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

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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.

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Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. drs. H. Bijl

Copromotor: Dr. ir. A.H. van Zuijlen

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. dr. ir. drs. H. Bijl Technische Universiteit Delft, promotor Dr. ir. A.H. van Zuijlen Technische Universiteit Delft, copromotor Prof. dr. ir. G.A.M. van Kuik Technische Universiteit Delft

Prof. dr. ir. L.L.M. Veldhuis Technische Universiteit Delft Prof. N.N. Sørensen Technical University of Denmark Dr. -Ing. Th. Lutz Universit¨at Stuttgart

Dr. Ir. K. Boorsma ECN

Prof. dr. F. Scarano Technische Universiteit Delft, reservelid

This research is funded by Agentschap NL (formerly Senternovem), an agency of the Dutch Ministry of Economic Affairs, under project num-ber EOS LT 09001

Printed by Ipskamp Drukkers, The Netherlands Copyright c_{2014 by J.J.H.M. Sterenborg}

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.

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Summary

Over the last years fluid-structure interactions have attained more interest emanat-ing 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 de-formations, 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 fluid-structure interactions. This complexity appears amongst others in the determination of unsteady loads on moving objects and unsteady wind tunnel wall corrections. Fur-thermore, 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 valid-ation data. Therefore, this thesis aims to enhance the possibilities for validvalid-ation of aeroelastic solvers used for the simulation of aeroelasticity of wind turbines. An aer-oelastic 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 alle-viation 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 simula-tions.

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

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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 model-ling 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. Subiter-ations 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.

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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 van-wege 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 inter-acties in toepassingen zijn soms onwenselijk, maar kunnen ook benut worden. Een voorbeeld van het laatste kan worden gevonden in belastingsreducties voor windtur-binebladen 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 vali-deren 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 instatio-naire 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 mogelijk-heden 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 belastingsreductiesys-temen met kleppen, de op-en-neergaande beweging van de gebruikte stijve vleugel genduceerd door een opgelegde klep beweging. De klep oscilleert in een sinus bewe-ging 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 reken-roosters 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

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op een gesloten lijn. Een experiment is uitgevoerd om de toepasbaarheid van Noca’s methode voor een vleugel met een bewegende klep te onderzoeken. Windtunnelcor-recties voor dit specifieke instationaire probleem zijn ook onderzocht. Conclusie is dat, gegeven de experimentele data, Noca’s methode relatief gevoelig is voor de ge-kozen 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 instan-tane 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 krachtencoeffici¨enten. Het is bekend dat onder andere een hogere resolutie voor de ruimte discretisatie en een hogere orde benadering voor de snel-heidsafgeleiden 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 massa-demper-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 ver-wacht 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. Aanna-mes 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 vereenvoudi-gingen 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 pane-len code en een URANS code. In de simulatiemodelpane-len zijn 2-D stationaire windtun-nelcorrecties gentegreerd. Alle stromingsmodellen zijn gekoppeld aan een structureel rekenmodel en de vloeistof-vaste stof interactie is zowel zwak en sterk gekoppeld op-gelost. 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 ampli-tudefouten 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

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gevon-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.

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6 Conclusions 115 7 Recommendations 119 A Wind tunnel corrections LTT wind tunnel 121 B Error classification 123 B.1 Experimental errors . . . 123 B.1.1 Systematic errors . . . 123 B.1.2 Random errors . . . 124 B.2 Numerical errors . . . 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

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Acknowledgements 167

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Nomenclature

Symbols

α Angle of attack [deg],[rad]

β Prandtl-Glauert compressibility factor

∆ Change of quantity

δ Flap deflection, positive downwards [deg],[rad]

˙δ Flap angular velocity, positive downwards [rad_/_s_]

¨

δ Flap angular acceleration, positive downwards [rad_/_s2_]

ǫ Blockage factor

ǫ Error

φ Phase angle [deg],[rad]

Γ Circulation [m2

s ]

γ Flux term Noca [m2_/_s2_]

Λ Shape factor

ρ Density [kg_/_m3_]

σ Wind tunnel correction parameter

θ Phase [deg],[rad]

ω Vorticity [1_/_s_]

ω Angular velocity [rad_/_s_]

a Pitch axis location (in semichords)

A0 Airfoil cross-sectional area [m2]

