Environmental Engineering Reference
In-Depth Information
34-m VAWT:
z
m
= 28.0
m
C
m
= 8.68
m
/
s
k
m
= 2.50
(2-21b)
The subscript
m
denotes a parameter at the mid-elevation of the rotor. The gross annual en-
ergy output in Equation (2-1) can now be expressed as
¥
AEO
G
=
ò
P
O
(
t
)
dt
=
A
ò
p
O
(
U
)
f
W
(
z
m
)
dU
(2-22)
year
0
where
AEO
G
= gross annual energy output (W/y)
p
O
= system output power density (W/m
2
)
The integration in Equation (2-14) is usually performed numerically, by summing the prod-
ucts of the last two columns in Table 2-2. The product
f
W
dU
has been replaced by a
histo-
gram
in which the duration in a wind speed interval or
bin
of width D
U
is calculated from
the Weibull model as
k
m
k
m
U
- D
U
/2
C
m
U
+ D
U
/2
C
m
D
t
(
U
) = 8,760 exp -
- exp -
(2-23)
where
D
t
= duration of (
U -
D
U
/2) £
U
£ (
U +
D
U
/2) (h/y)
Using the reference annual wind energy inputs from Equations (2-10) and the gross an-
nual energy outputs calculated in accordance with Table 2-2, the gross coeficients of energy
for the example wind turbines are
Mod-5B:
C
E
=
12,040
MWh
/
y
41,710
MWh
/
y
= 0.29
(2-24a)
1,240
MWh
/
y
3,640
MWh
/
y
34-m VAWT:
C
E
=
= 0.34
(2-24b)
Coeficients of energy tend to increase somewhat at lower hub-level wind speeds, as
illustrated in Figure 2-19 for representative current commercial and early prototype wind
turbines. The aerodynamic designs of early 2-bladed prototype rotors established a level of
performance that designers of modern wind turbines now seek to achieve and exceed. The
design energy production of large-scale 3-bladed wind turbines is now roughly 45 percent to
70 percent of the theoretical
Lanchester-Betz
limit of 0.593.
Wind tunnel testing of a scale-model rotor can be used to verify design power coef-
icients if the tip-speed ratio, l, of the model is approximately equal to that of the full-scale
turbine. This leads to the following scaling requirements:
U
M
»
U
; W
M
» W(
R
/
R
M
)
(2-25)
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