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

owid - offshore wind design parameter

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