A1, A2 Coefficients indicial function

b Semi chord [m]

b1, b2 Exponents indicial function

C Closed contour [m] c Chord [m] c Damping coefficient [kg_/_s_] cD 3-D drag coefficient cd 2-D drag coefficient ¯

cd Mean 2-D drag coefficient

C(k) Theodorsens function

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cl 2-D lift coefficient ¯

cl Mean 2-D lift coefficient

cM 3-D moment coefficient (1/4c) cm 2-D moment coefficient (1/4c)

D Drag [N]

d Distance [m]

e Flap hinge location (in semichords)

F Force [N]

f Frequency [Hz]

f Fluctuating quantity

F1, F4, F10, F11 Geometric flap parameter

F 0 Forcing amplitude [N]

H Structural state vector

h Wind tunnel height [m]

I Identity tensor

k Reduced frequency

k Spring stiffness [N_/_m_]

L Lift [N]

l Characteristic length scale [m]

l Line element [m]

M Mach number

m Mass [kg]

N Dimension of the flow field

N Number of samples

ˆ

n Normal unit tensor

p Pressure [Pa]

q Derived quantity

q∞ Undisturbed dynamic pressure [N]

S Surface [m2_]

T Temperature [K],[ ◦

C]

t Time [s]

t Thickness airfoil [m]

T Viscous stress tensor [kg_/_m/s2_]

U Flow velocity [m_/_s_]

u Undisturbed flow velocity [m_/_s_]

~u Flow velocity vector [m_/_s_]

u Velocity tensor [m_/_s_] x Horizontal displacement [m] ~x Position vector [m] ˙x Horizontal velocity [m_/_s_] ¨ x Horizontal acceleration [m_/_s2_] ˆ

x Non-dimensional horizontal displacement

x Position tensor [m]

Y Displacement amplitude [m]

y Vertical displacement [m]

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¨

y Vertical acceleration [m_/_s2_]

ˆ

y Non-dimensional vertical displacement

Z Aerodynamic state vector

Subscripts cd,cD Belonging to drag cl,cL Belonging to lift cM Belonging to moment δ Belonging to flap ∞ Undisturbed

y_/_c _{Belonging to vertical displacement}

˙y Belonging to vertical velocity

amp Amplitude b Body c Circulatory cg Center of gravity d Damping eq Equivalent exp Experiment f Flap int Interval KJ Kutta-Joukowski l Left side l Low LC Load cells

mean Mean value

MF Momentum Flux (Noca)

min Minimum ms Mini step n Natural n Normal nc Non-circulatory p Plates PC Panel code qs Quasi-steady r Right side r Residence s Surface body s Springs sb Solid blockage SG Strain gauges t Tangential t Wind tunnel u Up w Wing wb Wake blockage

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Abbreviations

BEM Blade element momentum

CMM Coordinate measuring machine

DAQ Data aquisition

DOF Degrees of freedom

FOV Field of view

FSI Fluid-structure interaction

LES Large eddy simulation

LTT Low turbulence tunnel

OJF Open Jet Facility

PIV Particle image velocimetry

RANS Reynolds averaged Navier-Stokes

RMS Root mean square

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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 pre-dictions 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 nu-merical fluid-structure interaction modelling is widely explored, see e.g. Garcia [2005],

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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 com-plexity 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 combina-tions 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 ex-periments 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 prob-lems 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 typ-ical 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 act-ive 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 labor-atory 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 de-forming 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.

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Numerical approaches FSI

Fluid-structure interaction problems can be solved in a monolithic (see e.g. H¨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 par-titioned 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 K¨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 stud-ies 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

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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 determ-ines 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 ex-plained 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 experiment-alists 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 cooper-atively, independence must be maintained in obtaining both the computational and experimental results.

• Guideline V: A hierarchy of experimental measurements of increasing computa-tional 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) experi-mental errors.

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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 undis-puted 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 comprehen-sion 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 sup-porting structure. The unsteady loads can also be indirectly derived from measured flow-field quantities. Examples of the latter are for example wake rake measure-ments, 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 sub-jected 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 deterior-ates 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 determ-ine 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 veloci-metry is also considered to be an appropriate measurement technique. Advantage is that both flow visualisations are obtained and loads can be deduced. Loads can

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be determined from PIV data using theory based on the exchange of momentum as presented by amongst others Unal et al. [1997], Baur and K¨ongeter [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 pres-sure 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 (sub-sequent) 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 combin-ation 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 multi-body 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 multi-body 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 engineer-ing 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

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for-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 com-plements 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]. Further-more, 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 valida-tion processes a better pinpointing of the origin of deviavalida-tions 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 tar-get 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 applic-ation and implementapplic-ation of Noca’s method for moving and/or deformable structures. Therefore it is decided to prior to the fluid-structure interaction experimental cam-paign 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

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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 measure-ments 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 quasi-2-D experiment as a quasi-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.

