide range of applications as a renewable energy resource. It is known that the total amount of theoretical wave energy that can be generated is approximately 3.7 TW [4]. In Japan particularly, which is surrounded by seas, an average of 36 GW of electric power can be obtained from wave energy [5]; 36 GW is a value that accounts for approximately 12% of Japan’s total power generation capacity, based on the 2016 standard. When the annual residential electricity use per capita is 7480 kWh [6], the value of 36 GW amounts to 4800 times as much. In the case of wind and solar power generation equipment, it is possible to generate electricity only for approximately 20–30% of the time in a day, whereas wave energy converters (WECs) have almost no time restrictions, and can generate electricity for up to 90% of the time in a day [7]. Therefore, at night when the electricity consumption is low, it is possible to store the generated power and use secondary energy resources that can be stored and transported in combination with a hydrogen production device. Approximately 37% of the world’s population lives within 90 km of a coast. As a result, mutual understanding of resource supply and demand is possible, enabling the installation of WECs in multiple locations [3]. From an environmental point of view, the negative impact of the wave energy recovery device on the environment is the lowest, thereby generating low environmental load [8].

^{2}) are obtainable in comparison with other types of WECs [26].

## 2. Materials and Methods

#### 2.1. Experimental Description

_{in}(0.02 m interval), 5 wave periods T (0.4 s interval), 5 initial water depths h (= 0.0475 m, ± 0.035 m, ± 0.05 m), and 2 different distances D (= 1.09 m, 1.45 m) from the reflection wall. Some cases (22 cases) showing unstable wave generating were excluded in this study owing to the limitations of wave generators. The installed position of the flap D was changed to examine the effects of the distance from the reflected wall on the characteristics of the flap behavior and power generation performance. In particular, this study focused on the effects of the node and anti-node positions at which maximum and minimum wave energy capturing performances were expected. Therefore, unidirectional regular waves were generated to form idealized standing waves in front of a reflected wall. D was set for including the node (D/L = 0.25) and anti-node (D/L = 0.5) positions of standing waves. D/L indicates the distance from the reflection wall D and the wavelength L ratio. For D = 1.09 m, D/L ranged from 0.1667 to 0.4463, and for D = 1.45 m, D/L ranged from 0.2217 to 0.5937. It is noted that D/L was confined in this study by varying wave periods and still water depths under the condition of the fixed flap position. Different water depths and wave heights were adopted to investigate the influences of still water depth and wave steepness on flap behaviors.

_{in}is the voltage converted to DC by the rectifier, and V

_{out}is the voltage measured by the data logger.

_{in}, one resistor of 15 kΩ and five resistors of 1 kΩ (total resistance of 20 kΩ) were connected in series on the breadboard. C is a condenser. V

_{in}was calculated using Equation (1) as follows:

_{x}of the flap was measured. The experiments were composed of two parts: investigating the natural oscillation period of the flap, and determining the power generation efficiency, depending on the hydraulic conditions. In the former experiment, a time series of the rotation angles of the flap was measured when the flap was tilted in one direction in still water and then released. The experiments were conducted six times each on both sides (12 times in total).

#### 2.2. Reflection Coefficient

_{r}was calculated according to the method proposed by Lin and Huang [44] based on four wave gages (W2–W5 in Figure 1) installed on the offshore side of the flap in Figure 1. Lin and Huang [44] extended the method of Mansard and Funke [45] to separate the free and bound waves of the incident and reflected waves based on four or more water level fluctuation data under the regular wave conditions. Lin and Huang’s method separates the first and nth harmonics of the free and bound waves of the incident and reflected waves using each water level fluctuation datum. Then, the reflection coefficient k

_{r}was calculated by Equation (2), based on each amplitude of the separated incident and reflected waves.

_{r}, only when the decomposed incident wave height is within ± 0.02 m of the targeted input wave height, are discussed in this paper.

#### 2.3. Estimation of Power Generation Efficiency

_{out}measured from the voltage divider circuit was converted to V

_{in}, as depicted in Figure 5, and the converted voltage is regarded as the output voltage obtained from the rotary generator (BLDC motor). The generated power P

_{wec_on}(shore direction) and P

_{wec_off}(offshore direction) were calculated from the relationship, P

_{wec_on/off}= V

_{in}/R

^{2}, using the resistance R (=V

_{0}/(I

_{satll}–I

_{idle})) based on the motor specifications, as presented in Table 3.

_{wec_both}was determined by the summation of P

_{wec_on}and P

_{wec_off}. As P

_{wec_both}changed with time owing to periodic wave motions, the average value P

_{WEC}for one wave period was calculated using Equation (3). The averaged value for each wave period was calculated for 15 wave periods of 100 s after the wave generation, and then the upper and lower 20% of P

_{WEC}were excluded to minimize the effects of temporal fluctuations. Consequently, P

_{WEC}was obtained by averaging the remaining six averaged values.

