The Answer is Blowing in the Wind… The Power of Wind Disclaimer aerospace!
•  I am not a wind wind expert!! Wind turbine blade on I-­‐29 north of Sioux Falls, 10 Oct 2008 What is a Wind Turbine •  Remember your bicycle dynamo? A turbine uses wind to turn shaL connected to a gearbox, followed by a generator to produce electricity How does a turbine work? Limits to 100 % Efficiency •  Power in the wind
•  Betz limit (air can not be slowed to zero)
•  59.7 % is maximum efficiency
•  Low speed losses - wake rotation
•  Drag losses – aerodynamics and blade
geometry
•  Generator and drive train inefficiencies
The Betz limit •  Albert Betz, a German physicist, concluded that a wind turbine can convert no more than 59.3% of the kineYc energy of the wind into mechanical energy turning a rotor (1919) •  For a wind turbine to be 100% efficient it would need to stop 100% of the wind –  This would be a solid, flat disk and have no kineYc energy vs. Wind Power…Power of the Wind •  Power in the wind =½ρAV3 •  Subject to: –  Effect of air density, ρ –  Effect of sweep area, A –  Effect of wind speed, V –  Swept Area, A = πR2 •  Area of the circle swept by the rotor. KineYc Energy = Work = ½mV2 R R
The Importance of Windspeed3 •  Wind speed is the most important factor in determining power •  Power is a cubic funcYon of wind speed: V X V X V •  20% increase in wind speed means 73% more power •  Doubling wind speed means 8 Ymes more power d V KineYc Energy = Work = ½mV2 Power = Work / t = KineYc Energy / t = ½mV2 / t = ½(ρAd)V2/t Redistribute: = ½ρAV2(d/t) = ½ρAV3 Power = ½ρAV3 Power of the wind turbine •  Power = ½ρAV3, but power of the turbine: •  Powerturbine= Cp½ρAV3 –  Cp = Power coefficient –  Cp is the percentage of potenYal power converted to actual power •  Limited by several factors •  A 1MW turbine with a 30% Cp produces ~2,600 MWh that can power 320 homes An Working Example •  Wind blows at 7 MPH = 3 m/s 3 Power =
½
ρAV
•  ρ = 1.6 kg/m3 •  Blade length = 50 cm → area = 0.785 m2 3
3
2
1
Power = 2 (1.6 kg /m )(0.785 m )(3m /s)
3
2
3
3
Newton 1
=
1.6
kg
/m
0.785
m
27
m
/s
)(
)(
)
2(
( )
( )
= 16.95kg m 2 /s3 = 16.95( kg m /s2 )( m /s)
= 16.95(N - m )/s = 16.95 Watts
How good does it get? •  ALer engineering requirements, the real world limit is well below the Betz Limit with values of 0.35-­‐0.45 •  ALer inefficiencies in the generator, bearings, power transmission, etc. only 10-­‐30% of the power of the wind is ever actually converted into usable electricity. €
An efficiency calculaYon Power of the wind (watts) = ½ ρ⋅A⋅V3
# power out &
% efficiency, η = %
( ×100
$ power in '
Wind turbine parameters: Sweep area = 4 m2 Wind speed = 5 m/sec Power output = 90 wars $
'
90
watts
) ×100
% efficiency, η = &
3
3
2
& 0.597 × 1 × 1.6 kg/m × 4m × (5 m/s) )
%
(
2
" 90 wattsout %
= $
' × 100
# 238.8 watts in &
€
% efficiency = (0.376) × 100 = 37.6 %
€
Factor in Betz limit Actual efficiency = 22.5 % The Beaufort Scale •  Gauging wind speed Wind Speed DistribuYon •  Average speed does not denote maximum •  Short bursts power carry V3 more power Weibull distribuYon hrp://www.ceere.org/rerl/about_wind/RERL_Fact_Sheet_1_Wind_Technology.pdf Modern Windmill Styles Ver%cal Axis •  Smaller footprint •  Urban use •  Subject to low windspeeds Darrieus-­‐style Horizontal Axis •  High power output •  Large foot Wind….it’s a Drag •  Goal: Maximize liL-­‐to-­‐drag raYo Relies on wind force only Uses aerodynamics of liL hrp://science.howstuffworks.com/wind-­‐power3.htm Blade Aerodynamics LiL •  Angle of arack (pitch) needs to be 10-­‐15° to get a high enough liL-­‐to-­‐drag raYo (> 10) Drag nasa.gov Blade Design 101 •  A balancing act to keep drag, wind resistance, Yp vorYces, etc. to a minimum while simultaneously puxng enough blade in the wind to capture it’s kineYc energy. •  Good blade design has: –  Smooth surfaces –  Tapered edges –  Sharp tail edge –  Low thickness-­‐to-­‐length raYon Blade Design 101 •  A balancing act to keep drag, wind resistance, Yp vorYces, etc. to a minimum while simultaneously puxng enough blade in the wind to capture it’s kineYc energy. Low angle of arack Medium angle of arack (10-­‐15°) High angle of arack (> 20°) Solidity, Speed, and Torque Low solidity (0.10) = low speed, high torque Solidity = 3a/A R a = total area of blades A = sweep area of blades High solidity (>0.80) = high speed, low torque How high does the Windmill need to be? •  Tower height of 30 feet wind power increased by 0 % •  Tower height of 60 feet wind power increased by 41% •  Tower height of 90 feet wind power increased by 75% •  Tower height of 120 feet wind power increased by 100 % •  Tower height of 150 feet wind power increased by 124% U.S. DOE Those blades look slow?!? •  Turbines usually operate at 30 – 60 RPMs •  Standard US electricity funcYons on 60 Hz AC power –  This amounts to a sinusoidal curve flipping from +1 to -­‐1 60 Ymes per second –  With a direct connecYon from blades to generator, the blades would have to spin at 1200-­‐1800 RPMs (20-­‐30 rev per second) –  This is roughly 2x the speed of sound •  Gearboxes are the key! –  Gear raYos can increase hub speed while keeping the blades turning at a moderate pace –  RaYos are typically 1:50 –  Blade rotaYons ~30 RPM Tip Speed RaYo, λ = Yp speed/wind speed •  Tip speed = 2πr/t (distance/Yme) •  Tip speed raYo is key to good blade design –  If blades are too slow, a lot of wind is “missed” –  If blades are too fast, the turbine acts like a solid disk •  The perfect Yp speed is determined to be: 4π/n, n is the number of blades •  For 3 blades, the opYmal TSR is 4.18 –  Knowing the average windspeed for an site, the best TSR can be calculated –  Adjustments in RPM can be made (speed) by increasing/
decreasing load on the turbine in design Blade Size and Sound hrp://www.awea.org hrp://www.omafra.gov.on.ca Sound decreases by -­‐6 dB on doubling distance noise Noise NOISE!!! •  Large wind turbines have a maximum sound level of 60-­‐70 dB •  Background noise of an office environment •  Most turbine noise is impercepYble at distances > 120m •  Noise is a human percepYon U.S. Wind Energy Map Current Wind Capacity hrp://www.awea.org/pubs/factsheets/Market_Update_Factsheet.pdf Wind Capacity by State Texas Iowa California Minnesota Washington Oregon New York Colorado Kansas Illinois Oklahoma Wyoming North Dakota Indiana New Mexico Wisconsin Pennsylvania West Virginia Montana South Dakota Missouri Nebraska Idaho Michigan Maine Hawaii Tennessee New Hampshire Utah New Jersey Ohio Vermont Massachusers Alaska Rhode Island Planned State Capacity 0 1000 2000 3000 4000 5000 Capacity (MW) Total US capacity: >20,000 mW (as of 9/2008) 6000 7000 8000 9000 Data compiled from NWEA Sites with More InformaYon •  KidWind Project: www.kidwind.org •  Danish Wind Industry: hrp://www.windpower.org/en/tour.htm •  American Wind Energy AssociaYon: hrp://www.awea.org/ •  The U.S. Department of Energy: hrp://www1.eere.energy.gov/windandhydro/ •  Wind turbine noise and percepYon: hrp://www.windpoweringamerica.gov/pdfs/workshops/
mwwg_turbine_noise.pdf