An offshore wind turbine can be considered as a relatively complex structural system since several environmental factors (e.g. wind and waves) affect its dynamic behavior by generating both an active load and a resistant force to the structure’s deformation induced by simultaneous actions. Besides the stochastic nature, also their mutual interaction should be considered as nonlinear phenomena could be crucial for optimal and cost-effective design. Another element of complexity lies in the presence of different parts, each one with its peculiar features, whose mutual interaction determines the overall dynamic response to non-stationary environmental and service loads. These are the reasons why a proper and safe approach to the analysis and design of offshore wind turbines requires a suitable technique for carrying out a structural and performances decomposition along with the adoption of advanced computation tools. In this work a finite element model for coupled windwaves analysis is presented and the results of the dynamic behavior of a monopiletype support structure for offshore wind turbine are shown.

1. Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear
Interaction
Manenti S., Petrini F.
University of Rome Sapienza, via Eudossiana, 18 – 00184 Rome (Italy)
Phone: +39 06 44 585 265
Fax: +39 06 48 848 52
e-mail: sauro.manenti@uniroma1.it - francesco.petrini@uniroma1.it
ABSTRACT
An offshore wind turbine can be considered as a relatively complex structural system
since several environmental factors (e.g. wind and waves) affect its dynamic
behavior by generating both an active load and a resistant force to the structure’s
deformation induced by simultaneous actions. Besides the stochastic nature, also
their mutual interaction should be considered as nonlinear phenomena could be
crucial for optimal and cost-effective design. Another element of complexity lies in
the presence of different parts, each one with its peculiar features, whose mutual
interaction determines the overall dynamic response to non-stationary environmental
and service loads. These are the reasons why a proper and safe approach to the
analysis and design of offshore wind turbines requires a suitable technique for
carrying out a structural and performances decomposition along with the adoption of
advanced computation tools. In this work a finite element model for coupled wind-
waves analysis is presented and the results of the dynamic behavior of a monopile-
type support structure for offshore wind turbine are shown.
INTRODUCTION
Owing to the major regularity and power of the wind forcing, open-sea turbines
could be an advantageous alternative with respect to analogous inland plants;
furthermore they could become competitive with respect to other conventional,
exhaustible and high environmental impact sources of energy if a proper design
approach is established assuring a good compromise between safety and costs related
aspects.
Anyway boundary conditions (i.e. loads and constraints) are highly time- and
space-dependent, along with mechanical properties of the materials that are subject
to significant variation over the structural life owing to fatigue, marine growth,
corrosion etc. Furthermore different configurations must be handled, passing from
complete functionality to rotor stop.
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2. As a consequence these structures can be defined “complex” and this requires
a critical revision of the design procedure according to a systemic approach
(Bontempi, 2008b), i.e. a systemic decomposition of the relevant elements both
physical (e.g. the constituting parts) and environmental related (i.e. identification of
the structural loads and constraints).
Different aspects and various performances under several load conditions
have to be investigated for this type of structures. Referring to all possible system
configurations that can be assumed by the blades and then by the rotor, one need
explicitly:
1. to ensure that the components are designed for the extreme loads
allowing a fair survivability;
2. to assure that the fatigue life of the components is guaranteed for
the service life;
3. to define component stiffness with respect to vibrations and
critical deflections in a way that the behavior of the turbine can
keep under control by a careful matching of stiffness.
In this context an important task concerns the proper definition of nonlinear
interaction between the forcings (e.g. wind and wave) that can influence significantly
the numerical prediction of the dynamic response and, consequently, the durability
and the cost-effectiveness of the turbine (OWTES, 2003).
Since an offshore wind turbine is generally planned for installation in
intermediate depth water (with respect to a representative design wave length), its
dynamic characteristics are fairly different from an offshore platform for oil industry:
the latter usually has a design natural frequency higher than the wave excitation,
while the former is wedged between the wind and wave frequency; so in the last case
nonlinear interaction between the environmental forcings should be properly
considered during the design phase as it can led to a beneficial aerodynamic damping
by lowering the structural stiffness of the turbine’s support: this would lead to both
an increase fatigue life and reduce the cost of the support.
Relevant codes and standards (BSH, DNV, GL, IEC) provides an accurate
description of the analytical methods for estimating the random action by wind and
waves separately; anyway nonlinear interaction phenomena still requires an in depth
and careful investigation with the aim to give reliable estimate of the loads: such an
aspect could play a crucial role in the calculation procedure of economical and safe
offshore wind turbines.