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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 Terminology

2.1.1 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:

tr= L

u. (2.1)

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}

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number: St =ωtr 2π = ωL 2πu = f L u . (2.2)

In this relation f is the frequency of the oscillating flow mechanism. In case of periodic motions an important parameter is the non-dimensional reduced frequency that relates the velocity of the motion to the undisturbed flow velocity u according to

k = πf c

u , (2.3)

where in this work f is the flap frequency and c is the chord. The reduced frequency is a measure for the degree to which unsteady phenomena are occurring.

2.1.2 Flap phase angle

The attitude of the flap of the wing model used is controlled using two servo engines. Besides static flap deflections, in this thesis harmonic flap deflections are prescribed. This means that the flap deflection δ can be written according to

δ = δmean+ δamp· sin

2π φ 360+ θδ

. (2.4)

In this equation φ is the flap phase angle in degrees, δmeanis the mean flap deflection and δamp is the amplitude of the deflection around the mean. By definition the phase angle θδ = 0 and can therefore be omitted.

The flap phase angle is used as reference signal in the experiments, but also as a reference signal in the post-processing of the measurement data and the numerical solutions.

2.1.3 Averaging methods

Based on the harmonic flap oscillations, the fact that attached flow is promoted and displacements are kept small, periodic flow phenomena and structural responses are expected. Consequently the data can be post-processed using phase averaging, where the flap deflection determines the phase angle φ. Hussain and Reynolds [1972] proposed a decomposition of an arbitrary fluctuating quantity f (~x, t) in three com-ponents, namely the classical time average ¯f (~x), a coherent fluctuation ˜f (~x, t) and an incoherent or random fluctuation f′

(~x, t): f (~x, t) = ¯f (~x) + ˜f (~x, t) + f′

(~x, t) =hf(~x, t)i + f′

(~x, t). (2.5)

Phase averaging will result in the sum of the time average and the coherent fluctu-ations, _{hf(~x, t)i by the elimination of the incoherent or random fluctuations f}′

(~x, t) from the input signal f (~x, t). Phase averaging is based on ensemble averaging, where the instance of evaluation is in this case based on the instantaneous flap phase angle φ(t): hf(~x, φ(t))i = _N1 N −1 X n=0 f (~x, φ(t + nT )). (2.6)

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In this relation T is the period belonging to the flap oscillation.

Prior to the described phase averaging, moving averaging is employed to reduce noise in the various quantities of interest. Mind that in this process the random fluctuations f′

(~x, t) are modified as well as the resolution of the quantities of interest. In a mathematical formulation the simple moving averaging process is described by

f (~x, φ(tint)) = 1 N X tǫ[t1,t2] f (~x, φ(t)), (2.7)

where tint is the discretized time at which the simple moving average for the interval t1 ≤ t ≤ t2 is assigned and t1 ≤ tint ≤ t2. The number of samples found within the interval equals N .

2.1.4 Data reduction

After averaging of the data, for each quantity the data is reduced to one full period of the flap phase angle φ. In the data reduction process it is investigated whether the periodic signal is harmonic. In case a harmonic signal is found, the quantity is fully determined by a mean value, an amplitude and a phase angle θ. It turns out that all quantities of interest are harmonic, except for the drag that deviates from a harmonic signal. Despite a small error is made, also for the drag the same characteristic values are used to represent the signal.

