Plunging motions of an elastically suspended wing with an oscillating flap an experimental and numerical assessment

Plunging motions of an elastically
suspended wing with an oscillating flap
An experimental and numerical assessment

PROEFSCHRIFT

ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben,
voorzitter van het College voor Promoties,
in het openbaar te verdedigen
op maandag 13 oktober 2014 om 10:00 uur
door

Joost Joachim Hermanus Marie STERENBORG

ingenieur luchtvaart en ruimtevaart
geboren te Nijmegen.


Dit proefschrift is goedgekeurd door de promotor:
Prof. dr. ir. drs. H. Bijl
Copromotor: Dr. ir. A.H. van Zuijlen

Samenstelling promotiecommissie:
Rector Magnificus
Prof. dr. ir. drs. H. Bijl
Dr. ir. A.H. van Zuijlen
Prof. dr. ir. G.A.M. van Kuik
Prof. dr. ir. L.L.M. Veldhuis
Prof. N.N. Sørensen

Dr. -Ing. Th. Lutz
Dr. Ir. K. Boorsma
Prof. dr. F. Scarano

voorzitter
Technische Universiteit Delft, promotor
Technische Universiteit Delft, copromotor
Technische Universiteit Delft
Technische Universiteit Delft
Technical University of Denmark
Universităat Stuttgart
ECN
Technische Universiteit Delft, reservelid

This research is funded by Agentschap NL
(formerly Senternovem), an agency of the Dutch
Ministry of Economic Affairs, under project number EOS LT 09001
Printed by Ipskamp Drukkers, The Netherlands
c 2014 by J.J.H.M. Sterenborg
Copyright
All rights reserved. No part of the material protected by this copyright notice may
be reproduced or utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and retrieval
system, without the prior permission of the author.
isbn: 978-94-6259-353-4

ii


Summary

Over the last years fluid-structure interactions have attained more interest emanating from applications, the availability of new numerical approaches for multi-physics
coupling and the improved computing capacity that enables simulations of complex
multi-physics problems. Fluid-structure interactions involved in applications can be
undesired but can also be benefited from. An example of the latter is the popular
research field of load alleviation for wind turbines based on aeroelastic blade deformations, like bend-twist coupling. Next to aeroelastic load alleviation, active load
mitigation systems for wind turbines also gain much attention. Also for these active
approaches, the aeroelastic system responses can be important to address.
Understanding and prediction of fluid-structure interactions can be achieved with
numerical simulations. One of the problems for numerical simulations of fluid-structure
interactions is the validation of the solvers. Main reason is the limited availability of
proper experimental data, partly due to the complexity of experiments involving fluidstructure interactions. This complexity appears amongst others in the determination
of unsteady loads on moving objects and unsteady wind tunnel wall corrections. Furthermore, the limited amount of data that are available are mostly for lower Reynolds
regimes and/or different structures.
Also for aeroelastic codes used to design wind turbines there is a lack of validation data. Therefore, this thesis aims to enhance the possibilities for validation of
aeroelastic solvers used for the simulation of aeroelasticity of wind turbines. An aeroelastic experiment is conducted using a wing based on the DU96-W-180 wind turbine
profile and a Reynolds number of 700 000. Furthermore, in line with active load alleviation systems employing control surfaces, the one degree of freedom plunging wing
motion is induced by controlled flap oscillations. The flap actuation is sinusoidal as
well as the resulting oscillations. A rigid body motion is used in the experiment in
order to eliminate spatial coupling between flow and structure in numerical simulations.
Three sub-objectives, elaborated on in the remainder, can be distinguished in
this thesis: 1) the assessment of experimental unsteady load determination, 2) a
one degree of freedom aeroelastic experiment to setup a validation database, and
3) a comparative numerical study using three 2-D aeroelastic solvers with different
levels of fidelity, partially also to identify implications of the numerical modelling in
combination with the experimental setup.
One option to determine the aerodynamic forces is to deduce the instantaneous
sectional loads from measured velocity fields using Noca’s method along any closed
contour. An experiment is conducted to investigate the application of Noca’s method
iii

first for an aerofoil with an oscillating trailing edge flap. Wind tunnel corrections for
this specific unsteady flow problem are considered. Conclusion of this assessment is
that for the experimental data Noca’s approach is relatively sensitive to the contour
location: applied to a set of contours a solution of the unsteady loads with an error
bandwidth of on average 6.39% of its mean instantaneous values is found. Also,
compared to Kutta-Joukowski’s theorem and panel code simulations, small offsets of
on average about 5% reduction are found in the force coefficients. Among others,
it is known a higher spatial resolution of the experimental data and more accurate
approximations of velocity gradients will improve the force prediction. Phase and
amplitude of the lift are in close agreement with 2-D panel computations including
modelled wind tunnel walls and a gap correction.
The aeroelastic experiment is conducted at an angle of attack of α = −0.95 ◦
yielding attached flow conditions. The flap deflects over a range of about ±2 ◦ with
reduced flap frequencies ranging from k = 0.1 to k = 0.3. The damped natural
frequency of the mass-damper-spring like structure expressed as a reduced frequency is
about k = 0.194. The obtained database contains displacements and time dependent
aerodynamic forces. It provides a clear insight in typical loads and motions and can
be used in comparative studies. As expected, the maximum displacement of the wing
is found near the system eigenfrequency. The lift is dominated by the flap motion
and the effective angle of attack due to the motion introduces phase shifts of the lift
signal with respect to the flap phase angle. Despite the experiment has been setup
and executed with the necessary precision, small ambiguities are found in the lift and
drag and the data should not be used for code validation. Structural assumptions (e.g.
mass-damper-spring, constant damping) are one of the causes for the ambiguities in
the lift. Both the data and experiences can be used to (re)design future experiments
to improve the quality of the data to the desired level of accuracy for validation.
Suggestions in this are the extension of the used measurement techniques with surface
pressure measurements and simplifications in the supporting structure by a reduction
of the number of components.

