This topic consists of two categories, a single Savonius wind rotor inside the wind tunnel and a single Savonius wind rotor in atmosphere. The geometries are illustrated in Figs. 3.1 and 3.2 and the corresponding information, such as the geometric data of the single Savonius wind rotor and the dimensions of the simulation domains are summarized in Tables 3.1 and 3.2.
4.1.1 A Single Savonius Wind Rotor inside the Wind Tunnel (Reference Case)
The reference case simulated in this work adopts the experimental one by
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Blackwell et al. [4], who investigated the performances of fifteen configurations of Savonius wind rotors tested in a low speed wind tunnel. The Savonius wind rotor, with a predetermined load provided by an air motor, was allowed to rotate in a steady wind speed 7 or 14 m/s. When a steady rotation was achieved, a data was taken. After that, the load was changed slightly, causing a new rotational speed to get another data. By repeating these steps, the functions between cp and tip-speed ratio in fixed wind speed were plotted. The experimental results in wind speeds of 7m/s and 14m/s are shown in Fig. 4.1. However, the turbine load is not considered in simulations, so the free spinning wind rotor cannot be fully simulated. The method in simulations is to specify constant rotational speeds and change the parameters to reveal freely moving wind rotor blades in experiments. The comparison between the predicted results and experimental measurements is given in this section.
The two and three dimensional simulations are carried out with the wind speeds of 7 and 14m/s and the tip speed ratios ranged from 0.4 to 1.2. 2-D model uses a grid number of 13115 and 3-D uses 741524, respectively. The parameters used are summarized in Table 4.1.
Table 4.1 Parameters for a single Savonius wind rotor inside the wind tunnel (Reference case)
To observe the flow field, α is firstly defined as the angle of rotating wind
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blade relative to the initial angle and illustrated in Fig. 4.2. The description of flow field in 2-D simulation is given for demonstrating the fundamental phenomenon. The resultant torque curve of one single Savonius wind rotor with wind speed 7 m/s and tip-speed ratio 0.9 in a rotation (360°) is shown in Fig. 4.3.
As shown in this figure, the maximal torque happens at α=10° and the minimal is at α=110°. The static pressure fields and velocity vector distributions around the single Savonus wind rotor at the two positions are demonstrated in Figs. 4.4 and 4.5, respectively. In Fig. 4.4, it shows that the pressure difference between the front and back sides of the retuning blade at α=110° is apparently higher than that at α=10°. A large vortex is generated around the tip at the low-pressure region behind the blade as shown in Fig 4.5 (b). This effect would produce a negative torque and thus causes a lower torque. On the other hand, as shown in Fig 4.5 (a) at α=10°, the pressure difference between the front and back sides of the retuning blade is smaller, and the generated vortices are also smaller.
Therefore, the negative torque is decreased, causing a higher torque.
Static pressure field and velocity vector distribution at a cross section at z = 1m (see Sec. 3.1) in 3-D simulations with tip-speed ratio 0.9 at α=10° and 110°
are shown in Figs. 4.6 and 4.7, respectively. Comparing these two figures with Figs. 4.4 and 4.5, the phenomena in 3-D simulation are quite similar to those in 2-D one, only the pressure values are apparently lower than those in 2-D simulation due to the existence of one more dimension in 3-D simulation. When the wind hits blades, as shown in Fig. 4.8, the velocity vector distribution at y = 0, the air close to the top and bottom of the wind rotor will escape upwardly and downwardly, leading to a decrease of pressure around the wind rotor.
The performance comparisons between 2-D and 3-D predictions and with the corresponding experimental data are shown in Fig. 4.9. Considering the
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experimental measurements, the error bars on all the experimental data are fixed at ±20% of the measured value. Such value is proposed by Howell et al. [6], who also applied Fluent to compare the performances of a single VAWT by using 2-D and 3-D predictions with measurements. In Fig. 4.9, it clearly shows that the 3-D simulation is more suitable than the 2-D one in dealing with this problem. It is resulted from the effect mentioned above that the air close to the top and bottom of the wind rotor escape upwardly and downwardly. Such effect decreases the energy gained from wind and thus causes a lower performance.
