turbine comparison

STATIC TORQUE ANALYSIS OF VARIOUS TWO-BLADED SAVONIUS WIND TURBINE

MODELS

Brandon [email protected]

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

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

Turbine Designs Studied• Vertical axis wind turbine• Savonius, two-bladed design• Blades of different radii

– 4” diameter– 5” diameter– 6” diameter

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

Mathematical Expressions• Rotor Area: • Angular Velocity: • Reynolds Number:• Tip Speed Ratio: • Torque Coefficient: • Power Coefficient:

Procedure•Two-part study

– ANSYS Fluent to simulate designs– Wind tunnel to measure torque

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

Mesh Created

4”ϴ blade design 5”ϴ blade design 6”ϴ blade design

5 m/s Vertical Airflow Pressure


5 m/s Horizontal Airflow Pressure


5 m/s Vertical Airflow Velocity


5 m/s Horizontal Airflow Velocity


Simulation Results

HorizontalAirflow

VerticalAirflow

MAX MIN4"ϴ DESIGN 18.6 -49.35"ϴ DESIGN 13.3 -25.76"ϴ DESIGN 11.8 -18.6

5 M/S LEFT-RIGHT VELOCITYPRESSURE (pascal)

MAX MIN4"ϴ DESIGN 9.71 0.02145"ϴ DESIGN 7.77 0.02126"ϴ DESIGN 7.04 0.0253

5 M/S LEFT-RIGHT VELOCITYVELOCITY (m/s)

MAX MIN4"ϴ DESIGN 68.5 -47.35"ϴ DESIGN 79.6 -1.496"ϴ DESIGN 81.9 -2.15

5 M/S UPWARDS VELOCITYPRESSURE (pascal)

MAX MIN4"ϴ DESIGN 13.5 0.0004655"ϴ DESIGN 11.5 0.001756"ϴ DESIGN 11.6 0.0026

5 M/S UPWARDS VELOCITYVELOCITY (m/s)

Experimental Setup• Wind Turbine in Georgia Southern Wind Research Laboratory

used to conduct experiments• Static torque measurement fixture utilized to collect data

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


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

Torque vs Blade Angle• 6 m/s

0 30 60 90 120 150

-0.1-0.08-0.06-0.04-0.02

00.020.040.060.08

0.1

4"ϴ Blade Design5"ϴ Blade Design6"ϴ Blade Design

Blade Angle, (degree)

Torq

ue, T

(N-m

)

Torque vs Blade Angle• 9 m/s

0 30 60 90 120 150

-0.05

0

0.05

0.1

0.15

0.2



Torq

ue, T

(N-m

)

Torque vs Blade Angle• 11.6 m/s

0 30 60 90 120 150

-0.1-0.05

00.05

0.10.15

0.20.25

0.30.35

0.4



Torq

ue, T

( N

-m)

Torque Coefficient Calculations

• From measured torque values, equation:used to calculate torque coefficient• T = Torque• ρ = Air Density (kg/m3)• A = Rotor Area• D = Overall Rotor Diameter• V = Wind Velocity (m/s)

Torque Coefficient vs Blade Angle• 6 m/s

0 30 60 90 120 150

-0.0800

-0.0600

-0.0400

-0.0200

0.0000

0.0200

0.0400

0.0600

0.0800


Blade Angle

Torq

ue C

oeffi

cient

Torque Coefficient vs Blade Angle• 9 m/s

0 30 60 90 120 150

-0.0400-0.02000.00000.02000.04000.06000.08000.10000.12000.14000.1600



Torq

ue C

oeffi

cien

t, Cq

Torque Coefficient vs Blade Angle• 11.6 m/s

0 30 60 90 120 150-0.0500

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000



Torq

ue C

oeffi

cien

t, Cq

Angular Velocity Calculations

• Revolutions per minute values of 60, 80, 100, 120, and 140 implemented to calculate power coefficient

• Equation: used to calculate angular velocity• N = revolutions per minute

Tip Speed Ratio Calculations

• From calculated angular velocity values, equation: used to calculate tip speed ratio