_{wave}was calculated by Equation (4) through applying the linear wave theory.

_{i}is the incident wave height, B

_{w}is the distance between the triangular faces of the flap, T is the incident wave period, L is the wavelength, and h is the water depth.

_{e}was calculated using Equation (5) by dividing P

_{wec}by P

_{wave}.

## 3. Results and Discussions

#### 3.1. Natural Frequency of the Flap

_{x}was negative (0° in the still water state). The natural frequency was calculated using the θ

_{x}data (up to 2 s after the release) within a range that was not affected by the turbulence around the flap after it returned to its original position. From the figure, it is clear that the natural period T

_{f}for the flap to return to its original position is 2 s (0.5 Hz), regardless of the initial tilted angle (≈35–55°). The flap hardly shook after returning to its original position.

#### 3.2. Behavioral Characteristics of the Flap

_{x}of the flap, and the brown and light blue dotted lines denote the output voltages of V

_{on}and V

_{off}.

- Pattern A (stable, 108 cases): the flap rotated stably with incident waves.
- Pattern B (fluctuation, 66 cases): the flap behavior changed with time.
- Pattern C (unstable, 40 cases): the behavior of the flap changed randomly during the experiment.
- Pattern D (loss, 65 cases): the flap did not return to its original position after moving several times so that the flap lost its restoring force and remained stationary in the water.
- Pattern E (P
_{WEC}= 0, 49 cases): the flap did not move during experiments.

_{on}and V

_{off}increased and decreased with the rotational direction of θ

_{x}. V

_{off}becomes maximum when θ

_{x}is maximum, whereas V

_{on}becomes maximum when θ

_{x}is minimum.

_{x}in pattern B fluctuates owing to the long period component contained in the main period component (see Figure 7b). The long period fluctuation in pattern B is a particular phenomenon induced by the closed experimental region in which an undoubtedly long period, such as resonance, occurs. This pattern can be generated by the interactions of the incident waves, the reflected waves from the reflecting wall, and the extra waves generated by the behavior of the flap. Pattern B also includes the cases in which the rotation angle θ

_{x}gradually increases or decreases over time. In pattern C, the rotation of the flap becomes irregular over time, as depicted in Figure 7c, and in some cases, the rotation of the flap is halted for a while. In pattern D, as depicted in Figure 7d, the flap does not rotate after it has tilted into the water and remains stationary. In pattern E, the pendulum does not rotate from the beginning. As a result, the output voltages V

_{on}and V

_{off}were 0 for the whole experimental time, as depicted in Figure 7e. Hereafter, patterns A and B are valid, and patterns C, D, and E are invalid, in terms of generating electricity.

_{i}/L, initial water depth h, and wave energy power P

_{wave}on the behavioral characteristics of the flap were investigated. Figure 8a,b depicts the tendency of the behavior of the flap depending on D/L and H

_{i}/L, and D/L and P

_{wave}, respectively. The results in Figure 8 include all experimental cases of different initial water depth. H

_{i}/L was calculated from the generated wave height H

_{i}and the wavelength L of the linear wave theory for respective experimental conditions. As depicted in Figure 8a, H

_{i}/L for patterns D and E increased linearly when D/L increased, and the rapid increase of H

_{i}/L was confirmed in the range of 0.4 < D/L < 0.5. In particular, pattern D was predominant at D/L ≈ 0.55. Additionally, as depicted in Figure 8b, in the designed WEC system, a P

_{wave}> 11 W is required in the range of D/L < 0.4, and a P

_{wave}of 16 W is required in the range of 0.4 < D/L < 0.45 for comfortably generating electricity. In the range of 0.58 < D/L, electricity can be produced at P

_{wave}> 4 W. From Figure 8, it is suggested that the flap installation position should avoid the range of 0.45 < D/L < 0.58. On the other hand, pattern C was observed randomly near the boundaries of patterns A and B and patterns D and E and in the area of A and B. H

_{i}/L and P

_{wave}for pattern C are similar to or larger than those of patterns D and E; thus, the tendency of pattern C occurring is considered to be affected by other factors rather than H

_{i}/L and P

_{wave}, such as the initial water depth.