Moreover, the influence of frictions by end plates would lower the performance, too. For these reasons, the 3-D simulation is more suitable than the 2-D one, ratio. It is because the Reynolds number around the blades increases with wind speed, causing a delayed separation; see Fig. 4.11, the velocity vector distribution at z = 1m. Therefore, the drags on the advancing blades decrease and then cause a higher cp.
4.1.2 A Single Savonius Wind Rotor in Atmosphere
To simulate a single Savonius wind rotor in atmosphere, its domain even with an application of symmetry is expected to be bigger than the one inside the wind tunnel. 2-D model uses a grid number of 15423, whereas 3-D model uses
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886676. The parameters used are summarized in Table 4.2 .
Table 4.2 Parameters for a single Savonius wind rotor in atmosphere
Wind Speed (m/s) 7 and 14 figure, the maximal torque happens at α=10° and the minimum is at α=110°. The static pressure field and velocity vector distribution in 2-D simulation around the single wind rotor at the above two positions are shown in Figs. 4.13 and 4.14, respectively. The results show that both the maximum and minimum of torque are happened at the same position inside the wind tunnel, and the differences in pressure field and velocity vector distribution between the two conditions are unapparent.
Static pressure field and velocity vector distribution at a cross section of z = 1m in 3-D simulations with tip-speed ratio 0.9 at α=10° and 110° are shown in Figs. 4.15 and 4.16, respectively. Comparing these two figures with Figs. 4.13 and 4.14, the phenomena in 3-D simulation are similar to those in 2-D one and its pressure values are apparently lower than the ones in 2-D simulation. The reasons are the same as the situation inside the wind rotor as mentioned in Section 4.1.1.
The simulation results are shown in Fig. 4.17. In 2-D simulations, the results show that the maximum of cp is 0.234 at wind speed 7 m/s and 0.236 at
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14 m/s. In 3-D, the maximum of cp is 0.182 at wind speed 7 m/s and 0.184 at 14 m/s. As shown in Fig. 4.17, the 2-D simulation results are apparently higher than 3-D ones, and the cp slightly increases with wind speeds at the same tip speed ratio in both 2-D and 3-D simulation. The reasons are the same as the case of a single Savonius wind rotor inside the wind tunnel discussed in Section 4.1.1.
4.1.3 Performance Comparison between One Single Savonius Wind Rotor Inside the Wind Tunnel and the One in Atmosphere
Comparing the streamlines between one single wind rotor inside the wind tunnel and the one in atmosphere, the generated vortices around the one in atmosphere are slightly larger than those inside the wind tunnel (see Figs. 4.18 and 4.19). The difference is resulted from that the wind tunnel is not large enough to simulate the condition in atmosphere completely; therefore, rotating wind rotor would cause a higher pressure field (see Figs. 4.4 and 4.13), causing the curved streamlines. In Figs. 4.18 and 4.19, it can be seen that the wake length caused by flow separations in atmosphere is longer than that inside the wind tunnel both at α=10° and α=110°. The larger wake flow field would make a higher difference in pressure between the front and back sides of the wind rotor, and then causes a higher drag. Therefore, the performance of one single Savonius wind rotor in atmosphere is lower than that inside the wind tunnel.
The performance comparisons between the one inside the wind tunnel and the one in atmosphere by 2-D and 3-D simulations are shown in Figs. 4.20 (a) and (b). As shown in these two figures, the cp of a single Savonius wind rotor in atmosphere is clearly lower than that inside the wind tunnel. The average difference is about 0.04 either in 2-D or 3-D simulation. The reasons have
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been mentioned above. Therefore, the simulations carried out in atmosphere are more practical.