Environmental Engineering Reference
In-Depth Information
2.74) = 0.251 m
-1
(note
that
U
wake
= U
for
these
tests),
and f & 0.2027/
(2H(0.1722 9 2.74)) = 0.166 from Eq.
8.9b
.
Equation
8.5a
, gives
x
n
=
U
¼
p
1
:
18
0
:
96
0
:
112
p
0
:
44
=ð
2
0
:
51
2
:
74
Þ
Þ ¼
0
:
251 m
1
;
ð
which is equal to that from USB as expected. From (
8.5b
)
f
¼
p
1
:
18
0
:
96
3
0
:
112
p
0
:
44
=ð
8
0
:
51
2
:
74
Þ
¼
0
:
120
Note that 0.120 9 (1 ? 0.51/(3 9 0.96))
2
= 1.66 as required form the results of
the previous Exercise.
Only the USB predictions from Eqs.
8.7
and
8.8
are shown in Fig.
8.7
because
the significantly higher damping from USB gives a better approximation to the
measured yaw response. This difference in damping is significant because the
hardest part of tail fin design is to provide sufficiently high damping. As is clear
from the Exercises 8.1 and 8.2, the agreement in natural frequency is due to the
small magnitude of the added mass term, K
3
, in comparison to the inertia. The tail
boom contributed 0.747 kg m
2
to I, and the steel tail fin 0.758 kg m
2
. The
remaining contributions to I come from the rotor, generator, and a lead weight
added to the tail to increase the inertia.
The simulation in Fig.
8.7
is fairly accurate and the tail fin has obviously
prevented the turbine from responding to the high frequency wind direction
changes, but it is reasonable to infer from the sequence 0-5 s, and from 15 to 25 s,
that the damping ratio of the tail fin is too low.
Example 8.3
How could the damping ratio of the tail fin described in Table
8.2
be
increased?
Answer The USB Eq.
8.9b
shows that it is necessary to increase K
2
without
increasing K
1
or I. This is not easy. The only parameter in K
2
that is absent from K
1
is the chord, c. Increasing c will increase the damping, but the effect may not be
Fig. 8.7 Measured and
calculated turbine yaw x
n
/
U = 0.25, f = 0.166 with
stationary blades, from
Wright [
21
]
0
wind vane
turbine
simulated
-20
-40
-60
-80
-100
0
5
10
15
20
25
30
16
14
12
10
8
6
0
5
10
15
20
25
30
time (s)
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