0475_ewec2006fullpaper

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Frequency domain fatigue calculationA quick comparison of 4 sites with 3D-scatterdiagrams from waveclimate.com

J. van der Tempel

*

, W. de Vries

*

, G.J. (Han) Wensink

+

*Duwind, Stevinweg 1, 2628 CN Delft, The Netherlands

Delft University of Technology [email protected] +31-15-278 6828

+ Argoss, PO box 61, 8325 ZH Vollenhove, The Netherlands

[email protected] +31-527 242 299

Key words: Design, fatigue, frequency domain, wind and wave data

1. INTRODUCTION

The design of offshore wind turbine support structures at present very much resembles the installation

method: the offshore contractor is responsible for the lower end; the turbine manufacturer supplies tower

and turbine. The fact that the structure will behave as an integrated dynamic system is only covered

superficially through crude combinations of simultaneous wind and wave responses. This separation indesign has been instigated because of the following:

• onshore, turbine and tower are the design responsibility of turbine manufacturers, the foundation

does not add design loads

• offshore structure design and design responsibility is preferably left to expert offshore contractors

• offshore contractors usually do not have expert turbine design programs or personnel qualified to

use it

• turbine manufacturers are reluctant to share detailed information of their turbine and control

system to improve the modelling capabilities for support structure design.

In offshore oil and gas, design of structures for fatigue loading is usually done in the frequency domain.

Although the loads are not entirely linear, linearized models give sufficiently accurate results. For offshore

wind turbines, current design practice prescribes time domain simulations with complete turbine dynamics

and control and simultaneous wind and wave loading. But, as described above, these complete models arenot always available. Furthermore, time domain simulations are still time consuming, especially when

several support structure options are to be compared or when the support structure is to be optimised for

every single location in the wind farm.

This paper describes a frequency domain approach for the fatigue load calculations of offshore wind

turbine support structures. The method divides the offshore wind turbine in a turbine, clamped at hub

height with no support structure dynamics and a support structure. The method enables easy, non-

commercial data transfer between turbine manufacturer and offshore contractor and enables the offshore

contractor to optimise the support structure in a quick and controllable manner without loss of detail.

The main steps of the frequency domain method are described in chapter 2. A comparison with traditional

time domain fatigue is also given. In chapter 3, the steps are applied to a model of the Blyth turbines. The

method is further applied to the more fatigue prone location off the Dutch coast of Egmond on a NEG-

Micon NM92 turbine. The lifetime fatigue is calculated in both the time and the frequency domain.

Fatigue calculations require the input of correlated wind and wave data. The internet database atwww.waveclimate.com consist of more than 20 years of a worldwide validated wind and wave

observations from satellites and more than 14 years of quality checked and physically consistent hindcast

data. This service was recently extended with a 3D scatter diagram option to serve fatigue calculations.

To show the effectiveness of the global wind and wave database in combination with the frequency domain

method, the following parameter study is carried out in chapter 5. For 4 sites planned for offshore wind

farm development in around 20m of water depth, the data was retrieved from the database and a lifetime

fatigue check was carried out for the exact same design as for the NM92 off the Dutch coast. By selecting 4

sites around the North Sea, the impact of location on fatigue can be shown. Chapter 6 gives the conclusions

and an outlook.



2. SETUP OF THE FREQUENCY DOMAIN METHOD

As mentioned in the introduction, the analysis of wave loads in the frequency domain is already common

practice. The focus of this chapter will therefore be primarily on analysing the wind load on the turbine.

The steps required to come to a fatigue calculation are depicted in Figure 2.1. In the time domain, on theleft hand side, the wind characteristics are used as input to create a three-dimensional turbulent wind field.

This field is then "shoved" through the rotor disk in a time domain model of the turbine. The program

incorporates all specific details: wind shear, tip corrections, wake influence, tower shadow, etc. The

program produces time series of bending moments and other response characteristics for different stations

along the support structure.

To calculate fatigue damage at a specific location, the stress time series is post-processed. First, the bending

moment is converted to bending stress, then the stress is rainflow counted (RFC) to find the stress range

variation histogram. With the proper S-N curve for the detail under consideration, the Miner sum gives the

fatigue damage value Dminer .

