energy in the wind walt musial senior engineer national wind technology center national renewable...
TRANSCRIPT
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Energy in the Wind
Walt Musial
Senior Engineer
National Wind Technology Center
National Renewable Energy Laboratory
Kidwind Teachers’ Workshop
May 14, 2005
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Wind Energy Technology
At it’s simplest, the wind turns the turbine’s blades, which spin a shaft connected to a generator that makes electricity. Large turbines can be grouped together to form a wind power plant, which feeds power to the electrical transmission system.
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Turbine Power Limited By
• Power in the wind
• Betz limit (air can not be slowed to zero)
• Low speed losses - wake rotation
• Drag losses – aerodynamics and blade geometry
• Generator and drivetrain inefficiencies
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The Difference Between Energy and Power
EnergyEnergy PowerPower
QuantityQuantity RateRate
UnitUnit kWhkWh kW, MW*kW, MW*
Water analogyWater analogy GallonsGallons Gal / MinGal / Min
Car analogy-Car analogy- - How far?- Gallon of gas- How far?- Gallon of gas
Engine HPEngine HP
Cost exampleCost example 12 ¢/kWh12 ¢/kWh $1,500,000/MW$1,500,000/MW
GridGrid Consumption & productionConsumption & production Installed capacityInstalled capacity
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Review of Power and Energy Relationships
Force = mass x acceleration F = ma
Typical Units – Pounds, Newtons
Energy = Work (W) = Force (F) x Distance (d)
Typical units - kilowatt hours, Joules, BTU
Power = P = W / time (t)
Typical units kilowatts, Watts , Horsepower
Power = Torque (Q) x Rotational Speed (Ω)
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Kinetic Energy in the Wind
Kinetic Energy = Work = ½mV2
Where:
M= mass of moving object
V = velocity of moving object
What is the mass of moving air?
= density (ρ) x volume (Area x distance)
= ρ x A x d
= (kg/m3) (m2) (m)
= kg
V
A
d
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Power in the Wind
Power = Work / t
= Kinetic Energy / t
= ½mV2 / t= ½(ρAd)V2/t
= ½ρAV2(d/t)
= ½ρAV3
d/t = V
Power in the Wind = ½ρAV3
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A couple things to remember…
• Swept Area – A = πR2 (m2) Area of the circle swept by the rotor.
• ρ = air density – in Colorado its about 1-kg/m3
Power in the Wind = ½ρAV3
R
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Example – Calculating Power in the Wind
V = 5 meters (m) per second (s) m/s
ρ = 1.0 kg/m3
R = .2 m >>>> A = .125 m2
Power in the Wind = ½ρAV3
= (.5)(1.0)(.125)(5)3
= 7.85 WattsUnits = (kg/m3)x (m2)x (m3/s3)
= (kg-m)/s2 x m/s= N-m/s = Watt
Power in the Wind = ½ρAV3
(kg-m)/s2 = Newton
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Wind Turbine Power
Power from a Wind Turbine Rotor = Cp½ρAV3
– Cp is called the power coefficient. – Cp is the percentage of power in the wind that is
converted into mechanical energy.
What is the maximum amount of energy that can be extracted from the wind?
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• Betz Limit when a = 1/3
• Vax = 2/3V1
• V2 = V1/3
Actuator Disk Model of a Wind Turbine
V1
(1) (2)
Where
Free stream velocity, V1
Wake velocity, V2=(1 2a)
Velocity at rotor, Vax = V1(1-a)
Induction factor, a
5926.27
16C max,p
Rotor Wake
Rotor Disc
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Reality Check
• What’s the most power the .2-m turbine in the example can produce in a 5 m/s wind?
7.85 Watts x .5926 (Betz Limit) = 4.65 Watts
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150 m2
250 m2
800 m2
1,800 m2
3,700 m2
19801985
1990
19952000
A= 12,000 m2
2005
How big will wind turbines be?
.