In a comparative study the one degree of freedom aeroelastic problem is simulated
with three different levels of fidelity 2-D aerodynamic models: Theodorsens model, a
panel code and a URANS solver. In the numerical models 2-D steady wind tunnel
corrections are implemented. All models are coupled to a structure solver and the
fluid-structure interaction is resolved in both a loosely coupled and strongly coupled
fashion. The applicability of the 2-D wind tunnel corrections instead of a full modelling is investigated and the accuracy of the different models is assessed. Trends in the
lift forces, moments and displacements are predicted according to the experimental
values, although some phase and amplitude errors are observed. Errors are amongst
others due to inherent 3-D flow effects in the experiment against 2-D simulations and
the application of steady wind tunnel corrections on an unsteady problem. Subiterations to reduce the coupling error only have a significant effect on the phase of the
lift. General conclusion is that compared to expensive 3-D simulations, less expensive
2-D solutions are found that approximate the experimental values for the unsteady
test cases. For Theodorsens model and the panel code this is achieved with a low
computational effort and for URANS the computational effort is moderate.

iv


Dompende bewegingen van een flexibel opgehangen vleugel
met een oscillerende klep
Een experimenteel en numeriek onderzoek

Samenvatting
De laatste jaren is vloeistof-vaste stof interactie onderwerp van onderzoek vanwege de vele toepassingen, de beschikbaarheid van nieuwe numerieke benaderingen
voor multi-fysische koppelingen en de verbeterde rekenkracht die het mogelijk maakt
om complexe, multi-fysische problemen door te rekenen. Vloeistof-vaste stof interacties in toepassingen zijn soms onwenselijk, maar kunnen ook benut worden. Een
voorbeeld van het laatste kan worden gevonden in belastingsreducties voor windturbinebladen door middel van bladvervormingen onder invloed van luchtkrachten, zoals
een buig-torsie koppeling. Hiernaast is er veel belangstelling voor actieve systemen
die belastingen reduceren op windturbinebladen. Voor deze actieve systemen kan het
ook belangrijk zijn om de vloeistof-vaste stof interactie te beschouwen.

Begrip van vloeistof-vaste stof interactie kan worden verkregen door numerieke
simulaties uit te voeren. Een van de problemen van numerieke simulaties is het valideren van de rekencodes. Belangrijkste reden is de erg gelimiteerde beschikbaarheid
van goede data, mede vanwege de complexiteit van experimenten. Deze complexiteit
komt onder andere voort uit de bepaling van de niet-stationaire krachten en instationaire windtunnelcorrecties. Daarnaast is de gelimiteerde data vaak alleen beschikbaar
voor lage Reynoldsgetallen en/of voor andere constructies.
Ook voor aero-elastische codes gebruikt voor het ontwerpen van windturbines is
een gebrek aan validatie data. Daarom is het doel van dit onderzoek om de mogelijkheden te vergroten om validaties uit te voeren van aero-elastische codes gebruikt voor
het simuleren van windturbines. Een aero-elastisch experiment is uitgevoerd, waarbij
een vleugel gebaseerd op het DU96-W-180 windturbine profiel en een Reynoldsgetal
van 700 000 zijn gebruikt. Daarnaast is, net zoals bij actieve belastingsreductiesystemen met kleppen, de op-en-neergaande beweging van de gebruikte stijve vleugel
genduceerd door een opgelegde klep beweging. De klep oscilleert in een sinus beweging en daardoor beweegt ook de vleugel in een zelfde patroon. Het gebruik van een
stijve vleugel zorgt er voor dat in numerieke simulaties de koppeling tussen de rekenroosters voor de vloeistof en de vaste stof buiten beschouwing gelaten kan worden.
Het onderzoek kan worden onderverdeeld in 3 delen, die in het vervolg worden
beschouwd: 1) onderzoek naar de experimentele bepaling van instationaire krachten,
2) het ´e´en vrijheids graden aero-elastische experiment voor het vergaren van validatie
materiaal, en 3) een vergelijkende studie van drie numerieke rekenmodellen met een
verschillende complexiteit, deels ook om de implicaties van de modellering en de
experimentele opstelling te beschouwen.
Een optie voor het bepalen van instationaire luchtkrachten is door de instantane
doorsnede krachten te bepalen uit snelheidsvelden middels Noca’s methode toegepast
v


op een gesloten lijn. Een experiment is uitgevoerd om de toepasbaarheid van Noca’s
methode voor een vleugel met een bewegende klep te onderzoeken. Windtunnelcorrecties voor dit specifieke instationaire probleem zijn ook onderzocht. Conclusie is
dat, gegeven de experimentele data, Noca’s methode relatief gevoelig is voor de gekozen ligging van de gesloten lijn: voor meerdere gesloten lijnen is een schatting van
de instationaire krachten met een bandbreedte van 6.39% van de gemiddelde instantane kracht bepaald. Verder zijn er, in vergelijking met Kutta-Joukowksi’s theorie
en panelen code simulaties, kleine afwijkingen met een gemiddelde verlaging van zo’n
5% gevonden in de krachtencoefficiăenten. Het is bekend dat onder andere een hogere
resolutie voor de ruimte discretisatie en een hogere orde benadering voor de snelheidsafgeleiden leiden tot een verbetering van de voorspelling van de krachten. De