The goal of the frequency domain method is to be able to optimise the design of the support structure. This

requires complete separation between turbine and support structure in the calculation method. Figure 1.1

shows the separate calculation of the turbine loads in step 1 and the derivation of the transfer function

between tower top load and support structure bending stress in step 3.Previous studies have demonstrated the effect of the operating turbine on support structure dynamics. The

rotor introduces aerodynamic damping, which should be taken into account in the further analysis of the

structure, step 2.

Steps 1 to 3 result in a transfer function per wind class for turbulent wind field to support structure bendingstress at any desired location along the structure. By multiplying the square of this transfer function with

the input turbulent wind spectrum, the stress response spectrum can be found.

In a separate process, the stress response to the wave loading is determined, step 4. By linearly summing

the ordinates per frequency of wind and wave induced stress response, the total response is found. This

response spectrum can then be used to determine the stress cycles and find the fatigue damage in step 5.



RFC

Wind

input

D D

Time Domain Frequency Domain

Cyclecounting

Aerodynamicdamping

( )

V S f

f

V wt

f

TRF V w→ F

w

F

V

F

σ

f

TRF F → σ

( )S f σ

f

f

TRF V w → σ

wV

σ

S

N

S

N

( )t σ

t

1

5

3

2

FE program

F top

Frequencydomain waves

( )S f σ

f

4

Figure 2.1 Fatigue calculation in time domain (left) and frequency domain (right)



Step 1: tower top loading

The non-linear behaviour of the wind turbine in different wind conditions cannot easily be linearized in an

overall and direct manner. Some form of time domain simulation to solve the blade element momentum

equations for different wind conditions will usually be required. This approach is used here in a pragmaticway.

During or preferably before the design of an offshore wind farm, a turbine manufacturer is selected. It can

be assumed that the manufacturer has a working computer model of his turbine, capable of performing all

typical design calculations prescribed for normal turbine design. To uncouple the turbine calculations from

the behaviour of the support structure, the structure can be modelled as a rigid structure.

The computer model can now be used to calculate time series of the tower top load due to specific wind

conditions with a mean wind speed, turbulence intensity and wind shear. As output, the tower top load is

recorded. When the time series of both the input wind field time trace and the tower top load are converted

to a spectrum, the transfer function can be derived by dividing both spectra and taking the square root as

shown in equation 1:

( )

( )

top F

Kármán

S f TRF

S f

= (eq. 1)

Step 2: Aerodynamic damping

For an operating turbine, support structure motion and turbine aerodynamics have a significant effect on

each other. When the turbine moves forward (against the wind), the blades experience an increase in total

wind speed. As a result of this increased wind speed, the instantaneous tower top load is increased through

basic aerodynamic action of the blades. This load is acting against the tower top motion. For backward

motion, the situation is analogous, now resulting in a reduced tower top load, also reducing the tower top

motion. This effect is known as aerodynamic damping [1] [2]. To separate turbine and support structure

calculations in the frequency domain approach, the aerodynamic damping needs to be calculated for each

wind speed and must be incorporated through an equivalent viscous damping in the dynamic model of the

support structure. To determine the aerodynamic damping, several methods exist, which were described in

[3].

Step 3: Dynamic behaviour of the support structure

In step 3, the dimensions of the support structure are processed in a finite element model (FEM). To take

the effect of aerodynamic damping into account, the structural damping factor is increased with the valuederived in step 2. Solving the equations of motion for one or more specific points along the structure under

time varying tower top loads will result in a transfer function between tower top load and bending stress at

a specific location.

The total transfer function between the turbulent wind field and bending stress can now be found as the

product of the derived transfer functions from steps 1 and 3. By multiplying the input wind spectrum with

the combined transfer function squared, we find the total bending stress spectrum for the location under

consideration.

The different steps to find the wind induced stress response in the frequency domain are shown in Figure

2.2.



top F σ →

Turbine, step 1

Support Structure, step 3

Aerodynamicdamping, step 2

Wind

input

( )

V S f

f

Aerodynamic

damping

f

( )top F S f

( )S f σ

f

Dynamic model

F t o p

( t )

t

FE program

F top

V wind t

f

TRF V wind → F top

ˆ

ˆtop

wind

F

V

ˆ

ˆtop F

σ

f

TRF F top→ σ

f

TRF V wind → σ

ˆ

ˆwind V

σ

Rigid model

Figure 2.2 Flowchart for frequency domain calculation

of the stress spectrum due to wind loading

Step 4: Incorporating stress response due to wave excitation

The previous section presented a method to derive the response spectrum for bending stress in the support

structure due to wind loads on the rotor. For the design of offshore oil & gas structures it is common

practice to use a frequency domain method for response calculations due to wave excitation. If the

responses due to wind and wave response are assumed to be fully independent, the combined response can

be determined by adding the respective response spectra. The effectiveness of this method was already

shown in [4]. The only interaction between the wind turbine and the response of the support structure due

to wave excitation is the aerodynamic damping. The flowchart in Figure 2.3 shows the steps to combine the

stress response spectra due to wind and wave loading to obtain the spectrum of the total stress response.



