Problem 10.111 [Difficulty: 2]
Given: NASA-DOE wind turbine generator
Find: Estimate rotor tip speed and power coefficient at maximum power condition
Solution:
Basic equations: CP
Pm
1
2ρV3
πR2
XωR
V
UωR η
Pm
Pideal
and we have ρ0.00237 slug
ft3
ω45 rpm4.712 rad
s
R63ft V 16 knot27.005 ft
s
P 135 hp η74%
The blade tip speed is: UωR297 ft
s
The tip speed ratio is: XωR
V10.994 (X will decrease at the wind speed increases.)
The mechanical work out is: PmP
η182.4 hp From this we can calculate the power coefficient:
CP
Pm
1
2ρV3
πR2
0.345