{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Wind_Energy_Essentials_Lecture 9

# Wind_Energy_Essentials_Lecture 9 - Wind Turbine...

This preview shows pages 1–6. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 =
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}