This document describes a numerical simulation approach for offshore wind turbines that couples aerodynamic, hydrodynamic, and structural dynamic effects. The approach uses an implicit finite element method extended with multibody system capabilities to model the turbine. Aerodynamic loads are calculated using blade element momentum theory. Hydrodynamic loads are determined using Morison's equation. Two examples are presented: analysis of dynamic coupling effects on a jacket-based turbine, and transient analysis of a floating turbine anchored to the seabed.

1. Numerical simulation of offshore wind turbines
by a coupled aerodynamic, hydrodynamic
and structural dynamic approach
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull
SAMTECH Iberica
E-08007 Barcelona
andreas.heege@samtech.com
Abstract particular in the case of floating offshore wind
turbines, a decoupled aero-elastic and
Central point of the present publication is an hydrodynamic formulation does not permit to
implicitly coupled aero-elastic, hydrodynamic and reproduce properly the global dynamic response of
structural approach which is dedicated to the the wind turbine. This is because the speed
simulation of offshore wind turbines. variations which are induced in the rotor plane by
dynamic operation deflections of the offshore wind
The applied mathematical approach relies on an turbine and/or by a floating wind turbine, affect
implicit non-linear dynamic Finite Element Method directly the aerodynamic loads and associated
which is extended by Multi-Body-System controller actions on the blade pitch position and/or
functionalities, aerodynamics based on the Blade on the generator torque. A major drawback of
Element Momentum theory, controller decoupled simplified approaches is that a proper
functionalities, hydrodynamic wave loads through tuning of controller parameters of floating offshore
the implementation of the Morison equation and wind turbines is not possible and as a consequence
finally buoyancy loads which account for variable the dynamic behavior might be wrongly evaluated.
wave height. In order to account for the hydro-
dynamic and structural coupling effects, the In order to remedy these deficiencies, the proposed
Morison equation is implemented in its extended mathematical approach is specifically formulated in
form which accounts for the dynamic response of order to capture dynamic coupling effects which
the loaded offshore structure. might be induced simultaneous by aero-elastic and
hydrodynamic loading of the offshore structure.
First, the impact of hydrodynamic and structural Accordingly, the relative velocity and acceleration
dynamic coupling effects is analyzed for a jacket fields which are induced by a floating and/or
based offshore wind turbine. As second example, vibrating offshore wind turbine are accounted in the
the aerodynamic and hydrodynamic coupling coupled aerodynamic and hydrodynamic
effects are put in evidence by a transient dynamic formulation.
analysis of a floating offshore wind turbine which is
anchored by structural cables to the seabed. The implementation of aerodynamic loads is based
on the Blade Element Theory where wind turbine
1 Introduction specific corrections for tip and hub losses, wake
effects and the impact of the tower shadow are
The operation deflection modes and associated accounted.
dynamic loads of offshore wind turbines originate,
on the one hand, from aero-elasticity and Hydrodynamic loads are composed of drag loads
hydrodynamic loading of the submerged offshore and of inertia loads which account for the relative
structure, and, on the other hand, from the proper velocity and acceleration fields in between the fluid
dynamics of the entire wind turbine system, and the moving and/or vibrating offshore structure.
including all control mechanisms. Two different applications of dynamic analysis of
Especially in the case of the numerical simulation of offshore wind turbines will be presented. The
floating offshore wind turbines, a decoupling of the applied wind turbine models are discretized by
dynamic offshore wind turbine system into sub- more than 3000 DOF and account for all mentioned
systems bears risks to miss coupling effects which coupling effects.
