owid - offshore wind design parameter
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law exponents (Hellmann exponents) for the profiles which
are clearly dependent on wind speed and the thermal strati-
fication of the MBL. For a complete description of the mean
profiles please refer to [2].
For small wind speeds and unstable stratification the expo-
nent is small (below 0.1) but for large wind speeds around 25
to 30 m/s we find mean exponents of 0.13. For stable stratifi-
cation mean values of 0.19 are observed, which is considera-
bly beyond the value of 0.14 as assumed in the IEC 61400-3.
Turbulence of the undisturbed MBL
Large efforts have been made to analyse the turbulence in
the MBL. Not only has the mean turbulence intensity (u/u)
been analysed but also the size of turbulence elements and
their inclination was investigated. Further, in addition to these
mean parameters that characterise the turbulence, it was
looked at the strength of temporal variations of isolated tur-
bulence elements (such as Mexican hats). Fig. 3 shows the
variation of the turbulence intensity with the mean wind
speed. For low wind speeds (below 10 to 12 m/s) considera-
ble parts of the turbulence are due to thermally induced tur-
bulence (convection in cold air over a warm sea surface).
Above 12 m/s turbulence intensity is increasing again withwind speed due to the increasing roughness of the sea sur-
face (higher waves). For values of the estimated extreme
wind with a 50-year return period (this is about 40 to 42 m/s
from the present data) we expect from extrapolation of the
data in Fig. 3 a turbulence intensity of about 0.10.
Fig. 4 shows the measured 90th percentiles of the turbulence
intensity in four different heights at FINO1. It turns out that
there are three wind speed ranges within which the parame-
terisation used in the IEC 61400-3 is not satisfying. One range
is below 7 m/s where the parameterised values are far below
the observed values. Another range is above about 20 m/s
where the parameterised values are slightly below the
observed values. Here, obviously the increase of turbulence
due to higher waves is somewhat underestimated. A third
range is around the most frequent wind speeds around 12
m/s. Here, the parameterisation, which is based on Prandtl-
layer theory, delivers too high values because the measure-
ment heights (30 to 90 m above sea level) are already within
the Ekman layer (the layer above the Prandtl layer) which
usually exhibits lower turbulence than the Prandtl layer.
A first suggestion to change this parameterisation has been
made in [2]. Based on this, we propose here
This leads to a better approximation in the whole range ofpossible hub height wind speeds. The first term copies
Prandtl-layer theory, the second term deals with the increase
Fig. 1: Vertical structure of the marine boundary layer as function of
the wave height (from [1]).
Fig. 2: Hellmann exponent as function of wind speed.
Fig. 3: Observed variation of turbulence intensity with 10 min mean
wind speed at 90 m at FINO1 in the period September 2003 to
August 2007.
Fig. 4: Measured 90th percentiles of the turbulence intensity for four
heights (30, 50, 70, and 90 m, red lines) compared to the
parameterisation used in the IEC 61400-3 (dotted black lines).
hub
hub
Ti
hub
hub
subVIsm
V
V
zz
Va 15
min,
0
, )/44,1(2
)/ln(
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DEWI MAGAZIN NO. 35, AUGUST 2009 75
towards low wind speeds, and the third term raises the curve
for high wind speeds.
Scanning the 10 Hz data has yielded examples (Fig. 6) and
statistics (Fig. 7) for Mexican hat-shaped turbulence struc-
tures (gusts) in the wind speed time series. Fig. 6 shows an
example of such a gust which in this case is only observ-
able at 80 m height. There are other cases where such gusts
appear in all three heights. A statistical evaluation shows that
Mexican hats with smaller duration (e.g. 8 s) are 1.6 times
more frequent than Mexican hats with 10.5 s duration (the
assumption which is made in the IEC 61400). Such gusts with
even longer duration (e.g. 14 s) are even less frequent (63%
compared to the 10.5 s gusts). Fig. 7 shows that Mexican
hats do not need to be upright. Actually, the statistics
reveal that about 57 % of all hats are negative hats (i.e. they
looked like hats turned upside down).
The turbulence length scale is slightly increasing with height
at FINO1. Mean values of 249 m (40 m), 280 m (60 m), and
302 m (80 m) have been found (Fig. 8). The inclination of the
large majority of the turbulence elements (Fig. 9) is forward.
Fig. 10 shows the frequency distribution of the maximum
wind direction change with time intervals of 6, 10, and 14 s
from 10 Hz data at FINO1. The mean value for 6 s is 10.7
degrees, for 10 s it is 11.3 degrees and for 14 s it is 11.7degrees. This behaviour is well described by the EDC model of
the IEC 61400.
CFD-Model for the Main Wind Characteristics in Offshore
Wind Farms
In the previous chapters we described the results of the
FINO1 data assessment of the mean and turbulence values of
the undisturbed offshore wind flow. To incorporate the
effects of surrounding wind turbines to the properties of the
wind field a Computational Fluid Dynamics (CFD) model has
been used.
