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6 DEWI MAGAZIN NO. 39, AUGUST 2011

EXTERNAL ARTICLE

A. Heege

ENGLISH

A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull;

SAMTECH Iberica

Numerical Simulation of

Offshore Wind Turbines by a

Coupled Aerodynamic,

Hydrodynamic and Structural

Dynamic Approach

Abstract

The central point of the present publicaon is an implicitly

coupled aerodynamic, hydrodynamic and structural dynam-

ic approach dedicated to oshore wind turbine simulaon.

The mathemacal approach relies on an implicit non-linear

dynamic Finite Element Method extended by Mul-Body-

System funconalies, aerodynamics based on the Blade

Element Momentum theory, controller funconalies and

hydrodynamic loads.

Oshore loads are formulated in terms of hydrostac buoy-

ancy and hydrodynamic wave loads which are approximat-

ed through Morisons equaon. Special aenon is focused

on the implementaon of Morisons equaon in order to

capture hydrodynamic coupling eects which are induced

by the dynamic response of the oshore wind turbine.

Two disnct applicaons of oshore wind turbines are ana-

lyzed. First, a jacket-based oshore wind turbine is loaded

hydro-dynamically through a wave eld described by Airys

linear wave theory. As a second example, the aerodynamic

and hydrodynamic coupling eects are put in evidence by a

transient dynamic analysis of a oang oshore wind tur-bine anchored to the seabed by structural cables.

Introducon

The operaonal deecon modes and associated dynamic

loads of oshore wind turbines originate, on one hand,

from the aerodynamic and hydrodynamic loading, and, on

the other hand, from the proper dynamic response of the

enre oshore wind turbine system, including all control

mechanisms.

A decoupling of the dynamic oshore wind turbine system

into sub-systems bears the risk of missing dynamic coupling

eects which might prevail in many operaonal modes. In

parcular in the case of oang oshore wind turbines,

a decoupled aero-elasc and hydrodynamic formulaon

does not permit to reproduce properly the global dynamic

response of the wind turbine. This is because the speed

variaons which are induced in the rotor plane by dynamic

deecons of the oshore wind turbine aect directly the

rotor aerodynamics and associated controller acons on

the blade pitch posion and on the generator torque. As a

consequence, an accurate tuning of controller parameters

is dicult with simplied, decoupled oshore wind turbine

models. In order to remedy these deciencies, the pro-posed mathemacal approach is specically formulated in

order to capture dynamic coupling eects which might be


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DEWI MAGAZIN NO. 39, AUGUST 2011 7

induced simultaneously by aero-elasc and hydrodynamic

loading of oshore structures. Accordingly, the relave

velocity and acceleraon elds induced by a oang and/

or vibrang oshore wind turbine are accounted for in the

proposed coupled aerodynamic and hydrodynamic formu-

laon.

The implementaon of aerodynamic loads is based on the

Blade Element Momentum theory where wind turbine spe-

cic correcons for p and hub losses, wake eects and theimpact of the tower shadow are accounted. Hydrodynamic

loads are composed of drag loads and of ineral loads and

account for the relave velocity and acceleraon elds in

between the uid and the moving and/or vibrang oshore

structure.

Two dierent applicaons of dynamic analysis of oshore

wind turbines are presented. The wind turbine models are

discrezed by more than 3,000 Degrees of Freedom (DOF)

and account for all the abovemenoned coupling eects.

Coupled Aero-elasc, Hydro-dynamic, Structural FEM &

MBS Analysis

The applied mathemacal approach is based on a non-lin-

ear Finite Element formalism, which accounts simultane-

ously for exible Mul-Body-System funconalies [1][2]

[3][4], control devices, aerodynamics in terms of the Blade

Element Momentum theory [1][2][4][5][6][7], hydrostac

buoyancy loads and nally hydrodynamic loads in terms of

the Morison equaon [2][5][10][11][12][13][14].

Mathemacal background

In the context of an Augmented Lagrangian Approach and

the one-step me integraon method of Newmark [1][3],

the incremental form of the equaons of moon in the pres-ence of constraints is given in equaon (1). According to the

denion of the residual vector ofequaon (1), the vectorg

assembles the sum of elasto-visco-plasc internal forcesInt.

g , complementary ineral forces where centrifugal and

gyroscopic eects are included, external forces Ext.g , the

aero-dynamic forces AeroF

and nally the hydro-dynamic

and hydrostac loads HydroF

. The vector introduces ad-

dional equaons of the generalized soluon

,q , whichare used to include general Mul-Body-System/MBS func-

onalies for the modelling of the power train, pitch and

yaw drives and nally further DOF which are related to con-

troller state variables for blade pitch, yaw orientaon and

generator modelling.