might prevail during many operation modes. In
Article submitted to EWEC 2011:
Numerical simulation of offshore wind turbines by a coupled aerodynamic, hydrodynamic and structural dynamic approach
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull

2. r r r
2 Coupled aero-elastic, hydro- ⎡[ M ] [0]⎤ ⎡ Δq ⎤ ⎡[C] [0]⎤ ⎡ Δq ⎤ ⎡[ K ] [BT ]⎤ ⎡ Δq ⎤
&&
r &
⎢ [0] [0]⎥ ⎢ &&⎥ + ⎢ ⎢ r⎥ + ⎢
⎥ & ⎥⎢ r⎥ =
⎣ ⎦ ⎣ Δλ ⎦ ⎣ [0] [0]⎦ ⎣ Δλ ⎦ ⎢[B] [0] ⎥ ⎣ Δλ ⎦
⎣ ⎦
dynamic, structural dynamic FEM r r r
⎡ R (q , q , t )⎤
&
and MBS analysis = ⎢ r r ⎥ + 0(Δ2 )
⎣ − φ (q , t ) ⎦
The applied mathematical approach is based on a (1)
non-linear Finite Element formalism, which Residual vector :
accounts simultaneously for flexible Multi-Body- r r r r r r r r r r
R(q, q, &&, t) = −g(q, q, &&, t) − [M]&& − [B T ]λ
& q & q q (2a)
System functionalities [1][2][3], control devices,
where :
aerodynamics in terms of the Blade Element
r r r r r r r r Hydro
Momentum Theory [3][4][5][6], buoyancy and g ( q , q , q , t ) = g Int. − g Ext. - F Aero − F
& && (2b)
hydrodynamic loads in terms of the Morsion Generalized solution at time T + ΔT and iteration It + 1 :
equation [7] [8][9][10][11]
[ ]
r r
[ ] [r rT
q, λ T + 1 T = q, λ + Δq, Δλ It + 1
It +
Δ ]
r r T + ΔT
(3)
The applied aero-elastic wind turbine models
Stiffness matrix : K, Damping matrix : C
include flexible component models through dynamic
Mass & Inertia matrix : M
Finite Element models, or respectively in its r
condensed form as Super Elements. Further on, the Constraint vector : φ
most relevant mechanisms like pitch and yaw drives Constraint Jacobian matrix : [B] = ∂φ /∂q
r r
[ ]
or detailed power train models are included in the r r r r
Internal forces : g Int. (q , q , &&, t )
& q
same aero-elastic analysis model [3]. r r r r
External forces : g Ext. (q , q , &&, t )
& q
2.1 Mathematical background Aerodynamic loads : F
r Aero r r
(q , q , t )
&
In the context of an “Augmented Lagrangian r Hydro r r r
Hydrodynamic loads : F (q , q , q , t )
& &&
Approach” and the “one-step time integration
method of Newmark” [1][2], the incremental form of 2.2 Aero-dynamic loads
the equations of motions in the presence of
constraints is stated in terms of equations (1,2,3). Blades are modeled through a non-linear FEM
formalism either in terms of Super Elements, or in
According to the definition of the residual vector of terms of non-linear beam elements. The implicit
r
equation (2a,b), the vector g assembles the sum of structural and aerodynamic coupling is performed at
elasto-visco-plastic internal forces r Int.
, discrete blade section nodes through the
g
connection of “Finite Blade Section Elements”
complementary inertia forces where centrifugal and
which contribute in terms of elemental aerodynamic
gyroscopic effects are included, external forces
r Aero
forces to the global equilibrium equation (1). The
r Ext.
g , the aero-dynamic forces F and finally the elemental aerodynamic forces are computed
r Hydro according to the Blade Element Momentum/BEM
hydro-dynamic and hydrostatic loads
r
The F .
theory including specific corrections in order to
Vector φ introduces additional equations of the
account for the tower shadow and tip and hub
generalized solution [q, λ ] , which are used to
r r
losses.
include general Multi-Body-System functionalities The discretisation of aerodynamic loads
for the modelling of the power train, pitch and yaw corresponds to the structural discretisation in terms
drives and finally further Degrees of Freedom/DOF of retained Super Element nodes or, respectively,
which are related to controller state variables for beam nodes and the aero-elastic coupling is
blade pitches, yaw orientation and generator performed generally at the ¼ chord length positions
modelling. of 15 equally spaced blade sections.
Further details on time integration procedure, error The a-priori unknown induced velocities are defined
estimators and solution strategies for equation in equations (6a,b,c) in terms of the induction
solvers, can be found in the SAMCEF-Mecano user normal to the rotor plane, i.e. the axial induction a,
manual [1]. and the induction tangential to the rotor plane a’
[4][5][6]. It is noted that the inductions in the normal
and the tangential rotor plane directions are
computed iteratively by solving a system of non-
linear equations which is resulting from expressions
(1), (4), (5) and (6a,b,c). The elemental
aerodynamic forces at each blade section are
assembled to the global aerodynamic force vector
r Aero r r
F ( q , q , t ) according to equations (1,2,3,4) and
&
Article submitted to EWEC 2011:
Numerical simulation of offshore wind turbines by a coupled aerodynamic, hydrodynamic and structural dynamic approach
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull

3. account for the empirica model for inductions [6 of
al 6]
equations (5
5,6).