2010
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Analytical wind turbine models Complexity adds more limitations
Stream tube model of flow behind rotating wind turbine blade
•Actuator Disk Theory•Momentum Theory/Wake Rotation (most common)
H. Glauret – Airscrew Theory, 1926•Lifting Line Theory•Lifting Surface Theory•Computation Flow Models
NREL Unsteady Aerodynamics Experiment NASA Ames Wind Tunnel
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Maximum Possible Power Coefficient
0.60
0.50
0.40
0.30
0.20
0.10
0.00
Cp
109876543210Tip Speed Ratio
Betz - Without Wake Rotation With Wake Rotation
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Tip-Speed Ratio
Tip-speed ratio is the ratio of the speed of the rotating blade tip to the speed of the free stream wind.
ΩRV
=
ΩR
R
Where,
Ω = rotational speed in radians /sec
R = Rotor Radius
V = Free Stream Velocity
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Blade Planform - SolidityBlade planform is the shape of the flatwise
blade surface
Solidity is the ratio of total rotor planform area to total swept area
Low solidity (0.10) = high speed, low torque
High solidity (>0.80) = low speed, high torque
R
A
a
Solidity = 3a/A
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Blade Planform Types Which should work the best??
Rectangular Reverse Linear Taper
Linear Taper
Parabolic Taper
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Airfoil Nomenclaturewind turbines use the same aerodynamic principals as aircraft
α
VR = Relative Wind
α = angle of attack = angle between the chord line and the direction of the relative wind, VR .
VR = wind speed seen by the airfoil – vector sum of V (free stream wind) and ΩR (tip speed).
V
ΩR Ωr
V
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Airfoil Behavior
• The Lift Force is perpendicular to the direction of motion. We want to make this force BIG.
• The Drag Force is parallel to the direction of motion. We want to make this force small.
α = low
α = medium<10 degrees
α = HighStall!!
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Airfoil in stall (with flow separation)
• Stall arises due to separation of flow from airfoil• Stall results in decreasing lift coefficient with
increasing angle of attack• Stall behavior complicated due to blade rotation
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• Gradual curves
• Sharp trailing edge
• Round leading edge
• Low thickness to chord ratio
• Smooth surfaces
Making Good Airfoils
Good
Not so good
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More Blade Geometry Terms• Twist Angle, θ – The angle of an airfoil’s chord line relative to a
reference chord line (usually at the blade tip). Typical blades have about 20 degrees from root to tip.
• Pitch angle, β, – The rotation angle of the whole blade measured from the plane of rotation from the tip chord line.
θ
Root Airfoil
Tip airfoil
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Energy Production Terms• Power in the Wind = 1/2AV3
• Betz Limit - 59% Max
• Power Coefficient - Cp
• Rated Power – Maximum power generator can produce.
• Capacity factor– Actual energy/maximum
energy
• Cut-in wind speed where energy production begins
• Cut-out wind speed where energy production ends.
Typical Power Curve
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Performance Over Range of Tip Speed Ratios
• Power Coefficient Varies with Tip Speed Ratio• Characterized by Cp vs Tip Speed Ratio Curve
0.4
0.3
0.2
0.1
0.0
Cp
121086420Tip Speed Ratio
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Considerations for Optimum Blade
• Optimum blade will have low solidity (10%) and tip speed
ratio, λ, about 5-7. (match speed to generator)
• High λ means lower pitch angle (blade tip is flat to the
plane of rotation).
• Lower λ means higher pitch angle (feathered).
• Pitch angles should be equal for all blades.
• Optimum blade has large chord and large twist near hub
and gets thinner near the tip.
• Optimum blade is only "optimum" for one tip speed ratio.
• The optimum blade will have smooth streamlined airfoils.
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Sirocco A warm wind of the Mediterranean area, either a
foehn or a hot southerly wind in advance of a low pressure area
moving from the Sahara or Arabian deserts
Questions