Waveinput

Aerodynamicdamping

FD windsee figure 2.2

( )S f σ

f

( )S f σ

f

FE program

wave excitation

( )S f σ

f

f

( )S f ζ

ˆ

ˆ

σ

ζ

f

TRF ζ→ σ

Figure 2.3 Flowchart for adding stress spectra due to wind and wave loading

Step 5: Fatigue damage calculation via spectra of the total stress response

The method presented in the previous sections will provide a response spectrum for the total stress due to

wind and wave loading. The final step is to process this spectrum to obtain the cumulative fatigue damage D Miner . Several solutions exist to derive the stress range distribution from the spectral moments of a stress

spectrum. The Dirlik method is used here, which is an empirical method based on four moments of the

spectrum. This method has been found to give results that compare best with time domain rainflowcounting [5].

3. APPLYING THE FREQUENCY DOMAIN METHOD TO THE BLYTH

TURBINES

To test the proposed method, an accurate model of an offshore wind turbine is needed. Within the OWTES

project [6], a detailed model was created of the Vestas V66 turbines, which were installed in 1999 off thecoast of Blyth, UK. The measurement and validation project assured that the model of the turbine is highly

accurate compared with reality. The turbine is modelled in the time domain program Bladed for Windows.To create transfer functions of the support structure, the offshore design program SESAM was used. Next to

standard finite element modelling, this package incorporates all hydrodynamic modelling features requiredfor offshore structure design.

For all simulations, the wind climate defined by Germanischer Lloyd was used [7]. GL prescribes a fixed

turbulence intensity of 12% for all wind speed classes. Although higher turbulence intensity at lower wind

speeds, as prescribed by other standards represents nature better, for the validation of the frequency domainmethod a fixed turbulence intensity is convenient and sufficient. For the wind shear the same standard was

used, giving a shear factor α = 0.12. This is again used for all wind speeds. Waves and currents are notincluded in these wind simulations.

Step 1: Transfer function for fluctuating wind speed to tower top load

First, a 3D turbulence field is created based on an improved Von Kármán spectrum for a mean wind speed

of 10 m/s and a turbulence intensity of 12% in longitudinal direction. Then a simulation is carried out for the offshore wind turbine model at Blyth. The modal analysis of the support structure is set not to

incorporate any modes, which effectively eliminates support structure dynamics. The blade modes are still

active.

After the simulation, a spectrum estimate is determined for the wind speed at the hub. This results in the

spectrum shown in Figure 3.1, when plotted on log-linear scale.



0 0.5 1 1.5 210

-3

10-2

10-1

100

101

102

103

Frequency [Hz]

s p e c t r a l d e n s i t y [ ( m / s ) 2

s ]

Improved Von Karman time simulation

Improved Von Karman theoretical

Figure 3.1 Wind spectrum, mean = 10 m/s, TI = 12%

For the resulting tower top load, the response spectrum is obtained by processing the time domainsimulation of the axial load on the rotor axis to a spectrum using the same spectral settings; the result is

presented in Figure 3.2. The effects of rotational sampling at 3P, 6P and 9P are clearly visible.

0 0.5 1 1.5 2 2.5 3 3.5 410

4

105

106

107

108

109

1010

1011

Frequency [Hz]

R e s p o n s e s p e c t r u m t o w e r t o p l o a d

[ N 2 * s ]

Figure 3.2 Response spectrum for tower top load

Now, the transfer function can be determined by taking the square root of the response spectrum divided by

the wind spectrum at each frequency. Because the spectral estimates have been created with equal settings,

the frequency intervals are the same, making the calculation of the transfer function very straightforward.

0 0.5 1 1.5 20

1

2

3

4

5

6x 10

4

Frequency [Hz]

T R F w i n d s p e e d t o t o w

e r t o p l o a d

[ N / ( m / s ) ]

Figure 3.3 Transfer function between wind speed and tower top load

The mean rotor speed in this simulation is 21 RPM = 0.35 Hz. The 1P peak cannot be distinguished, the 3Pspeed at 1.05 Hz is clearly visible. It has to be noted that the 1

stblade flapping frequency also lies in this

range, which is, based on the "Campbell-diagram" approach, not entirely an ideal situation.



