5 - Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear Interaction

EARTH & SPACE 2010 – March 14-17 Honolulu HI 1/16
INTRODUCTION MODEL DESCRIPTION RESULTS CONCLUSIONS
Dynamic Analysis of an Offshore Wind Turbine:
Wind-Waves Nonlinear Interaction
S. Manenti, F. Petrini
sauro.manenti@uniroma1.it
University of Rome Sapienza
Faculty of Engineering
Department of Structural Engineering

PURPOSE AND CONTENTS OF THE WORK
In this work the dynamic analysis of a monopile supported offshore wind turbine forced
by a random wind a wave excitation in the frequency and time domain is carried out by
means of the ANSYS finite element model.
The effects of non-linear interaction is investigated for possible reduction of vibration
peaks in the structural response.
In the following:
1. an introduction to the problem and the analysis methodology adopted is given;
2. the main features of the finite element model and the analytical model for simulating
wind-wave random forcing are illustrated;
3. the results of the analyses carried out are discussed by pointing out the nonlinear effect
induced by wind-waves interaction;
4. final conclusions concerning the study are then illustrated.

INTRODUCTION
Offshore wind turbines represent rather complex structural systems.
ENVIRONMENT STRUCTURE
STOCHASTIC
INTERACTING
TIME-VARYING
Though the major regularity and power of the offshore wind forcing, they could become
competitive if a proper design approach is established by taking into account the above
factors and assuring a good compromise between safety and costs related aspects.
STRUCTURAL BEHAVIOR
LOADS
(wind, wave,
current etc.)
CONSTRAINTS
(soil etc.)
PROPERTIES
(mechanical,
geometrical etc.)
MULTI-SCALE
(support,
junctions etc.)

INTRODUCTION
To obtain such a goal, design method of an offshore wind turbine requires a critical revision
according to the systemic approach.
Systemic Decomposition
sub-problem sub-problem sub-problem
ENVIRONMENT
LOADS
(wind, wave,
current etc.)
CONSTRAINTS
(soil etc.)
STRUCTURE
PROPERTIES
(mechanical,
geometrical etc.)
MULTI-SCALE
(support,
junctions etc.)
STOCHASTIC
INTERACTING
TIME-VARYING
STRUCTURAL BEHAVIOR
sub-problem sub-problem
complexity

INTRODUCTION
The natural frequency of a typical offshore wind turbine operating in intermediate-depth water
is wedged between the wind and wave excitation frequency; in this context simulation of
wind-wave nonlinear interaction become a crucial aspect as it can led to a beneficial
damping by selecting proper structural stiffness of the turbine’s support: this would lead to an
increase fatigue life and reduce the cost of the support.
WIND excit.
STRUCTURE
WAVE excit.
frequency
Nonlinear
Interaction
INTERNATIONAL
CODES AND
STANDARDS

F.E. MODEL DESCRIPTION
The In the present work a 5MW 3-bladed offshore wind turbine with monopile-type support
is considered as economically convenient for intermediate water depth purposes: it represents
a structure of interest for possible planning of an offshore wind farm in the Mediterranean Sea
near the south-eastern cost of Italy.
Monopile type support
Z
Y X
Aerodynamic
Fluid-
dynamic
Geotechnical
Foundation
Submerged
Emergent
d
lfound
H
mud line Z
Y X
Z
Y X
Aerodynamic
Fluid-
dynamic
Geotechnical
Foundation
Submerged
Emergent
d
lfound
H
mud line
H = 100m
d=35m
lfound=40m
D =5m
tw=0.05m
Dfound=6m
D = diameter of the tubular tower;
tw = thickness of the tower tubular
member;
FIXED
effects of
foundation are
neglected (the
lower node is
fixed at the
sea bottom)
beam elements
(BEAM4) for
simulating the
tower
blades and
nacelle replaced
by a
concentrated
mass (MASS21)

