gravesen wind
DESCRIPTION
Wave & Wind LoadTRANSCRIPT
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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
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Wind and wave forces
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
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Wind and wave forces
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Wind and wave forces
Figure 2: Sketch of foundation types. Monopile, steel tripod, concrete
tripod and gravity foundation.
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Wind and wave forces
Met-ocean conditions
Figure 3: Wind rose (DHI).
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Wind and wave forces
Wave Rose
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Wind and wave forces
Met-ocean conditions
Figure 5: Current rose (DHI).
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Wind and wave forces
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions
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.
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions
Design scatter table of wave steepness Sop and wave height
Hm0. The numbers indicate the number of events per 10
years.
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Wind and wave forces
Met-ocean conditions
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Wind and wave forces
Met-ocean conditions: Wave height statistics derived from the
design correlation between wind velocity and wave height.
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Wind and wave forces
Met-ocean conditions:
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Wind and wave forces
Met-ocean conditions:
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Wind and wave forces
Met-ocean conditions:
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Wind and wave forces
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.
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Wind and wave forces
Force exceedance distribution
Figure 7: Force exceedance distributions calculate d with the
Lundgren/Boussinesq method. Example.
offsetxXP
kF +
>=
))(log(exp(1
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Wind and wave forces
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
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Wind and wave forces
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
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Wind and wave forces
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
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Wind and wave forces
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.
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Wind and wave forces
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
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Wind and wave forces
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
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Wind and wave forces
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
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Wind and wave forces
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).
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Wind and wave forces
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.
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Wind and wave forces
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
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Wind and wave forces
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.
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Wind and wave forces
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.
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Wind and wave forces
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.
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Wind and wave forces
Initial Boussinesq simulations
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Wind and wave forces
Add to Boussinesq simulations
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Improved Boussinesq
Linear correction to Boussinesq simulations
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Improved Boussinesq
Corrected input spectrum
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Improved Boussinesq
Force spectra Boussinesq witout and with linear correction