This work is part and continues an early study on the modeling and design of
offshore wind turbines (Bontempi, 2009); its approach follows structural and
performances decomposition in order to organize the qualitative and quantitative
assessment in various sub-problems, which can be faced by sub-models of different
complexity both for structural behavior and load scenarios.
In the present work the dynamic analysis of a turbine and its monopile
support structure in the frequency domain is carried out by means of the ANSYS
finite element model. Initially the loading induced by wind and random waves acting
separately is considered; subsequently the nonlinear effects by their mutual
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3. interaction are accounted with the aim of pointing out the implication on the design
procedure.
The outline of the paper is as follow:
• the main features of both the ANSYS finite element and the
analytical models for the wind and wave random forcing
are illustrated;
• the results of the analyses carried out are discussed by
pointing out the nonlinear effect induced by wind-waves
interaction;
• final conclusions concerning the study are then illustrated at
the end of the paper.
MODEL DESCRIPTION
In the present work a 5MW 3-bladed offshore wind turbine with monopile-type
support is considered for carrying out the coupled wind-wave spectral analysis: 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.
Tab. 1. Main geometrical characteristics of the structure.
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;
The main geometrical characteristics are summarized in Tab. 1: a Vestas-V90
turbine with rotor diameter of 100m; the hub height is positioned 100m above mean
sea level (m.s.l.); the tower, with a steel tubular section, has a diameter of 5m with a
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4. thickness of 50mm; water depth is 35m. At this stage of investigation the effect of
foundation medium has been neglected and the lower node of the pile is assumed
fixed at the sea bottom.
Even if such an hypothesis looks like far from the actual behavior of the
structure, it has been possible, during an early phase, to check the numerical model
by comparing the numerical results with the analytical solution for an equivalent
one-degree of freedom body. Additional investigations have to be carried out for
introducing the effect of marine soil on the dynamic response of the wind turbine and
the support (here after the structure).
The monopile support has been selected as it appear economically convenient
for intermediate water depth purposes: according to the DNV (2004) classification its
range of application is around 25m water depth and it would be a possible design
solution for planning an offshore wind farm in the southern Adriatic Sea.
Moreover it is a relatively simple support structure and this allow to reduce
the uncertainties related to the wave-induced loads estimation on submerged sloping
members (Chakrabarti et al., 1975).
In this work the analysis is performed by considering typical wind and waves
forcing with relatively small recurrence period (i.e. exercise load condition) that
could be crucial for fatigue-induced long term damage; an early investigation based
on extreme events for monopile-type and other support structure has been yet carried
out in Bontempi (2008a).
In the following subsections a description of the main features relevant to the
finite element model is provided; then the analytical models for the estimate of wind
and waves random loads are shown separately.
z
y
x,x’
z’
y’
W
ater level (medium)
Mud line
Waves
Medium
wind
Current
P
(t)vP
(t)wP
(t)uP
Turbulent
wind Vm(zP)
P
Water level (medium)
Mud line
Hub level
R
H
h
vw(z’)
Vcur(z’)
z
y
z
y
x,x’
z’
y’
x,x’
z’
y’
W
ater level (medium)
Mud line
Waves
Medium
wind
Current
P
(t)vP
(t)wP
(t)uP
P
(t)vP
(t)wP
(t)uP
Turbulent
wind Vm(zP)
P
Water level (medium)
Mud line
Hub level
R
H
h
vw(z’)
Vcur(z’)
Fig. 1 Problem sketch and actions configuration.
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5. Model Features. The finite element model is realized with the ANSYS finite
element code by adopting beam elements (BEAM4) for simulating the tower, while
the blades and nacelle have been represented by a concentrated mass Mtop on the
tower top by means of MASS21 element on which is applied the random horizontal
force caused by the wind trust. The tower base is assumed to be fixed for the reasons
explained above.
A suitable discretization of the exposed structure is carried out for load
application; at each node a spectral force is specified which corresponds to the effect
of random waves (for nodes below the mean sea level) or wind excitation acting on
the corresponding area of pertinence.
Calculation of the force spectrum for both environmental factors has been
carried out by applying the analytical models described in the following. Tab. 2
summarizes the principal mechanical parameters for calculation of the random loads:
E is the elastic modulus, ρ is the density, cD is the drag coefficient, cM is the
hydrodynamic added mass coefficient and cL is the lift coefficient.