The OWID Wake model uses the commercial flow simulation
software version Phoenics 3.4 as numerical core. The model
is used in parabolic mode, which means that the calculation
advances downstream only. The variables in the model used
are the wind speed, the turbulent kinetic energy k and the
dsspaton of the turbulent knetc energy . The wnd farm
area and a one kilometre buffer around it is covered with a
cartesian grid with a resolution of 10m in all three spatial
directions. In the vertical direction the grid spacing is increased
above 300m (over sea level) up to the top of the model at
1000m altitude. A 10m resolution in the relevant area is sup-
posed to be sufficient to resolve the relevant effects on wind
turbines within this model.
In a CFD run the mean wind speeds and the corresponding
turbulence intensities at each wind turbine are calculated.The effect of the wind turbines on the flow field is dependent
on the hub height, the rotor diameter and the C t -curve. The
Fig. 5: Measured 90th percentiles of the turbulence intensity for 90 m
height (full line) compared to the modified parameterization
proposed above (dotted line) with a=.63, b=.0012, I15=4.9%,
Vti,min=12 m/s.
Fig. 6: Example of a Mexican hat-shaped gust at 80 m above sea
level (upper curve). This gust is not present at 40 and 60 m
height (lower two curves).
Fig. 7: Amplitude statistics for Mexican hat-like turbulence gusts
with 10.5 s duration at 80 m height (440 cases in the year
2005).
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reduction of wind speeds at the rotor level is determined
approximately from the ct-curve and the actuator disc
model. Wake meandering has been incorporated by super-
imposing shifted versions of the flow field and according to a
two-dimensional Gaussian distri bution.
Validation of the Model
The consistency of the model results were checked with
measurements that were taken from a flat terrain onshore
site and also with data that was provided by the Horns Rev
wind farm operator. Onshore comparison shows that for the
average wind speed, both the depth and the width of the
wake are well predicted. The increase of the turbulence
intensity as a function of the wind speed is in good accor-
dance in the relevant range. The comparison with Horns Rev
data shows also good agreement. The steady decrease of the
energy yield along a series of wind turbines is well repro-
duced [3].
Wind Farm Results
The geometry of the modelled example wind farm is a simple
rectangular grid with the rows heading east-west and the
columns heading north-south. The spacing between the windenergy converters is seven rotor diameters in the directions
of the rows and columns. The hub height is 90m. The position
of the wind farm is supposed to be near the FINO1 platform,
therefore FINO1 [4] wind data is used directly as input for the
model. For a whole wind farm calculation all relevant wind
speeds and wind directions are calculated as described in the
previous chapter. These results are combined according to
the distributions evaluated from FINO1 measurements and
the effective turbulence [5,6,7] is calculated with a Whler
coefficient of 10. As a result, it can be seen in fig. 12 that the
highest effective turbulence intensity values (>11%) within
the wind farm appear slightly off-centre which is consistent
with the dominant wind direction south west. Lowest values
of the turbulence intensity (>8%) can be found at the south
west corner, where free flow occurs most often for the FINO1
wind distribution.
Discussion of the Sten Frandsen Model
The Sten Frandsen model [5] has been applied for the same
situation and park geometry as in fig. 12, the result is plotted
in fig. 13. A direct comparison reveals substantial differences.
The most striking difference is the overestimation of the gen-
eral turbulence intensity, especially in the north-east corner,
opposite to the main wind direction. Lowest values can be
found in the centre which is also in opposition to the flow
model results. In general however the effective turbulence isfound to be 3-4% higher than the one calculated with the
flow model.
Fig. 8: Frequency distribution of the turbulent length scale in three
different heights (40, 60, and 80 m).
Fig. 9: Frequency distribution of the inclination of the turbulence ele-
ments between 40 and 60 m height at FINO1. Positive values
mean forward inclination (i.e. the upper edge arrives first), nega-
tive values indicate a backward inclination. (The gap at zero
degree inclination (perfectly upright elements) is due to the
limited temporal resolution (10 Hz) of the available turbulence
data.)
Fig. 10: Frequency distribution of the maximum wind direction change
for three different time intervals (6, 10, and 14 s).
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78 DEWI MAGAZIN NO. 35, AUGUST 2009
versus the use of the real distribution of turbulence intensi-ties in the FINO1 observation. Fig. 16 again shows the load
spectrum for the blade root bending moment, but for differ-
ent turbulence intensities. It can be concluded that the 90 %
quantile approach is conservative compared to the calcula-
tions with the real FINO1 distribution. A 75 % quantile
assumption is not conservative in all cases but it produces
nearly comparable results. This statement is consistent with
all load components of the system.
Fatigue Loads in the Model Wind Farm
The Frandsen model has been compared to the CFD-approach
that has been developed in this project. The wind and turbu-
lence spectra as measured at FINO1 are supplemented by the
wind farm effects of the CFD model and than transformed as
input for load calculations via a transfer matrix. This transfer
matrix gives the relative share for each wind turbine, wind
speed bin and turbulence bin for the FINO1 site.
