Problem 10.114 [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 ρ1.23 kg
m3
ω70 rpm R5m H18m A 110 m2
UωR36.652 m
s
From Fig. 10.45: CP0.34when X 5.3(maximum power condition) If we replace the πR2
term in the power coefficient
with the swept area we will get: P1
2CP
ρV3
A
Here are the results, calculated using Excel:
A =110.00m
2Power coefficient data were taken from Fig. 10.45
ρ = 1.23 kg/m3
U = 36.65 m/s
V (kt) V (m/s) X
C
P
P
(kW)
10.0 5.14 7.125 0.00 0.00
12.5 6.43 5.700 0.30 5.40
15.0 7.72 4.750 0.32 9.95
17.5 9.00 4.071 0.20 9.87
20.0 10.29 3.562 0.10 7.37
22.5 11.57 3.167 0.05 4.72
25.0 12.86 2.850 0.02 2.88
30.0 15.43 2.375 0.00 0.00
Power Versus Wind Speed
0
2
4
6
8
10
12
5 101520253035
V (knots)
P (kW)