1. Actual Power Developed by A Rotor
P M V Subbarao
Professor
Mechanical Engineering Department
Design by Neglecting Drag in Lifting Machine.....
Consider the effect of Drag While Computing Performance

2. The Blade : Heart of a Wind Turbine

3. Generally used Airfoils for Wind Turbine Blades
There are many types of airfoils used in construction of wind turbine blades.
A few examples of ones that have been used in wind turbine designs are:
TheNACA0012 is a 12% thick symmetric airfoil.
The NACA 63(2)-215 is a 15% thick airfoil with a slight camber, and the
LS(1)-0417 is a 17% thick airfoil with a larger camber.

4. Lift and drag coefficients for the NACA 0012 symmetric airfoil : Preferred Reynolds Number Range

5. Lift and drag coefficients for the NACA 63(2)-215 airfoil : Preferred Reynolds Number Range

6. Lift and drag coefficients for the LS(1)-0417 airfoil : Preferred Reynolds Number Range

7. Iterative Method of Solution
1. Guess values of a and a’.
2. Calculate the angle of the relative wind from Equation (3.63).
3. Calculate the angle of attack from  =p+ and then Cl and Cd.
4. Update a and a’ from Equations:
5. The process is then repeated until the newly calculated induction factors are within some acceptable tolerance of the previous ones.

8. Calculation of Power Coefficient
Once a has been obtained from each section, the overall rotor power coefficient may be calculated from the following equation
Actual local torque generated by rotor element:
Actual local power generated by rotor element:

9. Universal form of Local Power Equation
Universal local Design variable for a Wind Turbine Rotor:
Local Blade Speed Ratio:

10. Universal form of Local Power Equation

11. Actual Power Developed by A Rotor
Integrate local power equation from hub to tip:
Actual Power Coefficient of a Rotor:

12. Actual Power Coefficient
Note that even though the axial induction factors were determined assuming Cd= 0, the drag is included here in the power coefficient calculation.
Usually this equation is solved numerically

13. Tip Loss: Effect on Power Coefficient
It is well-known fact that the pressure on the suction side of a blade is lower than that on the pressure side.
Air tends to flow around the tip from the lower to upper surface.
This reduces the lift and hence power production near the tip.
This effect is most noticeable with fewer, wider blades.

14. Method to Account Tip Losses
A number of methods have been suggested for including the effect of the tip loss.
The most straightforward approach to use is one developed by Prandtl.
According to this method, a correction factor, F (0<F<1), must be introduced into the previously discussed equations.
This correction factor is a function of the number of blades, the angle of relative wind, and the position on the blade.
Based on Prandtl’s method:
where the angle resulting from the inverse cosine function is assumed to be in radians.

15. Useful Design Equations with tip Loss Correction

16. Actual Power Coefficient with tip Loss Correction