This document analyzes the static torque of various two-bladed Savonius wind turbine models through computational fluid dynamics simulations and wind tunnel experiments. It finds that a turbine with 5-inch diameter curved blades produced the highest average torque across wind speeds of 6, 9, and 11.6 m/s. Simulations were conducted in ANSYS Fluent to compare pressure and velocity fields, while experiments measured torque at varying blade angles and revolutions per minute to calculate torque, power, and tip speed ratios.

1. STATIC TORQUE ANALYSIS OF
VARIOUS TWO-BLADED
SAVONIUS WIND TURBINE
MODELS
Brandon Byrnes
brandonrbyrnes@gmail.com

2. Purpose of Research
• Determine the most efficient wind turbine design when
considering a specific type with only one variable
• Designs chosen were two-blade vertical axis wind turbines
with the same diameter
• Variable tested was diameter of the curved blades

3. Wind Turbines
• Used to convert naturally occurring wind into electric power
• Blades mounted around a central axis capture the wind
• Captured wind causes the turbines to rotate
• Two types of wind turbines: horizontal axis wind turbines and
vertical axis wind turbines

4. Turbine Designs Studied
• Vertical axis wind turbine
• Savonius, two-bladed design
• Blades of different radii
– 4” diameter
– 5” diameter
– 6” diameter

5. List of Symbols
• Symbol Explanation
• A Rotor Area
• D Overall Rotor Diameter
• d Blade Diameter
• H Rotor Height
• V Wind Velocity (m/s)
• N Revolutions Per Minute
• ν Kinematic Viscosity (m2/s)
• ρ Air Density (kg/m3)
• ω Angular Velocity (rad/sec)
• Re Reynolds Number
• λ Tip Speed Ratio
• T Torque
• P Power
• Cq Torque Coefficient
• Cp Power Coefficient

6. Mathematical Expressions
• Rotor Area: 𝐴 = 𝐷. 𝐻
• Angular Velocity: 𝜔 =
2𝜋𝑁
60
• Reynolds Number:𝑅𝑒 =
𝑉𝐷
𝜈
• Tip Speed Ratio: 𝜆 =
𝜔𝐷
2𝑉
• Torque Coefficient: 𝐶 𝑞 =
𝑇
1
4
𝜌𝐴𝐷𝑉2
• Power Coefficient: 𝐶 𝑝 =
𝑃
1
2
𝜌𝐴𝑉3
=
𝑇𝜔
1
2
𝜌𝐴𝑉3
= 𝐶𝑞

7. Procedure
• Two-part study
– ANSYS Fluent to simulate designs
– Wind tunnel to measure torque

8. Static Simulation
• Conduct in a 2D format
• Designs created in Geometry function as cross-section
• Sketches imported into Mesh function
• Mesh imported into Fluent function
• Simulation executed in vertical and horizontal airflow

9. Mesh Created
4”ϴ blade design 5”ϴ blade design 6”ϴ blade design

10. 5 m/s Vertical Airflow Pressure
4”ϴ blade design 5”ϴ blade design 6”ϴ blade design

11. 5 m/s Horizontal Airflow Pressure
4”ϴ blade design 5”ϴ blade design 6”ϴ blade design

12. 5 m/s Vertical Airflow Velocity
4”ϴ blade design 5”ϴ blade design 6”ϴ blade design

13. 5 m/s Horizontal Airflow Velocity
4”ϴ blade design 5”ϴ blade design 6”ϴ blade design

14. Simulation Results
Horizontal
Airflow
Vertical
Airflow
MAX MIN
4"ϴ DESIGN 18.6 -49.3
5"ϴ DESIGN 13.3 -25.7
6"ϴ DESIGN 11.8 -18.6
5 M/S LEFT-RIGHT VELOCITY
PRESSURE (pascal)
MAX MIN
4"ϴ DESIGN 9.71 0.0214
5"ϴ DESIGN 7.77 0.0212
6"ϴ DESIGN 7.04 0.0253
5 M/S LEFT-RIGHT VELOCITY
VELOCITY (m/s)
MAX MIN
4"ϴ DESIGN 68.5 -47.3
5"ϴ DESIGN 79.6 -1.49
6"ϴ DESIGN 81.9 -2.15
5 M/S UPWARDS VELOCITY
PRESSURE (pascal)
MAX MIN
4"ϴ DESIGN 13.5 0.000465
5"ϴ DESIGN 11.5 0.00175
6"ϴ DESIGN 11.6 0.0026
5 M/S UPWARDS VELOCITY
VELOCITY (m/s)