_{f}. Figure 9 depicts the patterns of the flap depending on h/h

_{f}and P

_{wave}. The results in the range of 0.45 < D/L < 0.58, in which the invalid pattern was dominant, were excluded in Figure 9 because the effect of D/L on the flap behavior was dominant rather than h. From Figure 9a, which depicts patterns C, D, and E, the behavior of the flap tends to become an invalid pattern despite a relatively large P

_{wave}in the water depth equal to and greater than the height of the flap (h/h

_{f}≥ 1). In particular, the P

_{wave}to become pattern E at h/h

_{f}≥ 1 is larger than the P

_{wave}at h/h

_{f}< 1. Similarly, it is confirmed in Figure 9b, which depicts patterns A and B, that more wave power is required to generate electricity normally at h/h

_{f}≥ 1. Focusing on pattern C at h/h

_{f}< 1, even with a P

_{wave}that is smaller than pattern E, pattern C can be observed at h/h

_{f}= 0.89 and 0.93 where the initial water depth is less than the height of the flap. For example, P

_{wave}= 1.74 W for h = 0.93 (D/L = 0.5870 in Figure 8b) and P

_{wave}= 4.67 W for h = 0.89 (D/L = 0.4328 in Figure 8b). Though pattern C is the invalid pattern as well, the flap is rotated irregularly for pattern C, differently from patterns D and E, which are halted without motion. Therefore, this implies that if the initial water depth is smaller than the height of the flap (h/h

_{f}< 1), the flap can easily rotate even with a relatively small P

_{wave}.

_{wave}> 10 W, which coexisted with patterns A and B, as shown in Figure 8b and Figure 9b; the relevant results can be found at h/h

_{f}≥ 1 in Figure 9a. This implies that the possibility of the behavior of a flap being unstable increases given the condition of h/h

_{f}≥ 1 for relatively small P

_{wave}. These tendencies suggest that it is more effective to install the flap in the condition of h/h

_{f}< 1 in terms of avoiding the invalid pattern.

_{r}from the flap. The results of patterns B and C were excluded because the reflection coefficients of patterns B and C have variability depending on the reference time. From the figure, it can be confirmed that k

_{r}increases as D/L approaches 0.5, whereas k

_{r}decreases rapidly when D/L > 0.5. The differences in k

_{r}at the same position (e.g., D/L ≈ 0.22 for pattern A or D/L ≈ 0.56 for pattern D) are the effect of H

_{i}/L; there is a tendency that k

_{r}increases as H

_{i}/L increases.

#### 3.3. Power Generation Characteristics

_{e}and D/L, and k

_{e}and H

_{i}/L depending on T/T

_{f}and h/h

_{f}, respectively. T/T

_{f}denotes the ratio of the wave period T and the natural period of the flap T

_{f}, and h/h

_{f}is the ratio of the initial water depth h and the flap height h

_{f}.

_{e}(=0.77) was obtained at D/L ≈ 0.32, which was the case for T/T

_{f}= 0.9 and 1.1 close to the natural period of the flap. However, confirming the results for T/T

_{f}= 0.9 and 1.1 at D/L ≈ 0.25 and 0.43, k

_{e}exhibited a low value (k

_{e}< 0.20) in comparison with other results. Therefore, it is considered that k

_{e}is affected more by the installation position than by the natural period of the flap. Focusing on the relationship between D/L and k

_{e}, it is theoretically well known that the maximum k

_{e}is obtained at the position of the node of the standing wave formed by the reflecting wall (D/L = 0.25), when the flap is extremely thin and the behavior of the flap does not affect the standing waves [39]. In contrast, the flap adopted in this experiment was the shape of an inverted triangular prism with a wide upper part, thereby overtopping or overflowing on the top of the flap occurs when incident waves propagate over the flap. This phenomenon leads to the loss of incident wave energy, and a slight phase delay is likely to occur in the rotation of the flap when the wave force acting on the flap is not enough to rotate owing to the energy loss; i.e., the flap rotates later than the propagation of the waves. Hence, a phase discrepancy can occur between the motion of the flap and the standing waves. Furthermore, not only the shape of the flap but also the damping of the PTO system contributes to the phase discrepancy. As a result, the position where the motion of the flap was maximized by synchronizing the direction of rotation of the flap and the motion direction of the water particles in the standing waves was considered to be D/L ≈ 0.32 in this study. The phase difference between the rotation of the flap and the standing wave is dependent on the ratio of the initial water depth and the flap height h/h

_{f}, as depicted in Figure 14b. For example, the maximum k

_{e}appears at the position of D/L ≈ 0.32, at the same (h/h

_{f}= 1.0) or lower water depths (h/h

_{f}= 0.89) as the flap height, and at the position of D/L ≈ 0.22 at a greater water depth (h/h

_{f}= 1.07, 1.11) than the flap height. Focusing on the relationship between k

_{e}and H

_{i}/L depicted in Figure 15, it can be confirmed that k

_{e}increases with H

_{i}/L. However, k

_{e}is small at H

_{i}/L ≥ 0.04, as D/L is close to 0.5. The results indicate that k

_{e}is more dependent on the installation position of the flap than the wave steepness. Moreover, as depicted in Figure 8a, the tendency that the behavior of the flap becomes unstable as H

_{i}/L becomes larger is considered to be an influential factor.

