2.2. Experimental Apparatus and Methods
An overview of the experimental apparatus is shown in Figure 3. The flow rate Q of water supplied by the pump was measured with an electromagnetic flow meter (Toshiba Corporation; LF620). The experiment was conducted under the condition of constant flow rate Q = 0.00285 m3/s. The load to the runner was controlled by a motor and an inverter, and the rotational speed was arbitrarily set. The rotational speed n and torque T were measured with a magnetic rotation detector (Ono Sokki Co., Ltd.; MP-981) and a torque detector (Ono Sokki Co., Ltd.; SS-005), respectively. The turbine output P was obtained by
Figure 3Experimental apparatus.
Here the torque T was corrected by measuring the idling torque without the runner. The effective head H is defined by the following as shown in Figure 4.
Figure 4Definition of performance evaluation.
Here the upstream water depth h3 was measured at the tank inlet in the vicinity of the wall surface on the +y-axis with a ruler. The downstream water depth h4 was measured by a point gauge (Kenek Corporation; PH-102) at five points from the vicinity of the wall surface on the +y-axis to the center at the position of 6D1 downstream from the downstream atmospheric opening from which the average water depth was obtained. The upstream velocity v3 and downstream velocity v4 were calculated by
Here B3 and B4 are the waterway widths of the tank inlet and downstream, respectively. In addition, the turbine efficiency η was calculated by
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).
3. Numerical Analysis Method and Conditions
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 , which is suitable for a flow field that has a clear interface between two phases and expresses the actual performance [13–17] in a free surface flow analysis of a water turbine, was also used. The working fluids were water and air. The governing equations were the mass conservation equation, momentum conservation equation, and volume conservation equation. A guideline for using a turbulence model that is suitable for the VOF method has not been clarified. Therefore, the shear stress transport (SST) model , which can model the actual performance [13, 16, 17] of a free surface flow analysis of a water turbine using the VOF method, has been used as the turbulence model.
The entire area of calculation is shown in Figure 5. This is divided into four main areas: runner, tank, upstream waterway, and downstream waterway. The downstream waterway is 10D1 in length from the atmospheric opening to the outlet boundary. The reference position of the upstream side was set to the tank inlet, which was the same as that in the experiment. The reference position of the downstream side was set to 6D1 downstream from the atmospheric opening of the downstream waterway. At these reference positions, the distribution of each water depth was obtained in the width direction, assuming that the water surface is equivalent to that of a water volume fraction of 0.5. The upstream water depth h3 and downstream water depth h4 are the averages obtained from the distribution of water depth in the width direction. As an example, the grids used in the runner and tank calculations are illustrated in Figures 6(a) and 6(b), respectively. The runner, tank, upstream waterway, and downstream waterway have approximately 446 ,000, 541 ,000, 434 ,000, and 780 ,000 computational elements, respectively, which totals to 2 ,201,000. Computational grids [14, 15] using an undershot cross-flow water turbine were prepared, as these are able to verify the free surface flow analysis and the experiments of the flow field relatively well. As boundary conditions, the mass flow rate (2.838 kg/s) was given to the inlet boundary, an open boundary (total pressure of 0 Pa for the inflow, or relative static pressure of 0 Pa for the outflow) to the outlet boundary, and an arbitrary rotational speed to the runner. In addition, the upper surfaces of the tank and downstream waterway were set to open boundaries (relative static pressure of 0 Pa) so that air could enter and exit freely. The wall surface was set to the no-slip condition. With reference to the calculations, a steady flow analysis was first conducted, followed by an unsteady flow analysis using the steady flow results as the initial conditions. In the unsteady flow analysis, the boundary between a rotational and a stationary area was connected using the transient rotor-stator method. The calculation continued until the flow became almost stable, as determined by its fluctuations. A total of 180 time steps were used, during which the runner completes one rotation.
Figure 5Calculating area.
Figure 6Computational grids.
4. Results and Discussion
4.1. Comparison of Water Turbine Performance
A comparison between the experimental and calculation results for this water turbine in relation to its performance is shown in Figures 7(a) and 7(b). It is observed that the experimental and calculation results are in good agreement in terms of torque , turbine output , turbine efficiency η, and effective head H. As the rotational speed n is increased, the torque T decreases and the effective head H increases marginally. The reasons for this appear to be that the increase of effective head H derives mainly from the increase of upstream water depth h3 and that the resistance of the runner increases with the increase of rotational speed n. Both turbine output P and turbine efficiency η show maximum values at the rotational speed n = 122 min−1. The maximum experimentally determined efficiency is approximately 0.354 at a specific speed of approximately 47 [min−1, kW, m].
(a) Torque and turbine output
(b) Turbine efficiency and effective head
Figure 7Turbine performance.