In this section, the analysis for four two-blade Savonius system subjected to the wind of 7 m/s is carried out. The phase angle difference adopted is 90 degree, originated from the conclusion of Feng’s [1] studied.
He found that such condition can result in the best performance. The computational domain is 26(L) x 38.5(W) x 15(H) in 3-D model and 26(L) x 38.5(W) in 2-D domain. The distance between two wind rotors is 1.12m, as shown in Fig. 3.4. The grid numbers in 3-D model and 2-D model are 1901050 and 49862, respectively. From Section 4.1.2, it found that the maximum value of power coefficient occurs at TSR = 0.82, therefore, the tip speed ratios are tested at 0.4, 0.6, 0.8, 0.82, 1.0 and 1.2, the related parameters are shown in Table 4.6. The four rotors rotate in the same direction, which is counterclockwise.
Table 4.6 Parameters for matrix system
Simulation Domain 3-D ( 26m x 38.5m x 15m)
Wind Speed 7 m/s
Tip-speed Ratio 0.4~1.2
The resultant torque curves for each Savonius rotor in system are shown in Fig. 4.27, at wind speed of 7 m/s and tip speed ratio of 0.82, where the maximum Cp occurs in single Savonius rotor. The pressure distribution and velocity vector field are shown in Figs. 4.28 and 4.29, respectively. In order to demonstrate the effect of system, each rotor is assigned a number, as marked in Fig. 4.28.
78 will provide extra momentum to # 3, and the similar action is duplicated from #3 to #2, and so on. This is the reason that the resultant torque on # 1 rotor is the highest.
From Fig. 4.28, it shows the pressure difference on the advancing blade for each rotor is pretty high, resulting in high drag force. From the velocity vector field in Fig. 4.29, #2 and #4 rotors rotate to 110 degree. In this situation, the returning blades of #2 and #4 rotors provide additional momentum to lateral (upward) direction. Thus, the nearby rotors #1 and
#3 can get the extra momentum. Each rotor provides and absorbs the momentum from other rotors during the rotation. This positive effect occurs and enhances the performance of the overall system.
Comparing with the performance of one single Savonius wind turbine, the power coefficient for four Savonius in system, 0.291, at tip speed ratio 0.82 is better than that (0.198) of the single one at wind velocity of 7m/s, as shown in Fig. 4.30. The power coefficient increases about 47%. The reason is that the flow interference occurs between Savonius turbines that produce positive interaction between them.
The simulation results for 2-D and 3-D are system is shown in Fig.
4.31. The maximum power coefficient occurs at tip speed ratio 0.82 for both conditions. The values are 0.338 and 0.291, respectively. The reason
79
for the difference is similar to that described in Section 4.1.2.
Figure 4.32 is a comparison made between the simulation and experiment. The experiment is carried out in the pilot plant in ChuBei city.
The simulation results showed that the maximum power coefficient, 0.291, is occurred at TSR 0.82. However, the performance (Cp) difference is apparently between the experimental and simulation results.
As expected, the simulation results are better than experimental ones.
This is because the mechanical efficiency and the generator’s efficiency need to be considered in experiment. Besides, the wind velocity and rotational speed are fixed in simulation. On the other hand, the gust always exists in real experiment. It will let the rotor runs at different TSR continuously due to the inertia effect. For instance, as the wind velocity drops down suddenly, the rotational speed of blade will not stop immediately, leading to a higher tip speed ratio. In other words, the inertia effect keeps the blades rotating continuously that cause maximal Cp to occur at a higher TSR = 1.0. And this is the reason for the up and down tendency appearing in experiment. The measured power coefficients as a function of TSR are shown in Fig. 4.33. The history of wind velocity variation during the experiment is given in Fig. 4.34. The average of wind velocity in this period is 6.53 m/s. The history of generated power is shown in Fig. 4.35. The average power outputs of Savonius engine are shown in Table 4.6. The simulated power outputs of single and systematic Savonius engines are 73.74 and 109.13 watts, respectively. It has a higher power output about 47% in system. The experimental power output in system is 73.62 watts, which is lower about
80
48% than the simulated result. The first reason to cause the difference is due to the lower wind speed in experiment. The wind power input is proportional to third power of wind velocity. Therefore, it results in about 23% of power input difference between the simulation and experiment.
The second reason is the mechanical efficiency loss of transmission that contributes to about 25% difference. Based on the above reasons, the difference between simulated and experiment is about 48%.