With the relati speeds at eac Blade Section/ of index I :
ive ch /BS
r rel
V
I I
[
r ow r BS r in
= V info V
- I
+ V nduced
I
]
BS I
S
Rotation opera from global coord. system to B - System :
ator c BS R
α I
Rotation opera from the BS - System to Aero - α - System :
ator o R
r BS BS I r
S I r r
with VI = R q and the unknown angle o attack α (q, q, t)
& u of &
α
the local aerody
ynami c loads can be defined in e
n each Aero - Sys
stem :
I r r
& )
1 I
2
I r r
& ( 2 r r
I
)
M Pitch (q, q, t) = C M α (q, q, t) ρVrel (q, q, t)A I
&
Figure 1: Aerodynamic Load Element
A c
I r r 1 I
(
I r r
)
2 r r
FLift (q, q, t) = C Lift α (q, q, t) ρVrel (q, q, t)A I
&
2
&
I
& 2.3 Hydro
o-dynamic & buoyan loads
c ncy
In the present work, offsho loads are idealized in
n t ore e n
I r r 1 I I r r
( 2 r r
)
FDrag (q, q, t) = C Drag α (q, q, t) ρVrel (q, q, t)A I
&
2
&
I
& te
erms of hyd
de
drostatic buo
efined in equation (8) a
oyancy loads which are
and hydrodyn
e
namic forcess
BS r I r r α I
F (q, q, t) = R F I
& [
Drag
r r r r
(q, q, t), F I (q, q, t F I
&
Lift
& t),
spanwise
] ac
ccording to the formula ation of Mor
rison [7][8][9
which is state in equations (9,10,11 Structura
ed 1).
9]
al
co
omponents of the o offshore sttructure aree
Aerodynami c load vector in global coordinate s
system : discretized in general th
n hrough non--linear beamm
Nb. BS
elements.
r Aero r r BS r I r r
F (q, q, t) = ∑ BS R I
& F (q, q, t)
& (4
4) Analogously to the aero-elastic modelling
c g
I =1
pproach, hyd
ap drodynamic loads are introduced in
n
te
erms of 1-noded Hydrodyna amic Loadd
⎡1 0 0 ⎤ Elements/HLE which are connected t the nodes
E to s
r
V induced = ⎢0 a'
⎡r
0 ⎥ V
r BS ⎤ of the FEM me of the of
f esh ffshore struct
ture.
⎢0 ⎢ inflow - V ⎥ (5
5)
⎣ 0 − a⎥⎣
⎦
⎦ Hydrodynamic Load Elements are form
c mulated in ann
mplicit mann
im ner in local convective coordinate
e e
with the induct
tion normal to the rotor plane is de
efined by :
sy
ystems whic are attach
ch hed to the n nodes of thee
a ≤ 0.4 : C T = 4 aF (1 - a) a)
(6a FEEM mesh of the off fshore comp ponents. As s
8 40 50
de
epicted in Fig
gures 2 & 3 the initial or
rientation and
d
2
a ≥ 0.4 : C T = + (4F - )a + (
a - 4F)a b)
(6b as
ssociated span of a Hydrodyn
s namic Load d
9 9 9
Elements is ddefined throu
ugh a span vector which h
and the inductio tangential to th rotorplane :
on he
otates with the vibratin or float
ro ng ting offshoree
2 st
tructure.
CP V
' N
a = )
(6c) 2.3.1 Coup
pled Moris
son equat
tion
2
4 F (1 - a) T
)V
with :
Morison’s for
M rmula was originally ap
o pplied to thee
coomputation o uncoupled hydrodynam forces on
of d mic n
Thrust coefficie t of the angula rotor segment of surface 2π r d :
en ar dr veertical, shallo water, fix
ow xed piles wit only wave
th e
lo
oading. It ha since bee extended to a three
as en d e-
dF thrus Nb Blades
st
CT = dimensional f formulation for arbitrary orientation
y n
ρV 2 π r dr
V moving struct
m tures, with both wave and curren nt
rpl
lo
oading [7][8][9 As stated in equation (7) to (11)
9]. d ns ),
Power coefficie t of the angular rotor segment o surface 2π r dr :
en r of r th
he coupled Morison equation p presents an n
dT torq V Nb Blades
que s emmpirical formmulation which describes the hydro o-
T dyynamic loads as a supe erposition of a fluid drag
f g
CP =
ρ 2 π r dr
ρV r Drag r Inertia
rpl F and an inertial term F
d which
h
F = Prandtl tip & hub loss coeff
p ficien t ccounts for the added fluid mas which is
ac d ss s
ac
ccelerated du to the fluid-structure in
ue nteraction.