WIND-WAVE SPECTRA
A typical wind-wave forcing with relatively small recurrence period is assumed in the following
calculations (exercise load): this could be crucial for fatigue-induced long term damage.
4
5.19
4
4
5
2
74.0
,
4
5
,0081.0
exp2)(








===














−⋅
⋅
=
mPM
pPMPM
p
PM
PM
V
g
g
S
β
ωβα
ω
ω
β
ω
α
πωηη
α






=
hub
hubmm
z
z
VzV )(
[ ] 6522
)(8701
)(
)(
4
/
i
m
i
i
ijij
zf.
zV
zLf
σ
(f,z)Sf
+
=
( )







+
−
−=
)()(2
)(
exp)()()(
22
kmjm
kjz
ikikijijijik
zVzV
zzCf
fSfSfS
π
wvui ,,=
( )[ ] 2
0
2
751)log(arctan116 *i u.zg.-σ +=
Pierson-Moskowitz wave spectrum
Wind velocity: mean and turbulent spectrum
z
y
x,x’
z’
y’
M
ean water level
Mud line
Waves
Mean
wind
Current
P
(t)vP
(t)w P
(t)uP
Turbulent
wind Vm(zP)
P
Mean water level
Mud line
Hub level
R
H
h
vw(z’)
Vcur(z’)
z
y
z
y
x,x’
z’
y’
x,x’
z’
y’
M
ean water level
Mud line
Waves
Mean
wind
Current
P
(t)vP
(t)w P
(t)uP
P
(t)vP
(t)w P
(t)uP
Turbulent
wind Vm(zP)
P
Mean water level
Mud line
Hub level
R
H
h
vw(z’)
Vcur(z’)
normalized half-side von Karman

Assuming linear wave theory and performing the Fourier transform of the elementary force
experienced by a structural member, force spectra are obtained for both wind and wave.
WIND-WAVE FORCE SPECTRA
d
|z|
z
x
d+z
dF(z,t)dz
A A Sect. A-A
D
tw
d
z
x
dF(z,t)dz
A A
Sect AA
D
tw
),(),(
8
),(),( tzxtzCtzxCtzdF xDI
&&& &σ
π
+=
Linearized Morison equation
[ ]2
),(
2
1
),( tzxdACtzdF DD
&ρ=
Aerodynamic drag force
[ ]
)(
)()cosh(
8
)cosh(
)sinh(
),( 2
2
2
ω
σ
π
ω
ω
ω ηηS
zkzC
kzC
kd
zS
ixiD
iI
iFF


















+






=
&
( ) ∫∫=
A
ikijDmkjFiFi dAdASCVzzS
2
),,( ρω
Wind force spectrum
Wave force spectrum

Assuming linear wave theory and performing the Fourier transform of the elementary force
experienced by a structural member, force spectra are obtained for both wind and wave.
WIND-WAVE FORCE SPECTRA
),(),(
8
),(),( tzxtzCtzxCtzdF xDI
&&& &σ
π
+=
Linearized Morison equation
[ ]2
),(
2
1
),( tzxdACtzdF DD
&ρ=
Aerodynamic drag force
[ ]
)(
)()cosh(
8
)cosh(
)sinh(
),( 2
2
2
ω
σ
π
ω
ω
ω ηηS
zkzC
kzC
kd
zS
ixiD
iI
iFF


















+






=
&
( ) ∫∫=
A
ikijDmkjFiFi dAdASCVzzS
2
),,( ρω
Wind force spectrum
Wave force spectrum
Vm hub = 20m/s
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E-04 1.E-02 1.E+00 1.E+02 1.E+04
freq [Hz]
Forcespectra[N2
/Hz]
Wind
Wave

RESPONSE SPECTRA: WAVE ONLY
The frequency of the first relative maximum corresponds to the peak frequency of the wave
force spectrum (about 0.1Hz); the absolute maximum of the structural response occurs
however at about 0.2Hz which is very close to the first vibration mode of the structure.
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E-04 1.E-02 1.E+00 1.E+02 1.E+04
freq [Hz]
Forcespectra[N2
/Hz]
Wind
Wave
fp = 0.1 Hz
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
freq [Hz]
Responsespectra[m
2
/Hz]
X direction
fp = 0.1 Hz
fn = 0.2 Hz

