Simulation of Aerodynamic Divergence and Flutter on Wind ...

<strong>Simulation</strong> <strong>of</strong> <strong>Aerodynamic</strong> <strong>Divergence</strong> <strong>and</strong> <strong>Flutter</strong> on
Wind Turbines using ANSYS-CFX
Drishtysingh Ramdenee 1 , Sorin Ion Minea 1 <strong>and</strong> Adrian Ilinca 1
1 Wind Energy Research Laboratory, Université Du Québec à Rimouski
ABSTRACT
Email: Author@eng.uwo.ca
The recent development <strong>of</strong> large wind turbines poses
new challenges with regard to underst<strong>and</strong>ing the
mechanisms surrounding unsteady flow-structure
interaction. The larger <strong>and</strong> more flexible blades
imply risks from an aeroelastic point <strong>of</strong> view <strong>and</strong>
urge the need to properly underst<strong>and</strong> <strong>and</strong> model these
phenomena. Due to limited experimental data
available in this field, Computational Fluid dynamics
(CFD) techniques provide an invaluable alternative to
identify <strong>and</strong> model aerodynamic <strong>and</strong> aeroelastic
phenomena around the wind blades. The study is part
<strong>of</strong> the coupling between aerodynamic <strong>and</strong> elastic
models <strong>of</strong> the commercial code - CFX with ANSYS,
respectively. In this paper we are modeling the
aeroelastic divergence. This article presents the the
studies aiming at modeling divergence. In this article
the results <strong>of</strong> the divergence modeling using ANSYS-
CFX will be presented <strong>and</strong> compared with results
from “Jennifer Heeg” [13]. The study is realized on
the NACA0012 airfoil for which experimental data
are available in literature. The ANSYS workbench is
used for the fluid structure interaction to simulate the
divergence phenomenon which is a structural
response imposed by aerodynamic loads due to
transient fluid flow.
1. INTRODUTION
An aeroelastic instability occurs when the variation in
the aerodynamic forces resulting from the blade
displacement tends to amplify the latter. The most
commonly occurring aeroelastic phenomena with
wind turbines are stall induced vibrations. <strong>Flutter</strong> is
another instability problem that needs to be inspected
<strong>and</strong> understood in an aim to mitigate it. Stall induced
vibrations occur in dynamic stall controlled wind
turbines. The gradient <strong>of</strong> the power coefficient curve
becomes negative when part <strong>of</strong> the blade is
subjected to stall, having as result a local negative
aerodynamic damping <strong>of</strong> the blade movement in the
direction <strong>of</strong> the lift. If the global aerodynamic
damping for a particular vibration mode is negative,
<strong>and</strong> exceeds (in magnitude) the structural modal
damping, then the oscillations can be amplified from
any initial perturbation independent <strong>of</strong> the ratio
between the normal frequency <strong>of</strong> the vibration mode
<strong>and</strong> the excitation frequencies. The first mode in each
direction is more prone to such a behavior as the
structural damping increases with the frequency
whereas the aerodynamic damping decreases. On the
other h<strong>and</strong>, flutter is a very dangerous phenomenon
which results from an interaction between elastic,
inertial <strong>and</strong> aerodynamic forces. It occurs when
structural damping becomes insufficient to damp
aerodynamically induced vibration motions. <strong>Flutter</strong> is
caused by the superposition <strong>of</strong> two structural modes –
pitch <strong>and</strong> plunge. The pitch mode is described by a
rotational movement about the elastic centre <strong>of</strong> the
airfoil whereas the plunge mode is a vertical up <strong>and</strong>
down motion at the blade tip. As wind speed
increases, the frequencies <strong>of</strong> these modes coalesce to
create the flutter motion. This is called flutter
resonance. Usually, flutter is initiated as the airfoil is
subjected to an initial rotation. As a divergence like
phenomena arises, the torsional stiffness <strong>of</strong> the blade
reacts to achieve zero rotation again. On the other
h<strong>and</strong>, the resistance to bending tries to restore a
neutral position <strong>and</strong> sets the airfoil in a nose down
rotation position. The amplified force causes
plunging <strong>and</strong> torsional stiffness to restore zero
rotation. With time, though [1] the plunging motion
tends to damp out, the rotation motion diverges till
failure.