V &V = n
normal & tangenti l rotorplane spe
ia eed without ind
duction
N T
It is stipulated that the ba
d asic Morison equation as
n s
sttated in refeerences [7][[8][9] might lead to ann
Article submitted to EW
e WEC 2011:
Numerical simula
ation of offshore w
wind turbines by a coupled aerodynamic, hydrodynam and structural dynamic approac
mic ch
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J Sanchez, P. Cucchini, A. Gaull
J.L. C

4. overestimation of hydrodynamic drag and/or inertia r r
∂u ∂v
loads, because hydrodynamic inductions and/or relative fluid-structure acceleration ( − )
∂t ∂t
wave dispersion are not accounted in that
which is projected onto the plane which is
formulation.
perpendicular to the span wise direction of the
As it is shown in Figure 1, the direction of drag is structural component.
determined in the aerodynamic and in the
Both mentioned inertia load components are
hydrodynamic implementation by the relative fluid-
contained in the same plane which is
structural velocity vector which is projected onto a
perpendicular to the span wise direction, but the
plane which is perpendicular to the span wise
respective vector orientations are not necessarily
direction.
aligned if the structure is vibrating and/or floating. It
The vector of the fluid drag formulated in equation is conjectured that the coupled Morison formulation
(9) and the vector of fluid inertia loads formulated might require further adaptations, because the first
in equation (10) are contained in the same plane term of equation (10) includes an uncoupled term
r
which is perpendicular to the span wise direction, eff r ∂u
but show generally different vector directions, i.e. ρV (q, t) which does not depend on the
∂t
the “angle of attack of the drag forces” and the
“angle of attack of the inertia forces” are frequently relative direction of the fluid-structure accelerations
r r
not coincident. ∂u ∂v
( − ) .
∂t ∂t
A coupled formulation of Morison’s approach is
exposed in several references [8][9] in a form
analogous to equation (10) and might be r Hydro r r r r Buoyancy r Morison r r r
F (q, q, &&, t) = F
& q (q, t) + F (q, q, &&, t)
& q (7)
interpreted as an extension of an empirical one-
dimensional formulation which was dedicated with :
initially to the modelling of uncoupled fluid loads [7] r Buoyancy r eff r r
to a coupled three-dimensional formulation. It is F (q, t) = − V (q, t) ρ g (8)
stipulated that the coupled Morison formulation
might require further adaptations in order to r Drag r r D eff r r r r r
F (q, q, t) = ρ L (q, t) C drag | u - v | (u - v)
& (9)
improve the precision of that empirical method. 2
r r r
Important hydrodynamic and structural dynamic r Inertia r r r eff r ∂u eff r ∂u ∂v
F (q, q, &&, t) = ρ V (q, t)
& q + ρ V (q, t) C ( − ) (10)
coupling effects might be induced by floating ∂t a ∂t ∂t
offshore structures, but the coupled formulation r Morison r r r r Drag r r r Inertia r r
exposed in references [8][9] include an “uncoupled F (q, q, &&, t) = F
& q (q, q, t) + F
& (q, &&, t)
q (11)
inertia term” which does not depend on the relative where :
dynamics of the fluid and the structure. It is r r
conjectured that the inclusion of an “uncoupled q : structural position, && : structural acceleration
q
inertia term” might not be indicated for a r
u : Fluid particle velocity component normal to element span
formulation which is prone to the simulation of r
v : Structural velocity component normal to element span
coupled hydrodynamic and structural dynamic
r
phenomena. g : gravity vector , ρ : fluid density
The direction of the Morison inertia load is D : Diameter associated to structural node
determined by 2 distinct contributions with a-priori eff r
2 different vector orientations: L (q, t) : Effective Spanwise Length
r eff r
eff r ∂u V (q, t) : effective submerged volume
a) The first term of equation (10) ρ V (q, t) ,
∂t
C : Drag coefficient
presents a vector component which direction drag
corresponds to the unperturbed fluid C : added mass coefficient
r a
∂u
acceleration which is projected into the C = 1 + C : Morison coefficient
∂t m a
plane which is perpendicular to the span wise
direction of the structural component.
b) The second term of equation (10)
r r
eff r ∂u ∂v
ρ V (q, t) C ( − ) , presents a vector
a ∂t ∂t
component which direction corresponds to the
Article submitted to EWEC 2011:
Numerical simulation of offshore wind turbines by a coupled aerodynamic, hydrodynamic and structural dynamic approach
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull

5. 2.3.2 Large transformations & variable The adopted time dependent span L (q, t) which
eff r
wave height enters in the computation of drag forces and the
In the case of nodes of structural FEM components eff r
resulting effective submerged volume V (q, t) for
which are subjected to large displacements &
rotations and/or a variable wave height, the relative the computation of buoyancy and Morison inertia
r
nodal position & rotation vector q(t) and the loads, are outlined in equations (13,14).