15. Experimental Setup
• Wind Turbine in Georgia Southern Wind Research Laboratory
used to conduct experiments
• Static torque measurement fixture utilized to collect data

16. Models Tested
• Models of 4”, 5”, and 6” diameter blades created
• Common 8 ½” overall diameter and 12” blade height
• Clear acrylic material construction
4”ϴ blade design 5”ϴ blade design 6”ϴ blade design

17. Data Acquisition
• Airflow rates of 6, 9, and 11.6 meters per second
– Calculated using anemometer
• Reynolds numbers calculated; indicate turbulent flow
• Rotational positions at 30º increments tested
• Torque measurement gathered at all wind speeds

18. Torque vs Blade Angle
• 6 m/s
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0 30 60 90 120 150
Torque,T(N-m)
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

19. Torque vs Blade Angle
• 9 m/s
-0.05
0
0.05
0.1
0.15
0.2
0 30 60 90 120 150
Torque,T(N-m)
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

20. Torque vs Blade Angle
• 11.6 m/s
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 30 60 90 120 150
Torque,T(N-m)
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

21. Torque Coefficient Calculations
• From measured torque values, equation:
𝐶 𝑞 =
𝑇
1
4
𝜌𝐴𝐷𝑉2
used to calculate torque coefficient
• T = Torque
• ρ = Air Density (kg/m3)
• A = Rotor Area
• D = Overall Rotor Diameter
• V = Wind Velocity (m/s)

22. Torque Coefficient vs Blade Angle
• 6 m/s
-0.0800
-0.0600
-0.0400
-0.0200
0.0000
0.0200
0.0400
0.0600
0.0800
0 30 60 90 120 150
TorqueCoefficient
Blade Angle
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

23. Torque Coefficient vs Blade Angle
• 9 m/s
-0.0400
-0.0200
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0.1400
0.1600
0 30 60 90 120 150
TorqueCoefficient,Cq
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

24. Torque Coefficient vs Blade Angle
• 11.6 m/s
-0.0500
0.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
0 30 60 90 120 150
TorqueCoefficient,Cq
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

25. Angular Velocity Calculations
• Revolutions per minute values of 60, 80, 100,
120, and 140 implemented to calculate power
coefficient
• Equation: 𝜔 =
2𝜋𝑁
60
used to calculate angular
velocity
• N = revolutions per minute

26. Tip Speed Ratio Calculations
• From calculated angular velocity values,
equation: 𝜆 =
𝜔𝐷
2𝑉
used to calculate tip speed
ratio
• 𝜔 = Angular Velocity (rad/sec)
• 𝐷 = Overall Rotor Diameter
• 𝑉 = Wind Speed Velocity (m/s)

27. Power Coefficient Calculations
• From calculated torque coefficient values,
equation:𝐶 𝑝 = 𝐶𝑞 used to calculate power
coefficient
•  = Tip Speed Ratio
• 𝐶𝑞 = Torque Coefficient

28. Power Coefficient vs Blade Angle
• 60 RPM considered
– Similar power coefficients
– Variable wind speed

29. Power Coefficient vs Blade Angle
• 60 RPM considered
• 6 m/s
-0.0100
-0.0080
-0.0060
-0.0040
-0.0020
0.0000
0.0020
0.0040
0.0060
0.0080
0.0100
0 30 60 90 120 150
PowerCoefficient,Cp
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

30. Power Coefficient vs Blade Angle
• 60 RPM considered
• 9 m/s
-0.0040
-0.0020
0.0000
0.0020
0.0040
0.0060
0.0080
0.0100
0.0120
0.0140
0.0160
0.0180
0 30 60 90 120 150
PowerCoefficient,Cp
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

31. Power Coefficient vs Blade Angle
• 60 RPM considered
• 11.6 m/s
-0.0100
-0.0050
0.0000
0.0050
0.0100
0.0150
0.0200
0.0250
0.0300
0.0350
0 30 60 90 120 150
PowerCoefficient,Cp
Blade Angle,  (degree)
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