2. CHALLENGE IN MODELING
AEROELASTIC PHENOMENA
Modeling <strong>of</strong> aeroelastic phenomena requires coupling
<strong>of</strong> aerodynamic <strong>and</strong> structural equations <strong>and</strong> such
represents a particular challenge. The need to obtain
solutions for several combinations <strong>of</strong> the parameters
<strong>of</strong> the structure <strong>and</strong> the fluid require very precise
modeling <strong>of</strong> the fluid model solutions <strong>and</strong> this is very
dem<strong>and</strong>ing from a computational point <strong>of</strong> view. For
several years the finite element model size has been
reduced. This has been possible by first finding the
Eigen modes <strong>and</strong> using a discrete set <strong>of</strong> values to

ebuild a discrete structure upon which the modeling
is performed. Lagrangian equations <strong>of</strong> classical
dynamics are made use <strong>of</strong> <strong>and</strong> the computational
requirements are appreciably reduced. Usually a
finite element structural model with some thous<strong>and</strong>s
<strong>of</strong> degree <strong>of</strong> freedom (DoF) can be reduced into one
<strong>of</strong> some ten DoF.[2]. Though, this method is highly
convenient in terms <strong>of</strong> computational needs, it is very
tedious <strong>and</strong> requires refined modeling at each step.
3. ANSYS-CFX COUPLING
In order to realize the fluid structure coupling study,
we make use <strong>of</strong> ANSYS multi domain (MFX). This
module was primarily developed for fluid-structure
interaction studies. On one side, the structural part is
solved using ANSYS Multiphysics <strong>and</strong> on the other
side, the fluid part is solved using ANSYS CFX. The
study needs to be conducted on a 3D geometry.
However, if the geometries used by ANSYS <strong>and</strong> CFX
need to have common surfaces (interfaces), the
meshes <strong>of</strong> these surfaces need not be identical [3].
The ANSYS code acts as the master code <strong>and</strong> reads
all the multi-domain comm<strong>and</strong>s. It recuperates the
interface meshes <strong>of</strong> the CFX code, creates the
mapping <strong>and</strong> communicates the parameters that
control the timescale <strong>and</strong> coupling loops to the CFX
code. The ANSYS generated mapping interpolates
the solicitations between the different meshes on each
side <strong>of</strong> the coupling. Each solver realizes a sequence
<strong>of</strong> multi-domain time steps <strong>and</strong> coupling iterations
between each time steps. For each iteration, each
solver recuperates its required solicitation from the
other domain <strong>and</strong> then solves it physical domain.
Each element <strong>of</strong> interface is initially divided into n
interpolation faces (IP) where n is the number <strong>of</strong>
nodes on that face. The 3D IP faces are transformed
into 2D polygons. We, then, create the intersection
between these polygons, on one h<strong>and</strong>, the solver
diffusing solicitations <strong>and</strong> on the other h<strong>and</strong>, the
solver receiving the solicitations. This intersection
creates a large number <strong>of</strong> surfaces called control
surfaces as illustrated in figure 1.
Figure 1: Transfer Surfaces <strong>and</strong> resolution scheme
These surfaces are made use <strong>of</strong> in order to transfer
the solicitation between the structural <strong>and</strong> fluid
domains. In the case <strong>of</strong> the divergence, it is the fluid
that imposes the solicitations on the solid such that
the CFX code will be the first to be solved followed
by the ANSYS code.
.