r r
instantaneous Free Water Level/FWL vector W(q, t) For each structural node which is subjected to
eff r hydrostatic or hydrodynamic loads, a time
define the effective depth E ( q, t ) of a node and dependent direction of the span wise component
the associated effective submerged component rSpan r
length is defined in terms of the vector L (q, t) . It
eff r
span L (q, t) .
rSpan r
is noted that the span wise length vector L (q, t)
Effective depth of structural node w.r.t. Free Water Level :
eff r rT r r r r is moving and rotating with the associated
E ( q, t ) = ( g / g ) ( q(t) - W(q, t)) (12) structural node. In case of a component which is
partially submerged below the free water level, the
eff
(E > 0. => node below FWL) proportion of the submerged span is approximated
through the projection of the span length vector
Effective submerged spanwise length :
rSpan r r
L (q, t) onto the gravity vector g yielding the
Span eff
for : L >E > 0 => span partially submerged =>
Proj
Span r
“projected span wise length” L (q, t) . Finally, the
eff r eff Span Proj
L (q, t) = L (E /L ) (13a)
Proj eff r
effectively submerged span wise length L (q, t) is
Span eff
for : L <E > 0 => span fully submerged => computed through equations (13a,b,c,d) and the
Proj
eff r
effectively submerged volume V (q, t) is
eff r
L (q, t) = L (13b)
resulting from equation (14).
Span eff
for : L <E < 0 => span partially submerged =>
Proj
eff r eff Span 2.3.3 Added Mass & Eigen-Modes
L (q, t) = L (1 - E /L ) (13c)
Proj
r Inertia
Span eff The inertia term F of the Morison equation
for : L >E < 0 => entire span out of fluid => (11) modifies the total mass associated to the
Proj
submerged offshore structure and as consequence
eff r the resulting Eigen-Modes of the offshore wind
L (q, t) = 0. (13d)
turbine.
Effective submerged volume :
As depicted in Figures 2 & 3 and as outlined in
eff r eff r 2 section 2.3.2, the implemented algorithm accounts
V (q, t) = L (q, t) ((π / 4) D ) (14)
for the large transformations induced by a floating
offshore wind turbine and the relative wave height.
with :
The total mass which is accounted in the Eigen-
r r
W(q, t) : Free Water Level/FWL vector (variable wave height) mode computation of the offshore structure is
complemented through the derivative of the inertia
rSpan r
L (q, t) : span length vector associated to structural node term of the Morison equation (11) with respect to
the relative accelerations in between the fluid and
Span r r T r rSpan r the vibrating and/or floating offshore structure.
L (q, t) = − ( g / g ) L (q, t) : Projected Span Length Equations (15,16) define the added mass term in
Proj
terms of the derivative of the Morison inertia force
rSpan with respect to the structural accelerations of the
L = Mod(L ) : span length associated to node (scalar value)
respective node of the FEM model. As stated in
equation (16), the “added fluid mass” which is
added to the global mass & inertia matrix of the
FEM equations stated in equation (1) is obtained
through the derivative of the Morison inertia term
and can be presented in terms of two contributions.
Article submitted to EWEC 2011:
Numerical simulation of offshore wind turbines by a coupled aerodynamic, hydrodynamic and structural dynamic approach
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull

6. The first co ontribution is determined by the dyadic
s d
r
product of the acceleration unit vector n . I is It
r
emphasized that the unit vector n is contained in the
d n
plane whic is perpen
ch ndicular to the span w wise
direction of the respective compone and migh be
ent ht
interpreted as the vecto which defin the direc
or nes ction
of the inert loads. Th second te
tia he erm of equaation
r
(16) depend not only on the vecto n , but as well
ds or
on the strucctural acceleration of the respective F
FEM
r
q
node && and on the de erivative of t
the accelera
ation
r
unit vector n . As a cons sequence the additional f
e fluid
mass which is include in the global mass and
h ed
inertia mat trix of equ uation (1) becomes time t
dependent and beco omes depe endent on the
instantaneoous spatial direction o the rela
of ative
acceleration which occu in between the fluid and
n urs
the subme erged offshore struct ture. As a
s
consequenc not only the Eigen-
ce, y -Frequencies of
s
the offshore wind turbin become t
e ne time dependdent,
but as well the Eigen-S Shapes are affected by the
added fluid mass, bec
d cause the a added mass is
s
directional.