The non-linear set ofequaons (1) is solved iteravely and

further details on the me integraon procedure, error es-

mators and soluon strategies can be found in the SAM-

CEF-Mecano user manual [1].

Aero-dynamic and structural coupling

Blades are modeled in the S4WT soware [1][2] through a

non-linear FEM formalism adapted to large transformaons

and large rotaons. For computaonal eciency, the struc-

tural blade model is presented either in terms of Super Ele-

ments [1][3], or in terms of non-linear beam elements. The

elemental aerodynamic forces are computed according tothe Blade Element Momentum/BEM theory including spe-

cic correcons and addional models for the p and hub

losses, turbulent wake state, tower shadow eect, dynamic

inow and dynamic stall [1][2][5][6][7][8][9].

The structural/aerodynamic coupling is performed implic-

itly at the blade secon nodes of the structural blade model

through the connecon of Aerodynamic Blade Secon Ele-

ments which contribute in terms of elemental aerodynam-

ic forces to the global equilibrium equaon (1). The discre-

saon of the aerodynamic loads corresponds to the FEM

discresaon of the structural blade model and the nodesfor the aero-elasc coupling are generally located at the

chord length posions of typically about 15 to 20 blade sec-

ons distributed along the blade span. Taking into account

that the aerodynamic loadsI

Pitch

I

Drag

I

Lift M,F,F presentedin equaon (2) are included in the residual vector ofequa-

on (1), once the iterave soluon ofequaon (1) to (8) is

found, the induced velocies, angles of aack, Prandtl loss

coecients, hydrodynamic forces and the global structural

dynamic response are consistent.

It is emphasized that this methodology features a strong

coupling, i.e. all equaons associated either with aerody-

namics, hydrodynamics, structures, mechanisms, or control

loops are solved simultaneously. A major advantage of astrong coupling is that blade vibraons induced by aero-

dynamic forces and/or hydrodynamic loads, implicitly aect

the structural response of the global dynamic wind turbine

model. Accordingly, the relave speeds relV

that enter in

the aerodynamic load computaon, account implicitly for

the aerodynamically induced speeds indV

and the result-

ing speeds BV of the structural Blade Secon nodes.

where a and a are respecvely the axial and tangenal in-

ducon factors. Details on the procedure applied in order

to compute the induced speed vector indV in terms of the

aerodynamic inducons are given in references [1][2][5].

Hydrostac buoyancy & hydrodynamic wave loads

In the present work, oshore loads are presented by hydro-

stac buoyancy loads and by hydrodynamic forces which

approximate wave loads. The hydrostac buoyancy loads

are composed of a buoyancy force vector ,t)q(Buoy

F and

of a buoyancy restoring moment ,t)q(Buoy

M . The hydro-

dynamic wave loads ,t)q,q,q(orison

F

are approximated

through Morisons equaon in terms of a drag and an iner-

a term [10][11][12].

Analogously to the aero-elasc coupling through the connec-

on of Aerodynamic Blade Secon Elements to the FEM

model of the rotor blades, the coupling of hydrodynamic

loads to the oshore structure is realized through Hydro-

dynamic Load Elements/HLE. In the context of a non-linear

FEM formalism, the Hydrodynamic Load Elements are

to be considered as 1-noded elements connected to the

nodes of the FEM mesh of the oshore structure. Accord-

ingly, each node of the FEM model of the oshore struc-

ture is loaded by a six-dimensional vector ,t)q,q,q(Hydro

F

according to equaon (3).