#### 3.4. Reflection Characteristics

_{i}/L and k

_{r}(in front of the flap) for patterns E and A. For pattern E, k

_{r}increases as h/h

_{f}decreases and H

_{i}/L increases. It is analogous to the general reflection tendency of a vertical wall because the flap does not rotate at all in pattern E. Consequently, the flap becomes the vertical wall in front of the reflection wall. In pattern A, k

_{r}tends to increase as H

_{i}/L increases similar to pattern E.

_{e}and k

_{r}for patterns A. In contrast, it is difficult to determine the correlation between k

_{e}and k

_{r}, as depicted in Figure 17. In general, a large rotation angle of the flap is accompanied by high k

_{e}so that less reflected waves are generated due to a large portion of the incident waves getting captured in the flap in terms of the conservation of wave energy. However, the case of high k

_{e}with low k

_{r}or vice versa is regarded as the flap tending to be tilted to one side, depending on the installation position (e.g., shore side for 0.25 < D/L < 0.5; offshore for 0.5 < D/L). The tilted flap to one side causes a different energy dissipation mechanism of the incident and reflected waves from the reflection wall for rotating the pendulum. As a result, k

_{r}is not proportional to k

_{e}, as depicted in Figure 17. The mechanism of energy dissipation depending on the motion of the flap and the relationship between k

_{e}and k

_{r}should be evaluated in further studies.

#### 3.5. Effects of T/T_{f} and h/h_{f} on P_{WEC}

_{e}= 0.2–0.4, regardless of H

_{i}/L, excluding the case of k

_{e}> 0.5 (surrounded by a red circle in Figure 14) and the case of D/L ≈ 0.43 (surrounded by a blue circle in Figure 14) near the positions of the anti-node of the standing waves. This relationship can be clearly observed in Figure 18, which depicts the relationship between P

_{wave}and P

_{WEC}. Figure 18 indicates that the larger the value of P

_{wave}, the greater the value of P

_{WEC}produced. The linear approximation line (black dotted line in Figure 18), excluding the data surrounded by the red and blue circles, denotes a relationship of y = 0.2935x, which indicates that power can be produced at a ratio of approximately 0.3 to wave power in this system. Focusing on T/T

_{f}in Figure 18a, no particular relationship is observed between T/T

_{f}and P

_{WEC}, which is analogous to the results in Section 3.3, whereas the case for T/T

_{f}= 0.9 except for the results surrounded by blue circles tending to exceed the approximation line. As illustrated in Figure 14a, the results are attributed to the location of the flap, for which T/T

_{f}= 0.9 is mainly in the range of 0.31 < D/L < 0.43, where the maximum k

_{e}appears (D/L ≈ 0.32). On the other hand, focusing on the other cases positioned above the approximation line for T/T

_{f}= 1.1, 1.3, and 1.5, most cases correspond to the cases at h/h

_{f}≤ 1.0 in Figure 18b. The influence of h/h

_{f}on P

_{WEC}, as depicted in Figure 18b, is largely classified by whether the water depth is larger than the flap height (h/h

_{f}> 1.0) or not (h/h

_{f}≤ 1.0). The correlation of P

_{WEC}according to h/h

_{f}increasing or decreasing was not observed, distinctly. Most cases larger than the approximation line in Figure 18b are observed at h/h

_{f}≤ 1.0 in the whole range of P

_{wave}. Focusing on the cases at h/h

_{f}> 1.0, P

_{WEC}is less than the approximation line in the range of P

_{wave}< 20 W, while P

_{WEC}in the range of P

_{wave}> 20 W exceeds the approximation line, occasionally. It implies that the effects of h/h

_{f}on P

_{WEC}become smaller under the relatively large P

_{wave}conditions although the condition of h/h

_{f}> 1.0 tends to become the invalid pattern of the flap and decrease P

_{WEC}in a relatively small P

_{wave}. However, most cases of h/h

_{f}> 1.0 in Figure 18b are confined by the cases of T/T

_{f}= 1.3 and 1.5 in Figure 18a. This was because only pattern A was analyzed for k

_{e}and P

_{WEC}in this study. The results of pattern B, which is a valid pattern to generate electricity normally as well, are not included. To more clearly identify the capability of the power generation under the condition of h/h

_{f}> 1.0, the emergence ratio of each pattern depending on h/h

_{f}and T/T

_{f}was investigated.