Derivative of e
external Morison inertia forces
n
r
w.r.t. structural accelerati ons q
&& :
r
r Morison ∂ ( ∂v )
add
M = ∂ rF = − ρ Vsub C r∂t (15)
∂&&
q a ∂&&
q Figure 2: S
S4WT wind turbine mode supported
t el
with accelerati on component pere
n endicul ar to span : by OC4 jaccket offshore structure
e
r
∂v = Proj
∂t ⎧
r
q
&& []
⎨ Span_plane ⎬ 2.3.4 Airy’ linear w
’s wave theor
ry
⎫
⎩ ⎭
r
with accelerati o unit vec tor n perpendicu lar t span orientatio n :
on to In the prese
n ent studies, the unpe erturbed fluid
r veelocity/accele
eration field is modeled through Airy
y's
∂v
n = r ∂t
r wave theory [10][11] which appro
w oximates thhe
∂v tra
ansient fluid dynamics of waves as a function of
o
∂t
paarameters like water d depth, wave height an
e nd
add
Added Mass M
Matrix M : peeriod (see equation (17)).
ij
⎡r r r ⎛ r ⎤ All the following applicati
ion example are based
es d
add r r r ⎞
n n + && ⎜ n ( ∂ r n ) + n ( ∂ r n )⎟
a⎢ i j ⎥ (16)
M = − ρ Vsub C q ⎜ on fluid/wate speed distributions which are
n er d e
ij k i ∂&& j k
q k ∂&& j i ⎟
q
⎣ ⎝ ⎠ ⎦ ge
enerated by the independ dent program Waveloads
m s
of the Univers of Hannover [10].
f sity
Airy' s wave sp
peed :
H 2 cosh(k(d + zz))
u fluid =
& ω sin(kx − ωt
t) (17)
2 sinh(kd)
with
H : wave heigh d : waterd
ht, depth (positive sign)
ω = 2ππ/ wave : angular freq
e quency of wave
e/fluid
z : distance of structural nod from Still Wa Level/SWL
f de ater L
k = 2pi/L wav : angular wave number [rad
ve a d/m]
Twave : wave period [s], L w
e wave : wave length[m]
Article submitted to EW
e WEC 2011:
Numerical simula
ation of offshore w
wind turbines by a coupled aerodynamic, hydrodynam and structural dynamic approac
mic ch
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J Sanchez, P. Cucchini, A. Gaull
J.L. C

7. pr
resented in terms of no
on-linear be
eam elements
an loaded by buoyancy and hydrodyn
nd y a namic loads.
Th following simulation results cor
he g rrespond to a
oad case wit wind field of a mean speed of 1
lo th d 10
[m and a wa definition according t Airy’s linea
m/s] ave n to ar
wave model (see equatio 17) with the followin
on ng
chharacteristics
s:
• Wave Height: 6 m
e
• Wave Period: 10 s
e
• Water Depth: 50 m
r
Fiigure 3 pres
sents the adoopted algoritthm in orderr
to approximate the effectiv
o vely submerg span for
ged r
th configura
he ations of noodes which are located d
beelow and respectively above the instantaneous
a s
fre
ee water level. Figure 4 pre esents the e
hyydrodynamic boundary c
c conditions fo the jacket
or t
noode#40 whic is located closely to the Still Water
ch r
Leevel/SWL. The location of the consid dered jacket t
noode#40 is d depicted in Figure 2. T The applied d
wave velocitie in longitu
es udinal XGL and vertical l
ZG directions refer to the left ordinate of Figure 4
GL s e e
an the wave height refer to the righ ordinate of
nd rs ht f
Fiigure 4.
It is mention ned that th spatial fluid speed
he d
distribution is obtained fro the exter
om rnal softwaree
Waveloads [10]. The cor
W rresponding acceleration n
fie of the e
eld external wav is compu
ve uted directlyy
fro the resp
om pective input speed tran
t nsient in thee
soolver SAM MCEF-Mecan no. Analogously, the e
re
elative structtural-fluid accelerations o equations
of s
(11,12), are accounted in the hy ydrodynamic c
element of th solver SA
he AMCEF-Mecano [1][2][3] ]
Figure 3: Effective submerged span for node
e an as a co
nd onsequence the resulti ing Morison n
above & below Free Water Level l/FWL inertia loads (s equation 11,12) acc
see ns count for the
e
sttructural dy ynamic resp ponse of the loaded d
offfshore structture.
3 Offshore applications Fi
igure 5 pres
sents for the node#40 the resulting
e g
There will b presented two distinc simulations of
be d ct bu
uoyancy and hydrodynam loads in terms of fluid
d mic d
offshore w wind turbine es. The f first applica
ation dr and in terms of the M
rag Morison inertia force.
corresponds to an offs
s shore wind t turbine whic is
ch
supported b a jacket s
by structure which correspo
onds
to the OC4 reference base line m
4 model [12]. The
second application ex xample pres sents a floaating
offshore wi ind turbine which floate and moo
er oring
lines correspond to the O
OC3 reference model [13 3].
