Environmental Engineering Reference
In-Depth Information
The relative velocity of the wind with respect to the moving rotor blade is computed
by transforming the wind velocity components from Equation (11-14) into the deformed
blade coordinates and then subtracting the blade velocity of Equation (1 l-16a). This gives
2
2
2
V
z
R
W
V
x
R
W
V
rel
R
W
=
V
h
R
W
+
+
(11-17a)
V
h
R
W
= -
r
c
q
p
- (
V
r
+ d
V
r
+ d
V
y
)
s
q
p
+
c
y [(d
V
x
+ f
V
r
)
c
q
p
+ f{(
d
+ b
0
r
)
c
q
p
+
v
}]
(11-17b)
V
h
R
W
= -
r
s
q
p
-
v
+ (
V
r
+ d
V
r
+ d
V
y
)
c
q
p
+
c
y[(d
V
x
+ f
V
r
)
s
q
p
f{(
d
+ b
0
r
)
s
q
p
}]
+
s
y
+
(11-17c)
_
{ (
c
V
r
)
s
q
p
- f(
r
c
q
p
)}
d
V
z
-
V
z
R
W
= - (
v
r
-
v
)
s
q
p
+
c
y(d
V
z
- c
V
r
) + (b
0
+
v c
q
p
)
V
r
+
s
y[d
V
x
+ f
V
r
+ f{
d
+ (
v
-
v
r
)
c
q
p
}]
(11-17d)
where
V
rel
= relative wind speed at airfoil section in h-z-x coordinates (m/s)
V
h
= relative chordwise wind speed at airfoil section (m/s)
V
z
= relative normal wind speed at airfoil section (m/s)
V
x
= relative spanwise wind speed at airfoil section (m/s)
Terms of order e
0
2
have been discarded in these equations. The following assumptions
have been made regarding the order of the velocity components:
Order
1
velocities
:
V
r
Order
e
0
velocities
:
d
V
r
, d
V
x
, d
V
y
, d
V
z
Acceleration Analysis
Referring again to Figure 11-1, our acceleration analysis will recognize the fact that
the mass of the blade is not all concentrated on the elastic axis but is distributed across the
airfoil section. Acceleration equations will, therefore, be derived for an arbitrary point
P
at coordinates (h,z) within the cross-section. The point
A
in the velocity analysis is the
same as
P
(0,0). Using the same a-b reference frame designations as for the velocity vector
analysis, the acceleration of
P
is given by the usual five-term acceleration equation as
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