Tab. 2. Summary of the most relevant model parameters.
Vm10 [m/s] 14.5
Esteel [kg/m2
] 2.059E+11
Eblade [kg/m2
] 3.100E+20
ρsteel [kg/m3
] 7.980E+3
ρwater [kg/m3
] 1.024E+3
cD hydr 1.05
cM hydr 1.00
cD tow 0.50
cD blade 0.15
cL blade 1.00
Mtop [kg] 1.1E+5
Wave Forcing. In the present work a Pierson-Moskowitz wave spectrum (for fully
developed sea condition) is adopted for dynamic analysis of the support structure for
the offshore wind turbine (Kamphuis, 2000):
4
4
4
5
2
74.0
,
4
5
,0081.0
exp2)(
⎟
⎠
⎞
⎜
⎝
⎛
===
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−⋅
⋅
=
V
g
g
S
PM
pPMPM
p
PM
PM
β
ωβα
ω
ω
β
ω
α
πωηη
(1)
with ω =2π/T=2π f angular frequency, ωp spectral peak angular frequency, η(t) local
free surface elevation with respect to the mean sea level (m.s.l.), V intensity of
characteristic wind speed at the reference height of 19.5m above m.s.l. (see Eq. (12)
for variation of the mean wind sped over the height).
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6. According to the linear wave theory and making use of complex algebra the
time evolution of the free surface elevation η and of the horizontal components of
the water particles velocity x& and acceleration x&& for each spectral wave component
of angular frequency ω are respectively:
),(),(
)(
sinh
cosh
),(
)exp()( 0
tzxitzx
t
kd
kz
tzx
tiat
&&&
&
ω
ηω
ωη
−=
⋅=
−=
; (2)
By applying the Fourier transform and its conjugate to the variable x& , the
spectrum of the horizontal velocity component of the water particles can be obtained:
)(
sinh
cosh
),(
2
ωωω ηηS
kd
kz
zS xx ⋅⎟
⎠
⎞
⎜
⎝
⎛
=&&
; (3)
where from Sηη is defined by Eq. (1); the standard deviation of the water particles
velocity component is then given by:
∫∫
∞∞
⋅⎟
⎠
⎞
⎜
⎝
⎛
==
0
2
0
2
)(
sinh
cosh
),()( ωωωωωσ ηη dS
kd
kz
dzSz xxx &&&
. (4)
In this work the Morison et al. (1950) empirical formula for evaluating the
force induced by a regular surface non-breaking wave on a slender and partially
submerged vertical cylinder is adopted.
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
Fig. 2 Specific force induced by regular wave on a partially submerged cylinder.
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7. According to the scheme in Fig. 2 the force per unit length on the column is:
),(),(),(),( tzxtzxCtzxCtzdF DI &&&& += (5)
which is the sum of two distinct contributions: i) inertial force, also called virtual
mass force, that is proportional to the horizontal component of the water particle
acceleration; ii) drag force, proportional to the square of the water particle horizontal
velocity.
The expression (5) implies that the axis of the cylinder is orthogonal to the
direction of wave advance; the horizontal components of both water particle velocity
and acceleration are evaluated at the column axis as if it was absent by adopting the
linear wave theory (Dean & Dalrymple, 1991).
The inertia and drag coefficients in Eq. (5) has the following expression for a
cylinder having circular section of diameter D:
DcCCCA
D
cC WDDAMWWMI ρρ
π
ρ
2
1
4
2
=+=+= . (6)
The inertia coefficient is made up of two contribution: the former is due to
hydrodynamic mass and the latter pertains the variation of the pressure gradient
within the accelerating fluid.
The added mass coefficient cM is tabulated for the geometries of technical
interest (Hooft, 1978); the drag coefficient cD is a function of the Reynolds number.
Moreover both coefficients depends also on the Keulegan-Carpenter number defined
as:
DTxKC max
&= , (7)
with maxx& the maximum horizontal component of the water-particle velocity, T is the
wave period and D is the cylinder diameter (Chakrabarti et al., 1976).
Assuming that the velocity of the fluid particles is a Gaussian process with
zero mean it is possible to eliminate nonlinearity from the drag term in Eq. (11)5 and
write the linearized Morison force per unit length as follows:
),(),(
8
),(),( tzxtzCtzxCtzdF xDI
&&& &σ
π
+= , (8)
being x&σ the standard deviation of the water-particle velocity component in x
direction given by Eq. (4).