Large transformaons & uid kinemacs

In parcular in the case of oang oshore wind turbines,

the enre wind turbine, or sub-components like for exam-

ple the mooring lines, might by subjected to large oscilla-ons which produce eventually large rotaons. In order to

account properly for large displacements, large rotaons


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length[m]wave:waveL[s],periodwave:waveT,[rad/m]numberwaveangular:wave2pi/Lk

Level/SWLWaterStilltodistance:zfrequency,wave:,waterdepth:dheight,wave:Hwith

(11)t)sin(kxsinh(kd)

z))cosh(k(d2

2

H

fluidu

(10)1,2,3kj,i,with)ia

jq(

ka)

ka

jq(ia

kq

jaia

aCsubV

add

ijM

tv

tv

a:spanthetolarperpendicuvectorunitonaccelerati

qSpan_plane

Projt

v:planespantheonprojectedvectoronaccelerati

(9)q

)t

v(

a

CsubVMorisonF

q

addM

tcoefficienMorison1,tcoefficienmassadded,tcoefficiendrag

volumesubmerged,diameter:Dspan,submerged

spanelementtonormalcomponentvelocitystructural&particlefluid&

(8)

(7)2

(6)

pointatsurfaceto)(nbody,submergedofsurfaceenvelope:)S(

levermomentrestoring:lFWL,w.r.t.depth:E,densityfluid:vectorgravity

(5),

(4),

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'a,),BSVinfowV(findVandindVBSVinfowVrel

Vwith

(2)it)A,q,q(2relVt),q,q(iC*2

1PitchM,DragF,LiftF

ForcesExternal,ForcesInternalwith

)(:vectorResidual

factorPenalty:pmatrix,JacobianConstraint:vectorConstraint:

matrixInertia&Mass:M:,matrixDamping:C,matrixStiffness:K

sMultiplierLagrangeofVector:,vectorvectorPosition

(1)2

0000

0

00

0

:aC

mC:

aC:

dragC

,t):q(effV,t):q(

effL

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)t

v

t

u(a

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D,t)q,q(

DragF

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DragF,t)q,q,q(

MorisonF

qnormal:,tq,tq

, :g

,t)qS(

dsg,t) q,t) E(q(n,t)q(l

,t)qS(

dsg,t) q,t) E(q(n,t)q(HstatF

,t)q(Buoy

M,t)q(BuoyF,t)q(

HstatF

,t)q(Buoy

M,t)q,q,q(MorisonF,t)q(

BuoyF,t)q,q,q(

HydroF

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Int.g

p]T[Bq[M]Ext.gHydroFAeroFInt.g,t)q,q,q(R

q/,[B]

onAccelerati:q,:q

)(,t)q(

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][[B]

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[B[K]

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4/10


and/or deformaons of the oshore wind turbine, the

kinemacal variables which are involved in the hydrostac

& hydrodynamic formulaon of equaons (3) to (8) are

formulated implicitly as a funcon of the soluon of the

respecve me integraon step of the global equilibrium

equaon (1). According to Fig. 1 and Fig.2, the eecvely

submerged depth ),q(eff

E t is measured w.r.t. to a me

variable Free Water Level/FWL dened by the wave height

t),q(W

. It is noted that a span length vector t),q(Span

L

and the associated envelope surface ),tqS( are aachedto each node of the FEM mesh of the oshore. The surface

normal vector ,t)q(n

ofequaon (5) is to be interpreted as

the outward normal for any point of the integral of the en-

velope surface ),tqS( . Since the span vector t),q(SpanL and

the envelope surface ),tqS( are moving and rotang with

the associated structural node of the FEM mesh, the uid

depth ),q(eff

E t depends implicitly on the soluon vector

(t)q

of the respecve me integraon step. As a conse-

quence, the buoyancy, drag and ineral loads ofequaons

(5) to (8) account implicitly for the soluon-dependent ef-

fecvely submerged span length ),q( teff

L and for the ef-

fecvely submerged volume ),q( teffV .

Hydrostac buoyancy force and restoring moment

Hydrodynamic loads are introduced through 1-noded Hy-

drodynamic Load Elements/HLE aached to each node

of the FEM mesh of the oshore component. According

to equaon (5), the buoyancy force ,t)q(Buoy

F and the

restoring moment ,t)q(Buoy

M are obtained from the in-

tegraon of the pressure distribuon that acts on the en-

velope surface of the submerged oshore components. In

case of cylindrical geometries, the integrals ofequaon (5)

are obtained analycally. According to the rst integral

term ofequaon (5), the direcon of the buoyancy force,t)q(

BuoyF

is opposed to the gravity vector and funcon

of the integral of the pressure acng on the submerged

envelope surface. The restoring moment ,t)q(Buoy

M is

determined by the second integral term of equaon (5)

where the lever vector ,t)q(l points from the origin of the

local coordinate system of the Hydrodynamic Load Ele-

ment to the respecve integraon point of the envelope

surface ),tqS( with the normal vector ,t)q(n .The orienta-

on of the local axis of the restoring moment ,t)q(Buoy

M

results from the integral soluon of the second term of

equaon (5) which is funcon of the inclinaon of the o-

shore component w.r.t. to the gravity vector.

