Experimental Study on Conversion Efficiency of A Floating OWC Pentagonal Backward Bent Duct Buoy Wave Energy Converter

Wave tank tests were carried out to evaluate the total efficiency of a floating OWC Pentagonal Backward Bent Duct Buoy (PBBDB). Two kinds of turbine generators were used in tests. The incident wave power, pneumatic power and electricity were measured. The test results show that the primary efficiency can reach up to 185.98% in regular waves and 85.86% in irregular waves. The total efficiency from wave to wire with Wells turbine-generator set is 33.43% in regular waves and 15.82% in irregular waves. The peak total efficiency of the PBBDB with check valves equipped with the impulse turbine-generator set is 41.68% in regular waves and 27.10% in irregular waves. The efficiency of the turbine-generator set is about 30% in the tests. Obviously, the total efficiency can be further improved with the increasing of turbine efficiency.


Introduction
A wide variety of devices have been proposed to extract power from ocean waves. Those devices can mostly be divided into Oscillating Water Column (OWC), Oscillating Bodies and Overtopping based on different working principles (Falcão, 2010). The Backward Bent Duct Buoy (BBDB), first proposed by Masuda and McCormick (1986), is a typical floating OWC device. As shown in Fig. 1, the BBDB consists of an L-shaped duct, a buoyancy chamber, an air chamber, a turbine and a generator (Imai et al., 2011). Wave energy is converted to electricity in three steps for the BBDB. First, Wave energy is transformed into the mechanical energy of the buoy. Second, the mechanical energy is converted into pneumatic energy. This stage from wave energy to pneumatic energy is called the primary conversion. Third, the pneumatic energy is converted into electric energy, and this stage is called the secondary conversion.
Researchers around the world have studied the energy conversion of the BBDB, including the Capture Width Ratio (CWR), which is defined as the ratio of the captured pneumatic power to the incident wave power in the width of wave crest through the converter, and generating efficiency. Toyota et al. (2008) studied the effect of hull shape on the primary efficiency of the BBDB. The results showed that the peak CWR was about 35% in regular waves. Liang et al. (1998) carried out regular wave tests on the BBDB with cuboid front and cylindrical behind floating room in a wave basin. The results showed that the wave-to-wire efficiency China Ocean Eng., 2019, Vol. 33, No. 3, P. 297-308 DOI: 10.1007/s13344-019-0029-1, ISSN 0890-5487 http://www.chinaoceanengin.cn/ E-mail: coe@nhri.cn could reach 37%. The CWR of the BBDB with different duct lengths in regular and irregular waves was measured and the CWR of optimal BBDB could reach 52% in irregular waves (Pathak et al., 1999). The CWR and total efficiency of the BBDB with different extended lengths mounted impulse turbine were measured. The results revealed that the maximum CWR of the cuboid BBDB was 78%. The peak value of generating efficiency was 49% (Imai et al., 2011), however, the response frequency band was relatively narrow. The BBDB equipped with Wells turbine-generator set was tested in real sea. According to the experimental results, the conversion efficiency from pneumatic power to electric power was about 30% (O'Sullivan et al., 2011). Kim et al. (2015) studied a floating wave energy device with a total efficiency of 19.7% by numerical and experimental methods. Recently, Wu et al. (2017) studied the CWR of a PBBDB and the experimental results showed that it could reach 87.1% in irregular waves.
The Power Take Off (PTO) system of the BBDB consists of an air turbine and a generator in general, so it can convert the pneumatic power to electric power. Common air turbines are Wells turbines and impulse turbines. The Wells turbine was invented in the mid-1970s by Wells (1976). Wells turbines have the advantages of simple structure and easiness in manufacturing and its high speed can match the generator easily. But it also has some disadvantages (Halder et al., 2017), such as low operating range, poor starting characteristics, low tangential force coefficient and a high axial thrust. The efficiency of the Wells turbine and the generator is about 60% in real sea (Heath, 2012). The impulse turbine is derived from the unidirectional impulse turbine in the traditional turbine, but in order to adapt to the reciprocating air-flow, the impulse turbine requires the guide blade to be strictly symmetrical. This requirement causes the airflow to have a shock loss on the guide blade on the outlet side, so the maximum efficiency of impulse turbine is generally not high. Setoguchi et al. (1996) proposed an impulse turbine with self-pitch-controlled guide vanes to solve the problem of shock loss, but it greatly increases the complexity of turbine machinery. It is a serious problem to ensure the self-pitch-controlled guide vanes working normally in a real sea. In recent years, a number of new turbines have been proposed, such as a twin unidirectional impulse turbine (Jayashankar et al., 2009) and a new radial bi-directional turbine (Moisel and Starzmann, 2013). Under the steady state flow, the performance of the novel turbines is better than that of the existing Wells turbine and impulse turbine. However, due to the unstable air-flow in the OWC technology, it is still to be studied on the new form of turbines.
In this paper, the CWR and total efficiency of the PBBDB were measured in regular and irregular waves. The PBBDB combined with two types of turbines: Wells turbine and impulse turbine. The Wells turbine was designed based on NACA airfoil shape. The impulse turbine was de-signed based on traditional steam turbine. In order to adapt to the reciprocating air-flow, some check valves with large cross-sectional area were used for rectification.