fase en de amplitude van de liftkracht komen goed overeen met 2-D simulaties met
een panelen code met gentegreerde windtunnelcorrecties en een sleuf correctie.
Het aero-elastische experiment is uitgevoerd voor een invalshoek van α = −0.95 ◦,
waarbij de stroming aanligt. Hierbij slaat de klep uit over ±2 ◦ met gereduceerde flap
frequenties van k = 0.1 tot k = 0.3. De gedempte natuurlijke frequentie van de massademper-veersysteem achtige constructie, uitgedrukt als een gereduceerde frequentie,
is ongeveer k = 0.194. Verplaatsingen en tijdsafhankelijke luchtkrachten zijn gemeten.
De resultaten geven een goed inzicht in de typische krachten en verplaatsingen die
kunnen worden gebruikt om vergelijkende onderzoeken te kunnen doen. Zoals verwacht is de verplaatsing van de vleugel maximaal rond de natuurlijke frequentie van de
constructie. De liftkracht is met name afhankelijk van de klepbeweging. De effectieve
invalshoek door de verticale beweging zorgt voor fase veranderingen in de liftkracht
ten opzichte van de klep fasehoek. Ondanks een zorgvuldige opzet en uitvoering van
het experiment, zijn er tegenstrijdigheden gevonden in de lift en weerstandskrachten
die er toe leiden dat de data niet direct voor validatie kan worden gebruikt. Aannames voor het structurele model (o.a. massa-demper-veersysteem, constante demping)
is een van de oorzaken voor de tegenstrijdigheden voor de liftkrachten. De gemeten
data en opgedane kennis kunnen worden gebruikt om een herontwerp te maken voor
nieuwe experimenten, zodat nieuwe data geschikt voor validatie kan worden gemeten.
Suggesties hiervoor zijn het uitvoeren van oppervlakte drukmetingen en vereenvoudigingen van de ondersteunende constructie door minder componenten te gebruiken.
In een vergelijkingsonderzoek is het aero-elastische probleem gesimuleerd met drie
2-D stromingsmodellen van verschillende complexiteit: Theodorsens model, een panelen code en een URANS code. In de simulatiemodellen zijn 2-D stationaire windtunnelcorrecties gentegreerd. Alle stromingsmodellen zijn gekoppeld aan een structureel
rekenmodel en de vloeistof-vaste stof interactie is zowel zwak en sterk gekoppeld opgelost. De toepasbaarheid van 2-D windtunnelcorrecties in plaats van het simuleren
van de volledige opstelling met windtunnel is onderzocht en de nauwkeurigheid van de
rekenmodellen is beschouwd. Trends in the liftkrachten, momenten en verplaatsingen
zijn overeenkomstig voorspeld met de experimentele data, alhoewel fase- en amplitudefouten zijn waargenomen. Fouten komen onder andere door de 2-D modellering
van een 3-D experiment en de toepassing van stationaraire windtunnelcorrecties voor
een instationair probleem. Subiteraties om de koppelingsfouten te reduceren hebben
alleen een waarneembaar effect op de fase van de liftkracht. De algemene conclusie is
dat ten opzicht van dure 3-D simulaties, minder dure 2-D voorspellingen zijn gevon-

vi

den die de resultaten van het experiment benaderen voor de instationaire problemen.
Voor Theodorsens model en de panelen code is dit bereikt met weinig rekentijd en
voor URANS is de rekentijd meer gemiddeld.

vii


viii


Contents

Summary

iii

Samenvatting

v

Contents

xii

1 Introduction
1.1 Motivation . . . . . . . . . . . .
1.2 Literature review of present state
1.3 Approach . . . . . . . . . . . . .
1.4 Outline . . . . . . . . . . . . . .

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2 Terminology, wind tunnel models and methodologies
2.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Characteristic (non-)dimensional numbers . . . .
2.1.2 Flap phase angle . . . . . . . . . . . . . . . . . .
2.1.3 Averaging methods . . . . . . . . . . . . . . . . .
2.1.4 Data reduction . . . . . . . . . . . . . . . . . . .
2.2 Wind tunnel model . . . . . . . . . . . . . . . . . . . . .
2.2.1 Model description . . . . . . . . . . . . . . . . .

2.2.2 Wing model derived with co-kriging . . . . . . .
2.3 Standard wind tunnel corrections for steady flow . . . .
2.3.1 Steady corrections closed wind tunnels . . . . . .
2.3.2 Steady corrections for open jet wind tunnels . . .
2.4 Wind tunnel measurements and FSI . . . . . . . . . . .
2.5 Particle Image Velocimetry . . . . . . . . . . . . . . . .
2.5.1 Principles of PIV . . . . . . . . . . . . . . . . . .
2.5.2 Phase-locked PIV . . . . . . . . . . . . . . . . . .
2.6 Methods to derive (un)steady forces . . . . . . . . . . .
2.6.1 Kutta-Joukowski’s circulatory approach . . . . .
2.6.2 Noca’s momentum flux equation . . . . . . . . .
2.6.3 Implementation of Noca’s method . . . . . . . .

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2.7

Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Experimental benchmark I and numerical comparison:
with actuated flap
3.1 Problem definition . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Low turbulence tunnel . . . . . . . . . . . . . . . .
3.1.2 The model and equipment . . . . . . . . . . . . . .
3.1.3 Steady and unsteady test cases . . . . . . . . . . .
3.1.4 PIV setup and apparatus . . . . . . . . . . . . . .
3.2 Numerical model . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 2-D panel code . . . . . . . . . . . . . . . . . . . .