A spectrum in the direction y orthogonal to the mean wind speed appears due to component
correlation. Two maxima occur for the peak frequency of the wind spectrum and close to
the first mode frequency of the structure.
RESPONSE SPECTRA: WIND ONLY
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E-04 1.E-02 1.E+00 1.E+02 1.E+04
freq [Hz]
Forcespectra[N2
/Hz]
Wind
Wave
fp = 0.1 Hz
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
freq [Hz]
Responsespectra[m
2
/Hz]
X direction
Y direction
fn = 0.2 Hz

The increasing roughness length of the sea surface owing to the presence of the wave field
has been modeled (iterative procedure).
No contribution is present in y-axis due to the absence of wave directional spreading.
RESPONSE SPECTRA: COMBINED WIND-WAVE
The in x-direction wind-wave
combination produces the
appearance of a relative
maximum at the wave peak
frequency.
The resultant response spectrum
appears to be the superposition
of the wind-only and wave-only
response.
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
freq [Hz]
Responsespectra[m2/Hz]
X direction
Y direction
fp = 0.1 Hz
fn = 0.2 Hz

The increasing roughness length of the sea surface owing to the presence of propagating
waves has been modeled (iterative procedure).
RESPONSE SPECTRA: COMBINED WIND-WAVE
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
freq [Hz]
Responsespectra[m2/Hz]
X direction
Y direction
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
freq [Hz]
Responsespectra[m
2
/Hz]
X direction
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
freq [Hz]
Responsespectra[m
2
/Hz]
X direction
Y direction
WIND ONLY
WAVE ONLY WIND + WAVE

A load time history is generated in time domain
with Montecarlo method;
both wind and wave actions associated with 4
different wind mean speeds are considered;
corresponding peak displacements at the hub
height are evaluated.
TIME DOMAIN ANALYSIS: COMBINED WIND-WAVE
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
200 700 1200 1700 2200 2700 3200
time [s]
dalong hub [m]
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500
15 20 25 30 35 40 45 50 55
Vm hub [m/s ]
dpeak
along hub [m]
Time domain
(* =samples)
Frequency domain
Comparison with results from spectral
analysis shows that nonlinear interaction
can be reasonably neglected for wind
speed lower than 20m/s;
Vm hub=20 [m/s]

A load time history is generated in time domain
with Montecarlo method;
both wind and wave actions associated with 4
different wind mean speeds are considered;
corresponding peak displacements at the hub
height are evaluated.
TIME DOMAIN ANALYSIS: COMBINED WIND-WAVE
Comparison with results from spectral
analysis shows that nonlinear interaction
can be neglected for wind speed lower
than 40m/s;
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
200 700 1200 1700 2200 2700 3200
time [s]
dacross hub [m]
Vm hub=20 [m/s]
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
15 20 25 30 35 40 45 50 55
Vm hub [m/s ]
dpeak
across hub [m]
Time domain
(* =samples)
Frequency domain

CONCLUSIONS
In this work a finite element model for the dynamic analysis in both time and frequency domain
of a monopile-type support structure for offshore wind turbine has been presented.
Excitation wind and wave spectra are calculated for typical exercise conditions and nonlinear
interaction is evaluated concerning the structural response spectrum.
The obtained results have shown that wind-wave nonlinear interaction becomes important
for elevated wind speed and should be considered in the design phase of a safe and cost-
effective offshore wind turbine.
This can be done performing a time-domain analysis which is however computationally
cumbersome: in order to obtain analogous results from the frequency-domain analysis, which
is intrinsically linear, the wind-wave spectra correlation and geometrical nonlinearity
should be introduced; this is currently under development.

5 - Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear Interaction

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