3.1 Offs
shore wind turbine s
d supported
d
by J
Jacket stru
ucture
Figure 2 p presents a S4WT wind turbine mo
d odel
[1][2[3] which is suppo
orted by a jacket struc cture
according t the OC4 reference m
to model [12]. The
applied win turbine model compr
nd m romises in t total
3732 DOF’s and include a detailed gearbox mo
s es odel,
pitch and y
yaw drives a
and further flexible struct
tural Figure 4: Zo
F oom on wave speed & w
e wave height
components like the be
s edplate and nnacelle struc
cture at node #40 located at limit to free f
0 l fluid surface
in terms of Super Elements. The jacket structur is
re of jacket
Article submitted to EW
e WEC 2011:
Numerical simula
ation of offshore w
wind turbines by a coupled aerodynamic, hydrodynam and structural dynamic approac
mic ch
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J Sanchez, P. Cucchini, A. Gaull
J.L. C

8. Th large osc
he cillations of the floating wind turbine e
induced impor rtant low freq
quent speed variations in n
th rotor plane In Figure 7 is clearly v
he e. visible the low
w
fre
equent spee and rotor torque vari
ed r iations whichh
ar induced by the glob tilt oscilla
re bal ations of thee
flo
oating turbin Some further controller tuning is
ne. s
re
equired in o order to re educe these oscillations
e s
induced by the floating win turbine co
e nd oncept.
Figure 5: Zoom on hydrodynam mic drag force,
f
Morison iinertia force & and bu
e uoyancy forc at
ce
node#40
The black p plot of Figur 5 present the buoya
re ts ancy
load transie the blue plot the fluid drag trans
ent, sient
and the red plot the Mo
d orison inertia load transi
a ient.
The Moriso inertia loa transients (red plot) show
on ad
Figure 6: S4W model of OC3 offsho 5-MW
F WT o ore
clearly visi ible importaant oscillatioons which are
baseline wind turbine
b d
induced by the structur vibrations of the offsh
ral s hore
jacket struccture at the w
wave impact. Within the t
. time
interval from 13.8 [s] to 17.6 [s], no
m o ode#40 is ou of
ut
the wave an as consequence buoy
nd yancy, drag and
Morison’s innertia load dr progress
rop sively to zero.
3.2 Floa
ating offsh
hore wind turbine
Figure 6 pr resents the S4WT mode of a float
el ting
offshore wi ind turbine which is supported by ay
floating stru
ucture accor
rding to the reference [1
13].
The applied wind turbine model c
d compromises in
s
total 3402 DOF’s and includes a detailed pow wer
train mode pitch and yaw drive and further
el, d es
flexible stru
uctural components like the moor
e ring
lines.
The simulat load case correspond to a cons
ted ds stant
wind field o a mean sp
of peed of 8 [m and a w
m/s] wave
definition a
according to equation (17) with the
o
following ch
haracteristics
s:
• Wave Height: 10 m
• Wave Period: 15 s
• Water Depth: 32 m
20 Figure 7: Spe
F eed, blade pitch & power
e
transients in
t nduced by t oscillation of the
tilt ns
As depicted in Figure 6 the floating offshore w
d 6, g wind floating offsh
f hore wind turbine
turbine is attached by 3 cable which are
es Fiigure 7 prese ents the blad pitch, spe and powe
de eed er
separated eeach by a rottation of 120 [degrees] w.r.t. tra
ansients of the presented floating offshore win nd
to the vertic reference axis. The length of ea
cal e ach tu
urbine. The presented t transients o blade pitc
of ch
cable is abo 700 [m]. In the S4W model of the
out WT anngle and the produced power show low frequent
e w
floating win turbine, the cables are presented
nd osscillations which are ind
w duced by the rotor plan
ne
either by non-linear cable elem ments (neither sppeed variatio ons which are produce by the t
ed tilt
compressioon, nor bending stiffness), or osscillations of the entire flo
oating wind turbine.
respectively by non-linear Beam Ele
y ements.