3.3 Wind tunnel corrections . . . . . . . . . . . . . . . . . . .
3.3.1 Wind tunnel wall corrections . . . . . . . . . . . .
3.3.2 Gap correction . . . . . . . . . . . . . . . . . . . .
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Force evaluation . . . . . . . . . . . . . . . . . . .
3.4.2 Steady cases . . . . . . . . . . . . . . . . . . . . .
3.4.3 Unsteady cases . . . . . . . . . . . . . . . . . . . .
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .

an aerofoil
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4 Experimental benchmark II: a free plunging wing with imposed
oscillations
4.1 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Open jet wind tunnel . . . . . . . . . . . . . . . . . . . . .
4.1.2 Wind tunnel model . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Supporting structure . . . . . . . . . . . . . . . . . . . . . .
4.1.4 Structural characteristics . . . . . . . . . . . . . . . . . . .
4.1.5 Steady and unsteady test cases . . . . . . . . . . . . . . . .
4.2 Measurements and post-processing . . . . . . . . . . . . . . . . . .
4.2.1 Measurement devices . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Force derivation . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Measurement procedure and post-processing . . . . . . . .
4.2.4 Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . .
4.2.5 PIV setup and apparatus . . . . . . . . . . . . . . . . . . .
4.2.6 Wind tunnel corrections . . . . . . . . . . . . . . . . . . . .
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Steady cases . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Unsteady case: 2-D PIV . . . . . . . . . . . . . . . . . . . .
4.3.3 Unsteady cases . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Comparative study of numerical models
with imposed flap oscillations
5.1 Problem definition . . . . . . . . . . . .
5.1.1 Test problem simplification . . .
5.1.2 Wind tunnel corrections . . . . .
5.2 Numerical methods . . . . . . . . . . . .

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for a free plunging aerofoil
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5.2.1
5.2.2
5.2.3

5.3

5.4

2-D Extended Theodorsens model . . . . . . . . . . . . . . . .
2-D panel code with structural model . . . . . . . . . . . . . .
2-D Unsteady Reynolds-averaged Navier Stokes solver with structural model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Steady cases . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Unsteady cases - description . . . . . . . . . . . . . . . . . . . .
5.3.3 Unsteady cases - subiterations . . . . . . . . . . . . . . . . . .
5.3.4 Unsteady cases - PIV test case . . . . . . . . . . . . . . . . . .
5.3.5 Unsteady cases - sensor test cases . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Conclusions

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7 Recommendations

119

A Wind tunnel corrections LTT wind tunnel

121

B Error classification
B.1 Experimental errors . .
B.1.1 Systematic errors
B.1.2 Random errors .
B.2 Numerical errors . . . .

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123
123
123
124
124

C Data interpolation
125

C.1 Bayesian inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C.2 Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
C.3 Co-kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
D Wing/Aerofoil measurements

131

E Flap motion algorithm

135

F Theodorsens model

137

G Tabulated numerical and experimental results

139

H Wind tunnel measurements DU96-W-180
147
H.1 Steady measurement data original DU96-W-180 . . . . . . . . . . . . . 147
H.2 Steady measurement data current model . . . . . . . . . . . . . . . . . 148
H.3 Combined graphs DU96-W-180 and current
wind tunnel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
I

Tabulated results grid and time step study (U)RANS solver

153

References

155

List of publications

165

xi


Acknowledgements

167

Curriculum Vitae

169

xii


Nomenclature

Symbols

ă











a
A0
A1 , A2
b
b1 , b2
C
c
c
cD
cd
cd
C(k)
cL

Angle of attack
Prandtl-Glauert compressibility factor
Change of quantity

Flap deflection, positive downwards
Flap angular velocity, positive downwards
Flap angular acceleration, positive downwards
Blockage factor
Error
Phase angle
Circulation
Flux term Noca
Shape factor
Density
Wind tunnel correction parameter
Phase
Vorticity
Angular velocity
Pitch axis location (in semichords)
Airfoil cross-sectional area
Coefficients indicial function
Semi chord
Exponents indicial function
Closed contour
Chord
Damping coefficient
3-D drag coefficient
2-D drag coefficient
Mean 2-D drag coefficient
Theodorsens function
3-D lift coefficient
xiii

[deg],[rad]

[deg],[rad]
[rad/s]
rad
[ /s2 ]

[deg],[rad]
2
[ ms ]
2
[m /s2 ]
[kg/m3 ]
[deg],[rad]
[1/s]
rad
[ /s]
[m2 ]
[m]
[m]
[m]
[kg/s]


cl
cl
cM
cm
D
d
e

F
f
f
F1 , F4 , F10 , F11
F0
H
h
I
k
k
L
l
l
M
m
N
N
n

p
q
q
S
T
t
t
T
U
u
~u

u
x
~x
x
x
ă
x

x
Y
y
y

2-D lift coefficient
Mean 2-D lift coefficient
3-D moment coefficient (1/4 c)
2-D moment coefficient (1/4 c)
Drag
Distance
Flap hinge location (in semichords)
Force
Frequency
Fluctuating quantity
Geometric flap parameter
Forcing amplitude
Structural state vector
Wind tunnel height
Identity tensor
Reduced frequency
Spring stiffness

Lift
Characteristic length scale
Line element
Mach number
Mass
Dimension of the flow field
Number of samples
Normal unit tensor
Pressure
Derived quantity
Undisturbed dynamic pressure
Surface
Temperature
Time
Thickness airfoil
Viscous stress tensor
Flow velocity
Undisturbed flow velocity
Flow velocity vector
Velocity tensor
Horizontal displacement
Position vector
Horizontal velocity
Horizontal acceleration
Non-dimensional horizontal displacement
Position tensor
Displacement amplitude
Vertical displacement
Vertical velocity

xiv

[N]
[m]
[N]
[Hz]

[N]
[m]

[N/m]
[N]
[m]
[m]
[kg]