_{f}and T/T

_{f}. For instance, “4 (6.1)” in the row of pattern A for the T/T

_{f}= 0.7 column indicates that the number of pattern As that emerged was four under the condition of T/T

_{f}= 0.7 and the percentage of the occurred number (=4) of pattern A over the total number (=66) of experiments for T/T

_{f}= 0.7 was 6.1%. On the other hand, “2 (50.0)” in the row of pattern A for the h/h

_{f}= 0.93 column denotes that two cases among the total number of pattern As emerging under the condition of T/T

_{f}= 0.7 were observed for h/h

_{f}= 0.93, and the percentage is 50%.

_{f}, the proportions of the valid pattern (patterns A and B) that accomplish power generation are 66.0% at T/T

_{f}= 1.5 (0.17 < D/L < 0.24), 58.2% at T/T

_{f}= 1.3 (0.19 < D/L < 0.29), 58.7% at T/T

_{f}= 1.1 (0.24 < D/L < 0.34), 49.2% at T/T

_{f}= 0.9 (0.30 < D/L < 0.43), and 33.4% at T/T

_{f}= 0.7 (0.42 < D/L < 0.59). Excluding the case of T/T

_{f}= 0.7 where the pendulum is located near D/L = 0.5, it can be confirmed that power can be generated in more than half of the cases, regardless of h/h

_{f}and H

_{i}/L for the respective values of T/T

_{f}. Additionally, because the ratio of the number of cases at h/h

_{f}≥ 1.07, where the water depth was greater than that of the flap, to the number of cases for overall patterns A and B, was 29.5% at T/T

_{f}= 1.5, 25.6% at T/T

_{f}= 1.3, 32.4% at T/T

_{f}= 1.1, and 27.3% at T/T

_{f}= 0.9; it is obvious that T/T

_{f}does not have a significant effect on power generation under the condition of h/h

_{f}≥ 1.07. Therefore, when considering pattern B, which is not included in the analysis, it is noticed that power can be generated at all wave periods except T/T

_{f}= 0.7, regardless of the flap installation depth. However, because it is difficult to specify the output power in pattern B as described above, further study is necessary under the condition that the long period component due to multiple reflections is not included. Although the effect of h/h

_{f}on patterns A and B is not significantly noticeable, the ratio of the number of cases at h/h

_{f}≥ 1.0 for the respective values of T/T

_{f}to the total number of cases of patterns C and D is extremely high, i.e., 76.9% at T/T

_{f}= 1.5, 73.7% at T/T

_{f}= 1.3, 70.0% at T/T

_{f}= 1.1, and 73.9% at T/T

_{f}= 0.7. As depicted in Figure 9a, the behavior of the flap tends to be unstable as the water depth increases. Therefore, as depicted in Figure 8b, when the flap is installed at h/h

_{f}≥ 1.0 greater than the flap height, the condition of wave power in the installation area should be considered to avoid instability of the flap. In other words, it is better to avoid a submerged type of flap in the area of relatively low wave energy.

#### 3.6. Behavior Characteristics of the Flap

_{e}≈ 0.3 for pattern A as shown in Figure 18 and the highest k

_{e}appeared at D/L ≈ 0.32. As discussed above, the position of D/L ≈ 0.32 is regarded as the position where the motion of the flap is maximized with a less phase discrepancy between the motion of the flap and the standing waves. In this section, the effects of the behavior characteristics of the flap on k

_{e}are examined.

_{e}at D/L ≈ 0.32. The flap rotates to the right (offshore) at t/T = 1/8 by the reflected waves from the reflection wall, and the flap is tilted to the rightmost side at t/T = 5/8. Then, the flap rotates to the left side (shore side) again by the incident wave from the right side and is tilted to the leftmost side at t/T = 9/8 (=1/8) after t/T = 8/8. It is confirmed that the flap rotates without any delay during one wave period. Other cases of D/L ≈ 0.32 also demonstrate a tendency to rotate smoothly without stay when rotating in the opposite direction after being most inclined.

_{e}. Pattern D in this study is a kind of latching effect, and it becomes a stationary state without any rotating owing to the dominant latching effect at a certain point in time. In the wave energy recovery system used in this study, it is considered that the cycle of the incident, and reflected waves contributing to the flap motion and the cycle of the rotation behavior of the flap including the damping of PTO system, are synchronized at the position of D/L ≈ 0.32. Hence, there is no temporal stationary phenomenon during rotation at D/L ≈ 0.32 and it results in the smooth rotation of the rotary generator in both directions. Therefore, k

_{e}increases at D/L ≈ 0.32. However, in other cases, it was regarded that was is a phase difference up to the force for operating the generator between the behavior of the flap and the waves near the flap so that the flap momentarily stopped. Consequently, the generator was stopped temporally during the latching phenomenon and it leads to decreased k

_{e}.

