Environmental Engineering Reference
In-Depth Information
dT
=
dm v
(
−
v
),
( 17)
1
3
r
( 18)
2
1
dT
=+
4(1
a
a
)2
p
r dr
v
2
and torque
( 19)
dQ
=
dm v r
,
t
2
2
2,
(20)
dQ
=
2
prw
r dr
v
r
3
( 21 )
dQ
=
4
pr
r
v
1
Ω
(1
−
a a
)
′
.
increment is obtained.
Now comparison with the forces resulting from the airfoil sections is performed.
From Fig. 8 the force coeffi cient in the infl ow direction is
(22 )
CC s
=
·
( )
a
+
Csin
·
( ).
a
NL
D
Here the fl ow angle
ϕ
can be computed from the velocity triangle.
(1
−
av
)
1
tan
()
j
=
.
( 23)
(1
+
ar
′
)
w
The angle of attack and the fl ow angle is related via the twist angle
ϑ
:
( 24 )
ajJ
=−
.
The square of the velocity is
2
2
2
( 25 )
w
=−
((1
a v
)
)
+
(
w
(1
+′
a
)) .
1
All relevant data is then calculated using an interaction scheme. It is to be noted that
in the inner part of a blade, values of greater than 0.5 and even 0.52 are observed.
Then the simple momentum theoretical value
c
T
(
a
) = 4(1 -
a
) ·
a
is no longer valid.
An empirical extension for 0.5 <
a
< 1.0 must be used. The deviation starts at
a
≈
0.3 and gives
c
T
(
a
= 1) of approximately 2.
Many engineering codes, such as the PROP Code of Walker and co-workers [18]
follow this approach. These codes rely heavily on measured aerodynamic data for
airfoils. In the early days of wind energy, airfoils from ordinary airplanes were used.
Since then, special airfoils for wind turbines have been developed, mainly at Stutt-
gart (FX-Series), Delft (DU profi les) and Risø. Today, not only power optimization
but also load reduction has to be included into profi le and blade design. Another
important issue is a phenomenon called stall delay within rotating boundary layers.
Since its fi rst observation by Himmelskamp [30] in 1945, it has become evident that
much behavior cannot be explained without the phenomenon, which is also impor-
tant for swept fl ow. For 3D boundary layers the ECN model [45]:
2
⎛⎞
c
f
=
3
( 26 )
⎜
⎝⎠
with
f
defi ned as
C
L ,3 D
=
C
L ,2 D
+
f
(2
p
α
-
C
L ,2 D
) is often used.
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