1. Design of Vertical Axis Wind Turbines
P M V Subbarao
Professor
Mechanical Engineering Department
A Stable and Rugged Configuration .....

2. General Configuration of a Vertical-Axis Wind Turbine

3. The Turbine Rotor Subsystem : VAWT
Blades are shaped to approximate a troposkien

4. Local Details of The VAWT
Z (m)
r (m)
V (m/s) 

5. Problem Statement

6. Annual Energy Fraction vs velocity
Bromma
Malamo
Visby

7. Power Law Wind Profile
The power law is used by many wind energy researchers.
From the roughness length
Lawn, water: z0 = 0.01 m
Bushland: z0 = 0.1 m
Towns, forests: z0 = 1m

8. Single Stream Tube (SST) ModelV V Vw 
VAWT blades project a cylinder that is parallel to the stream tube.
The blades cross the normal actuator disc twice along their upwind and downwind path.
The induction factor:
 azimuth angle

9. Local Instantaneous Airfoil velocity and Force diagrams
The relative velocity component (VR) 
Normalized relative velocity

10. Local Details of The VAWT
Z (m)
r (m)

11. Rotor and blade element coordinate system
Rotor coordinate system
Top view
Blade element coordinate system

12. Kinetics Vs Kinematics of VWAT
Normalized relative velocity
angle of attack
Normal Force Coefficient
Tangential Force Coefficient

13. Local Instantaneous Torque per Blade
The local instantaneous Tangential force (dFti) on one single airfoil at certain θ is
The local instantaneous Torque (di) on one single airfoil at certain θ is
A single blade passes each stream tube twice per revolution in the upstream and downsteam.

14. Local Details of The VAWT
Z (m)
r (m)

15.  
VR(m/s) CL CD

16. Submitted By: Lt Col Vivek Bandal 2016MET2570 Ajay Singh 2016MET2563
Wind Power Farm Assgn:6
Submitted By:
Lt Col Vivek Bandal 2016MET2570
Ajay Singh 2016MET2563

17. 1st Quadrant θ in degrees α in degrees Vr Cl Cd 34.27054 0.00575 10 10
0.1427 20
0.2793 30
0.4202 40
0.5793 50
0.7225 60
0.8143
0.0119 70
0.8723 80
0.9142 90
0.9418

18. 2nd Quadrant θ in degrees α in degrees Vr Cl Cd 90 8.270232 30.00832
0.9418
100
0.9497
110
0.9366
0.0141
120
0.9024
0.0134
130
0.8453
140
0.7599
150
0.5819
160
0.3772
170
0.1929
180
1.28E-15

19. 3rd Quadrant θ in degrees α in degrees Vr Cl Cd 180 1.28E-15 25.12196
190
200
0.0076
210
220
230
-0.904
240
250
260
270

20. 4th Quadrant θ in degrees α in degrees Vr Cl Cd 270 -9.24207 30.08682
280
-8.851
-0.989
290
300
310
320
-0.626
0.0098
330
340
350
360
-1.9E-15

21. z=23.80m;r=16.63m;Vo=3.89;Lambda=4.4; me1130645
Theta (degree)
Relative velocity
alfa (degree) Cl Cd
df/dh
dT/dh
21.01
0.00
0.01 10
20.91
1.83
0.19
3.05
50.74 20
20.73
3.60
0.38
12.99
216.04 30
20.46
5.28
0.57
28.38
472.04 40
20.11
6.84
0.80
50.62
841.79 50
19.70
8.27
0.97
71.28 60
19.22
9.53
1.05
0.02
84.46 70
18.68
10.59
1.11
94.12 80
18.11
11.43
1.16
99.22 90
17.50
12.00
1.18
99.27
100
16.87
12.28
1.20
95.45
110
16.23
12.21
87.70
120
15.61
11.76
1.17
76.49
130
15.01
10.88
1.13
63.14
140
14.46
9.54
47.93
797.12
150
13.98
7.74
0.94
32.36
538.10
160
13.60
5.49
0.61
14.03
233.24
170
13.35
2.87
0.30
3.33
55.40
180
13.23