_{f}and affects the reflection coefficient k

_{r}at the front of the flap. k

_{r}is also influenced by the characteristics of the flap with the wide upper part inducing overflow and overtopping when waves pass above the flap, as depicted in Figure 19 (t/T = 7/8) and Figure 21 (t/T = 5/8). However, as these phenomena and the energy loss induced by the tilted pendulum occur irregularly for each condition, it is considered that there is no clear correlation between k

_{e}and k

_{r}in Figure 17.

## 4. Conclusions

_{i}/L, and distance from the reflecting wall D can be classified into patterns A and B that can generate power stably, pattern C that is unstable but that can generate power, and patterns D and E that cannot generate power. The effect of the position from the reflection wall is dominant on the flap pattern, and the flap tends to be unstable as the ratio of the wavelength and the distance from the reflection wall to the flap, i.e., D/L, approaches 0.5, which is the anti-node position of the standing wave. Moreover, when the water depth is greater than the flap height, the flap tends to be unstable. Therefore, the installation location of the bottom-hinged WEC with a reflection wall should avoid the condition D/L ≈ 0.5, and if the wave power of the installation location is relatively small, it is suggested that the flap height should be greater than the water depth for stable power generation. As a result of the power generation characteristics in pattern A that can generate power stably, it was demonstrated that the wave power capturing ability of the wave power generation system used in the experiment is 30%, and the maximum power generation efficiency k

_{e}is 0.77 at D/L ≈ 0.32. Theoretically, it is well known that the maximum k

_{e}can be obtained at D/L = 0.25, which is the node of the standing wave formed by the reflection wall. However, the position of D/L at which the maximum k

_{e}appears can be changed by the effects of the flap shape on the flow fields around the flap and the resistance of the PTO system on the phase difference between the reciprocating behavior of the flap and the period of the standing wave. Based on the relationship between k

_{e}and the characteristics of the flap motion, the flap tends to be temporary latching on the offshore or shore side during the pitching motion, and the rotational center of the flap is tilted to one side depending on D/L and h. These phenomena contribute to the reduction of the wave power capturing ability such that it is considered that the maximum k

_{e}appears at D/L ≈ 0.32, where there is no latching effect and there is a lesser tendency of tilting of the rotational center of the flap. As the effects of the damping PTO system and the flap shape on the flap motion during rotation were not clarified in this study, further research is required to consider these types of effects on power generation performance.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematic sketch of the experimental setup: (

**a**) side view, (

**b**) plan view. W1–W7 denote the water level gauges; h is the water depth; D indicates the distance between the flap and reflection wall; d is the submergence depth of the flap; and B and b are the width and length of the upper part of an inverted triangular prism, respectively.

**Figure 6.**Results of free fluctuation tests of the flap for (

**a**) the time variation of the rotation angle θ

_{x}measured by the gyro sensor and (

**b**) the natural frequency. L1–6 and R1–6 denote the cases of the flap initially tilted to the onshore (left side) and offshore sides (right side), respectively.

**Figure 7.**Behavioral characteristics of the flap for (

**a**) pattern A (stable), (

**b**) pattern B (fluctuation), (

**c**) pattern C (unstable), (

**d**) pattern D (loss), and (

**e**) pattern E (P

_{wec}= 0). Capitals of each subtitle indicate experimental conditions; e.g., D109_h42.5_T3.0_H12 denotes the distance from the reflection wall D (=1.09 m), water depth h (=0.425 m), wave period T (=3.0 s), and wave height H

_{i}(=0.12 m).

**Figure 8.**Tendency for the respective patterns depending on (

**a**) D/L and H

_{i}/L, and (

**b**) D/L and P

_{wave}.

**Figure 9.**Effects of h and P

_{wave}on the behavior of the flap: (

**a**) patterns C (unstable), D (loss), and E (P

_{wec}= 0); (

**b**) patterns A (stable) and B (fluctuation). The results in the range of 0.45 < D/L < 0.58 were excluded.

**Figure 10.**Screenshots for pattern E for the case of D = 1.09 m, h = 0.425 m, T = 1.4 s, and H

_{i}= 0.08 m at (

**a**) t/T = 1/4, (

**b**) t/T = 2/4, (

**c**) t/T = 3/4, and (

**d**) t/T = 4/4. D/L was 0.4463.

**Figure 11.**Screenshots for pattern D for the case of D = 1.45 m, h = 0.51 m, T = 1.4 s, and H

_{i}= 0.12 m at (

**a**) t/T = 1/4, (

**b**) t/T = 2/4, (

**c**) t/T = 3/4, and (

**d**) t/T = 4/4. D/L was 0.56. The blue solid line denotes the water surface.

**Figure 12.**Screenshots for pattern D for the case of D = 1.09 m, h = 0.475 m, T = 1.4 s, and H

_{i}= 0.12 m at (

**a**) t/T = 1/4, (

**b**) t/T = 2/4, (

**c**) t/T = 3/4, and (

**d**) t/T = 4/4. D/L was 0.4306. The blue solid line denotes the water surface.

**Figure 14.**Relationship between k

_{e}and D/L depending on (

**a**) T/T

_{f}, and (

**b**) h/h

_{f}. Open red and blue circles denote the range of high and low k

_{e}, respectively, owing to the effects of D/L.