Step 2: Incorporating aerodynamic damping

The critical step in the frequency domain method is to incorporate the only interaction between turbine

operation and structural dynamics: aerodynamic damping. To determine its magnitude, several options areavailable, which are detailed in [3]. For this paper, a damping of 4% of the critical damping is used for all

wind speed ranges. Although this is not the most accurate figure, it approaches reality sufficiently for the

frequency domain method to be demonstrated.

Step 3: Modelling the support structure

The finite element program SESAM was used to derive the transfer function for tower top load to mudline

bending stress. A model of the offshore wind turbine was made and the natural frequency in SESAM was

found to compare very well with the measured natural frequency and the natural frequency as modelled in

Bladed. The structural damping was set to 1% and 1 + 4 = 5% of the critical damping, with and without

aerodynamic damping, respectively. Then a sinusoidal tower top load was applied of 1000 N. This load

was applied with increasing frequency from 0.01 Hz to 2 Hz in steps of 0.001 Hz, which resulted in the

transfer functions shown in Figure 3.4. The effect of incorporating the aerodynamic damping is clearly verylarge.

0 0.5 1 1.5 2

0

1000

2000

3000

4000

5000

6000

7000

Frequency [Hz]

T R F t o w e r t o p l o a d t o

m u d l i n e b e n d i n g s t r e s s [ ( N / m 2 ) / N ]

TRF without aerodynamic damping

TRF with aerodynamic damping

Figure 3.4 Transfer function of mudline bending stress per unit tower top load as function of frequency with only

structural damping (1%) and 4% additional aerodynamic damping

By combining the transfer functions of Figure 3.3 and Figure 3.4, the combined transfer function as shown

in Figure 3.5 is derived.

0 0.5 1 1.5 20

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

6

Frequency [Hz]

T R F w i n d s p e e d t o

m u d l i n e b e n d i n g s t r e s s [ ( N / m 2 ) / ( m / s ) ]

Figure 3.5 Combined transfer function of mudline bending stress per unit wind speed as function of frequency,

including aerodynamic damping

By multiplying the combined transfer function squared with the input wind spectrum, we can determine theresponse spectrum for bending stress at the mudline, as shown in Figure 3.6. In the time domain, the time

series of the mudline bending stress for the same conditions can be found by using a full dynamic model of



the offshore wind turbine (turbine and support structure). The resulting time series of the varying bending

stress can next be transformed to a spectrum through Fast Fourier Transform (FFT). This spectrum is also

shown in Figure 3.6.

Figure 3.6 shows that the results match very well. The shapes are identical and only the peak at 1 Hz, whichcorresponds with both the 3P-blade passing frequency and the first blade flap frequency, is slightly lower

when calculated in the frequency domain. Apparently the overlapping of these frequencies influences the

support structure when all dynamics are modelled in the time domain.

0 0.5 1 1.5 20

0.5

1

1.5

2

2.5

3x 10

12

Frequency [Hz]

R e s p o n s e s p e c t r u m

m u d l i n

e b e n d i n g s t r e s s [ ( N / m 2 ) 2 * s ) ]

Time domain simulationincluding aerodynamic damping

Frequency domain calculationincluding aerodynamic damping

Figure 3.6 Mudline bending stress response spectra for frequency and time domain calculations

Step 4: Adding waves

Now that the stress response spectrum for turbulent wind has been found, the stress response spectrum for

wave loading can be determined. Based on the assumption that wind and waves are completely independent

(except for the aerodynamic damping) the wave response is calculated in the frequency domain programSESAM . Figure 3.7 shows the input wave spectrum with H s = 1.75 m and T z = 6 s and the resulting response

spectrum for mudline bending stress. As no wave energy is present at the natural frequency at 0.48 Hz, only

quasi static response is visible in the right-hand side plot.

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

Frequency [Hz]

W a v e s p e c t r u m [ m 2 * s ]

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

9

10x 10

11

Frequency [Hz]

S t r e s s r e s p o n s e d u e t o w a v e s [ ( N / m 2 ) 2 * s ]

Figure 3.7 Input wave spectrum with H s = 1.75 m and T z = 6 sand the resulting response spectrum for mudline bending stress

The combined stress response spectrum can now be found by combining the wind and wave responsespectra: per frequency step, the spectral ordinates are added to find the combined response as shown in

Figure 3.8 where the frequency domain spectrum is compared to the time domain spectrum.



