Page 67 - Fluid Power Engineering

Aerodynamics of W ind T urbine Blades 45

Relative velocity Gamma
140 90
80
Relative Velocity, m/s 100 60 γ, degs
120
70
80
50
40
60
30
40
20
10
0 20
0
0 10 20 30 40 50
Distance from hub, meters
FIGURE 4-6 Plot of relative velocity and angle between wind velocity vector
and the relative velocity vector.
For purposes of illustration, the impact of changing γ on blade
design, the relationship between γ and angle of attack is discussed
next. As stated in the previous section, there is an optimal angle of
attack, which is the angle between the chord of the airfoil and the
relative velocity vector v rel . This optimal angle of attack will yield
high lift and low drag forces. In order to maintain an optimal angle
of attack α along the entire length of the blade while γ changes as a
function of radius, the orientation of chord has to change along the
length of blade. This orientation is called the pitch, φ. Pitch is the angle
between the chord and the direction of motion, as shown in Fig. 4-7.
If the angle of attack is held constant, then the pitch of the blade
has to decrease from the root of the blade to the tip of the blade. Close
to the root of the blade, the pitch (φ) is approximately 90-α.Asthe
distance from root, r, increases, the value of φ decreases (see Fig. 4-9).

Direction of φ
motion of blade α
y
φ
x α
φ
V r
α V r V t =10 m/s
γ V r γ V t =5 m/s γ
V t =1 m/s
V 1 =10 m/s V 1 =10 m/s V 1 =10 m/s
r=3m r=15m r=30m

FIGURE 4-7 Velocity of wind relative to the blade at three locations on the
blade, r = R/10, R/2, and R. The wind speed is constant at 10 m/s along
the x-axis. Angular velocity
= 20 rpm, R = 30 m. Tangential velocity of
blade is in –y direction. Angle of attack α is constant.