Energy in the Wind Walt Musial Senior Engineer National Wind Technology Center National Renewable Energy Laboratory Kidwind Teachers’ Workshop May 14,

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