We considered several ways to calculate the fatigue loads in
the wind farm: The CFD approach with(a1)/without(a2) wind
speed reduction and Frandsen approach with approximated
(a3) and real ct-curve (a4). A few examples are shown for the
blade bending moment for a real 5MW wind turbine in fig. 17
and for the tower top tilt moment in fig. 18.
For the bending moment the load factors in the Frandsenscheme are about 10-15% higher according to the CFD model
approach. For the tower top tilt moment 10-20% higher val-
ues are found.
This holds to the general trend, where it could be found that
in the Frandsen model the loads are overestimated by several
10%, especially when using the approximated ct-curve.
Conclusion
To summarize the following conclusions can be made:
The assessment of FINO1-data reveals substantial differ-
ences to the height exponent and the turbulence inten-
sities that are assumed in the IEC 61400 - 3 (1)
The FINO1-data are the basis for the suggestion of an
enhanced parameterization for the turbulence intensity
as function of wind speed, which leads to a better approxi-
mation in the whole range of possible hub height wind
speeds.
The analysis of gusts has shown that Mexican hat-like
structures with a duration somewhat smaller than the
10.5 s duration assumed in the IEC 61400 - 3 (1) are more
frequent.
CFD Models can be applied successfully for large offshore
wind farms.
The Frandsen Model leads to systematically higher tur-
bulences and fatigue loads compared to the CFD approach
(especially with approximated Ct).
Fig. 16: Fatigue load spectrum for different distributions of the turbu-
lence intensities. The 75% and 90% quantile and the real
distribution as found from FINO1 measurements.
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
v40 (m/s) [Klassenobergrenzen]
Hhenexponenta
1
10
100
1000
10000
100000
numberofa-values
mean
maximumminimummedian10%-quantile
25%-quantile75%-quantile90%-quantilenumber of a-values
10 100 1 103
1 104
1 105
1 106
1 107
1 108
1 109
alpha = 90% Quantil
alpha = 0.14
alpha = 0.15alpha = 0.16
alpha = 0.17
alpha = 0.18
alpha = 0.19
alpha = 0.2
alpha = "real"
Mehrstufenkollektiv Blattwurzelschlagmoment
Anzahl Schwingspiele
Schwingweite
Fig. 14: Distribution of alpha as found from the FINO1 measurements
with different quantile values.Fig. 15: Fatigue load spectrum for different values of height exponent
alpha, for 90% quantile and for the real distribution as found
from FINO1 measurements.
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DEWI MAGAZIN NO. 35, AUGUST 2009 79
The 90% quantile approach of the turbulence intensity(IEC) is conservative.
For the a bending moment: a height exponent = 0.18
had to be assumed to match the real case loads (IEC
= 0.14).
OWID has laid the basis for further projects. The findings on
turbulence presented here in Section 3 will be further evalu-
ated in order to enhance the turbulence parameterisation in
numerical wind field models in the project VERITAS (PTJ, FKZ
0325060) which has now become part of the joint project
OWEA (PTJ, FKZ 0327696) in which the OWID results can be
validated in a real case (alpha ventus).
Acknowledgements
OWID has been funded by the German Federal Ministry for
the Environment, Nature Conservation and Nuclear Safety
(BMU) within the Project OWID (Offshore Wind Design
parameter) via PTJ (FKZ: 0329961) together with ENERCON
GmbH, GE-Wind Energy, Areva Multibrid GmbH and
REpower AG
References:
[1] Emeis, S., M. Trk, 2009: Wind-driven wave heights in the German Bight.
Ocean Dynamics, 59, 463-475.
[2] Trk, M., 2008: Ermittlung designrelevanter Belastungsparameter fr
Offshore-Windkraftanlagen. Dissertation Universitt zu Kln. Verfgbar
unter: http://kups.ub.uni-koeln.de/volltexte/2009/2799/pdf/
Dissertation_Tuerk_Publikation.pdf
[3] V. Riedel, T. Neumann, M. Strack, Beyond the Ainslie Model:, 3D Navier-
Stokes Simulation of Wind Flow through Large Offshore Wind Farms,
DEWEK 2006.
[4] T. Neumann, V. Riedel. FINO 1 Platform: Update of the Offshore Wind
Statistics. DEWI Magazin Nr. 28, February 2006
[5] Sten Trons Frandsen: Turbulence and turbulencegenerated structural
loading in wind turbine clusters, Ris National Laboratory, Roskilde,
Denmark, 2007.
[6] IEC 61400-1 Wind turbine generator systems Part 1: Safety require-
ments, 2nd edition 1999-02
[7] IEC 61400-3 Wind turbines - Part 3: Design requirements for offshore
wind turbines, 1st edition CDV
Fig. 17: Ratio of the bending moment fatigue loads in Frandsen model(a2)and CFD (a4), m=10
Fig. 18: Ratio of the tower top tilt moment fatigue loads in Frandsen
model (a2) and CFD model (a4), m=10
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