Page 89 - Fluid Power Engineering

Advanced Aerodynamics of W ind T urbine Blades 67

1200
Power Output, kW 1000

800
600
400
200

0
2 4 6 8 10 12 14 16 18 20 22 24
Wind speed m/s

FIGURE 5-2 Power output of a turbine with Prandtl tip loss factor and Glauert
correction.

1 3 2 2 1 3
Power P = Qω = ρv π R λ 8b (1 − a) μ dμ (5-22)
0
2
0
1
1
2 3
3
Coefficient of power, C p = Qω ρπ R v 0 = λ 2 8b(1 − a)μ dμ
2
0 (5-23)
A sample theoretical power curve is in Fig. 5-2. The relationship above
between C p and λ = ωR/v 0 is not simple quadratic. For most blade
designs, the peak value of C p of approximately 0.5 occurs for values
of λ between about 8 and 10 (see Fig. 5-3). Note that λ determines β,
which influences the values of a and b.

0.5
C p
0.4 φ=0

0.3

0.2

0.1
φ=20 φ=15 φ=10 φ=5 φ=3

5 10 λ 15 20 25
FIGURE 5-3 Typical power coefficient versus tip speed ratio (λ = ωR/v 0 ) for
different values of pitch (φ, in degrees).