Environmental Engineering Reference
In-Depth Information
0.9
Beam1+BEM lin
Bea
m
1+BE
M
nonl
i
n (to
w
e
r
excit
.
)
Beam2+FreeWake (tower excit.)
m
easure
m
ents (
OM
A)
30
0.8
25
0.7
20
15
0.6
10
0.5
5
0.4
0
0.3
-5
6
8
10
12
14
16
18
20
6
8
10
12
14
16
18
20
Wind speed (m/s)
Wind speed (m/s)
Figure 16: Frequency and damping variation of the tower lateral bending mode.
100
0.9
Beam1+BEM lin
Bea
m
1+BE
M
non
l
in (pi
t
ch ex
.
)
Beam1+BEM nonlin (tower excit.)
Bea
m
2+Free
W
ake
(pitch
exci
t
.)
measurements (OMA)
0.8
80
0.7
60
0.6
40
0.5
20
0.4
0.3
0
6
8 0 2 4 6 8 0
6
8 0 2 4 6 8 0
wind speed (m/s)
wind speed (m/s)
Figure 17 : Frequency and damping variation of the tower longitudinal bending mode.
loads with a total duration of several hours. Three sets of simulation results are
shown. The “Beam1+BEM” results were obtained using Euler-Bernoulli beam
theory for the structure and BEM theory for the aerodynamics. Models of this kind
represent the current state of art and can be used either in their linearized form
(denoted as “lin”) or in their original non-linear form (denoted as “nonlin”). The
“Beam2 + FreeWake” results have been obtained using the second order beam
theory outlined in Section 7.2 and the free wake aerodynamic model described in
[34]. Free wake aerodynamic modelling is a 3D model with signifi cantly higher
computational cost and therefore is regarded as a research tool.
Figures 16 and17 show the results for the two tower bending modes. Both pre-
dictions and measurements clearly indicate that the lateral bending mode is the
one less damped. However for this particular case predictions signifi cantly under-
estimate the damping. In the specifi c simulations, this underestimation is due to
the fact that the generator dynamics were not included which as already mentioned
improves stability. Another point is that the scatter of the measurements was large
and so of non-negligible uncertainty. Otherwise there is a noticeable mirror effect
between the linear and non-linear results for the lateral mode near the rated wind
speed (13 m/s). Contrary to linear models which give over this range minimum
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