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# Energy in wind

## by nasir76 on Oct 27, 2011

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WIND MILL POWER station and formulas

WIND MILL POWER station and formulas

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## Energy in windPresentation 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 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   Energy Power   Quantity Rate Unit kWh kW, MW* Water analogy Gallons Gal / Min Car analogy- - How far? - Gallon of gas Engine HP Cost example 12 ¢/kWh \$1,500,000/MW Grid Consumption & production Installed 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 = ½mV 2
• 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/m 3 ) (m 2 ) (m)
• = kg
V A d
• Power in the Wind
• Power = Work / t
• = Kinetic Energy / t
• = ½mV 2 / t
• = ½ρAV 2 (d/t)
• = ½ρAV 3
d/t = V Power in the Wind = ½ρAV 3
• A couple things to remember…
• Swept Area – A = πR 2 (m 2 ) Area of the circle swept by the rotor.
• ρ = air density – in Colorado its about 1-kg/m 3
Power in the Wind = ½ρAV 3 R
• Example – Calculating Power in the Wind
• V = 5 meters (m) per second (s) m/s
• ρ = 1.0 kg/m 3
• R = .2 m >>>> A = .125 m 2
• Power in the Wind = ½ρAV 3
• = (.5)(1.0)(.125)(5) 3
• = 7.85 Watts
• Units = (kg/m 3 )x (m 2 )x (m 3 /s 3 )
• = (kg-m)/s 2 x m/s
• = N-m/s = Watt
Power in the Wind = ½ρAV 3 (kg-m)/s 2 = Newton
• Wind Turbine Power
• Power from a Wind Turbine Rotor = C p ½ρAV 3
• C p is called the power coefficient .
• C p 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
• V ax = 2/3V 1
• V 2 = V 1 /3
Actuator Disk Model of a Wind Turbine
• Where
• Free stream velocity, V 1
• Wake velocity, V 2 =(1 2a)
• Velocity at rotor, V ax = V 1 (1-a)
• Induction factor , a
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 m 2 250 m 2 800 m 2 1,800 m 2 3,700 m 2 1980 1985 1990 1995 2000 A= 12,000 m 2 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
• 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 = ΩR R Where, Ω = rotational speed in radians /sec R = Rotor Radius V = Free Stream Velocity
• 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 Nomenclature w ind turbines use the same aerodynamic principals as aircraft α V R = Relative Wind α = angle of attack = angle between the chord line and the direction of the relative wind, V R . V R = 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 = 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
• Sharp trailing edge
• Low thickness to chord ratio
• Smooth surfaces
Making Good Airfoils 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 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 = 1/2  AV 3
• Betz Limit - 59% Max
• Power Coefficient - C p
• 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