PBBDB model and experimental facility
The PBBDB was designed and fabricated based on previous research results of the models (Wu et al., 2017). Its hull as shown in Fig. 2 was made of steel. It is 4.0 m long, 1.79 m wide and 1.82 m high. The total weight of the experimental device is about 1.3 t. The draft is about 1.2 m. Single point mooring is adopted. In the initial, the CWR and generating performance of the PBBDB equipped Wells turbine-generator set were measured. Afterwards, the PBBDB was slightly modified via adding several check valves, which made the device output power through the single-action air-flow. The CWR and generating performance of the PBBDB equipped with unidirectional impulse turbine-generator set were also measured.
The experimental campaigns were performed in a wave tank in Sun Yat-Sen University from September to October in 2017. The tank is 200 m long and 6 m wide, with a water depth of 2.81 m. The PBBDB was located 45 m away from the wave maker.

Measuring apparatus
The experimental platform is shown in Fig. 3. The parameters that were measured during the tests are mainly the instantaneous free surface elevation in the tank and inside the OWC chamber, the air differential pressure between the OWC chamber and exterior atmosphere, and the electric power.
The measuring instruments and equipment are listed below: (1) The digital wave height meter (YWH200-DXX) was installed between the wave maker and the experimental device (see Fig. 2) to measure the wave height and period.
(2) The analog wave height meter (YWH201-AXX) and the pressure gage (PY301) were installed on the top plate of the air chamber (see Fig. 4) to measure the relative fluctuation of the indoor free surface and the pressure difference between the air chamber and exterior atmosphere, respectively.
(3) The synchronous sampling signals output by YWH201-AXX and PY301 were collected and processed through capture card RBH8251-19 (see Fig. 3) and computer.
(4) The multi-channel Ainuo power analyzer AN87500 (see Fig. 3) can measure the voltage, current and electric power. 12 V lead-acid battery, 24 V lead-acid battery, a rectifier and a slide rheostat are shown in Fig. 3.
(5) Wells turbine-generator set is shown in Fig. 4 and the diameter of the turbine impeller is 200 mm. Impulse turbine-generator set is shown in Fig. 5 and the diameter of the turbine impeller is 300 mm.

Data analysis
To describe the primary conversion of a WEC, CWR is usually adopted (Babarit, 2015). CWR is defined as the ratio of the absorbed wave power (in kW) to the incident wave power (in kW). As for an OWC WEC, the pneumatic power is treated as .
J B where is the wave energy flux (in kW/m), is the wave crest width through the WEC and it is equivalent to the width of the PBBDB in this paper. The unit of CWR is a dimensionless parameter.

P air
In the experiments, the pressure difference is not exceeding 2 kPa and the incompressible air-flow can be assumed. The PBBDB mainly oscillates under the action of waves and the free surface inside the chamber is weakly affected by waves. So the free surface is assumed to be flat. The oscillating free surface inside the chamber moves in a piston-like motion. YWH201-AXX was installed in the symmetrical profile of the chamber to measure the motion. The average pneumatic power is given via the pressure difference and the water free surface elevation difference as follows (Wu et al., 2017): where is the i-th pressure difference, and are the i-th and (i+1)-th sample points of free surface elevation in the chamber respectively, is the waterline cross-sectional area of the air chamber, is the total sampling number and is the sampling time interval. The average air flow and average pressure are significant to design matched air turbines for the OWC converters (Wu et al., 2017).
In this paper, the subscripts 'reg' and 'irr' indicate regular and irregular wave, respectively. In the linear wave theory, the incident wave power per unit width (energy flux) and incident wave power are given by (Mc-Cormick, 1981): where is the water density, is the gravitational acceleration, is the incident wave height, is the group velocity of the incident wave given by: where is the water depth, is the phase velocity defined as , is the wave number defined as , is the wave period, is the wave length calculated by (McCormick, 1981). With the application of the random wave theory, the mean power of irregular waves in finite water depth is given by (Zhang et al., 2012): where is the power spectrum of irregular wave and . In infinite water depth, the mean power of irregular waves is given by: where is the significant wave height, is the mean energy period. The mean power of irregular waves is computed via the equation below (Pathak et al., 1999): T z where is the mean period of irregular wave.
For an OWC WEC, the CWR is expressed as follows: where is the power of incident wave, including regular wave and irregular wave.
Irregular wave P E U I P To measure the generating performance, the lead-acid battery was used as the consumption load. The average electric power ( ) was measured directly by the power analyzer. The measured parameters contain voltage ( ), current ( ) and electric power ( ). η Total efficiency of the WEC can be evaluated by incident wave power and the average electric power. The total efficiency is expressed as : where is the power of incident wave, including regular wave and irregular wave.