**Figure 18.**Relationship between P

_{wave}and P

_{WEC}depending on (

**a**) T/T

_{f}, and (

**b**) h/h

_{f}. Open red and blue circles denote the ranges of high and low k

_{e}.

**Figure 19.**Screenshots of the flap motions for the case of D = 1.09 m, h = 0.425 m, T = 1.8 s, and H

_{i}= 0.12 m at (

**a**) t/T = 1/8 to (

**h**) 8/8. D/L is 0.3253 and k

_{e}= 0.76. The blue arrow denotes the wave direction acting on the flap, and the white dotted line indicates the rotational neutral axis of the flap. The blue solid line denotes the water surface.

**Figure 20.**Screenshots of the flap motions for the case of D = 1.45 m, h = 0.425 m, T = 2.6 s, and H

_{i}= 0.12 m at (

**a**) t/T = 1/8 to (

**h**) 8/8. D/L is 0.2852 and k

_{e}= 0.44. The blue arrow denotes the wave direction acting on the flap, and the white dotted line indicates the rotational neutral axis of the flap. The blue solid line denotes the water surface.

**Figure 21.**Screenshots of the flap motions for the case of D = 1.09 m, h = 0.525 m, T = 2.2 s, and H

_{i}= 0.12 m at (

**a**) t/T = 1/8 to (

**h**) 8/8. D/L is 0.2355 and k

_{e}= 0.18. The blue arrow denotes the wave direction acting on the flap, and the white dotted line indicates the rotational neutral axis of the flap. The blue solid line denotes the water surface.

Case No. | Distance to the Reflection Wall D (m) | Water Depth h (m) (Submergence Depth d (m)) | Wave Period T (s) | Wave Height H (m) |
---|---|---|---|---|

1–328 | 1.09 | 0.425 (−0.05) | 1.4 | 0.04 |

0.06 | ||||

0.440 (−0.035) | 1.8 | 0.08 | ||

2.2 | 0.10 | |||

2.6 | 0.12 | |||

0.14 | ||||

0.475 (0.0) | 3.0 | 0.16 | ||

0.510 (+0.035) | ||||

1.45 | 0.525 (+0.05) |

Internal Diameter (mm) | External Diameter (mm) | Width (mm) | Number of Teeth | Total Length (mm) | |
---|---|---|---|---|---|

Rack gear | - | - | 5 | - | 560 |

Gear1 | 15 | 60 | 10 | 60 | - |

Gear2 | 35 | 60 | 60 | - | |

Cam Clutch | 15 | 35 | - | - | |

Gear3 | 6 | 18 | 18 | - | |

Shaft | - | - | - | - | 600 |

Model | Rated Voltage V_{0} (V) | No-Load Speed (rpm) | No-Load Current I_{idle} (A) | Rated Load Speed (rpm) | Rated-Load Current I_{stall} (A) |
---|---|---|---|---|---|

24J36SBLA2 | 24 | 4200 | 0.12 | 3600 | 0.3 |

**Table 4.**The number of the emergence of each pattern for h/h

_{f}and T/T

_{f}. The values in parentheses “()” of No. columns represent the percentages of the number of emerged cases for each h/h

_{f}over the total number of experiments for T/T

_{f}in each pattern. The value in parentheses “()” of Total No. columns denotes a percentage of the number of occurrences of each pattern from the total number of experiments for each T/T

_{f}.

Pattern | h/h_{f} | T/T_{f} = 0.7 | T/T_{f} = 0.9 | T/T_{f} = 1.1 | T/T_{f} = 1.3 | T/T_{f} = 1.5 | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

No. | Total No. | No. | Total No. | No. | Total No. | No. | Total No. | No. | Total No. | ||

