gravesen wind

Wind and wave forces

Helge Gravesen and Sren L. Srensen (Carl Bro as):

Wind and wave design forces.

Examples based on Boussinesq simulation used for wind farmBorkum Riffgrund

Improved Boussinesq simulations

Borkum Riffgrund Project developed by:

ENERGI E2 + Plambech Neuen Energien

77 turbines 3.6-4.5 MW

40 km from shore

Water depth 23-29 m

No sand waves


Met-ocean conditions

Return

period

(years)

Wind

velocity

el. 10

m (m/s)

Significant

wave

height (m)

Low

water

level

(m)

High

water

level

(m)

Current

speed

(m/s)

1 22.1 6.5 -1.7 2.1 1.1

10 26.6 7.7 -2.1 2.7 1.2

50 29.7 8.5 -2.3 3.1 1.3

Table 1: Parameters for nature load determination (DHI)

Depth below MWL

(m)

Marine growth

thickness (mm)

0-10 50

10-20 45

20-25 65

25-32 90

Table 2: Marine growth


Figure 2: Sketch of foundation types. Monopile, steel tripod, concrete

tripod and gravity foundation.



Figure 3: Wind rose (DHI).


Wave Rose



Figure 5: Current rose (DHI).



Wind

Speed

(m/s)

0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 All

Hm0 (m)

7.0- 7.5 0 0 0 0 0 0 0 0 0 0 3 7 0 0 0 10

6.5- 7.0 0 0 0 0 0 0 0 0 0 3 15 5 0 3 0 26

6.0- 6.5 0 0 0 0 0 0 0 0 2 18 34 6 1 0 1 62

5.5- 6.0 0 0 0 0 0 0 0 0 18 77 31 3 2 3 0 134

5.0- 5.5 0 0 0 0 0 0 0 7 92 111 15 4 0 0 0 229

4.5- 5.0 0 0 0 0 0 0 2 133 351 106 8 1 0 0 0 601

4.0- 4.5 0 0 0 0 0 0 64 553 376 50 2 0 0 0 0 1045

3.5- 4.0 0 0 0 0 1 26 499 889 279 21 1 0 0 0 0 1716

3.0- 3.5 0 0 0 2 16 433 1415 1003 148 0 0 0 0 0 0 3017

2.5- 3.0 0 0 2 20 312 1692 2184 575 17 1 0 0 0 0 0 4803

2.0- 2.5 1 10 45 373 2302 4088 1968 89 2 0 0 0 0 0 0 8878

1.5- 2.0 32 144 670 2595 6056 4040 278 2 0 0 0 0 0 0 0 13817

1.0- 1.5 376 1617 4510 8259 6293 657 8 1 0 0 0 0 0 0 0 21721

0.5- 1.0 1697 6073 10238 6655 614 7 0 0 0 0 0 0 0 0 0 25284

0.0- 0.5 1295 3367 1510 132 1 0 0 0 0 0 0 0 0 0 0 6305

All 3401 11211 16975 18036 15595 10943 6418 3252 1285 387 109 26 3 6 1 87648

1.



Design scatter table of wave steepness Sop and wave height

Hm0. The numbers indicate the number of events per 10

years.


Met-ocean conditions: Wave height statistics derived from the

design correlation between wind velocity and wave height.


Met-ocean conditions:


This approach allows for:

adding the pressure arising

from the difference in

surface elevation

taking account for non-linear

pressure gradients

inclusion of an improved

estimate of the phase

difference on e.g. tripods

and gravity foundations.

Figure 6: Force determination with the Lundgren/Boussinesq method.


Force exceedance distribution

Figure 7: Force exceedance distributions calculate d with the

Lundgren/Boussinesq method. Example.

offsetxXP

kF +

>=

))(log(exp(1


Generalized force exceedanc distribution

10-5

10-4

10-3

100

0

1000

2000

3000

4000

5000

6000

Hs= 1m

Hs= 2m

Hs= 3m

Hs= 4m

Hs= 5m

Hs= 6m

Hs= 7m

Hs= 8m

Hs= 9m

Figure 8: Generalized force exceedance distributions calculated with

the Lundgren/Boussinesq method


Integration of wave forces

10-2

10-1

100

101

102

0

1000

2000

3000

4000

5000

6000H

s = 6.75 m

Hs = 7.25 m

Hs = 7.75 m

Hs = 8.25 m

Hs = 8.75 m

Hs = 9.25 m

Hs = 9.75 m

Hs = 10.25 m

Hs = 10.75 m

Sum

Figure 9: Integration of the wave force distributions in figure 8 and

t he wave height distribution


Lundgren-Morison. comparison

10-4

10-3

10-2

10-1

100

0

500

1000

1500

2000

2500

3000LundgrenMorison

Figure 10: Example of comparison of wave force distributions

calculated with the Lundgren method and the Morison equation. Both

are based on Boussinesq data. In the present project the Lundgren

method is applied


Lundgren-Morison. Comparison

0 0.1 0.2 0.3 0.4 0.5 0.60

1

2

3

4

5

6

7LundgrenMorison

Figur e 11: Example of comparison of wave force spectra calculated

with the Lundgren method and the Morison equation. Both are based

on Boussinesq data.