The Eq. (5) holds for a vertical cylinder (not necessary circular); when
dealing with certain structures containing some members forming an angle with the
vertical direction, such as steel lattice type, there is no general agreement on how the
Morison Eq. should be extended to deal with. A method has been proposed in
Chakrabarti et al. (1975) that generalize the formulation given in (5) for a vertical
cylinder.
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8. The force dF acting per unit length on the wet part of the support structure
associated to a random sea state with spectral energy density Sηη as defined by Eq.
(1) can be obtained by considering the expression of η, xx &&& and in (8) and substituting
into Eq. (5):
)()()cosh(
8
)cosh(
sinh
),( tzkzCkziC
kd
tzF xDI ησ
π
ω
ω
⎥
⎦
⎤
⎢
⎣
⎡
+−= &
, (9)
being k=2π/L the wave number and L the wave length; note that the complex
response method is adopted for representation of the harmonic variables (i denotes
the imaginary unit).
By making the Fourier transform of such an expression the force spectrum is
obtained as a function of the wave energy spectral density:
[ ] )()()cosh(
8
)cosh(
)sinh(
),(
2
2
2
ωσ
π
ω
ω
ω ηηSzkzCkzC
kd
zS xDIFF ⋅
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
+⎥
⎦
⎤
⎢
⎣
⎡
= &
, (10)
where the expression between braces in Eq. (10) is the force transfer function.
Wind Forcing. Concerning the wind modeling for computing the aerodynamic
actions, a Cartesian three-dimensional coordinate system (x,y,z), with origin at water
level and the z-axis oriented upward is adopted as shown in Fig. 1.
Focusing on a short time period analysis the three components of the wind
velocity field Vx(j), Vy(j), Vz(j) at each spatial point j (the variation with time is
omitted for simplicity) can be expressed as the sum of an averaged (time-invariant)
value Vm and the turbulent components u(j), v(j), w(j) with zero mean.
Assuming that Vm is non zero only in x direction, the three components of the
total velocity are given by:
)()();()();()()( jwjVjvjVjujVjV zymx ==+= . (11)
The mean velocity Vm(j) can be determined by a database of values recorded
at or near the site, and evaluated as the record average over a proper time interval
(e.g. 10 minutes).
The variation of the mean velocity Vm with z over an horizontal surface of
homogeneous roughness can be described, as usual, by an exponential law:
α
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
hub
hubm
z
z
VzV )( . (12)
In this expressions, Vhub is the reference wind velocity at the rotor elevation
zhub, α=0.14 for extreme wind conditions; Vhub it is usually obtained as the mean of
the wind velocity on a 10 minutes time period V10.
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9. The turbulent components of the wind velocity are modeled as zero-mean
Gaussian ergodic independent processes; by adopting an Eulerian description and a
discretization of the spatial domain in N points representing the locations where the
wind acts on the structure, each Gaussian process is completely characterized by the
power spectral density matrix [S]i, (i = u, v, w). The diagonal terms Sijij(n, z) (i = u, v,
w and j = 1,2,…,N) of [S]i are given by the normalized half-side von Karman’s
power spectral density (Solari and Piccardo, 2001):
[ ] 6522
8701
4
/
i
i
ijij
(z)n.
n
σ
(n,z)nS
i
+
= , (13)
where n is the current frequency (in Hz), z is the height (in m), σi
2
is the variance of
the velocity fluctuations, given by (Solari and Piccardo, 2001):
( )[ ] 2
0
2
751logarctan116 *i u.)(zg.-σ += , (14)
with z0 is the roughness length, u* is the friction or shear velocity (in m/s), given by:
(0.006)1/2
Vm(z=10), while ni(z) is a non-dimensional height dependent frequency
given by:
)(
)(
)(
zV
znL
zn
m
i
i = . (15)
The integral scale Li(z) of the turbulent component can be derived
respectively for i = u, v, w according to the procedure given in ESDU (2001).
The out of diagonal terms Sijik(n, z) (k = 1,2,…,N) of [S]i are given by:
))(exp()()()( nfnSnSnS jkikikijijijik −= , (15)
being:
( ))()(2
)(
)(
22
kmjm
kjz
jk
zVzV
zzCn
nf
+
−
=
π
, (16)
where Cz represents the decay coefficient, that is inversely proportional to the spatial
correlation of the process.