0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4x 10

12

Frequency [Hz]


m u d l i n e b e n d i n g s t r e s s [ ( N / m

2 ) 2 * s ]

Bladed case 4

FD case 4

Figure 3.8 Mudline bending stress response spectra for combined wind and wave loading

compared to time domain simulations

The combination created in Figure 3.8 is designated case 4 in table 1. This table is a selection of typical

environmental states at Blyth. These 5 states were modelled in both the time and the frequency domain and

their resulting mudline bending stress response spectra are plotted in Figure 3.9

Table 1. Selection of 5 typical states for testing the frequency domain method against the time domain method from [8]

case H s T z V w % of

occurence

1 0.25 2.0 5.0 20.47

2 0.25 4.0 11.8 21.76

3 0.75 5.3 5.8 13.25

4 1.75 6.0 9.9 4.83

5 3.3 9.7 18.7 0.14

Figure 3.9 Comparison for 4 wind and wave load cases between frequency domain and time domain response spectra

for the mudline bending stress

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

9 x 1011

Frequency [Hz]


m u d l i n e b e n d i n g s t r e s s [ ( N / m 2 ) 2 * s ] Bladed case 1

FD case 1

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 1012

Frequency [Hz]


m u d l i n e b e n d i n g s t r e s s [ ( N / m 2 ) 2 * s ] Bladed case 2

FD case 2

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6x 10

13

Frequency [Hz]


m u d l i n e b e n d i n g s t r e s s [ ( N / m

2 ) 2 * s ] Bladed case 5

FD case 5

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

9x 10

11

Frequency [Hz]


m u d l i n e b e n d i n g s t r e s s [ ( N /

m 2 ) 2 * s ] Bladed case 3

FD case 3



The figures prove that the frequency domain method works, at least when looking at the graphic

representation. The aerodynamic damping of 4% is a functional estimate making the resonance peak at 0.48

Hz match between both methods. Furthermore, the superposition of separate wave and wind induced stress

results in a realistic combined response spectrum. For Blyth the influence of waves on the bending stress isrelatively small. This is of course to be expected as the site is only 6 m deep. Furthermore, the waves do not

have any energy in the range of the structure's natural frequency, which means that no significant wave

induced resonance is to be expected.

4. LIFETIME FATIGUE ASSESSMENT IN TIME AND FREQUENCY DOMAIN FOR

THE EGMOND SITE

To assess the effectiveness of the frequency domain method with regard to lifetime fatigue calculations(step 5), another turbine and site were selected where wave induced resonance will make fatigue a critical

design issue. In 2006 the Near Shore Windfarm off Egmond in the Netherlands will be constructed.

Although for the eventual site the Vestas V90 turbines will be used, previous designs were based on the

NEG-Micon NM 92 turbine. Since the merger of both companies though, this model has been discontinued.

A model of this turbine in Bladed was available for this paper and, as the site coincides with previous

studies [1] [9], the site conditions are known to a high degree of detail. The design under consideration hasa 2.75 MW turbine, a hub height of 70 m above mean sea level and stands in 20 m of water. Furthermore,an 8 m deep scour hole is anticipated in the design. The structure has a natural frequency of 0.31 Hz,

making it susceptible to wave induced resonance.The wind and wave data for the site comprise 7 full years of hind-cast data. These have been processed to a

3 dimensional scatter diagram where per wind speed interval of 2 m/s for the operational range of the

turbine (so 4, 6, 8, .. 24 m/s) a wave scatter diagram for significant wave height ( H s) and zero-crossing period (T z ) was produced. This resulted in 112 environmental states. All wind and waves are assumed to

come from only 1 direction. Directionality was neglected for these tests. The 112 states were all simulatedfor a 1 hour period in the time domain in Bladed and directly through the frequency domain method. To

find the cycles to perform the Miner sum fatigue damage check in the frequency domain, the Dirlik methodwas used. At present, the Dirlik method matches the outcome of time domain rainflow counting most

precisely and is therefore the best method to be used for this typical comparison. Current developments in

this field have seen the arrival of new and improved methods based on more theoretical foundations [10], but for this paper these have not yet been implemented.

