Geoscience Reference
In-Depth Information
A.5 Gust Duration and Wind Acceleration in Gusts
Gusts are characterized by a rapid increase in wind speed and a subsequent
decrease. For load estimations, a so-called ''Mexican hat'' shape of the gust (see,
e.g., Fig.
7.29
below) is assumed (e.g., in the standard IEC 61400-1) for wind
turbine load calculations, which starts with a wind speed decrease before the rapid
increase and a similar overshooting for the wind speed decrease directly afterwards
[see (
A.39
)]. The maximum expected gust amplitude over the rotor-swept area is
assumed to be:
8
<
:
0
1
9
=
;
r
u
1
þ
0
:
1
@
A
u
gust
¼
min
1
:
35
ð
u
e1
u
Þ;
3
:
3
ð
A
:
38
Þ
K
1
where u
e1
is the extreme 3 s gust with a recurrence period of 1 year, D is the rotor
diameter in m and K
1
is a turbulent length scale parameter, which in IEC 61400-1
is put to 42 m for larger wind turbines with hub heights above 60 m The time
variation of wind speed in such a ''Mexican hat'' gust event is assumed to be (see
Fig.
5.29
for an example):
(
u
ð
t
Þ¼
u
0
;
37u
gust
sin
ð
3pt
=
T
Þð
1
cos
ð
2pt
=
T
ÞÞ
for 0
t
T
ð
A
:
39
Þ
u
otherwise
where T is assumed to be 10.5 s. This ''Mexican hat'' model implies an increase of
wind speed from the lowest value to the highest value in about 4 s. Investigations
at the FINO1 platform in the German Bight (Türk
2008
) have shown that gusts
with a time period of 8 s are even more frequent than those with 10.5 s (see
Sect. 5.4
for more details).
A.6 Size of Turbulence Elements
The size of turbulent elements depends on the distance to the surface underneath,
as this distance is a limiting factor for the growth of these elements. One method to
estimate the size of turbulent elements in a turbulent flow is to analyse the
autocorrelation function (
A.12
). The integral over the autocorrelation function to
the first zero crossing of the autocorrelation function indicates the longitudinal
time scale T
u
of a turbulence element at a given position.
T
u
¼
Z
1
R
u
0
u
0
ð
s
Þ
ds
ð
A
:
40
Þ
0
Because the autocorrelation function is usually an exponential function (Foken
2008
), this time scale can be approximated as the time lag, s at which the
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