Results and discussion
3.1 CWR and generating efficiency of the PBBDB with reciprocating air-flow Some experimental conditions are as follows. The nozzle area ratio ( ) which is defined as the ratio of the nozzle area ( ) to the cross-sectional area of the air chamber is . The single point mooring was adopted. The anchoring hanging point was located at the turning point of L-duct in the symmetry plane (see Fig. 2). The single anchor chain was 5 m long. The total mass of the experimental device was about 1.3 t adjusted by adding appropriate ballast.

Primary conversion characteristics
The CWR of the PBBDB with reciprocating air-flow was tested with different wave periods and heights in regular and irregular waves. Different regular wave period tests were carried out. The wave height was about 0.15 m and the wave period varied from 1.8 s to 3.0 s. The captured by PBBDB and the CWR varying with the wave period are shown in Fig. 6. The results reveal that there was a peak CWR at the optimal wave period (about 2.45 s). The optimal response performance of the PBBDB is shown in Table 1. In regular waves, as shown in Fig. 7a, the free surface elevation, air pressure difference in the air chamber and pneumatic power are shown in Fig. 7b.
Different regular wave height tests were carried out. The wave period was 2.45 s and the wave height varied from 0.05 m to 0.30 m. The average pneumatic power and CWR varying with the wave height are shown in Fig. 8. The results indicate that with the increase of the wave height, the average pneumatic power increased correspondingly. However, as the incident wave power was proportional to the square of the wave height, the CWR firstly increased and then decreased instead of increasing with the increase of wave height, as shown in Fig. 8. When the wave height exceeded 0.1 m, the CWR gradually decreased. The optimal response performance of the PBBDB is shown in Under the same experimental condition with the regular waves, the CWR of the PBBDB were tested in irregular waves with different spectral peak periods. In order to guarantee the randomness of the irregular wave, the duration of each generating wave was 5 minutes to make the number of waves more than 100. The experimental data and results are shown in Table 2. The CWR of the PBBDB is shown in Fig. 9. In irregular waves, as shown in Fig. 10a, the free surface el-    were designed and manufactured using the method (Starzmann and Carolus, 2014). The permanent magnet alternator was combined with it as shown in Fig. 4. Firstly, the electric energy output by the generator was rectified. Then slide rheostat, 12 V and 24 V lead-acid battery were acted as consumption loads respectively. Finally, 24V lead-acid battery was selected as the load by comparing the results. Under regular waves, the generating efficiency experiment was carried out. The wave height was 0.15 m, and the wave peri-od was 2.35-2.65 s. The generating performance is as follows in Fig. 11. The CWR, mean electric power, total efficiency and efficiency of turbine-generator set are shown in Figs. 11a-11d. When the wave period was 2.45 s or 2.50 s, the excellent response performance is shown in Table 3. Under the action of the regular waves, as shown in Fig. 12a, charging voltage (U), current (I) and electric power (P) measured by the power analyzer are shown in Fig. 12b.
As can be seen from Fig. 11, when the regular wave period was 2.45 s, the PBBDB had an optimal response and the total efficiency was as high as 33.43%. The experimental data in Fig. 12b show that Wells turbine started slowly but rotated at a high speed. It can output power steadily. The charging current and voltage were relatively stable, so it played a positive role in the battery life.
The generating performance of the device in irregular waves was also tested. The results are shown in Table 4. Under the action of irregular waves as shown in Fig. 13a, U, I and P measured by the power analyzer are shown in Fig.  13b. The results show that the unstable irregular incident wave power led to the turbine-generator set outputting unstable electric power. The total efficiency of the WEC was low and the max value was 15.82%.