Hydrodynamic wave loads according to Morisons equa-

on

Morisons formula was originally applied to the computa-

on of uncoupled hydrodynamic forces on vercal, xed

piles with shallow water wave loading. It has since been

extended to a three-dimensional formulaon for arbitrar-

ily oriented moving structures, with both wave and cur-

rent loadings [10][11][12]. As stated in equaons (6) to

(8), the coupled Morison equaon presents an empirical

formulaon that describes the hydro-dynamic loads as a

superposion of a uid drag DragF

and an ineral term

InertiaF

that accounts for the added uid mass acceler-ated due to the uid-structure interacon.

DEWI oers an independent service

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Wind Turbine inspecTion


5/10


The uid drag vector formulated in equaon (7) and the u-

id ineral load vector formulated in equaon (8) are both

contained in the plane perpendicular to the span direcon,

but show generally dierent direcons, i.e. the angle of

aack of the drag forces and the angle of aack of the

inera forces do not generally coincide.

A coupled formulaon of Morisons approach is exposed

in references [11][12] in a form analogous to equaon (8)

where the direcon of the Morison inera load vector is

determined by 2 disnct contribuons with a-priori 2 dif-

ferent vector orientaons. The rst term of the Morison

equaon (8),

t

u

t),q(eff

V ,

contributes to the Morison inera forces, if the unperturbed

uid ow is accelerated. The direcon of that vector compo-

nent corresponds to the direcon of the unperturbed uid

direcon, but projected into the plane which is perpendicu-

lar to the span direcon of the oshore component. The

second term of the Morison equaon (8) contributes to theinera forces through the relave uid-structure accelera-

on

)(t

v

t

u

which results from the unperturbed uid ow accelera-

on and from the dynamic response of the oshore struc -

ture. It should be noted that both vector components

ofequaon (8) are projected onto the same plane which is

perpendicular to the span wise direcon, but the respecve

vector orientaons of these two terms are not necessarily

aligned if the structure vibrates and/or oats.

It is conjectured that the inclusion of the uncoupled inera

term of the Morison equaon (8) might not be straighor-

ward for a formulaon dedicated to the simulaon of cou-

pled hydrodynamic and structural dynamic phenomena.

It is spulated that the basic Morison equaon as stated in

references [10][11][12] might lead to an overesmaon of

hydrodynamic drag and/or inera loads, because hydrody-

namic inducons and/or wave dispersion are not accounted

for in that formulaon.

Added Mass & Eigen-ModesThe inera term InertiaF

of the Morison equaon (8) mod-

ies the total mass associated to the submerged oshore

Fig. 1: S4WT wind turbine model supported by

OC4 jacket oshore structure


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Fig. 2: Submerged span for node above Free Water Level/FWL and below FWL

structure and as a consequence the Eigen-Modes of the o-

shore wind turbine are aected.

As outlined, the implemented algorithm for the hydrody-

namic loads accounts implicitly for the kinemacs induced

by a heavily moving oshore wind turbine and transient

wave height. The total mass taken into account in the Ei-

gen-mode computaon of the oshore structure is comple-

mented through the derivave of the inera term of the

Morison equaon (8) with respect to the relave accelera-

ons in between the uid and the vibrang and/or oang

oshore structure. Equaons (9, 10) dene the added mass

term in terms of the derivave of the Morison inera force

with respect to the structural acceleraons of the respec-

ve node of the FEM model. As stated in equaon (10) in

tensorial form using the Einstein summaon convenon,

the added uid mass is obtained through the derivave of

the Morison inera term and can be presented in terms of

two contribuons. The rst contribuon is determined by

the added massa

Csub

V mulplied by the dyadic productof the acceleraon unit vector aa

. It is emphasized that

the unit vector a is contained in the plane perpendicular tothe span wise direcon of the respecve component and

might be interpreted as the vector dening the direcon of

the inera loads. The second term ofequaon (10) depends

not only on the vector a

, but as well on the structural ac-

celeraon of the respecve FEM node q and on the deriva-

ve of the acceleraon unit vector a

. As a consequence

the addional uid mass included in the global mass and

inera matrix of equaon (1) becomes me dependent

and also dependent on the instantaneous spaal direcon

of the relave acceleraon which occurs in between the

uid and the submerged oshore structure. Therefore, not

only do the Eigen-Frequencies of the oshore wind turbine

become me dependent, but also the Eigen-Shapes are af-

fected by the added uid mass, because the added mass is

direconal.