Table 4.6 The average power outputs of Savonius wind rotors Wind speed
(m/s)
Averaged Power (W/per turbine)
Single Savonius 7 73.74
Four Savonius in
system 7 109.13
Four Savonius in
system (exp.) 6.53 73.62
81
Fig. 4.1 The definition of overlap ratio
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30
Power coefficient (Cp)
Overlap ratio
Present simulation Blackwell et al. study [9]
Fig. 4.2 The power coefficient of Savonius wind turbine with different overlap ratio
D ratio d Overlap
82
(a)
(b)
83
(c)
Fig. 4.3 The streamline with different overlap ratio (a) overlap ratio 0.1 (b) overlap ratio 0.15 (c) overlap ratio 0.3
Fig. 4.4 The defined angle
of rotating wind blade relative to the initial angle84
0 60 120 180 240 300 360
0 2 4 6 8 10 12 14
Torque(N*m)
angle
Fig. 4.5 Torque curve of one single Savonius wind turbine with wind speed 7 m/s at tip speed ratio 0.82
(a)
Stagnation point
Overlap jet Counter rotating vortices
Recirculation flow
85
(b)
Fig. 4.6 Pressure distribution around one single Savonius wind rotor in atmosphere in 3-D simulation at z=1.21m and
(a) α=20°; (b) α=110°
(a)
Stagnation point
Recirculation flow Overlap jet
Counter rotating vortices Recirculation flow
Overlap jet
86
(b)
Fig. 4.7 Velocity vector around one single Savonius wind rotor in atmosphere in 3-D simulation at z=1.21m and
(a) α=20°; (b) α=110°
Fig. 4.8 The performance comparison between 2-D and 3-D in atmosphere
0.4 0.6 0.8 1.0 1.2
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Power coefficient (Cp)
tip speed ratio
2D single Savonius in atmosphere 3D single Sanonius in atmosphere
Recirculation flow Overlap jet
87
(a)
(b)
Fig. 4.9 Velocity vector distribution in 3-D simulation at y=0 around (a) the top end plate (b) the bottom end plate
88
Fig. 4.10 Velocity vector distribution in 3-D simulation at z=1.21m
0.4 0.6 0.8 1.0 1.2
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Power coefficient (Cp)
tip speed ratio
in atmosphere inside the wind tunnel
Fig. 4.11 The comparison between one single Savonius wind turbine in atmosphere and inside wind tunnel
89
(a)
(b)
Fig. 4.12 Pressure distribution around one single Savonius wind rotor inside the wind tunnel in 3-D simulation at z=1.21m and
(a) α=20°; (b) α=110°
90
(a)
(b)
Fig. 4.13 Velocity vector around one single Savonius wind rotor inside the wind tunnel
(a) α=20°; (b) α=110°
91
(a)
(b)
Fig. 4.14 Streamlines around one single Savonius wind rotor at α=110°
(a) inside the wind tunnel ; (b) in atmosphere
92
Fig. 4.15 The defined angle
of rotating wind blade relative to the initial angle(a)
93
(b)
(c)
94
(d)
(e)
Fig. 4.16 Pressure distribution around the blade of H-typed wind rotor in 3-D simulation at z=0.45m
(a) ;(b) ;(c) ;(d) ;(e) 325 180 115 30 225
95
(a)
(b)
96
(c)
(d)
97
(e)
Fig. 4.17 Velocity vector around the blade of H-typed wind rotor in 3-D simulation at z=0.45m
(a) ; (b) ; (c) ;(d) ;(e)
(a) 325
180 115 30 225 Blade 1
Blade 2
Blade 3
Blade 4 Blade 5
98
(b)
Fig. 4.18 Pressure distribution of the of overall H-typed blades in 3-D simulation at z=0.45m
(a) ; (b)
(a)
Blade 1
Blade 2
Blade 3
Blade 4 Blade 5
28
38
99
(b)
Fig. 4.19 Velocity vector of the of overall H-typed blades in 3-D simulation at z=0.45m
(a) ;(b)
Fig. 4.20 The H-type performance comparison between 2-D and 3-D in simulation
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Power coefficient (Cp)
tip speed ratio
H-type in 2D H-type in 3D
28
38
100
(a)
(b)
(c)
Fig. 4.21 Velocity vector distribution in 3-D simulation at (a) the top of the blade;(b) the bottom of the blade (c) z=0.45m
101
Fig. 4.22 The comparison between reference case and present study of one single Savonius wind turbine in atmosphere
0.4 0.6 0.8 1.0 1.2
Blackwell et al. [9] experiment Simulated Blackwell's study
Fig. 4.23 The comparison between reference case and present study of one single Savonius wind turbine inside the wind tunnel
102
Fig. 4.24 The simulation result of H-type wind turbine compares with reference study
Fig. 4.25 The comparison between Savonius and H-type wind turbine
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
103
(a)
(b)
Fig. 4.26 The schemetic diagram with different tip speed ratio (a) with tip speed ratio 2.5 (b) with tip speed ratio 1.5
104
Fig. 4.27 Torque curves of system at TSR 0.82
Fig. 4.28 Pressure distribution around four Savonius wind rotors with phase angle difference 90°
Rotor No.1
Rotor No.2
Rotor No.3
Rotor No.4
105
Fig. 4.29 Velocity vector four Savonius wind rotors with phase angle difference 90°
0.4 0.6 0.8 1.0 1.2
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
Power coefficient (Cp)
tip speed ratio
Savonius in system
Single Savonius wind turbine Rotor No.1
Rotor No.2
Rotor No.3
Rotor No.4
106
Fig. 4.30 The performance comparison of single and system of Savonius wind turbine
Fig. 4.31 The power coefficient of System of Savonius between 2-D and 3-D
0.4 0.6 0.8 1.0 1.2
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Power coefficient (Cp)
tip speed ratio
System of Savonius in 2D System of Savonius in 3D
107
Fig. 4.32 The performance of Savonius wind turbines in system
Fig. 4.33 The system of Savonius wind turbines in experiment
Fig. 4.34 Wind velocity variation and the average of wind velocity
0.2 0.4 0.6 0.8 1.0 1.2
-0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Measured point Curved fit
Power coefficient (Cp)
tip speed ratio
108
Fig. 4.35 The generated power in experiment
12:00 12:20 12:40 13:00 13:20 13:40 14:00 0
100 200 300 400 500 600 700 800
Generated Power (W)
time
109