A | 1.11 | 0 (0.0) | 4 (6.1) | 1 (9.1) | 11 (16.9) | 5 (22.7) | 22 (34.9) | 0 (0.0) | 31 (46.3) | 5 (12.5) | 40 (60.0) |

1.07 | 0 (0.0) | 0 (0.0) | 6 (27.3) | 2 (6.4) | 8 (20.0) | ||||||

1.0 | 1 (25.0) | 1 (9.1) | 3 (13.6) | 8 (25.8) | 10 (25.0) | ||||||

0.93 | 2 (50.0) | 7 (63.6) | 2 (9.1) | 10 (32.3) | 7 (17.5) | ||||||

0.89 | 1 (25.0) | 2 (18.2) | 6 (27.3) | 11 (35.5) | 10 (25.0) | ||||||

B | 1.11 | 0 (0.0) | 18 (27.3) | 4 (19.1) | 21 (32.3) | 0 (0.0) | 15 (23.8) | 3 (37.5) | 8 (11.9) | 0 (0.0) | 4 (6.0) |

1.07 | 0 (0.0) | 4 (19.1) | 1 (6.7) | 5 (62.5) | 0 (0.0) | ||||||

1.0 | 4 (22.2) | 3 (14.3) | 3 (20.0) | 0 (0.0) | 0 (0.0) | ||||||

0.93 | 8 (44.4) | 4 (19.1) | 8 (53.3) | 0 (0.0) | 3 (75.0) | ||||||

0.89 | 6 (33.3) | 6 (28.6) | 3 (20.0) | 0 (0.0) | 1 (25.0) | ||||||

C | 1.11 | 0 (0.00) | 3 (4.6) | 3 (21.4) | 14 (21.5) | 3 (37.5) | 8 (12.7) | 3 (33.3) | 9 (13.4) | 2 (33.3) | 6 (9.0) |

1.07 | 0 (0.00) | 3 (21.4) | 1 (12.5) | 2 (22.2) | 0 (0.0) | ||||||

1.0 | 1 (33.3) | 3 (21.4) | 1 (12.5) | 3 (33.3) | 1 (16.7) | ||||||

0.93 | 1 (33.3) | 1 (7.1) | 0 (0.0) | 1 (11.1) | 2 (33.3) | ||||||

0.89 | 1 (33.3) | 4 (28.6) | 3 (37.5) | 0 (0.0) | 1 (16.7) | ||||||

D | 1.11 | 9 (33.3) | 27 (40.9) | 2 (22.2) | 9 (13.9) | 3 (25.0) | 12 (19.1) | 3 (30.0) | 10 (14.9) | 2 (28.6) | 7 (10.5) |

1.07 | 8 (29.6) | 2 (22.2) | 4 (33.3) | 1 (10.0) | 2 (28.6) | ||||||

1.0 | 6 (22.2) | 4 (44.4) | 2 (16.7) | 2 (20.0) | 3 (42.9) | ||||||

0.93 | 1 (3.7) | 1 (1.1) | 2 (16.7) | 2 (20.0) | 0 (0.0) | ||||||

0.89 | 3 (11.1) | 0 (0.0) | 1 (8.3) | 2 (20.0) | 0 (0.0) | ||||||

E | 1.11 | 3 (21.4) | 14 (21.2) | 2 (20.0) | 10 (15.4) | 1 (16.7) | 6 (9.5) | 3 (33.3) | 9 (13.4) | 3 (30.0) | 10 (14.9) |

1.07 | 4 (28.6) | 3 (30.0) | 0 (0.0) | 3 (33.3) | 3 (4.5) | ||||||

1.0 | 2 (14.3) | 2 (20.0) | 2 (33.3) | 1 (11.1) | 0 (0.0) | ||||||

0.93 | 2 (14.3) | 1 (10.0) | 2 (33.3) | 1 (11.1) | 2 (20.0) | ||||||

0.89 | 3 (21.4) | 2 (20.0) | 1 (16.7) | 1 (11.1) | 2 (20.0) |

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**MDPI and ACS Style**

Cho, Y.-H.; Nakamura, T.; Mizutani, N.; Lee, K.-H.
An Experimental Study of a Bottom-Hinged Wave Energy Converter with a Reflection Wall in Regular Waves—Focusing on Behavioral Characteristics. *Appl. Sci.* **2020**, *10*, 6734.
https://doi.org/10.3390/app10196734

**AMA Style**

Cho Y-H, Nakamura T, Mizutani N, Lee K-H.
An Experimental Study of a Bottom-Hinged Wave Energy Converter with a Reflection Wall in Regular Waves—Focusing on Behavioral Characteristics. *Applied Sciences*. 2020; 10(19):6734.
https://doi.org/10.3390/app10196734

**Chicago/Turabian Style**

Cho, Yong-Hwan, Tomoaki Nakamura, Norimi Mizutani, and Kwang-Ho Lee.
2020. "An Experimental Study of a Bottom-Hinged Wave Energy Converter with a Reflection Wall in Regular Waves—Focusing on Behavioral Characteristics" *Applied Sciences* 10, no. 19: 6734.
https://doi.org/10.3390/app10196734