[Pa]
[N]
[m2 ]
[K],[ ◦ C]
[s]
[m]
[kg/m/s2 ]
[m/s]
[m/s]
[m/s]
[m/s]
[m]
[m]
[m/s]

m
[ /s2 ]
[m]
[m]
[m]
[m/s]


yă
y
Z

Vertical acceleration
Non-dimensional vertical displacement
Aerodynamic state vector

Subscripts
cd ,cD
cl ,cL
cM


y/c
y
amp
b
c
cg
d
eq

exp
f
int
KJ
l
l
LC
mean
MF
min
ms
n
n
nc
p
PC
qs
r
r
s
s
sb
SG
t
t
u
w
wb

Belonging to drag

Belonging to lift
Belonging to moment
Belonging to flap
Undisturbed
Belonging to vertical displacement
Belonging to vertical velocity
Amplitude
Body
Circulatory
Center of gravity
Damping
Equivalent
Experiment
Flap
Interval
Kutta-Joukowski
Left side
Low
Load cells
Mean value
Momentum Flux (Noca)
Minimum
Mini step
Natural
Normal
Non-circulatory
Plates
Panel code
Quasi-steady
Right side

Residence
Surface body
Springs
Solid blockage
Strain gauges
Tangential
Wind tunnel
Up
Wing
Wake blockage

xv

[m/s2 ]


Abbreviations
BEM
CMM
DAQ
DOF
FOV
FSI
LES
LTT
OJF
PIV
RANS
RMS
URANS

Blade element momentum
Coordinate measuring machine
Data aquisition
Degrees of freedom
Field of view
Fluid-structure interaction
Large eddy simulation
Low turbulence tunnel
Open Jet Facility
Particle image velocimetry
Reynolds averaged Navier-Stokes
Root mean square
Unsteady Reynolds averaged Navier-Stokes

xvi


Chapter

1

Introduction
1.1

Motivation

Dynamic interactions between a fluid flow and a structure play a pronounced role in
current designs. Amongst others reasons are that in many applications engineers are
deemed to create designs which are as light as possible or to design structures where

(static) interaction is intentionally part of the design philosophy. An example of the
latter can be found in the field of mechanical engineering, where passively deformable
spoilers are applied on race cars, see Heinze [2007]. In aeronautics aeroelasticity plays
a major role in e.g. micro air vehicle wings, see Wootton [1981], Shyy et al. [2010], and
in helicopter blades as discussed by e.g. Friedmann and Hodges [2003], Lim and Lee
[2009]. But also in civil engineering the understanding and prediction of interactions
between constructions like buildings and bridges is of utmost importance to prevent
occasions like the well-known Tacoma Narrows bridge disaster of 1940. In the field of
bio mechanics fluid-structure interactions cannot be ignored in for example arterial
blood flows and the lungs, see Bertram Fung [1997], Fern´
andez [2011].
In the wind turbine industry there is much interest in fluid-structure interactions.
Firstly, in the past aeroelastic unstable situations have been reported for wind turbines
and for the next generation of turbines this must be prevented. Hereto, proper predictions of aeroelastic responses are required as discussed by amongst others Hansen
[2007]. Secondly, there is still a trend to increase rotor diameters in order to make
wind turbines economically more attractive. One of the drawbacks of larger rotors is
the larger susceptibility to aeroelastic effects, see e.g. Hansen et al. [2006]. Thirdly, a
promising option is to use smart wind turbine blades, see van Wingerden et al. [2008],
which are tailored to reduce the aerodynamic loading based on e.g. measured wind
fields, blade root moments or the blade bending. Hereby, especially for slender, long
blades the aeroelastic response to the instantaneously changing loads is important to
consider.
Numerical models can be used to simulate and predict fluid-structure interactions
for wind turbines, as reported by e.g. Chaviaropoulos et al. [2003a]. In general numerical fluid-structure interaction modelling is widely explored, see e.g. Garcia [2005],
1


Gardner et al. [2008] or Riziotis et al. [2004]. Despite the fact that many engineers
rely on these simulations, the validation of the numerical fluid-structure interaction
models with measurement data is limited and relatively unexplored. This is certainly

true for fluid-structure interactions for wind turbines yielding high Reynolds numbers.
Main cause is the limited availability of good experimental data, amongst others due
to the complexity of aeroelastic wind tunnel experiments. An example of such a complexity is unsteady wind tunnel interference. Furthermore, there is a restriction on
the available data in the sense it has a limited applicability due to specific combinations of Reynolds numbers and structure types. Examples of such experiments are for
instance work of Gerontakos and Lee [2008] who assessed the unsteady aerodynamics
around a prescribed oscillatory aerofoil with trailing edge flap or aeroelastic flutter experiments performed by Rivera et al. [1991] with the aim to obtain experimental data
for validation purposes. In the latter research for a large range of Mach numbers from
low subsonic to transonic, pitch and plunge magnitudes and phases are determined
as well as unsteady surface pressure measurements are performed. Reynolds numbers
are approximately in the order of a few million. Although not all flow parameters are
known, together with the structural parameters this is a valuable data set that can
be used in the development of aeroelastic codes.
The lack of experimental validation material for fluid-structure interaction problems for wind turbine applications is the main motivation for this doctoral research
work. Within the INNWIND project where this thesis is part of, research activities
are defined to improve the aeroelastic modelling. One of the main tasks in this is
to obtain validation data for aeroelastic simulations, where for wind turbines typical Reynolds numbers of > 500 000 are considered and the structural shape is a
good representation of a wind turbine section. Furthermore, in the framework of active control strategies it is beneficial to integrate a controllable flap in the structure.
Therefore, the main target of this research is defined to obtain validation material for
fluid-structure problems for wind turbine related Reynolds numbers and structures.
A numerical benchmark study is part of the research to obtain amongst others more
insight in possible issues in modelling the validation experiment.

