Page 44 - Fluid Power Engineering

22 Chapter Tw o

Power Curve of 1MW WTG with Betz limit
5000
4500
4000
3500
3000
Power, kW 2500

2000
1500
1000
500
0
0 2 4 6 8 10 12 14
Wind Speed m/s
FIGURE 2-9 Dashed line is the power curve of 1-MW wind turbine generator
(WTG) with rotor diameter = 70 m. The solid curve is the Betz limit curve for
the same rotor.

Since the power rating of turbine is greater than the maximum power
that can be extracted, this turbine rotor, therefore, does not pass the
Betz limit test; at 12 m/s, the turbine cannot produce 2 KW of power,
unless it uses a shroud or some other means to enhance axial wind
speed.

Example 3
As a third example, consider a vertical axis wind turbine (VAWT) in
Fig. 2-10. The height (h) = 6.1 m, diameter (d) = 1.2 m, and swept
2
area = h · d = 7.43 m .
Power rating of rotor at 12 m/s = 1.2 kW.

ρA r v 0 3 1.22π · 7.43 · 12 3
P ideal = = = 7.8 kW (2-37)
2 2
P Betz = 0.59 P ideal = 4.6 kW (2-38)

This VAWT passes the Betz limit test.

Wind versus Water
How do the limits on capturing energy from wind compare with limits
of capturing energy from water in a hydrorotor?