4. STATE OF THE ART
There has been little, if not, no article that pondered
on the modeling <strong>of</strong> divergence modeling as from subcritical
conditions till failure. This can be explained
by the difficulties encountered by s<strong>of</strong>tware to model
acute gradients in the proximity <strong>of</strong> divergence <strong>and</strong>,
also, due to the fact that the primary importance is
only to analyze stability <strong>and</strong> sub-critical speed <strong>and</strong> to
design the system in order for the latter to stay within
these conditions at all time. [3] has illustrated the
dramatic reduction in the divergence speed for a
reversed arrow wing. [4] went further with the works
presented in [3] <strong>and</strong> proposes an analytical method to
calculate the divergence speed <strong>of</strong> the airfoils. [5]
clearly illustrated the destructive nature <strong>of</strong> divergence
<strong>and</strong> the possibility <strong>of</strong> controlling the latter. [6]
realized wind tunnel experiments which showed the
fundamental relationship between the angle <strong>of</strong> the
blade, the orientation <strong>of</strong> the material fibers <strong>and</strong> the
divergence speed. “Rodney H.Ricketts, <strong>and</strong> Robert
V.Doggett, Jr” [7] makes use <strong>of</strong> flat plate models
with varying geometries <strong>and</strong> their subcritical
response testing techniques were formulated <strong>and</strong>
evaluated for accuracy in predicting static
divergence. “Sefic, Walter J., <strong>and</strong> Cleo M.Maxwell”
[8] did experiments to correlate flight data with
predicted structural stability <strong>and</strong> determination <strong>of</strong>
aeroservoelastic stability margins. “Stanley R. Cole,
James R. Florance, Lee B. Thmpson, Charles
V.Spain <strong>and</strong> Ellen P.Bullock” [9] made use <strong>of</strong>
experimental data obtained from supersonic tests at
the Unitary Plan Wind Tunnel at the NASA Langley
Research Center to examine the divergence <strong>of</strong> all
moveable parts. [10] has performed experiments to
correlate flight results with predicted structural
stability <strong>and</strong> the determination <strong>of</strong> aerservoelastic
stability. A more detailed literature review is
available in previous works [11] <strong>and</strong> [12]. The
literature surrounding the divergence phenomenon is
very large <strong>and</strong> includes several models all mostly
aiming at modeling sub-critical velocity, dynamic
pressure <strong>and</strong> the modal frequency within the stability
zone. Most works dealing with experimental analysis
have lengthily discussed on the errors <strong>and</strong> the
graphical results provide a domain <strong>of</strong> divergence
rather than a fixed value. The consulted literature has
been very broad, though, not exhaustive, <strong>and</strong> the

fundamental philosophy has been the same: the
objective <strong>of</strong> most aeroelastic work have most <strong>of</strong> the
time underlined the consequences <strong>of</strong> divergence <strong>and</strong>
flutter, the sub-critical behavior <strong>of</strong> structures in order
to be able to know how far we are from the critical
zones in order to avoid them. Modeling <strong>of</strong> these
phenomena has only been a very limited part <strong>of</strong> the
works.
5. EXPERIMENTAL VALIDATION
In 2000, Jennifer Heeg [13] realised aeroelastic
experiments at the Duke University wind Tunnel.
The aim was to validate analytical calculations <strong>of</strong> non
critical characteristic modes <strong>and</strong> explicitly examine
the aerodynamic divergence phenomenon. The
simplest model was built <strong>and</strong> tested. A NACA 0012
airfoil was used <strong>and</strong> the structure was only allowed a
single DoF, i.e., in torsion. A chord length <strong>of</strong> 8 inches
<strong>and</strong> a blade length <strong>of</strong> 21 inches were made use <strong>of</strong>.
The wing was made out <strong>of</strong> an aluminum shell <strong>of</strong> 1/32
inches in thickness. A spring constant <strong>of</strong> 5.826
N·m/rad was used. The structural dynamic
parameters for this model are summarized in table 1:
Elastic
Constant Kα
[N∙m/rad]
Natural
pulsation ωα
[rad/sec]
Natural
Frequency fα
[Hz]
Damping ratio
5.8262 49.5 7.88 0.053
Table 1: Structural dynamic parameters associated to
the model used for the wind tunnel experiment from
[13]
The objectives <strong>of</strong> the studies in [13] were to : 1)
calculate the dynamic pressure at divergence, 2)
examine the modal characteristics <strong>of</strong> non critical
modes, 3) examine the behavior <strong>of</strong> Eigen vectors.The
aim <strong>of</strong> our simulations is to be able to simulate the
same using ANSYS- CFX coupling.
6. SIMULATION MODEL
The model <strong>of</strong> the experiment was simulated at a
reduced scale, in order to reduce the calculation time
by reducing the dimensions <strong>of</strong> the fluid domain. The
span <strong>of</strong> the airfoil was reduced 262.5 times, from 21
inches to 0.08 inches or 2.032 mm, while the chord <strong>of</strong>
the airfoil was maintained at 8 inch or 203.2 mm. We
used a cylinder to simulate the torsion spring used in
the configuration <strong>of</strong> the experiment that was detailed
in the previous section. The constant <strong>of</strong> the original
spring is K = 5.8262 N∙m/rad <strong>and</strong> since we used a
reduced model, with an span 262.5 times smaller than
the original, the dimensions <strong>and</strong> properties <strong>of</strong> the
cylinder are such that:
= 0.022195 N∙ m/ rad
ζ
The mass <strong>of</strong> the considered configuration <strong>of</strong> the
original model is 2.2864 kg, <strong>and</strong> the mass <strong>of</strong> our
model is 262.5 times smaller, that is 0.00871 kg. The
moment <strong>of</strong> inertia is such that our model has the
same fundamental frequency as the original that is
7.88 Hz. Figure 2 illustrates the model built on
ANSYS.