1.2

Literature review of present state

Fluid-structure interactions (FSI) of wind turbines can be investigated by performing
field measurements, conducting numerical assessments or by doing controlled laboratory experiments. The incentive of this thesis and the used approach is based on
existing research and common practices on the numerical and experimental side. A
short overview of this background information is presented before the approach is

discussed.
FSI problem classification
Fluid-structure interaction is about the interaction between a fluid flow and a deforming or moving structure. Depending on the fluid and structural properties, the
interaction can be qualified as weak or strong. In general weakly coupled problems
most often deal with stiff structures which are with respect to the fluid heavy. Strongly
coupled problems deal typically with flexible, more light-weight structures.

2


Numerical approaches FSI
Fluid-structure interaction problems can be solved in a monolithic (see e.g. Hă
ubner
et al. [2004], Michler et al. [2004], Ryzhakov et al. [2010]) or a partitioned manner
(see e.g. Felippa and Geers [1988], Piperno et al. [1995]). In the monolithic approach,
a dedicated solver is needed where the flow and the structure are combined in one
physical model. Advantage is that no spatial and temporal coupling interface exists
between the flow and the structure. Drawback is the fact a dedicated solver needs to
be developed, maintained and updated which is relatively expensive. Furthermore,
monolithic solvers are often limited to a class of problems for which it is specifically
designed.
The drawbacks of monolithic solvers are such that most often one relies on partitioned solvers, where (commercially available) separate flow and structure solvers
are coupled. For partitioned codes a coupling interface is needed where the spatial
and temporal discretisations of the flow and structure solver are linked. The spatial
coupling consists of an interpolation technique needed for non-matching fluid and
structure computational meshes. The temporal coupling is needed to take care of the
communication of structure and flow solutions when the simulation advances in time.
For weakly coupled problems it is often sufficient to evaluate the coupling terms only
once per time step leaving a temporal coupling error. For strongly coupled problems
multiple evaluations are required to obtain a converged solution and an acceptable

temporal coupling error. Strong interactions can impose numerical instabilities and
require stability enhancing measures like relaxation techniques (see Kă
uttler and Wall
[2008]). Reduction of the computational effort for strongly coupled problems can be
achieved by application of e.g the Newton-Krylov solving strategy as discussed by
Michler et al. [2005] or multigrid algorithms as laid down by van Zuijlen and Bijl
[2009].
For both the monolithic and partitioned approaches validation is required to assess
the accuracy of the model. Besides implementation errors, for monolithic solvers the
validation covers flow and structure modelling errors and discretisation errors. For
partitioned solvers, the solvers are usually validated separately for a wide range of
test problems and validation is at least required to assess the implementation of the
spatial and temporal coupling between the flow and structure solvers.
Due to the lack of experimental data, academic test problems or benchmark studies are often used to assess fluid-structure interaction solvers. Disadvantage is that in
general only analytical solutions exist of physically simple test problems. For more
challenging, real physical problems one has to fall back on experiments. Numerical
benchmark studies, where solutions of different codes are compared, provide a good
means of a first analysis of the code, however the check with reality still lacks.
Laboratory experimental FSI
Experiments are performed to check numerical results or directly assess fluid-structure
interaction cases. As mentioned, for validation purposes not much data is available
and the available data is mostly confined to specific combinations of Reynolds numbers
and structure types. Examples of aeroelastic experiments are e.g. work by Dietz
et al. [2004], Tang and Dowell [2011] about flutter and Neumann and Mai [2013] on

3


an aeroelastic gust response of a wing.
In setting up a fluid-structure interaction experiment for validation purposes,

amongst others the following considerations need to be addressed before a detailed
experimental design can be made:
• Validation purpose(s)
• Measurement data needed (minimum)
• Reynolds classification
• Conformability level of numerical modelling wrt. experiment
• Structure type and degrees of freedom
With validation purpose is meant whether a specific part(s) of a numerical algorithm
or the complete solver is to be validated and roughly for which boundary conditions
this should be enabled. The conformability level of the numerical modelling determines how much effort it takes to model the experiment in the numerical setup: keep
in mind that in case an experiment is designed that is very complex to model in a
numerical solver, it is not particular suited for general validation purposes. Based on
the set incentives the experiment can be designed in detail, whereby the guidelines
described in the next section should be taken into consideration.
Validation experiments
Validation experiments need to comply to certain requirements as thoroughly explained in e.g. Oberkampf [2001], Oberkampf and Trucano [2002], Oberkampf and
Barone [2006]. Six guidelines are defined by Oberkampf [2001] for designing and
conducting validation experiments, which are:
• Guideline I: A validation experiment should be jointly designed by experimentalists and code developers or analysts working closely together throughout the
program, from inception to documentation, with complete candor about the
strengths and weaknesses of each approach.
• Guideline II: A validation experiment should be designed to capture the essential
physics of interest, including all relevant physical modelling data and initial and
boundary conditions required by the code.
• Guideline III: A validation experiment should strive to emphasize the inherent
synergism between computational and experimental approaches.
• Guideline IV: Although the experimental design should be developed cooperatively, independence must be maintained in obtaining both the computational
and experimental results.
• Guideline V: A hierarchy of experimental measurements of increasing computational difficulty and specificity should be made.
• Guideline VI: The experimental design should be constructed to analyze and

estimate the components of random (precision) and bias (systematic) experimental errors.