Airys linear wave theory

In the present studies, the unperturbed uid velocity/accel-

eraon eld is modelled according to equaon (11) through

Airys wave theory [13][14] that approximates the transient

uid dynamics of waves as a funcon of parameters like wa-

ter depth, wave height and period.

The following application examples are based on fluid/

water speed distributions according to equation (11) andare generated by the independent program Waveloads of

the University of Hannover [13].

Fig. 3: Zoom on wave speed & wave height at node #40 located at limit

to free uid surface of jacket

Fig. 4: hydrodynamic drag force, Morison inera force & and buoyancy

force at node#40


7/10


Applicaon Examples

Two disnct simulaons of oshore wind turbines are

presented. Even though the implemented methodologysupports the implementaon of very complex oshore

structures in terms of general FEM models, in the present

examples the oshore structures are modelled by non-line-

ar beam elements of circular geometry.

The rst applicaon corresponds to an oshore wind tur-

bine supported by a jacket structure that corresponds to

the OC4 reference base line model [15]. The second exam-

ple presents a oang oshore wind turbine whose oater

and mooring lines correspond to the OC3 reference model

[16].

Oshore wind turbine supported by Jacket structure

Fig. 1 presents the S4WT wind turbine model supported by a

jacket structure according to the OC4 reference model [15].

The applied wind turbine model comprises in total 3732

DOFs and includes a detailed gearbox model, pitch and yaw

drives and further exible structural components like the

bedplate and nacelle structure in terms of Super Elements.

The jacket structure is modelled by non-linear beam ele-

ments and loaded by buoyancy and hydrodynamic loads.

The following simulaon results correspond to a load case

with wind eld of a mean speed of 10 [m/s] and a wave

denion according to Airys linear wave model with the

following characteriscs:

Wave Height: 6m, Wave Period: 10s, Water Depth: 50m

Angle in between wave & wind direction: 0 [deg.]

Note that the spaal uid speed distribuon is obtained

from the external soware Waveloads [13]. The corre-

sponding acceleraon eld of the external wave and the

relave structural-uid acceleraons of equaons (8) are

computed in the hydrodynamic element of the solver SAM-CEF-Mecano.

Fig. 3 presents the hydrodynamic boundary condions for

the jacket node #40 located closely to the Sll Water Level/

SWL. The applied wave velocies in longitudinal XGL and

vercal ZGL direcons refer to the le ordinate ofFig. 3 and

the wave height refers to the right ordinate of Fig. 3. The

locaon of the jacket node #40 considered here is depicted

in Fig. 1. Fig. 4 presents for node #40 the resulng buoyancy

force, the uid drag and nally the Morison inera force.

Floang oshore wind turbine

Fig. 5 presents the S4WT model of a floating offshore wind

turbine supported by a floating structure according to ref-

erence [16]. The wind turbine model comprises in total

3402 DOFs and includes a detailed power train model, pitch

and yaw drives and further flexible structural components

like the mooring lines.

The simulated load case corresponds to a constant wind

eld of a mean speed of 16 [m/s] and a wave denion ac-

cording to equaon (11) with the following characteriscs:

Wave Height: 6m, Wave Period: 10s, Water Depth:

320m

Angle in between wave & wind direction: 45 [deg.]

As depicted in Fig. 5, the floating offshore wind turbine is

attached by 3 cables which are separated each by a rotationof 120 [degrees] w.r.t. to the vertical reference axis. The

length of each cable is about 700 [m]. In S4WTs floating

Fig. 5: S4WT model of OC3 oshore 5-MW baseline wind turbine


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Werbung

Samtech

1/1

4c


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Fig. 6: Generator speed, blade pitch & power transients induced by the oang wind turbine oscillaons

wind turbine model, the cables are presented either by

non-linear cable elements (neither compression, nor bend-

ing stiffness), or respectively by non-linear Beam Ele-

ments.

The large oscillations of the floating wind turbine induce

large low frequency speed variations in the rotor plane.