• = Angular Velocity (rad/sec)• = Overall Rotor Diameter• = Wind Speed Velocity (m/s)

Power Coefficient Calculations

• From calculated torque coefficient values, equation: used to calculate power coefficient

• = Tip Speed Ratio• = Torque Coefficient

Power Coefficient vs Blade Angle

• 60 RPM considered– Similar power coefficients– Variable wind speed

Power Coefficient vs Blade Angle• 60 RPM considered• 6 m/s

0 30 60 90 120 150

-0.0100-0.0080-0.0060-0.0040-0.00200.00000.00200.00400.00600.00800.0100



Pow

er C

oeffi

cient

, Cp

Power Coefficient vs Blade Angle• 60 RPM considered• 9 m/s

0 30 60 90 120 150

-0.0050

0.0000

0.0050

0.0100

0.0150

0.0200



Pow

er C

oeffi

cient

, Cp

Power Coefficient vs Blade Angle• 60 RPM considered• 11.6 m/s

0 30 60 90 120 150

-0.0100-0.00500.00000.00500.01000.01500.02000.02500.03000.0350



Pow

er C

oeffi

cient

, Cp

Power Coefficient vs Tip Speed• 6 m/s• 60, 80, 100, 120, and 140 RPM considered• Various tip speeds calculated• Parallel (0º) position

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.280

0.00050.001

0.00150.002

0.00250.003

0.00350.004

0.0045


Tip Speed Ratio, λ

Pow

er C

oeffi

cient

, Cp

Power Coefficient vs Tip Speed• 6 m/s• 60, 80, 100, 120, and 140 RPM considered• Various tip speeds calculated• Perpendicular (90º) position

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0


Tip Speed Ratio, λ

Pow

er C

oeffi

cient

, C

p

Power Coefficient vs Tip Speed• 9 m/s• 60, 80, 100, 120, and 140 RPM considered• Various tip speeds calculated• Parallel (0º) position

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.280

0.00050.001

0.00150.002

0.00250.003

0.00350.004

0.00450.005


Tip Speed Ratio, λ

Pow

er C

oeffi

cient

, Cp

Power Coefficient vs Tip Speed• 9 m/s• 60, 80, 100, 120, and 140 RPM considered• Various tip speeds calculated• Perpendicular (90º) position

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0


Tip Speed Ratio, λ

Pow

er C

oeffi

cient

, Cp

Power Coefficient vs Tip Speed• 11.6 m/s• 60, 80, 100, 120, and 140 RPM considered• Various tip speeds calculated• Parallel (0º) position

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.280

0.002

0.004

0.006

0.008

0.01

0.012

0.014


Tip Speed Ratio, λ

Pow

er C

oeffi

cient

, Cp

Power Coefficient vs Tip Speed• 11.6 m/s• 60, 80, 100, 120, and 140 RPM considered• Various tip speeds calculated• Perpendicular (90º) position

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28

-0.01-0.008-0.006-0.004-0.002

00.0020.0040.0060.008

0.01


Tip Speed Ratio, λ

Pow

er C

oeffi

cient

, Cp

Experiment Results

Blade Angle

4"ϴ Torque N-

m

5"ϴ Torque N-

m

6"ϴ Torque N-

m0 0.0068 0.0147 0.009030 0.0181 0.0490 0.056560 0.0486 0.0804 0.078090 -0.0045 -0.0049 -0.0102

120 -0.0904 0.0412 0.0000150 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-

m0 0.0147 0.0206 0.013630 0.0926 0.1216 0.120960 0.1006 0.1746 0.165090 -0.0090 -0.0245 -0.0215

120 -0.0181 0.0510 0.0113150 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-

m0 0.0621 0.0510 0.024930 0.1672 0.1961 0.201160 0.2757 0.3324 0.277990 0.0350 -0.0382 0.0000

120 -0.0203 0.0510 0.0271150 0.0610 -0.0039 -0.0147

AVERAGE 0.0968 0.0981 0.0861

11.6 M/S Torque

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

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

turbine comparison

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