# Download Walt Musial: Power in the Wind (National Wind Tech Center)

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Transcript
```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
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
Unit
Water analogy
Car analogy-
Cost example
Grid
Energy
Power
Quantity
kWh
Gallons
- How far?
- Gallon of gas
12 ¢/kWh
Rate
kW, MW*
Gal / Min
Engine HP
Consumption &
production
Installed capacity
\$1,500,000/MW
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)
=ρxAxd
= (kg/m3) (m2) (m)
= kg
A
V
d
Power in the Wind
Power
= Work / t
= Kinetic Energy / t
= ½mV2 / t
= ½ρAV2(d/t)
= ½ρAV3
d/t = V
Power in the Wind = ½ρAV3
A couple things to remember…
Power in the Wind = ½ρAV3
• Swept Area – A = πR2 (m2) Area
of the circle swept by the rotor.
• ρ = air density – in Colorado its
R
Example – Calculating Power in the Wind
Power in the Wind = ½ρAV3
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 Watts
Units
= (kg/m3)x (m2)x (m3/s3)
2 x m/s
=
(kg-m)/s
2
(kg-m)/s = Newton
= N-m/s = Watt
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?
Actuator Disk Model of a Wind Turbine
Rotor Disc
Where
Free stream velocity, V1
Wake velocity, V2=(1 2a)
Velocity at rotor, Vax = V1(1-a)
Rotor Wake
Induction factor, a
• Betz Limit when a = 1/3
• Vax = 2/3V1
• V2 = V1/3
C p ,max
16

 .5926
27
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
How big will wind turbines be?
2005
.
1980
1985
150 m2
1990
250 m2
2000
1995
800 m2
A= 12,000 m2
1,800 m2
3,700 m2
2010
Analytical wind turbine models
•Actuator Disk Theory
•Momentum Theory/Wake Rotation (most common)
H. Glauret – Airscrew Theory, 1926
•Lifting Line Theory
•Lifting Surface Theory
•Computation Flow Models
Stream tube model of flow behind
Experiment NASA Ames Wind Tunnel
Maximum Possible Power Coefficient
0.60
0.50
0.40
Cp
0.30
Betz - Without Wake Rotation
With Wake Rotation
0.20
0.10
0.00
0
1
2
3
4
5
6
7
Tip Speed Ratio
8
9
10
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.
ΩR
=
V
Where,
Ω = rotational speed in radians /sec
V = Free Stream Velocity
ΩR
R
-
Solidity
Blade planform is the shape of the
Solidity is the ratio of total rotor planform
area to total swept area
R
a
Low solidity (0.10) = high speed, low torque
A
High solidity (>0.80) = low speed, high torque
Solidity = 3a/A
Which should work the best??
Rectangular
Reverse
Linear
Taper
Linear
Taper
Parabolic Taper
Airfoil Nomenclature
wind turbines use the same aerodynamic principals as aircraft
ΩR
V
Ωr
α
V
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).
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 = High
Stall!!
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
Making Good Airfoils
•
•
•
•
Sharp trailing edge
Low thickness to
chord ratio
• Smooth surfaces
Good
Not so good
• Twist Angle, θ – The angle of an airfoil’s chord line
relative to a reference chord line (usually at the blade
to tip.
Tip airfoil
θ
Root Airfoil
• Pitch angle, β, – The rotation angle of the whole
blade measured from the plane of rotation from the
tip chord line.
Energy Production Terms
• Power in the Wind = 1/2AV3
• 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
Cp
0.3
0.2
0.1
0.0
0
2
4
6
8
Tip Speed Ratio
10
12
• 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.
Questions
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
```