The outcome of the time and frequency domain lifetime fatigue checks is presented in table 2. The value

given in the Miner sum fatigue damage, which must be less than 1 for the structural detail to satisfy thefatigue limit check. In the frequency domain, two estimates of aerodynamic damping were used: the

engineering estimate of 4% for all wind speed classes and a variable aerodynamic damping determinedwith the non-linear simulation method [3].

Table 2. Results of lifetime fatigue check in the time and frequency domainfor 112 uni-directional environmental states

Bladed time domain Frequency domain

engineering estimate

Frequency domain

non-lin simulation

Dlife

0.56 0.50 0.74

The results of the fatigue check show that the frequency domain method gives very good results compared

to time domain simulations. The aerodynamic damping is still not fully captured by the current methods

and will require more study. For preliminary design on the other hand, the engineering estimate and thenon-linear simulation method already give very usable results.

5. PARAMETER STUDY: 4 SITES WITH 20M WATER DEPTH

The effectiveness of the frequency domain method was shown in the previous two chapters. To perform a

lifetime fatigue check, correlated wind and wave data for the offshore wind farm site are required.

Although it is still common to install an offshore met-mast to collect site specific data, it is not a very

effective way of gathering information: the structure is expensive and measures for too short a time to be

statistically reliable. A far more economical way would be to use all data already available for the site.



To accommodate this desire for data, the off-the-shelf www.waveclimate.com database holds world-wide

data of wind and (spectral) wave parameters. The data is based on an ever growing amount of satellite

measurements, but has been extended with a hindcast model, fed by numerous local wind and wave

measurements (buoys, platforms). The hindcast data is integrated with the satellite observations and allmade physically consistent.

The online database offers a wide range of wind and wave parameters and the option to compile combined

statistics in scatter diagrams. If required all wave spectral parameters can easily be transferred to different

water depths allowing analysis of fatigue at different water depths of the site of interest.

For offshore wind turbine fatigue calculations, an extra output option was recently added: 3D scatter diagram of significant wave height ( H s), zero-crossing period (T z ), and mean wind speed (V w). The data is

presented in a wave scatter diagram per wind speed range, but can also be downloaded as a text file with

the 3 parameters and their probability of occurrence. Figure 5.1 shows the internet-database interface for

site selection and a screen shot of the 3D scatter diagram.

Figure 5.1 Screen shots of www.waveclimate.com: site selection,

near shore climate definition and retrieval of 3D scatter diagram

For a design of an offshore wind turbine for example at 20 m of water depth, a parameter study can easily be carried out. Here, we select four actual offshore wind farm sites currently under development and check the relative impact of fatigue on the design of the support structure. Figure 5.2 shows the four sites: Horns

Rev II (DK), London Array (UK), Thornton Bank (BE) and Borkum (DE) and the site for which the design

was originally made: Egmond (NL).

Figure 5.2 The Egmond reference site and 4 sites around the North Sea with approximately 20m water depth

The locations of the planned offshore wind farms differ significantly with respect to the exposure to the

mostly westerly wind climate. This means that for London Array the potential wave build-up due to the

wind is much smaller than for Borkum and Horns Rev II, where the wind has a full width of the North Seato build up waves.

Thornton Bank

Horns Rev II

London Array

Egmond

Borkum



The parameter variation assumes wind and waves to come from the same direction. The design for the

support structure from Egmond is assumed to suffice for every location and only the fatigue damage is

checked. All wave spectra are Pierson-Moskowitz and the wind turbulence is 12% for all wind speeds.

The outcome for every site is shown in table 3. These figures were calculated, including site selection and

data retrieval from www.waveclimate.com, in less than 10 minutes each.

Table 3. Outcome of lifetime fatigue check for 5 sites

The outcome clearly shows the impact of the offshore wind farm site on fatigue of the support structure.

The sheltered area of the Thornton Bank and London Array, where the land mass of the UK prevents wave

build-up from westerly winds significantly reduces the fatigue of the support structure.

