Topic 1-WT fundamentals & Aerodynamics

Question 1

An empirical formula,
E = 2.5AV^3
, can also be used to make a rough estimate of the
annual electricity production in kWh. Comment on the reasons for the difference.

Answer 1

The difference is due to the following factors:
(1) The Betz limit is a theoretical upper limit for wind turbines. It is normally less than 50% for
operational wind turbines;
(2) The turbine availability is normally about 90% rather than 100% as assumed in the
empirical formula.

Question 2

Discuss how to vary the pitch angle ( along the blade (twist) from the root to the tip to
maintain the same incidence for the cross sectional aerofoils for a given wind velocity.
If the pitch angle can be controlled during the wind turbine operation, how would you
change the pitch angle as the wind becomes weaker?

Answer 2

Along the blade from the root, the radius increases, so does the rotational speed 2r. From
the velocity triangle diagram, it implies a decrease in .
Since  to maintain incidence , the pitch angle needs to be decreased gradually from
the root to the tip.
 
L
D
FU

VT
Vr
U
From the velocity triangle diagram, as the wind speed reduces, decreases. To operate at the
design incidence, the pitch should be reduced.