Figure 2: Meshed ANSYS simulated model
Details about the used fluid model are available from
[14].
7. RESULTS
In a preliminary stage, prior to divergence <strong>and</strong> zer<strong>of</strong>requency
flutter modeling, the lift coefficient curve
for the model at a velocity <strong>of</strong> 20 m/s was constructed
using ANSYS <strong>and</strong> was compared to results from
[13]. Furthermore, the ANSYS-CFX coupling was
verified.
7.1 Construction <strong>of</strong> the curve
The curve was constructed for a velocity <strong>of</strong> 20 m/s,
which is between a velocity <strong>of</strong> 19.15 m/s estimated
by [13] <strong>and</strong> 20.16 m/s which [13] used as comparison
from experimental studies. For the validation <strong>of</strong> our
simulation, we have used experimental data from
[15] for Re numbers <strong>of</strong> Re = 1.7x10 5 <strong>and</strong> 3.3x10 5
from which we interpolated values for Re =2.6x10 5
corresponding to values used in our ANSYS-CFX
simulation. The result is shown in figure 3:
CL
1,2
1
0,8
0,6
0,4
0,2
Lift coefficient - CL(α)
0
0 2 4 6 8 10 12 14
Figure 3: Lift coefficient curve <strong>of</strong> the NACA 0012 for Re =
2.6x10 5 calculated using ANSYS-CFX <strong>and</strong> experimental
results from Sheldahl & Klimas (blue circle for increasing
angle <strong>and</strong> yellow triangle for decreasing angle)
α

The results from ANSYS-CFX are in close
accordance with experimental data till an AoA <strong>of</strong>
12°. At 2.5°, the results from CFX are inferior by
13%, at à 4.5° by 20% <strong>and</strong> at 6.5° by 6%. The
maximum value <strong>of</strong> the lift coefficient is achieved
around 12° <strong>and</strong> is 0.96 <strong>and</strong> 0.9 at 10.5°. As for CFX
achieved results, the maximum value is again
achieved at around 12° <strong>and</strong> is 0.924 <strong>and</strong> 0.899 at
10.5°. The difference in the values can be explained
by the fact that Sheldahl & Klimas have extrapolated
the obtained results from experiments using the
s<strong>of</strong>tware PROFILE to estimate the aerodynamic
coefficients from other Re numbers. Linearization <strong>of</strong>
the polars for low AoA had, also, been performed.
7.2 Verification <strong>of</strong> the Coupling
In order to verify the coupling between Mechanical
APDL <strong>and</strong> CFX, we performed a simulation at a
constant flow below divergence. The pr<strong>of</strong>ile in [13]
was fixed at α0 = 4°, restricted to one DoF <strong>and</strong>
subjected to vair = 15 m/s as a shock wave. Figure 4
illustrates the ANSYS-CFX generated response. The
represented variable is the vertical displacement <strong>of</strong>
the trailing edge. The equilibrium position induced
force obtained from CFX is FL = 0.0363787 N. The
AoA corresponding to a displacement <strong>of</strong> 0.006 m is,
α = arcsine (sin (α0) + 0.006 / y0) = 7.022°, where y0
= 0.1143 m. At this angle, the elastic moment is ME =
K · (α – α0) = 0,022195 · 0.05275 = 0.00117 Nm.
We obtain the same aerodynamic moment value from
CFX.
Figure 4: Oscillatory response <strong>of</strong> the pr<strong>of</strong>ile subjected
to a sudden shock wave <strong>of</strong> 15 m/s
7.3 <strong>Divergence</strong> <strong>and</strong> flutter simulation
The model from [13] was restricted from all DoF <strong>and</strong>
fixed to an AoA <strong>of</strong> 5°. For convergence needs, it was
subjected to a constant velocity <strong>of</strong> 1 m/s till
stabilisation <strong>of</strong> the flow. The fixation is then removed
leaving a rotation about the elastic axis <strong>and</strong> the
velocity is increased according to the expression V =
15.84 14.84*exp (-3*t) till 15.805 m/s at the end <strong>of</strong>
the simulation. A time step <strong>of</strong> 3.8 10 -4 s is used
though it would have been more interesting to use a
variable time step to adjust with the Courant number.