Fig. 6 clearly shows the low frequency speed and rotor

torque variations induced by the global tilt oscillations of

the floating turbine. It can be noted that further controller

tuning would be required in order to reduce these oscilla-

tions induced by the floating wind turbine concept.Fig. 6 presents the blade pitch, speed and power transients

of the presented oang oshore wind turbine. The pre-

sented transients of blade pitch angle and the produced

power show low frequency oscillaons induced by the ro-

tor plane speed variaons due to the lt oscillaons of the

enre oang wind turbine.

The tower-top trajectory in longitudinal XGL direcon (direc-

on of incoming wind) and in the horizontal YGL, is shown

on the top-right corner ofFig. 5. The maximum oscillaon

of the tower-top of the oang wind turbine in the longi-

tudinal direcon is evaluated from -1.5 [m] to 9 [m], i.e. a

total displacement range of the tower-top of nearly 14[m]

in the longitudinal direcon. In the case of the simulated

wave height of 6 [m], due to the induced buoyancy loads,

the wind turbine top oscillates approximately 2[m] in the

vercal direcon.

On the lower right poron ofFig. 5, the external hydrody-

namic uid loads applied on a specic node of the mooring

line FEM model are presented. The locaon of mooring line

node #49 is presented in Fig. 5. It is noted that the Morison

inera force module presents a phase oset with respect

to the drag force. The drag and ineral forces are both con-

tained in the same plane perpendicular to the span direc-

on, but the orientaon of both force components do not

generally coincide.

Conclusions

Morisons equaon was implemented in the solver SAM-

CEF-Mecano in an extended form proposed in several refer-

ences such as [11] and [12] in order to account for struc-

tural dynamics and hydrodynamics coupling eects. The

coupled form of the Morison equaon is interpreted as an

empirical approximaon for the modelling of hydrodynamic

currents and/or waves and can be decomposed into two

principal contribuons. On the one hand, an uncoupled in-

era term which is only funcon of the acceleraon of theuid ow, and, on the other hand, a coupled inera term

which is funcon of the relave acceleraon in between

the oshore structure and the unperturbed uid ow. It

is conjectured that the precision and applicaon range of

the coupled form of Morisons equaon might be improved

with some further modicaons. First, it might be conven-

ient to formulate not only the second term, but as well the

rst term of the Morison equaon (8) implicitly as a func-

on of the dynamic response of the oshore structure. Sec-

ond, Morisons model does not account for hydrodynamic

inducons on the unperturbed uid speeds and/or accel-

eraons which would result from the uid-structure inter-

acon. Analogously, the dispersion of an impacng wave

on the oshore structure is not accounted for in Morisons

empirical model. As a consequence, it is spulated that the

applicaon of the Morison equaon might tend to an over-

esmaon of hydrodynamic drag and/or uid inera loads.

It is conjectured that the empirical formulaon of Morison

might be improved if the added mass coecient, or respec-

vely the Morison coecient, is formulated as an empirical

decay funcon of the rao between the hydraulic diameter

and the wavelength, as stated by MacCamy and Fuchs [17].

These empirical decay funcons might approximate roughly

the eect of uid-structure inducons and/or wave disper-

sion, as it has been already reected in some recommendedpracces regarding oshore structures [18]. Future imple-

mentaons will be devoted to automacally modifying the


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Morison coecient taking into account these experimental

observaons and the corresponding wave dynamics. The

fully coupledphilosophy of the current code will be kept

during this new development, so the eects of the struc-

ture kinemacs will be considered during hydrodynamic

load computaon.

Two disnct oshore wind turbines have been analyzed by

a fully coupled aerodynamic, hydrodynamic and structural

dynamic approach. In the rst applicaon example, theOC4 reference oshore wind turbine model was chosen.

The corresponding aero-elasc S4WT wind turbine model

is supported by a hydro-dynamically loaded jacket FEM

model, includes exible MBS models of the major mecha-

nisms like the power train including the gearbox, the yaw

and the pitch drives, and comprises in total 3732 Degrees

of Freedom. The required CPU me for transient analysis

on a standard Intel Duo Core 3.2GHz computer, was similar

compared to standard onshore high delity wind turbine

models with a CPU me factor of about 45 with respect to

real me. It is menoned that required CPU mes depend

strongly on the number of Degrees of Freedom and on the

excited frequency content of the respecve model. In the

case of simplied wind turbine models that comprise less

than 1000 DOFs, the required CPU is generally less than a

factor of 10 with respect to real me.

