A Study on Fluidic Diode for Wave Energy Conversion-Effect of Bypass Geometry on the Turbine Performance

A twin-impulse turbine for bi-directional flow has been developed for wave energy converter. However, the previous studies elucidated that the mean efficiency of the twin turbine is much lower than that of the impulse turbine for a unidirectional flow because a portion of airflow passes through the reverse flow turbine whose efficiency is very low. Therefore, a fluidic diode was adopted in the twin-impulse turbine in order to reduce the air flow through the reverse flow turbine. In this study, the rectification effect of the fluidic diode was investigated where a bypass is introduced into a blunt body. A computational fluid dynamics (CFD) analysis was conducted to investigate the effect of fluidic diodes on the turbine performance. In this analysis, RANS equations were used as the governing equations and the standard k-ε model was used as the turbulence model. The computational domain is composed of a circular tube and fluidic diode, and the domain meshed with an approximately 1.5 million mesh elements. As a result, it was found that the rectification effect of the fluidic diode is enhanced by installing a blunt body with a bypass hole of 5 ̊ taper angle.


Introduction
Japan is surrounded by the ocean, and abundant wave energy exists around the country. Wave energy converter is one of the wave energy utilization techniques, and there are three types of converters, namely, movable body type, over topping type and oscillating water column type.
In this study, the oscillating water column (OWC) type wave energy converter was used because of its simple structure and the characteristic feature of the use in abnormal sea conditions. The OWC-based power generator converts the wave energy into the electrical energy driving an air turbine coupled with an electrical generator by means of the reciprocating air flow generated in the air chamber [1]. A twin-impulse turbine as shown in Figure 1 has been developed for the OWC-based wave energy converter. A more details of the turbine cascade can be found in Refs. [2] [3]. Since, an impulse turbine, which is used for unidirectional airflow, cannot obtain a high efficiency in a reverse flow. Thus, a fluidic diode has been used to alleviate this problem by rectifying the flow in the turbine [4].
However, the rectification effect of the current fluid diode is about 70%, which is not feasible to use in a practical application, so far. Therefore, in this study, the flow rectification performance of fluidic diode was investigated by a computational fluid dynamics (CFD) analysis. Specifically, in order to achieve a further improvement in the rectification characteristics, the rectification effect of the fluidic diode was investigated when a bypass, aimed at increasing the flow rate in the forward flow turbine, was provided into a blunt body.

Fluidic Diode
In the twin-impulse turbine, a fluidic diode is installed as shown in Figure 1  The previous studies shown that the rectifying characteristics are improved by  providing a bypass on the blunt body in Figure 2(B). From a subsequent research, it was found that the bypass shape as shown in Figure 2(C), wherein a long and narrow rod was installed at the center of the bypass, can further improve the rectification characteristics.
In this study, in order to achieve further improvement in the rectification characteristics, a "taper cylindrical type" bypass as shown in Figure 2(D) was installed where the taper angle θ is ranging between 0˚ and 15˚.

Methodologies
The rectification effect of the fluidic diode has been investigated by using a computational fluid dynamics (CFD) analysis. The shape of the fluidic diode was varied as mentioned in the previous section, in order to investigate its effect. The  Figure 3 shows the effect of the taper angle of bypass hole on the ratio of pressure differences. It is found from the figure that the preferable angle is θ = 5˚ in the tested range. Therefore, this value of taper angle of bypass hole is adopted in this study.     In Figure 4(A), the vortex generated in a hollow (H) at the back and the air flowing from the bypass collides with each other; leads to a separation. In Figure   4(B), the vortex generated at the depression and the airflow from the bypass flows smoothly without collision. As a result, the pressure distribution in Figure   6 shows that Δp f for the taper cylindrical type fluidic diode is low. Figure 5 shows the velocity distribution in the fluidic diode in the case of reverse flow. It can be seen from Figure 5 that the taper cylindrical type fluidic diode has a larger bypass area than the cylindrical type; however, the flow does not change significantly. As a result, the pressure distribution in Figure 7 shows that taper cylindrical type has a higher rectification effect.    In the estimation, the flow rates through the twin turbines were obtained by using the steady flow characteristics and solving these equations simultaneously.

Results and Discussion
f r const.
ω ω ω where Q and T o denote the flow rate through the turbine system and output torque. Subscripts f and r mean turbines in forward and reverse flows, respectively.    the flow coefficient φ, and the efficiency is considered to be lower than that of a turbine without a diode. From this fact, it is considered that the installation of a fluidic diode in a twin impulse turbine to improve the commutation effect is effective only in the range of low flow coefficients.

Conclusions
In this study, in order to improve the performance of the fluidic diodes used in twin-impulse turbines for wave energy conversion, the effect of some bypass shapes to the fluidic diode on its rectification effect was investigated by a computational fluid dynamics (CFD) analysis. The obtained results are summarized below: 1) It was found that the installation of bypass with taper hole to the blunt body of the fluidic diode is effective to improve the rectification effect.
2) The preferred angle of taper cylindrical type bypass hole obtained is at θ = 5˚ in the tested range.
3) From the results, the flow rate in the forward flow turbine found increases