Article submitted to EW
e WEC 2011:
Numerical simula
ation of offshore w
wind turbines by a coupled aerodynamic, hydrodynam and structural dynamic approac
mic ch
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J Sanchez, P. Cucchini, A. Gaull
J.L. C

9. Figure 8 pr resents the t trajectories o two nodes of
of
the tower in the plane which is formed by the
vertical ZG direction and the lo
GL ongitudinal XXGL
direction (direction of in
ncoming wind & wave). A it
d As
is shown in the red plo of Figure 8 the maxim
n ot 8, mum
movement of the towe top of th floating w
er he wind
turbine in loongitudinal d
direction is eevaluated fro -
om
14.5 [m] to 19.8 [m], i.e a total disp
e. placement raange
of the tow wer top of nearly 35[m movemen in
n m] nt
longitudinal direction. Taking into a
T account that the
center of til rotation of the floating wind turbin is
lt f g ne
below the s water le
still evel, the indduced maxim mum
inclination o the wind tu
of urbine is abo 15 [degre
out ees]
for the simuulated load case. In vertic direction, the
cal ,
wind turbi ine shows a displa acement ra ange
approximate ely 1.5 [m] to 4.5[m] That ver
] ]. rtical Figure 9: H
Hydrodynami loads in mooring
ic
oscillations of about 3 [m] of the entire wind turb bine line node#449
are induced by the buoy
d yancy loads w which compu uted
in case of a simulated wave height of 10 [m]. The
t 4 Conclusions
trajectory o a node which is located at the
of In case of the OC4 offsho reference wind turbine,
n ore e
connection of the tower bottom and the top of the
d f which is suppported by a jacket offsh hore structure,
offshore floaater is depic
cted in the bl plot of fig
lue gure no specific difficulties w
o were encou untered whe en
8. ru
unning the fully coupled aero-elastic, structural an
a nd
Due to the moving fl
e loating struc
cture, impor
rtant hy
ydrodynamic analysis. Ta
c aking into ac
ccount that th
he
speed variaations in the rotor plane were indu
e e uced co
orrespondingg SAMCEF-Mecano o model
and difficulties in stab
bilizing the w
wind turbine by
e co
ompromises 3732 DOF the CPU time on a
F, U
adaptation of controller paramet ters had b been st
tandard com mputer Intel Duo Core 3GHz wa
e as
encountered d. similar compaared to standdard “onshor high fidelity
re
wind turbine models” which run with a CPU tim
h me
fa
actor of about 60 with respect to real t
time.
In case of the OC3 flo
n oating offsho ore referenc ce
model, nume
m erical and modelling ch
m hallenges ar re
suubstantially higher, bec cause the wind turbin ne
model is not s
m stabilized by explicit fixations like in th
he
ca of the clamped jacke supports. In case of th
ase et he
flo
oating offsh hore wind turbine, t the dynam mic
eqquilibrium is strongly influenced by couple
s ed
buuoyancy, hy ydrodynamic and aero-
c -elastic load ds
which induce mutually e
e excitations a and controlle er
acctions. In particular the lo frequent oscillations of
ow
th
he floating turbine in nduce impo ortant spee ed
vaariations in th rotor plan The requi
he ne. ired CPU tim me
Figure 8: Trajectory of the tower top & of the
e on a standard computer was about a factor of 8
n d 80
tower ba ase of the floating wind turbine in n with respect to real time.
o
vertical a longitudi
and inal plane In the prese
n ent work, M Morison’s eq quation was s
Figure 9 presents a zoom on the exte n ernal im
mplemented in its extended form as it is proposed
t d
hydrodynam fluid loads which ar applied o a
mic re on in several re eferences in order to account fo
n or
specific nod of the F
de FEM model of the moo oring sttructural dyn namic and hydrodynam mic coupling g
lines. The location of mooring line node#49 is
f 9 efffects. As it w outlined in the prese work, the
was d ent e
presented in Figure 6. As it can be s
n A seen in Figur 9,
re exxtended form of the co
m oupled Moris son equation n
the Morison inertia forc has a di
n ce ifferent direc
ction ca be decom
an mposed in tw contribut
wo tions, on the
e
than the ass sociated dra force. This is because the
ag s e on hand, a “c
ne coupled inert term” whic is function
tia ch n
angle of atttack is deterrmined for th drag force by
he e of the relative acceleration in between the offshore
f n n e
the relative velocity field and the an
d ngle of attac of
ck sttructure and the unpertur rbed fluid flow and, on the
w e
the Morison inertia fo orce is deteermined by the otther hand, a further “uncoupled inertia term m”
relative accelerations in between ex xternal wave and which is only function of the acceleration of the
y f e
structural FE nodes.
EM unnperturbed f fluid flow. Even though the coupled d
Morison equa
M ation is understood as an empirica al
model, it migh be not stra
m ht aightforward to include an n
Article submitted to EW
e WEC 2011:
Numerical simula
ation of offshore w
wind turbines by a coupled aerodynamic, hydrodynam and structural dynamic approac
mic ch
A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J Sanchez, P. Cucchini, A. Gaull
J.L. C