The combination of the waveclimate.com 3D scatter diagrams with the frequency domain fatigue method

has been very successful. With a turbine and support structure modelled, the downloading of data and theexecution of the fatigue calculation can be executed in less than 10 minutes for each site

6. CONCLUSIONS AND OUTLOOK

The frequency domain method for calculating the fatigue damage of support structures of offshore wind

turbines delivers results which are very comparable to the outcome of time domain simulations, bothgraphically, when looking at the stress response spectra and in the final outcome of the fatigue check. The

method severs the turbine at the yaw bearing and leaves support structure optimisation to the offshorecontractor while the turbine manufacturer only needs to provide a set of tower top loading transfer functions to a turbine on a support structure without dynamics. The method enables rapid support structure

optimisation. Simple adjustment of the finite element model of the support structure and recreation of transfer functions are fed into the excel sheet and yield a lifetime fatigue damage within 2 minutes. A

further advantage of the frequency domain is the direct graphic visibility of peaks in the input, transfer and

output graphs. This makes it very clear which features need to be targeted to optimise the structure even

further. For instance, the effect of aerodynamic damping is easily illustrated, an increase will drastically

reduce the fatigue damage even further when the input load spectra contain energy in that area.

The correlated wind and wave data needed for fatigue calculations can be gathered from numerous sources.The use of the global wind and wave internet database waveclimate.com was shown to be very effective for

quick site assessment. A new feature in the database is to generate a 3D scatter diagram of mean wind

speed, significant wave height and wave zero-crossing period. Using these scatter diagrams as input to the

frequency domain tool delivers very fast and accurate fatigue results in less than 10 minutes. A comparison

of 4 sites with the Egmond design of the NM92 turbine shows the influence of the location on the fatiguedamage: sites in the more sheltered area of the southern North Sea suffer much less fatigue damage and

allow further optimisation of the support structure in that respect.

The functioning of the frequency domain method has only been proven for two structures at present.

Research is ongoing to further optimise the method with respect to the more detailed estimation of

aerodynamic damping. Further structures and sites will be studied in the near future to prove the generalapplicability. The method is also able to model other structures than just the monopile. Design studies in

this area are ongoing. The execution of the method is currently done in an Excel sheet. This may be altered

to make the method more robust for general use. A project to implement the method at the engineering

department of a large offshore contractor has recently started.

Egmond

Borkum

Horns Rev II

Thornton bank

London Array

0.83

0.82

0.87

0.51

0.35

Lifetime fatigue at mudline

20 years, unidirectional wind and waves



The current status of the frequency domain method is that it can be used for preliminary design. Further

development and standardisation of the different steps may eventually make it suitable for general

application as a final design tool, as is already the case with frequency domain fatigue assessment for

offshore structures subjected to waves only.

This paper is part of the PhD thesis "Design of support structures for offshore wind turbines" which will be

available at the end of April 2006 [11].

REFERENCES

[1] Kühn, M (2001) Dynamics and Design Optimisation of Offshore Wind Energy Conversion Systems

Institute for Wind Energy, Delft University of Technology ISBN 90-76468-07-9

[2] Matthies, HG, et al (1995) Study of Offshore Wind Energy in the EC , Joule I (JOUR 0072) Verlag

Natürliche Energie. Brekendorf

[3] Cerda Salzmann, D, Tempel, J van der (2005) Aerodynamic damping in the design of support

structures for offshore wind turbines, Proceedings of the Offshore Wind Energy Conference,

Copenhagen Denmark

[4] Tempel, J van der (2000) Lifetime Fatigue of an Offshore wind Turbine Support Structure Section

Offshore Technology & Section Wind Energy, Delft University of Technology

[5] Dirlik, T (1985) Application of computers in fatigue analysis Ph.D. Thesis, Warwick University

[6] Camp, TR et al (2003) Design methods of offshore wind turbines at exposed sites, EU Joule III

project JOR3-CT95-0284 Garrad-Hassan & Partners

[7] Germanischer Lloyd (2000), Rules & Guidelines 2000: IV Non-marine Technology - Regulations

for the Certification of (Offshore) Wind Energy Conversion Systems

[8] Tempel, J van der (ed.) et al. (2003) Robustness of Design Load Calculations for Offshore Wind

Turbines OWTES task 4.3, EW-03191, DUWIND, Delft University of Technology

[9] Ferguson, MC (ed.) et al. (1998) Opti-OWECS Final Report Vol.4: A typical Design Solution for

an Offshore Wind Energy Conversion System Institute for Wind Energy, Delft University of

Technology

[10] Benasciutti, D, Tovo, R (2005), Spectral methods for lifetime prediction under wide-band

stationary random processes, International Journal of fatigue, 27 pp. 867-877

[11] Tempel, J van der (2006, forthcoming) Design of support structures for offshore wind turbines

Offshore Engineering & Wind Energy, Delft University of Technology