A gravitation vortex type water turbine, which mainly comprises a runner and a tank, generates electricity by introducing a flow of water into the tank and using the gravitation vortex generated when the water drains from the bottom of the tank. This water turbine is capable of generating electricity using a low head and a low flow rate with relatively simple structure. However, because its flow field has a free surface, this water turbine is extremely complicated, and thus its relevance to performance for the generation of electricity has not been clarified. This study aims to clarify the performance and flow field of a gravitation vortex type water turbine. We conducted experiments and numerical analysis, taking the free surface into consideration. As a result, the experimental and computational values of the torque, turbine output, turbine efficiency, and effective head agreed with one another. The performance of this water turbine can be predicted by this analysis. It has been shown that when the rotational speed increases at the runner inlet, the forward flow area expands. However, when the air area decreases, the backward flow area also expands.
Many large-scale conventional hydraulic power generations mainly use medium- or high-heads and water turbines [
Therefore, we focused on a water turbine used in the Gravitation Water Vortex Power Plant (GWVPP) [
In light of this background, this study aims to clarify the performance of a gravitation vortex type water turbine and elucidate its flow field. We performed numerical analysis by considering the free surface, conducted a performance test and a visualization experiment, and verified the validity of our analysis. Furthermore, we examined the flow field around the runner at the center of the blade width in detail using a numerical analysis.
An overview of the gravitation vortex type water turbine is shown in Figure
Specifications of runner.
Outer diameter: | 0.14 m |
Inner diameter: | 0.09 m |
Inlet width: | 0.091 m |
Outlet width: | 0.091 m |
Inlet angle: | 71.9° |
Outlet angle: | 19.0° |
Tip clearance: | 0.5 mm |
Number of blades: | 20 |
Test water turbine.
Runner.
An overview of the experimental apparatus is shown in Figure
Experimental apparatus.
Here the torque
Definition of performance evaluation.
Here the upstream water depth
Here
A digital camera (Casio Computer Co., Ltd.; EXILIM EX-F1) was used to visualize the flow field at a frame rate of 30 frames per second (fps).
In this study, three-dimensional unsteady flow analysis was performed by considering the free surface. The general-purpose thermal fluid analysis software, ANSYS CFX15.0 (ANSYS, Inc.), was used for the calculations. Moreover, the volume of fluid (VOF) method [
The entire area of calculation is shown in Figure
Calculating area.
Computational grids.
Runner
Tank
A comparison between the experimental and calculation results for this water turbine in relation to its performance is shown in Figures
Turbine performance.
Torque and turbine output
Turbine efficiency and effective head
The experimental results for the free surface flow field of this water turbine are shown in Figures
Flow field by experiment.
Flow field by calculation.
First, in order to identify the water/air interface, the circumferential distribution of water volume fraction VF1 obtained numerically for a runner inlet at the center of the blade width is shown in Figure
Volume fraction of water at runner inlet (Cal.).
Here velocity triangles of the water turbine are illustrated in Figure
Velocity triangles.
Absolute velocity at runner inlet (Cal.).
Radial component
Axial component
Circumferential component
From Figure
The numerically determined circumferential distribution of the relative flow angle
Relative flow angle at runner inlet (Cal.).
The numerically determined circumferential distribution of water volume fraction VF2 of a runner outlet at the center of the blade width is shown in Figure
Volume fraction of water at runner outlet (Cal.).
Figures
Absolute velocity at runner outlet (Cal.).
Radial component
Axial component
Circumferential component
The flow rate and the angular momentum per unit time that flow in and out at the runner inlet and outlet relates to the torque of a water turbine studied.
The flow rates
Here
Therefore, the angular momentums,
The relationship between the rotational speed,
Flow rate per unit blade width.
Angular momentum per unit blade width and unit time.
In Figure
In Figure
Figures
Relative velocity vectors and volume fraction of water (Cal.).
The following matters were determined by our research of the performance of a gravitation vortex type water turbine and the flow field at the center of blade width through experiments and free surface flow analysis: The experimental and computational values of the torque, turbine output, turbine efficiency, and effective head agree well with one another. Thus, the performance of this water turbine can be predicted by this analysis. With increase in the rotational speed at a runner inlet, the forward flow area increases, as does the backward flow area because of the reduction in the air area. However, the flow rate that flows in from the center of the blade width barely changes. The flow in the tank of this water turbine is not a perfect free vortex, and it is greatly influenced by the rotation of the runner near the runner inlet. The water area of a runner outlet is considerably smaller than that of a runner inlet and does not change with the rotational speed. In addition, backward flow does not occur at a runner outlet. When the rotational speed changes, the angular momentum per unit time that flows from the runner inlet is nearly constant. The angular momentum per unit time that flows from the runner outlet shows a large negative value at low-speed rotations and a large positive value at high-speed rotations. It also has a large influence on the torque when the rotational speed changes.
Blade width m
Waterway width m
Runner diameter m
Gravitational acceleration m/s2
Water depth m
The difference in height between the bottom surface of tank and the bottom surface of downstream waterway m
Effective head m
Angular momentum per unit blade width and unit time N·m/mm·s
Rotational speed min−1
Specific speed min−1, kW, m
Turbine output W
Flow rate per unit blade width m3/mm·s
Flow rate m3/s
Torque N·m
Circumferential velocity m/s
Absolute velocity m/s
Volume fraction of water
Relative velocity m/s
Relative flow angle °
Blade angle °
Turbine efficiency
Circumferential angle °
Density of water kg/m3
Water area
Runner inlet
Runner outlet
Upstream
Downstream
Axial component
Hub
Radial component
Tip
Circumferential component.
The authors declare that they have no conflicts of interest regarding the publication of this paper.
The authors acknowledge the support of Shinoda Co., Ltd. in the design and production of the experimental apparatus. They are also grateful to Tomoaki Tanemura and Kentaro Hatano, graduate students of Ibaraki University at the time, who supported us with the experiments and numerical analysis. Here, we express our sincere gratitude for their cooperation.