By considering a drag and lift force produced by undisturbed wind velocity
acting on exposed turbine parts, the proposed model allows to estimate the force
spectrum at the j-point of the structure. When considering mobile structural parts
such as the rotor blades, relative wind speed (in a frame of reference moving with the
blade) should be assumed for drag and lift force computation. For more details about
such topics refers to Bontempi et al. (2008a).
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10. DISCUSSION OF RESULTS
In the following results for the analyses carried out are discussed: first wave and
wind forcing are treated separately and then their mutual interaction is investigated;
the values adopted for the most relevant model parameters are summarized in Tab. 2.
Fig. 3 shows the input spectra to the finite element model: both have been
plotted for a mean wind speed of 14.5m/s at 10m elevation above m.s.l. directed in x-
direction and correspond to the parametric formulation given in previous Sections.
1.0E-01
1.0E+01
1.0E+03
1.0E+05
1.0E+07
1.0E+09
1.0E+11
1.E-04 1.E-02 1.E+00 1.E+02 1.E+04
freq [Hz]
Forcespectra[N
2
/Hz]
Wind
Wave
Fig. 3 Wind and wave force energy density spectra.
Wave Forcing. Fig. 4 shows the results for the case of wave forcing acting alone on
the structure.
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
Fig. 4 Response spectra for wave forcing only.
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11. The frequency of the first relative peak corresponds to the peak frequency of
the wave force spectrum (about 0.1Hz); the maximum of the structural response
occurs however at about 0.2Hz which is very close to the first vibration mode of the
structure.
Wind Forcing. Fig. 5 shows the results for the case of wind forcing acting alone on
the structure.
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
Fig. 5 Response spectra for wind forcing only.
In this case the structural response in y-direction (i.e. orthogonal with respect
to the mean wind direction) is non-zero since the two speed turbulent components are
correlated as explained above.
The spectral response is however higher along the x-direction as expected
since the wind energy distribution is greater.
In both cases a maximum peak appear for the peak frequency of the wind
spectrum and close to the first mode frequency of the structure.
Combined Wind-Wave. When considering the effects of both wind and
wave on the structure, the increasing roughness length of the sea surface owing to the
presence of propagating waves has been modeled according to an iterative process
following Holmes 2001.
Fig. 6 shows calculated response spectra in each coordinate horizontal
direction.
While along the y-axis the results are not affected by the presence of waves
propagating in the orthogonal direction, when considering the x-oriented response
spectrum it shows, in addition to the case of wind only (Fig. 5), the characteristic
relative maximum at the wave peak frequency (about 1Hz); furthermore, at the
structure’s natural frequency (i.e. 0.2Hz) the curve is above the value of 1.0m2
/Hz
but it is not exactly the summation of those related to the wind and the wave alone
(Fig. 4 and 5).
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12. 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
Fig. 6 Response spectra for combined wind-wave forcing.
The phenomenon described above is the result of a destructive interference
between wind and wave forcings: the resultant energy density of the response spectra
at the structure’s natural frequency is less than the sum of the corresponding values
related to the wind and wave acting separately.
CONCLUSIONS
In this work a finite element model for the dynamic analysis of a monopile-type
support structure for offshore wind turbine has been presented.
The structural response in the frequency domain has been analyzed for both
wind and wave spectral forcings obtained starting from a characteristic wind velocity
which is representative of the exercise condition to be adopted for fatigue-damage
analysis.
These forcings have been considering as acting separately in the first phase,
and then their mutual interaction has been simulated.
Obtained results have shown that the response spectrum at the natural
frequency of the structure exhibit a destructive interference between wind and wave
forcings acting simultaneously.
As a consequence, nonlinear interaction should be considered in the design
phase of a safe and cost-effective offshore wind turbine as the actual load on the
structure could be lower than that extrapolated from the linear superposition of the
effects produced by the single forcings acting separately.
ACKNOWLEDGEMENTS
The present work has been developed within the research project
“SICUREZZA ED AFFIDABILITA' DEI SISTEMI DELL'INGEGNERIA CIVILE:
IL CASO DELLE TURBINE EOLICHE OFFSHORE", C26A08EFYR, financed by
University of Rome La Sapienza Fruitful discussions with Prof. Franco Bontempi are
also acknowledged
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