4


For a more in depth discussion of these guidelines the reader is referred to the specified
source. In this work it is aimed for to adhere to all guidelines, whereby guideline V
is considered to be partly beyond the scope of this work. Mind these guidelines do
not specify strict requirements in terms of the desired accuracy levels and acceptable
uncertainties. Furthermore, for validation it is clear that there must be an undisputed confidence in the experimental data meaning among others no ambiguities are
observed.
Experimental measurement techniques
A wide variety of qualitative and quantitative aerodynamic measurement techniques
have been developed. Qualitative techniques can be of added value in the comprehension of flow features, but are not sufficient for the validation purposes foreseen with
this work. The intrusiveness of measurement techniques is also important to consider
when a suitable measurement technique is selected.
Non-intrusive and accurate load measurements on objects that can deform or move
are often not trivial. For these experiments, as long as e.g electric wires or pressure
tubes are no obstruction to (free) motions, unsteady forces can be measured directly
with high accuracy by using e.g. load cells or strain gauges, see Hillenherms et al.
[2004]. When using load cells or strain gauges special attention should be given to the
possible contamination of measured forces with e.g. structural responses of the supporting structure. The unsteady loads can also be indirectly derived from measured
flow-field quantities. Examples of the latter are for example wake rake measurements, measurements with pressure sensitive paint (McLachlan and Bell [1995] and
Klein et al. [2005]) and pressure taps. For unsteady flow, pressure orifices based
measurements require relatively expensive sensors that are prone to drift when subjected to multiple pressure cycles. This means the accuracy reduces over time unless
frequent calibrations are performed, which is undesired. Pressure sensitive paint is
non-intrusive and can be applied to unsteady flows, although the sensitivity deteriorates with decreasing Mach number. For velocities beyond the low-subsonic range this
method can be applied with enough accuracy. However in this work the low-subsonic
range is covered and pressure sensitive paint lacks accuracy. Surface stress-sensitive
film is also suited for low-subsonic flows and additionally measures skin friction forces,

see e.g. Fonov et al. [2005]. Problem is that even the smallest vibration in the camera
setup deteriorates the accuracy of the measurement of the applied film layer thickness
and cameras must be focused on the moving surface when recording.
In previous research mainly strain gauges and pressure sensors are used to determine loads and/or deflections for an aerofoil with moving flap. This includes work of
Frederick et al. [2008], van Wingerden et al. [2008], Bak et al. [2010] and Heinz et al.
[2011] who performed an experimental and numerical investigation on control surfaces
for aerofoils with success. Tang and Dowell [2007] used strain gauges in flutter related
experiments. Based on these experiences strain gauge measurements are selected for
load measurements. Also load cells are used to have amongst others redundancy in
the measurements.
For research on fluid-structure interactions non-intrusive particle image velocimetry is also considered to be an appropriate measurement technique. Advantage
is that both flow visualisations are obtained and loads can be deduced. Loads can

5


be determined from PIV data using theory based on the exchange of momentum as
presented by amongst others Unal et al. [1997], Baur and Kăongeter [1999] and Noca
et al. [1999]. Unal and Baur used the velocity field to derive pressure differences from
the momentum equation. The local pressures are found by integration of the pressure differences in the domain starting from one side, leading to an accumulation of
numerical errors. Noca came up with another method to determine (un)steady loads
that only needs the velocity field and its derivatives, which directly follow from (subsequent) velocity fields. Noca’s approach suffers only from local spatial and temporal
discretisation errors and is therefore applied in this thesis.
Aerodynamic and structural solvers for wind turbines
For wind turbines fluid-structure interactions became important with the significant
upscaling in the last decades of the 20th century. Various aeroelastic solvers have been
developed which mainly rely on engineering models. Hansen et al. [2006] provided a
detailed description of commonly used solution strategies and the outlook for future
improvements. Buhl and Manjock [2006] have presented an overview of the aeroelastic
codes used for certification.

The aerodynamic part is often treated using the blade-element-momentum theory
(BEM), as laid down by Glauert [1963]. In BEM spanwise blade sections in combination with 1-D momentum theory is considered, where for the sectional aerodynamic
properties aerofoil data is required as input. In general the 2-D aerofoil data needs
to be corrected for e.g. tip losses, dynamic stall and Coriolis and centrifugal forces.
In order to have a more sound modelling of the 3-D flow field including the wake the
lifting line theory of Prandtl [1918] can be used, which also needs aerodynamic data
as input. The vortex lattice method and in(viscid) panel codes compute the 3-D flow
field including the lifting surface characteristics, see e.g. Katz and Plotkin [2001]. The
most detailed and best physical approximation are the Navier-Stokes solvers in e.g.
the Reynolds-averaged form (RANS) or as a large-eddy simulation (LES). However,
due to the computational effort of this type of solvers, BEM is still widely used for
wind turbine design.
For the structural modelling of wind turbines often is relied on a multi-body model,
a modal shape based analysis or a full finite element discretisation. In the multibody approach the various wind turbine components are modelled as multiple rigid
or flexible bodies inter-connected with joints or hinges, as described by e.g. Cook
[1987], Shabana [2005]. The type of connection determines the degrees of freedom
between the bodies. A full model of the structure using finite elements, see e.g.
Zienkiewicz [1989], is more accurate but also more expensive compared to the multibody approach. The finite elements contain the physical structural properties like the
axial stiffness, the bending stiffness and the torsional stiffness. As an intermediate
solution, a modal shape approximation can be used. In this method the mode shapes
are first determined with a finite element analysis using unit loads. In the further
analysis, linear combinations of a limited selection of mode shapes is used to calculate
the structural state for each type of loading.
The majority of aeroelastic solvers used in the wind turbine industry are engineering codes where a compromise is made between accuracy and computational effort.
As an example, FLEX makes use of a coupling between BEM and a multi-body for-

6


mulation, see for example Øye [1996]. GH Bladed is also based on the combination

of BEM and a multi-body approach for the structure, see Bossanyi [2003].