In the case of the OC3 oshore reference model, the oat-

ing wind turbine model is not restrained by xaons as in

the case of clamped jacket supports. Instead, the oater is

aached to exible mooring lines aached to the seabed.

As a consequence, the dynamic equilibrium of the oscillat-

ing oang wind turbine is strongly inuenced by coupled

buoyancy, hydrodynamic and aero-elasc loads which all

strongly mutually interact together with controller acons.

In parcular the low frequency oscillaons of the oangturbine induce large speed variaons in the rotor plane.

In order to reduce the observed rotor plane speed varia-

ons induced by the oscillang oang wind turbine, spe-

cic controller tuning for blade pitch and generator torque

would be required. Future research will include specic

control strategies in order to reduce these oscillaons, for

instance via the integraon of acve damping techniques.

References

[1]. SAMCEF-Mecano User Manual Version 14.1,

http://www.samtech.com

[2]. S4WT V3.1, SAMCEF for Wind Turbine User Manual,

http://www.samtech.com

[3]. Geradin, M. and Cardona, A., Flexible Multibody Dynamics: A Finite

Element Approach. John Wiley and Sons Ltd, 2001

[4]. Heege A., Betran J., Radovcic Y., Fatigue Load Computation of Wind

Turbine Gearboxes by Coupled Finite Element, Multi-Body-System

and Aerodynamic Analysis, Wind Energy, vol. 10:395-413, 2007.

[5]. Heege A., Bonnet P., Bastard L., Horcas S. G., Sanchez J.L., Cucchini P.,

Gaull A., Numerical simulation of offshore wind turbines by a cou-

pled aerodynamic, hydrodynamic and structural dynamic approach,

Proceedings EWEA 2011 conference, 14-17 March 2011, Brussels/

Belgium.

[6]. Bossanyi, E. A., GH-Bladed User Manual, Issue 14, Garrad Hassan and

Partners Limited, Bristol, UK, 2004

[7]. AeroDyn Theory Manual, December 2005 NREL/EL-500-36881,

Patrick J. Moriarty, National Renewable Energy Laboratory Golden,

Colorado A. Craig Hansen Windward Engineering, Salt Lake City,

Utah

[8]. Snel H., Schepers J. G., Joint Investigation of Dynamic Inflow Effects

and Implementation of an Engineering Method, ECN Report ECN-

C--94-107, 1995.

[9]. Hansen M. H., Gaunaa M., Madsen H. A., A Beddoes-Leishman type

dynamic stall model in state-space and indicial formulations, Riso

Report Riso-R-1354(EN), 2004.

[10]. Morison, J. R., O Brien, M. P., Johnson, J. W. and Schaaf, S. A., The

forces exerted by surface waves on piles. Petroleum Transactions.

189 (TP 2846), p 149, 1950

[11]. Germanischer Lloyd Wind Energie GmbH, Guideline for the Certifica-

tion of Offshore Wind Turbines. 1st June 2005

[12]. American Petroleum Institute. Recommended Practice for FlexiblePipe, API Recommended Practice 17B. Third Edition, March 2002

[13]. K.Mittendorf,B.Nguyen and M.Blmel. WaveLoads, A computer pro-

gram to calculate wave loading on vertical and inclined tubes.User

manual. Gigawind, Universitt Hannover. Version 1.01, August 2005

[14]. Robert G.Dean, Robert A. Dalrymple. Advanced Series on Ocean En-

gineering, Volume 2: Water wave mechanics for engineers and scien-

tists. World Scientific Publishing Co. Singapore, 1991

[15]. F. Vorpahl, W. Popko, D. Kaufer. Description of a basic model of the

Upwind reference jacket for code comparison in the OC4 project

under IEA Wind Annex XXX; Fraunhofer Institute for Wind Energy and

Energy System Technology (IWES), 4 February 2011

[16]. J. Jonkman, Definition of the Floating System for Phase IV of

OC3,Technical Report, NREL/TP-500-47535, National Renewable En-

ergy Laboratory Golden Colorado/USA, May 2010.

[17]. MacCamy, R.C., Fuchs, R.A., Wave forces on piles: A diffraction theo-

ry, U.S. Army Corps of Engineers, Beach Erosion Board, Tech. Memo

No. 69,1954

[18]. American Petroleum Institute. Recommended Practice for Planning,

Designing, and Constructing Tension Leg Platforms, API Recommend-

ed Practice 2T. Second Edition. August 1997

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