Spectra of simulated Boussinesq-waves

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.510

2

103

10 4

10 5

10 6

10 7

108

10 9Water depth h = 32 m (12 m in Boussinesq simulation)

Frequency

Surface elevation power spectru

Old dataNew dataOld cut-off frequency

New cut-off frequencyTail function, F=const*etaTail function, F=const*eta*T

Tail function, F=const*eta*T 2

10 -3 10 -2 10 -1 10 00

1000

2000

3000

4000

5000

6000

Exceedance probability

Force [kN]

Old dataNew data


Spectra of simulated Boussinesq-waves

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.510

2

103

104

105

106

107

108

109

Old dataNew dataOld cut-off frequencyNew cut-off frequencyTail function, F=const*etaTail function, F=const*eta*T

Tail function, F=const*eta*T2


Results of force calculations

Water depth h = 25 m

Wave data Stream

function/Morison Boussinesq/

Lundgren Jonswap/Morison

Deviat. % Deviat. %

Sop Hs Tp F0.1% M0.1% Arm F0.1% M0.1% F0.1% M0.1

% F0.1% M0.1% F0.1% M0.1%

0.044 8 10.8 3.56 72.6 20.4 3.62 66.6 1.5 -8.3 3.98 68.0 11.6 -6.2

0.036 8 11.9 3.59 72.2 20.1 3.66 67.3 2.0 -6.8 3.66 59.2 2.0 -18.0

0.030 8 13.1 3.63 72.8 20.0 3.70 68.0 1.7 -6.6 3.51 58.6 -3.4 -19.5

Water depth h = 32 m

Wave data Stream

function/Morison Boussinesq/

Lundgren Jonswap/Morison

Deviat. % Deviat. %

Sop Hs Tp F0.1% M0.1% Arm F0.1% M0.1% F

0.1% M

0.1% F0.1% M0.1% F

0.1% M

0.1%

0.044 8 10.8 3.84 94.3 24.5 3.94 91.7 2.6 -2.8 4.14 89.4 7.7 -5.2

0.036 8 11.9 3.81 92.3 24.2 3.91 91.0 2.6 -1.4 3.91 79.8 2.6 -13.5

0.030 8 13.1 3.82 91.5 24.0 3.92 91.1 2.6 -0.5 3.72 77.4 -2.5 -15.4


Comparison physical model tests and calculations

Monopile, water depth h=25m

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5 6 7 8 9 10

Significant wave height (m

Fo

rce

(kN

)

Model tests

Boussinesq/Lundgren

Figure 12: Comparison of Boussinesq/ Lundgren and physical model

tests (AU).


Dynamic amplification

Interaction factor, DME, m=4

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

0 5 10 15 20 25 30

Wind velocity, hub height (m

DM

E

Figure 13: Dynamic amplification factor for fatigue loads. Example

from FLEX 5 simulations.


Design formulas

Extreme forces:

Fmax,wind+waves=Fmean,wind+((Fmax,wind-Fmean,wind)2+Fmax,waves

2)0.5

Fatigue:

FE,wind+waves=DFE(FE,wind2+FE,waves

2)0.5


Inertia coefficient

Inertia coefficien

0

0.5

1

1.5

2

2.5

0 10 20 30 40

KC

CM

DNV (2004)

ISO 19902

Reference value

Figure 14: Inertia force coefficients from the DNV and ISO standards.

In the present project the ISO values are applied.


Drag coefficient

Drag coefficien

0

0.5

1

1.5

2

2.5

0 10 20 30 40

KC

CD

DNV (2004)

ISO 19902

Reference value

Figure 15: Drag force coefficients from the DNV and ISO standards.

In the present project the ISO values are appl ied.


Total correctionsThe wave spreading is included as a general factor of 0.91 to inertia

forces and 0.82 to drag forces.

Water depth h=25m

-25

-20

-15

-10

-5

0

5

10

15

0 0.5 1 1.5

Total correction factor

z (m

)

CM

CD

Figure 16: Corrections of hydrodynamic coefficients taking account

for depth variations in the KC number, marine growth and wave

spreading. The reference values are CD=1 and CM=2.


Initial Boussinesq simulations


Add to Boussinesq simulations

Improved Boussinesq

Linear correction to Boussinesq simulations

Improved Boussinesq

Corrected input spectrum

Improved Boussinesq

Force spectra Boussinesq witout and with linear correction

gravesen wind

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