22. z=23.80m;r=16.63m;Vo=3.89;Lambda=4.4; me1130645
Theta (degree)
Relative velocity
alfa (degree) Cl Cd
df/dh
dT/dh
180
13.23
0.00
0.01
190
13.26
-2.95
-0.31
4.76
79.10
200
13.45
-5.81
-0.65
19.25
320.11
210
13.78
-8.38
-0.98
43.25
719.29
220
14.25
-10.54
-1.11
0.02
65.57
230
14.82
-12.19
-1.20
88.68
240
15.48
-13.30
-1.24
0.03
110.41
250
16.18
-13.88
-1.26
128.44
260
16.90
-13.97
141.19
270
17.61
-13.61
148.16
280
18.29
-12.88
-1.22
146.66
290
18.93
-11.83
-1.18
138.84
300
19.50
-10.52
122.40
310
19.99
-9.01
-1.02
101.42
320
20.39
-7.34
-0.87
74.08
330
20.69
-5.57
-0.62
41.54
690.85
340
20.90
-3.73
-0.39
18.44
306.70
350
21.00
-1.86
-0.20
5.06
84.21

23. Tutorial 6 z
19.5 m
Uinf
3.67 m/s
a/sin(Theta)
0.07 r
12.2 m
lambda
3.4 Re
5.49E+05
Theta
Rad
alfa rad
alfa deg Vr Cl Cd
dFti/dH
dTi
16.148 10
0.2357 20
0.4685 30
0.7564 40
0.1475
0.9787 50
10.252
1.0854 60
1.1708
0.0212 70
1.2359 80
1.2707 90
1.29

24. z=43.2m theta alfa(degrees) Vr cl cd dFt dtau 8.494759206 0.00665 10
0.4063 20
0.8597 30
1.1712 40
1.3334
0.0298 50
1.3197 60
1.183 70 80 90

25. z=43.2m theta alfa(degrees) Vr cl cd dFt dtau 270 34.03455601
280
290
300
1.1171
0.1875
310
1.2441
320
1.3591
330
1.2029
340
0.9149
350
0.4168

26. z 45.9 : U∞ 4.74 NACA0015 θ α Vr Cl Cd dFti/dh dτ/dh 0.00 36.45 0.01
NACA0015 θ α Vr Cl Cd
dFti/dh
dτ/dh
0.00
36.45
0.01
-12.96 10
1.29
36.34
0.14
252.87 20
2.52
36.12
0.27
311.64 30
3.64
35.78
0.39 40
4.64
35.34
0.49 50
5.48
34.81
0.59 60
6.15
34.19
0.68 70
6.63
33.52
0.75
401.06 80
6.92
32.79
0.79
721.15 90
7.01
32.03
0.80
784.96
100
6.91
31.25
0.78
637.59
110
6.60
30.47
0.74
299.34
120
6.11
29.71
0.67
130
5.43
29.00
0.58
140
4.59
28.36
150
3.60
27.81
0.38
160
2.48
27.38
184.39
170
1.27
27.10
137.76
180
26.97
-7.10

27. z 45.9 : U∞ 4.74 NACA0015 θ α Vr Cl Cd dFti/dh dτ/dh 190 -1.30 27.01
NACA0015 θ α Vr Cl Cd
dFti/dh
dτ/dh
190
-1.30
27.01
-0.14
0.01
140.70
200
-2.58
27.22
-0.28
166.52
210
-3.80
27.60
-0.41
220
-4.92
28.13
-0.52
230
-5.90
28.79
-0.64
240
-6.70
29.54
-0.76
376.35
250
-7.30
30.37
-0.84
950.08
260
-7.67
31.23
-0.89
270
-7.80
32.10
-0.91
280
-7.69
32.95
290
-7.33
33.74
300
-6.75
34.46
572.96
310
-5.95
35.09
-0.65
320
-4.97
35.61
-0.53
330
-3.84
36.01
340
-2.61
36.28
284.19
350
-1.31
36.43
-0.15
269.61
360
0.00
36.45
-12.96

28. Time Averaged Local Torque
The time averaged local torque generated by “B” blades and twice per revolution can be expressed as
The time averaged total torque generated by “B” blades and twice per revolution can be expressed as

29. Local Details of The VAWT
Z (m)
r (m)
V (m/s) 
davg,loc