Motivation:
- Wind energy is a useful alternative energy source
- Most commercially available wind turbines have low power coefficients
- Wind conditions are different at different locations. Customized designs are
necessary for each location.
Theory:
Under the ideal conditions, it can be shown that the maximum Power Coefficient (Cp) of a
wind turbine is 0.5926. This value is knwon as the Betz limit. Because of the Betz limit,
the maximum energy extracted from the wind is limited to 59.3%. The power coefficient (Cp)
reaches the Betz limit when the Axial Indiuction Factor (a) is 0.33.
\[ C_p = \frac{\text{power extracted}} {\text{power in the wind}} = 4a(1-a)^2 \]
For practical wind turbines the following factors need to be considered.
- Wake Rotation
- Finite # of blades
- Drag force
- Tip losses
Blade Element- Momentum Theory:
\[ \lambda - \text{tip speed ratio}\] \[ \lambda_r - \text{local tip speed ratio}\] \[ \Psi - \text{local tip speed ratio}\] \[ C_d - \text{drag coefficient}\] \[ C_l - \text{lift coefficient}\] \[ F - \text{tip loss factor}\]