CWR and generating efficiency of the PBBDB with check valves
Based on previous experimental studies, several check valves with appropriate total cross-sectional area were added to the air chamber of the PBBDB. As shown in Fig. 5, the ratio between the total cross-sectional area of the check valves and the cross-sectional area of the air chamber was 0.1. When the oscillating water compressed air out of the air chamber, all of the check valves closed automatically and the air flowed through the nozzle to drive the turbine. When the air chamber inhaled air, the check valves were open. Because the total cross-sectional area of the valves was far more than the turbine flow passage area, the air would predominantly enter the air chamber through the open check valves. When the chamber inhaled air, the damping was so small that the oscillation amplitude of the water column would be clearly strengthened. Although there was no output power during the process of inhaling, the flow of air and the pressure difference increased during the process of exhausting. The experiment shows that the pneumatic power was not halved. The traditional single-action impulse tur-   bine as shown in Fig. 5 was applied and the turbine area ratio is . Regular and irregular wave tests were carried out to evaluate the CWR and generating performance of the PBBDB with check valves. The electrical energy output by the generator was rectified. 12V lead-acid battery was selected as the consumption load. The CWR and generating per-formance of the PBBDB device with check valves were experimentally measured under the same mooring state condition and the total mass. According to the preceding results, experiments with incident wave periods of 2.4 s, 2.45 s and 2.5 s were conducted only. The results are shown in Table 5. In regular waves, as shown in Fig. 14a, free surface elevation, air pressure difference and pneumatic power are shown LI Meng et al. China Ocean Eng., 2019, Vol. 33, No. 3, P. 297-308 305 in Fig. 14b. U, I and P measured by the power analyzer are shown in Fig. 14c. According to the results, under the action of regular waves, the PBBDB with check valves oscillated and the air chamber output the pneumatic power driven by the oscillating water column. During the process of exhalation, the check valves were closed automatically and useful pneumatic power was output. During the process of inhaling, the air would predominantly enter the air chamber through the open check valves almost without damping. The pressure difference was approximately null, so there was no output power. In conclusion, although work time was reduced by half, the average pneumatic power was not largely reduced. Its capture characteristic did not become bad and the maximum CWR can reach 129.75%. The impulse turbine was driven by the unidirectional air-flow during the exhaust process. Satisfyingly, impulse turbine could start to work immediately and it had a high efficiency. The total efficiency of the PBBDB with the impulse turbine-generator set was higher than that with Wells turbine-generator set and it was as high as 41.68%.
The performance of the PBBDB in irregular waves was also tested. Plenty of tests were carried out to study the primary conversion efficiency and total efficiency of the PBBDB with check valves. The peak factor was set at γ = 3.3 γ = 4 γ = 5 , and . The spectral peak periods were 2.35 s, 2.45 s and 2.55 s. The significant wave heights were 0.15 m, 0.18 m and 0.20 m. The results are shown in Table 6 and Fig. 16 .
In irregular waves, according to the results which can be seen clearly in Table 6, the PBBDB with check valves equipped with the impulse turbine-generator set had a high total efficiency and the peak value is 27.10%. Many experimental results show that the total efficiency was more than 20% far better than that of the PBBDB with Wells turbinegenerator set. In these tests, the captured pneumatic power was also measured. The CWR of the PBBDB with check valves was as high as 96.16% in irregular waves. The results confirm that the CWR of the PBBDB with check valves was still high, even though it only worked during the exhaust process with a single-action air-flow. When T P was 2.381 s and H s was 0.2215 m, the average electric power was 22.55 W. Under the action of the above-mentioned irregular waves shown in Fig. 15a, free surface elevation, air pressure difference and the pneumatic power are shown in Fig. 15b. U, I and P are shown in Fig. 15c.
To verify the reliability of the above experimental results, National Ocean Technology Center (NOTC in Tianjin, China) was commissioned to measure the total efficiency of the PBBDB equipped with impulsive turbine generator sets in a basin. This basin is 130 m long, 18 m wide with a water depth of 4.52 m. The test equipment was provided by NOTC. Similarly, with the 12V lead-acid battery as the load, the peak conversion efficiency of the PBBDB could reach 35.65% in regular waves and it was as high as 26.66% in irregular waves as reported by NOTC.

Conclusion
The PBBDB was designed and fabricated for experiment. The CWR and total efficiency of the PBBDB equipped with two types of turbine-generator sets were tested in regular and irregular waves in wave tanks.
For the reciprocating air-flow, the mean CWR of the PBBDB was as high as 185.98% in regular waves, 85.86% in irregular waves. However, when the matched Wells turbine-generator set was equipped to measure the average electric power, the maximum total efficiency was only 33.43% in regular waves, 15.82% in irregular waves. The test results also indicate that the Wells turbine-generator set did not play its best performance. As a result, there is room for improvement of the conversion efficiency of the Wells turbine-generator set as well as the total efficiency of this WEC.
In addition, check valves with appropriate cross-sectional area were installed on the PBBDB. The CWR and generating efficiency were evaluated. According to the results, the CWR was as high as 129.75% and the total efficiency could reach up to 41.68% in regular waves. The CWR was as high as 96.16% and the total efficiency could reach up to 27.10% in irregular waves. The results of the verification experiment in NOTC also confirmed the validity of the test results in Sun Yat-Sen University.