This section consists of two categories: one is single Savonius wind turbine in atmosphere and the other inside the wind tunnel. The geometric data and the corresponding information have been provided in Tables 3.1 and Figs. 3.2 and 3.3.
4.1.1 Overlap Ratio
Before conducting the parametric study, the structure of single Savonius wind turbine is tested firstly to identify the optimum performance. One of the most influential parameters on the performance of wind turbine is overlap ratio, whose definition is shown in Fig 4.1. The results of the experiment of Blackwell et al. [9] and present simulation
66 maximum power coefficient is 0.199, occurred at the overlap ratio of 0.15 in atmosphere with the tip speed ratio of 0.8 and wind velocity of 7m/s.
Fig. 4.3 shows streamline distributions for the overlap ratios of 0.1, 0.15 and 0.3, respectively. The comparison of overlap ratios of 0.1 (Figs. 4.3 (a)) and 0.15 (Fig. 4.3 (b)) is given firstly. It can be seen that the overlap jet between the gap is so small in Fig 4.3 (a) that the flow passes through the gap and the resultant jet weakly hits the returning blade, consequently, the performance with overlap ratio less than 0.15 is worse than that of 0.15. For the comparison between the overlap ratios of 0.15 and 0.3, it can be seen in Figs. 4.3 (b) and 4.3 (c). The gap for overlap ratio of 0.3 is too large that the passing flow is so slow that it weakly hits the advancing blade, so the performance with overlap ratio larger than 0.15 becomes worse. Besides, with the larger overlap ratio, it will increase the losses because the larger vortices are formed in the overlap to reduce the performance. Therefore, the optimal performance occurs at the overlap ratio of 0.15,.
However, due to turbine’s structure and construction in real establishment, the present study chooses the overlap ratio of 0.14 instead, which is very close to the predicted optimum value of 0.15 and still within the range found by Ref. [9]. The corresponding power coefficient
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is 0.198.
4.1.2 The Performance Comparison between One Single Savonius in Atmosphere and Inside the Wind Turbine
The two and three dimensional simulations are carried out with the wind speed of 7 m/s, and the tip speed ratios ranged from 0.4 to 1.2. The 3-D model uses a grid number of 1,063,108, and the 2-D one uses 23,152.
The parameters used are summarized in Table 4.3.
Table 4.3 Parameters for single Savonius wind turbine in atmosphere
In order to study the flow field, is firstly defined as the rotating angle of wind blade, which is illustrated graphically in Fig. 4.4.
Figure 4.5 presents the torque curve of one single Sanonius wind turbine in one rotation at the tip speed ratio of 0.82, where has the best performance. In the figure, the maximum torque happens at 110 and the minimum one at 20.
The pressure fields and velocity vector distributions around single Savonius rotor at 110and 20 in the x-y plane at z =1.21m are demonstrated in Figs.4.6 and 4.7, respectively. In Fig.4.6 (a), the pressure
Simulation Domain
2-D ( 26m x 12m ) 3-D ( 26m x 12m x 15m)
Wind Speed 7 m/s
Tip-speed Ratio 0.4~1.2
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difference on the returning blade is larger at 20 that causes a higher negative torque and reduces the net torque. Referring to Fig. 4.7(a), it can be seen that a vortex generated around the tip at low pressure region around the blade is so large that leads to the momentum loss and the lower net torque. On the contrary, the pressure difference on the returning blade is relatively smaller at 110 and the vortex is much smaller, as shown in Figs. 4.6(b) and 4.7(b). The negative torque is smaller at this position and therefore the net torque becomes larger. This is the typical characteristics of drag device.
As the air flow passes through the blade, as shown in Fig. 4.7 (a), a recirculation flow (vortex) occurs at the advancing blade of the concave side. In the meantime, Fig. 4.6 (a) shows the vortex area is a low pressure region. It can suck the flow into the advancing tip blade to reduce the flow impingement on the concave side of the advancing blade. Second, the overlap jet occurs and is formed on the concave side of the advancing blade, and affects the returning blade. The velocity growth in this region indicates that the negative contribution of the returning blade is reduced, and then enhances the overall torque. Next, some counter-rotating vortices are observed as well. They are induced from the overlap jet and evolved into bigger structures downstream of the blade. This overall wake structure can be regarded as similar to the Von Kármán vortex street.
The momentum is reduced by this vortex. Finally, a stagnation point, facing directly the incoming wind, can be identified on the returning blade, whose value is about 95pascal. The higher pressure region on the convex side gives a negative torque at this position.
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Figures 4.6 (b) and 4.7 (b) are the pressure and velocity vector distributions at 110. The high pressure region on the convex side provides the positive effect because the flow can pass through the blade smoothly and the stagnation point does not happen in this position. The recirculation occurs as well, but the counter-rotating vortices are not so apparent that the momentum loss is small at this position.
Figure 4.8 shows the power coefficients (performances) as a function of tip speed ratio for both 2-D and 3-D simulations. From this figure, the trends for both 2-D and 3-D are quite similar. The maximal power coefficient in 2-D and 3-D are 0.232 and 0.198, respectively, at the tip speed ratio of 0.82. Of course, it is expected that the performance of 2-D simulation should be better. As shown in Figs. 4.9 and 4.10, when wind hits the blades, the part of the incoming flow can escape upwardly and downwardly from the top and bottom of the wind turbine, leading to a decrease of momentum passing through the wind turbine. Besides, the frictions by end plates would influence the performance as well.
The parameters of the simulation inside the wind tunnel are given in Table 4.4. The grid number used in the 3-D model is 857,364.
Table 4.4 Parameters for single Savonius wind turbine inside the wind tunnel
Simulation Domain 3-D ( 11.9m x 3.6m x 3.5m)
Wind Speed 7 m/s
Tip-speed Ratio 0.4~1.2
The definition of the rotating angle was given previously. The
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maximal and minimal Cps inside the wind tunnel occur at = 110o and 20o, respectively, that are exactly the same as those in atmosphere. The corresponding pressure and velocity vector fields are shown in Figs. 4.12 and 4.13, which are similar to those in Figs. 4.6 and 4.7.
Figure 4.11 is Cps as a function of TSR for wind turbines in atmosphere and inside the wind tunnel. The maximum Cps are 0.198 and 0.262 in atmosphere and inside the wind tunnel, respectively. It has a higher performance about 32% inside the wind tunnel. The differences in pressure distributions can be seen in Figs 4.6 and 4.12. From Figs 4.6 (b) and 4.12 (b), the pressure differences on the advancing blade is 75 pascal and 95 pascal, respectively, which causes a higher drag force inside the wind tunnel. This phenomenon can be explained as the boundary conditions for the wind tunnel, which are enclosed by solid walls.
Therefore, the momentum of flow should be more concentrated to act on the turbine, resulting in a higher power coefficient. Furthermore, the difference can also be seen in Fig. 4.14, which shows the streamlines for both conditions in atmosphere and inside the wind tunnel. In Fig. 4.14 (b), the counter-rotating vortices behind the blade in atmosphere are apparently larger than that inside the wind tunnel, as shown in Fig. 4.14 (a). The larger vortex will cause more secondary losses that reduce the performance.