1.3

Approach

The main incentive of this research is to conduct an aeroelastic experiment that complements the available, limited database with aeroelastic experimental data. Focus
is on data that can be used for wind turbine applications. Hereby one can think of
validation of e.g. high fidelity aeroelastic solvers, but also structurally coupled BEM
codes including its input databases.
Relevant aeroelastic motions for wind turbines are flapwise, edgewise and pitching
motions, see e.g. Petersen et al. [1998] and Chaviaropoulos et al. [2003b]. Furthermore, wind turbines operate at moderate to large angles of attack whereby dynamic
stall can occur. In order to capture most of these relevant aspects, an experimental
setup is designed with which plunging and pitching motions can be investigated,
either combined or isolated. Based on the authors experience level, it is decided to
commence in this research with the assessment of an isolated plunging or pitching
structure and the combined motion is left as next step. There is no strong preference
to start with either pitching motions or plunging motions, although plunging motions
are expected to be more challenging regarding the PIV measurements. It is simply
decided to start with plunging motions.
Starting point is to achieve a low complexity level of the experiment to: 1) limit
the amount of possible error sources in the experimental data, 2) enable in validation processes a better pinpointing of the origin of deviations in the numerical data
compared to the experimental data, and 3) make sure the emphasis can be put on
the coupling of the flow and structure solvers. Reduction of the complexity level can
be arranged on the aerodynamic part by amongst others moderate angles of attack
to prevent dynamic flow attachments and detachments. On the structure part the
number of degrees of freedom can be reduced to cancel higher order mode shapes. In
this context, the decision is made to use a rigid wing with one degree of freedom and
a controllable flap to generate time varying forces. The setup is intended to result
in quasi-2-D flow, the Reynolds number is chosen such that it complements on the

Reynolds regimes of other aeroelastic data. Next to aeroelastic data, also existing
measurement data for the same wing shape are taken into consideration: for the target Reynolds number other steady measurement data are available that can serve as
reference.
The measurement techniques which are used are well-known, except for the application and implementation of Noca’s method for moving and/or deformable structures.
Therefore it is decided to prior to the fluid-structure interaction experimental campaign assess Noca’s method for a deformable structure: a wing (similar as used in the
fluid-structure interaction campaign) with a moving trailing edge flap.
For the application of PIV with moving objects, a decision must be made upon
the part of the flow field that must be captured for each location of the structure.
In combination with the desired flow field resolution this determines eventually the
number of cameras that is needed or how many separate camera setups are needed

7


in case of repeatable experiments. Initial knowledge about the expected structural
displacements is hereby needed. Hereto, a numerical model based on Theodorsens
model is applied to roughly estimate the structural properties and the accompanying
structural responses.
The aeroelastic experiment is designed using Theodorsens model: the measurements to conduct and the structural properties are determined from simulations.
Hereby, a trade-off for the structural parameters is made keeping in mind the amount
of camera setups for PIV, the frequency limits of the flap, the desired frequency range
to cover (0.5 / ω/ωn / 1.5) and the aim to have only low to moderate induced angles
of attack due to the structural velocities. The experiment is conducted in the open
jet facility to have the best optical access to the structure and since wing blockage
effects might be influential in the closed tunnel.
Finally, in this thesis the fluid-structure interaction cases under consideration are
simulated with three levels of fidelity numerical models: Theodorsens model, a panel
code and an URANS solver. The emphasis is on the possibility of modelling the quasi2-D experiment as a 2-D case with corrections for the wind tunnel influences, in order
to reduce the computational time. The impact of the modelling choices is assessed
based on a comparison with the experimental data and the other computations.

1.4

Outline

The outline of this thesis follows roughly the setup as described in the approach.
In Chapter 2 first some fundamental concepts, implementations and post-processing
techniques are described. The first experiment treating the application of Noca’s
method to deformable structures is treated in Chapter 3. Chapter 4 discusses the
fluid-structure interaction experiment followed by the numerical simulations of the
experiment in Chapter 5. Conclusions and recommendations are finally presented in
Chapters 6 and 7.

8


Chapter

2

Terminology, wind tunnel models
and methodologies
In this chapter background information is provided about used terminology, existing
methodologies and the wind tunnel model. Background information that is specific
for topics treated in the various chapters, is discussed in those chapters separately.
In this chapter first some general terminology is explained and averaging and data
reduction methods are discussed. Background information is provided about the wind
tunnel model and the 2-D numerical representation of this model. Measurements are
conducted in a closed wind tunnel and an open jet tunnel, as elaborated on in Sections
3.1 and 4.1. For both tunnels a discussion about wind tunnel corrections is provided.

Next the load determination using particle image velocimetry (PIV) is discussed.
Regarding the post-processing next to the data reduction the uncertainty analysis is
treated. Parts of this chapter are based on two papers: Sterenborg et al. [2014a] and
Sterenborg et al. [2014b]. Section 2.2 is based on work done by Boon et al. [2012].

2.1
2.1.1

Terminology
Characteristic (non-)dimensional numbers

First consider a quasi-steady or unsteady periodic flow. Classification of these types of
flows can be arranged using non-dimensional numbers. In fluid dynamics the residence
time tr can be expressed as a function of a characteristic length scale L and the
undisturbed flow velocity u as follows:
L
.
(2.1)
u
For unsteady flows with some periodic flow feature, the residence time can be related
to some periodic time scale ω −1 . The resulting quantity is known as the Strouhal
tr =

9