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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
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.
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
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
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)
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
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
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
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
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?
• 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
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
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
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
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
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
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
Blade Planform Types Which should work the best??
Rectangular Reverse Linear Taper
Linear Taper
Parabolic Taper
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
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!!
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
• Gradual curves
• Sharp trailing edge
• Round leading edge
• Low thickness to chord ratio
• Smooth surfaces
Making Good Airfoils
Good
Not so good
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
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
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
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.
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