32. Power Coefficient vs Tip Speed
• 6 m/s
• 60, 80, 100, 120, and 140 RPM considered
• Various tip speeds calculated
• Parallel (0º) position
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0 0.05 0.1 0.15 0.2 0.25 0.3
PowerCoefficient,Cp
Tip Speed Ratio, λ
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

33. Power Coefficient vs Tip Speed
• 6 m/s
• 60, 80, 100, 120, and 140 RPM considered
• Various tip speeds calculated
• Perpendicular (90º) position
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
0 0.05 0.1 0.15 0.2 0.25 0.3
PowerCoefficient,Cp
Tip Speed Ratio, λ
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

34. Power Coefficient vs Tip Speed
• 9 m/s
• 60, 80, 100, 120, and 140 RPM considered
• Various tip speeds calculated
• Parallel (0º) position
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
0 0.05 0.1 0.15 0.2 0.25 0.3
PowerCoefficient,Cp
Tip Speed Ratio, λ
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

35. Power Coefficient vs Tip Speed
• 9 m/s
• 60, 80, 100, 120, and 140 RPM considered
• Various tip speeds calculated
• Perpendicular (90º) position
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0
0 0.05 0.1 0.15 0.2 0.25 0.3
PowerCoefficient,Cp
Tip Speed Ratio, λ
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

36. Power Coefficient vs Tip Speed
• 11.6 m/s
• 60, 80, 100, 120, and 140 RPM considered
• Various tip speeds calculated
• Parallel (0º) position
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 0.05 0.1 0.15 0.2 0.25 0.3
PowerCoefficient,Cp
Tip Speed Ratio, λ
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

37. Power Coefficient vs Tip Speed
• 11.6 m/s
• 60, 80, 100, 120, and 140 RPM considered
• Various tip speeds calculated
• Perpendicular (90º) position
-0.01
-0.008
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0.008
0.01
0 0.05 0.1 0.15 0.2 0.25 0.3
PowerCoefficient,Cp
Tip Speed Ratio, λ
4"ϴ Blade Design
5"ϴ Blade Design
6"ϴ Blade Design

38. Experiment Results
Blade
Angle
4"ϴ
Torque N-
m
5"ϴ
Torque N-
m
6"ϴ
Torque N-
m
0 0.0068 0.0147 0.0090
30 0.0181 0.0490 0.0565
60 0.0486 0.0804 0.0780
90 -0.0045 -0.0049 -0.0102
120 -0.0904 0.0412 0.0000
150 0.0226 0.0245 -0.0136
AVERAGE 0.0002 0.0342 0.0200
6 M/S Torque
Blade
Angle
4"ϴ
Torque N-
m
5"ϴ
Torque N-
m
6"ϴ
Torque N-
m
0 0.0147 0.0206 0.0136
30 0.0926 0.1216 0.1209
60 0.1006 0.1746 0.1650
90 -0.0090 -0.0245 -0.0215
120 -0.0181 0.0510 0.0113
150 0.0362 0.0196 -0.0147
AVERAGE 0.0362 0.0605 0.0458
9 M/S Torque
Blade
Angle
4"ϴ
Torque N-
m
5"ϴ
Torque N-
m
6"ϴ
Torque N-
m
0 0.0621 0.0510 0.0249
30 0.1672 0.1961 0.2011
60 0.2757 0.3324 0.2779
90 0.0350 -0.0382 0.0000
120 -0.0203 0.0510 0.0271
150 0.0610 -0.0039 -0.0147
AVERAGE 0.0968 0.0981 0.0861
11.6 M/S Torque

39. Discussion
• Considering pressure, 4” diameter blade design most efficient
– Pressure localized to cup of blade
• Considering velocity, 6” diameter blade design most efficient
– High velocity at blade tip, low profile
• Considering torque, 5” diameter blade design most efficient
– Highest average torque
• Considering power coefficient vs tip speed ratio, 4” diameter
blade design most efficient

40. Conclusion
• 5” diameter design overall most efficient design
– Highest average torque
– Although 4” diameter blade design more efficient considering pressure
and power coefficient vs tip speed, orientations calculated at 0° and 90°
showed smallest torque
– Although 6” diameter blade design more efficient considering velocity,
minimal differences between designs was shown in simulation