Page 269 - Wind Energy Handbook

BLADE LOADS DURING OPERATION 243

U
A
r
radius
Ωr

R B
C

v L A s
v T A
A
2 2
s 2 s 3
2r sin Ωτ v L B B
2 v r
C B
s Uτ
1
Figure 5.17 Geometry for the Derivation of the Velocity Autocorrelation Function for a
Point on a Rotating Blade

B
the corresponding function for velocity components (v A and v ) in a direction
T
T
perpendicular to AB. s 1 is the separation of points A and B measured in the along-
wind direction, Uô. Noting that the distance between points A and C on the rotor
disc is 2r sin(Ùô=2), we have
2 2
2
2
2
s ¼ U ô þ 4r sin (Ùô=2) (5:36)
Hence
2 " 2 # 2 2
Uô Uô Uô 2r sin (Ùô=2)
k u (~ s,0) ¼ k L (s) þk T (s)1 ¼ k L (s) þk T (s)
s
s s s s
(5:37)

For incompressible flow, it can also be shown (Batchelor, 1953) that

s dk L (s)
k T (s) ¼ k L (s) þ (5:38)
2 ds