Figures 5 <strong>and</strong> 6 illustrate the response <strong>of</strong> the blade
provided by ANSYS-CFX. The represented variable
is the AoA <strong>of</strong> the airfoil.
Figure 5: nstability simulation obtained for an AoA
<strong>of</strong> 5 for configuration #2 from [13]
Figure 6: Instability simulation obtained for an AoA
<strong>of</strong> 5 0 for configuration #2 from [13] with details
The AoA <strong>of</strong> the airfoil increases progressively until it
enters a region <strong>of</strong> stall controlled dynamic
equilibrium. As the speed tends to 15.84 m/s, the
AoA stays temporarily small, resting in equilibrium
between the aerodynamic moment <strong>and</strong> the elastic
moment between 10° <strong>and</strong> 10.5°. The onset <strong>of</strong> flutter
is very quick due to the high gradient <strong>of</strong> the used
velocity pr<strong>of</strong>ile which avoids any possibility <strong>of</strong> stall
stabilization. The simulation was stopped at 15 0
because the Courant number ( ) reached 81.84
which is much larger than the recommended value
such that with the used time step, the analysis cannot
go beyond 15°.
7.4 Discussion
Due to numerical computation limitations, we can
only verify the frequency <strong>of</strong> the movement in a

velocity range between 15.6 <strong>and</strong> 15.8 m/s
corresponding to a small error <strong>of</strong> 1.26 % which we
judge very close to experimental data. The obtained
frequencies in these conditions vary between 5.822
Hz <strong>and</strong> 6.326 Hz which is close to the 6 Hz obtained
from the experiments conducted in [13]. In this case,
it will be more difficult to determine the flutter speed
as the airfoil achieves equilibrium in the stall zone
with the flow velocity still increasing. Due to this
perturbation, the flutter will start at a speed smaller
than that used in the experiments. In order improve
on the results, the simulation running time should be
longer <strong>and</strong> the simulation parameters more precise.
However, due to computational frontiers, we had to
limit ourselves to the presented simulation.
7.5 <strong>Divergence</strong> <strong>and</strong> flutter illustration
Figures 7 to 9 illustrate the airflow <strong>and</strong> the airfoil
movement at certain time steps <strong>of</strong> the simulation with
the air speed as the represented variable. In order to
ease eddy visualization, we have used a narrow speed
range <strong>of</strong> 14 m/s to 18 m/s for the color scale. In the
dark blue zones, the airflow is less than 14 m/s <strong>and</strong> in
the red regions, the speed is larger than 18 m/s.
Figure 7 illustrates the flow at the moment noted 1on
figure 6, when the oscillation is its minimum, =
6.53° <strong>and</strong> the maximum airflow, U= 26.95 m/s.
Figure 8 illustrates the airflow at moment noted 2 on
figure 6 at an intermediate point <strong>of</strong> the oscillation,
where = 10.78 0 <strong>and</strong> U = 33.65 m/s. Figure 9
illustrates timestep at moment 3, at a crest <strong>of</strong> the
oscillation with = 14.58 0 <strong>and</strong> U = 215.38 m/s.
Figure 7: Instability <strong>Simulation</strong> at t=1.8449 s,
AoA=6.53 0 , U=26.95 m/s
Figure 8: Instability <strong>Simulation</strong> at t=1.88822 s,
AoA=10.78 0 , U=33.65 m/s
Figure 9: Instability <strong>Simulation</strong> at t=1.93154 s,
AoA=14.58 0 , U=215.38 m/s
8. CONCLUSION
This article pondered on the divergence <strong>and</strong> zer<strong>of</strong>requency
flutter phenomena. The ANSYS-CFX
coupling to model fluid-structure interaction has been
very useful <strong>and</strong> we have been able to satisfactorily
model these phenomena within limits bounded by
computational capacity. It seems that the threshold
between divergence <strong>and</strong> flutter is very narrow. The
modeling <strong>of</strong> such phenomena is very complex <strong>and</strong> we

see that it is, still, very difficult to produce closely
reproducible results. The problem lies in
computational capacities <strong>and</strong>, also, some refinements
to be added into analytical modeling. The obtained
results are very encouraging in anticipating good
results for a 3D blade analysis. The expected
precision for a 3D blade will mainly depend on the
mesh size, the turbulence model <strong>and</strong> the
computational capacity that will allow us to use very
refined time steps.
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