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Wind_Energy_Essentials_Lecture 9

Wind_Energy_Essentials_Lecture 9 - Wind Turbine...

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11/9/2010 1 Wind Turbine Aerodynamics and Aeroacoustics Roger E. A. Arndt Professor Emeritus Saint Anthony Falls Laboratory 612-625-2883 [email protected] Outline Brief Historical Review Basic Concepts Betz Theory Rotor Aerodynamics Principles of Aerodynamic Lift Rotor Design Elements of Acoustics A Brief Primer on Rotor Noise
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11/9/2010 2 Types of Turbines Many types have been tried over the years. These are probably the two most important. VAWT or Darrieus HAWT This type of turbine will be installed at U of M Umore Park Our emphasis will be on HAWTs Source: Sandia National Laboratory and Clipper: How Much Power Can We Generate? Betz Momentum Theory The power available per unit area is ½ ρ V 3. The cross sectional area of a rotor is π R 2 We can define a power coefficient as Cp can be thought of as an efficiency. Can this value approach unity? The answer lies in the analyses of Betz (1919) and Glauert (1935) 2 3 2 1 p R V P C π ρ =
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11/9/2010 3 Betz Actuator Disk Theory U V 2 V’ U ) a 1 ( V = Using conservation of momentum,Betz (1919) showed that C p = 4(1 – a) 2 a Maximum power is obtained when a = 1/3 Ideal C p = 16/27 = 0.593 Define U – V’ = aU 2 3 2 1 p R V P C π ρ = Glauert Improved the Betz Theory The Glauert analysis added conservation of angular momentum
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11/9/2010 4 Aerodynamic Lift The in-plane component of the lift provides torque Rotation φ Blade Element Theory By integrating the applied torque over the entire rotor an expression for the power output can be found: φ ρ = R 0 L 2 R 2 1 rdr cos cB C V T Ω = T P [ ] 2 2 2 2 R R V ) a 1 ( V Ω + = B = number of blades C L = lift coefficient c = chord length Note that there are several parameters, some interrelated, that dictate the design of a rotor.
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11/9/2010 5 Blade Element Theory Twist is defined as β (r) Pitch is defined as β (R). Many machines can vary this parameter as wind velocity increases or decreases (this is approximate since rotation in the wake has not been considered) φ = α + β , where α depends on the lift coefficient of the blade element C L
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