dynamic analysis of an offshore wind turbine: wind-waves nonlinear interactions

8/13/2019 Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear Interactions

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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: [email protected] [email protected]

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 structures

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.

INTRODUCTIONOwing 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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Earth and Space 2010: Engineering, Science, Construction,

and Operations in Challenging Environments 2010 ASCE

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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 loadsallowing a fair survivability;

2. to assure that the fatigue life of the components is guaranteed forthe service life;

3. to define component stiffness with respect to vibrations andcritical 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 dampingby lowering the structural stiffness of the turbines 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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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 theanalytical models for the wind and wave random forcing

are illustrated;

the results of the analyses carried out are discussed bypointing out the nonlinear effect induced by wind-waves

interaction;

final conclusions concerning the study are then illustrated atthe 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: itrepresents 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 = 100md=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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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 modelby 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 (Chakrabartiet al., 1975).

In this work the analysis is performed by considering typical wind and wavesforcing 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 inBontempi(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

Waterlevel(medium)

Mudline

Waves

Medium

wind

Current

P

(t)vP

(t)w P

(t)u P

Turbulent

wind Vm

(zP

)P

Waterleve

l(medium

)

Mudline

Hublevel

R

H

h

vw(z)

Vcur(z)

z

y

z

y

x,x

z

y

x,x

z

y

Waterlevel(medium)

Mudline

Waves

Medium

wind

Current

P

(t)vP

(t)w P

(t)u P

P

(t)vP

(t)w P

(t)u P

Turbulent

wind Vm

(zP

)P

Waterleve

l(medium

)

Mudline

Hublevel

R

H

h

vw(z)

Vcur(z)

Fig. 1 Problem sketch and actions configuration.

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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 reasonsexplained 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, is the density, cD is the drag coefficient, cM is thehydrodynamic added mass coefficient and cLis 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

steel[kg/m3] 7.980E+3

water[kg/m3] 1.024E+3

cD hydr 1.05

c hydr 1.00

cD tow 0.50

cD blade 0.15

cL blade 1.00Mtop[kg] 1.1E+5

Wave Forcing. In the present work a Pierson-Moskowitzwave 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

gS

PM

pPMPM

p

PMPM

(1)

with =2/T=2fangular frequency, pspectral peak angular frequency, (t) localfree 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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According to the linear wave theory and making use of complex algebra the

time evolution of the free surface elevation and of the horizontal components ofthe water particles velocity x& and acceleration x&& for each spectral wave component

of angular frequency are respectively:

),(),(

)(sinh

cosh),(

)exp()( 0

tzxitzx

tkd

kztzx

tiat

&&&

&

=

=

=

; (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

Skd

kz

zSxx

=

&&

; (3)

where from S is defined by Eq. (1); the standard deviation of the water particles

velocity component is then given by:

==

0

2

0

2 )(sinh

cosh),()( dS

kd

kzdzSz

xxx &&&. (4)

In this work the Morisonet 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 ASect AA

D

tw

Fig. 2 Specific force induced by regular wave on a partially submerged cylinder.

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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 virtualmass 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 diameterD:

DcCCCA

D

cC WDDAMWWMI

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 cDis a function of theReynoldsnumber.

Moreover both coefficients depends also on theKeulegan-Carpenternumber defined

as:

DTxKC max&= , (7)

withmaxx& the maximum horizontal component of the water-particle velocity, Tis the

wave period andDis the cylinder diameter (Chakrabartiet 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 linearizedMorisonforce per unit length as follows:

),(),(8

),(),( tzxtzCtzxCtzdF xDI &&& &

+= , (8)

beingx& 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); whendealing 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

Chakrabartiet al. (1975) that generalize the formulation given in (5) for a vertical

cylinder.

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The force dFacting per unit length on the wet part of the support structure

associated to a random sea state with spectral energy density Sas defined by Eq.

(1) can be obtained by considering the expression of , xx &&& and in (8) and substituting

into Eq. (5):

)()()cosh(8

)cosh(sinh

),( tzkzCkziCkd

tzF xDI

+=

&, (9)

being k=2/L the wave number and L the wave length; note that the complexresponse method is adopted for representation of the harmonic variables (idenotes

the imaginary unit).

By making theFouriertransform 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

SzkzCkzCkdzS 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 thez-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 Vmand the turbulent components u(j), v(j), w(j) with zero mean.

Assuming that Vmis non zero only inxdirection, the three components of thetotal 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 Vmwith zover an horizontal surface of

homogeneous roughness can be described, as usual, by an exponential law:

=

hub

hubm z

z

VzV )( . (12)

In this expressions, Vhubis the reference wind velocity at the rotor elevation

zhub,=0.14for extreme wind conditions; Vhubit is usually obtained as the mean ofthe wind velocity on a 10minutes time period V10.

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The turbulent components of the wind velocity are modeled as zero-mean

Gaussianergodic independent processes; by adopting an Euleriandescription and a

discretization of the spatial domain in Npoints representing the locations where the

wind acts on the structure, each Gaussianprocess 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 Karmans

power spectral density (SolariandPiccardo, 2001):

[ ] 6522 87014

/

i

i

ijij

(z)n.

n

(n,z)nS

i+

= , (13)

where nis the current frequency (in Hz),zis the height (in m), i2

is the variance of

the velocity fluctuations, given by (SolariandPiccardo, 2001):

( )[ ] 202 751logarctan116 *i u.)(zg.- += , (14)

withz0is 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

znLzn

m

ii =

. (15)

The integral scaleLi(z) of the turbulent component can be derived

respectivelyfor i = u, v, waccording to the procedure given in ESDU (2001).

The out of diagonal terms Sijik(n, z) (k = 1,2,,N) of [S]iare given by:

))(exp()()()( nfnSnSnS jkikikijijijik =

, (15)

being:

( ))()(2)(

)(

22

kmjm

kjz

jkzVzV

zzCnnf

+

=

, (16)

where Czrepresents 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 partssuch 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 toBontempiet al. (2008a).

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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 inx-

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[N2/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 onthe 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]

Re

sponsespectra[m

2/Hz]

X direction

Fig. 4 Response spectra for wave forcing only.

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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]

Respo

nsespectra[m

2/Hz]

X direction

Y direction

Fig. 5 Response spectra for wind forcing only.

In this case the structural response iny-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 expectedsince 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

followingHolmes2001.

Fig. 6 shows calculated response spectra in each coordinate horizontal

direction.

While along they-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

structures 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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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. 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 structures 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-damageanalysis.

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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dynamic analysis of an offshore wind turbine: wind-waves nonlinear interactions

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