2.2 Wind tunnel model

2.2.1 Model description

The used wind tunnel model is a wing based on the 18% thick DU96-W-180 wind turbine aerofoil. Reason for this choice is the amount of available data for this aerofoil, mainly measured in the same facility, see Timmer and van Rooij [2003], Timmer [2010] and Appendix H. The wing is untwisted and untapered and has a chord of 0.5 m, a span of 1.8 m and a 0.2c flap. Except for the wing span, which is based on wind tunnel dimensions, the wing size is driven by the desired Reynolds numbers and the fact that flap engines must be housed inside the wing. In Chapter 1 it was elaborated that a rigid wing with a controllable flap is used such that the flow topology and the structure dynamics can adequately be controlled. This will help to bound the overall complexity and more straightforward validations are foreseen. To achieve a good rigidity and a low mass, the wing is made of carbon fibre. The flap is hinged at the lower surface of the carbon fibre wing using continuous hinges. This suspension allows the flap to move in upward and downward directions over a range of at least _±25◦

. Gap flow between the wing and flap as reported by Liggett and Smith [2013] is prevented by seals covering the gaps on both the suction and pressure side. The manufacturing tolerance is about 1 mm, meaning the actual shape differs from the DU96-W-180. The wing span has a manufacturing tolerance of 5 mm. In the following section (2.2.2) this is more elaborated on.

The Reynolds number for the tests is around Re=700 000, for which in steady flow natural transition is expected somewhere mid/aft of the chord of the model. In the

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majority of the experiments the flap is oscillating and for the aeroelastic experiments the wing plunges, which might affect the transition location. In the end the transition location is not known and it is helpful to force transition with tripping wires. This to reduce uncertainty in e.g. calculated force coefficients since also in simulations the transition location is difficult to predict. For each experiment, details about the tripping wire setup are presented in the experimental setup descriptions, see Section 3.1.2 and Section 4.1.2.

2.2.2 Wing model derived with co-kriging

For modelling purposes, the actual geometry including seals has been measured using two different approaches. Using these two measurement data sets as input for co-kriging, the wing model shape is determined as described by Boon et al. [2012]. In this section a summary is given of the results presented by Boon et al. [2012].

For the first measurement approach at seven spanwise stations the cross-sectional shape is measured with a coordinate measuring machine (CMM). The resulting 2-D profiles are subjected to a measurement uncertainty of about 0.25 mm. The second measurement has been conducted with an optical technique called photogrammetry, see e.g. Li [1993]. With this technique 3-D coordinates of the wing are determined. This technique is based on images taken with calibrated cameras from various ob-servation locations with respect to the wing. The wing is marked with yellow labels to identify specific locations, as can be seen in appendix D. A computer algorithm extracts the location of the marks from the pictures and computes the belonging coordinates of the three-dimensional object. The accuracy of the photogrammetry measurements is determined to be 0.10 mm.

With co-kriging the low-fidelity CMM measurement data and the high-fidelity, but low resolution 3-D photogrammetry measurement data can be combined to obtain a high fidelity wing model. Co-kriging is explained by Kennedy and O’Hagan [2000, 2001] as a method that interpolates outputs by combining multiple data sources, considering also the uncertainty and the smoothness of the data. Based on kriging, this technique uses the assumption of Gaussian processes. A more detailed description of co-kriging is given in appendix C.

In the high fidelity shape determination, the variances used in co-kriging for the input data are based on the accuracy of the measurements: 0.25 mm for the low fidelity data and 0.10 mm for the high fidelity data. Figure 2.1 shows the measurements of the geometry and the high fidelity wing representation obtained using co-kriging.

From the data presented in Figures 2.1 and D.2 it can be concluded that the wing planform is not two-dimensional as it is supposed to be. In general, this implies that in 3-D simulations this determined shape should be modelled accordingly. In the 2-D numerical simulations in this research a 2-D cross-sectional shape is used by taking the mean of the 35 reconstructed aerofoils along the span displayed in Figure 2.1b. In appendix D this geometry is tabulated and the variance on the mean shape with respect to the 35 sections is presented. Although not further reported here, Boon et al. [2012] investigated the propagated uncertainty of amongst others the use of this mean geometry in the computed force and moment coefficients for steady flow. Mind also that due to the reported shape deviations, a fair comparison with the DU96-W-180 data measured by Timmer [2010] and presented in Appendix H is not possible.

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x[m] y [m ] z[m] -0.9-0.6 -0.3 0 0.30.6 0.9 0 0.1 0.2 0.3 0.4 -0.2 -0.1 0 0.1 0.2

(a) Geometry measurements.

x[m] y [m ] z[m] -0.9-0.6 -0.3 0 0.30.6 0.9 0 0.1 0.2 0.3 0.4 -0.2 -0.1 0 0.1 0.2

(b) Co-kriging wing model.

Figure 2.1: CMM measurements (blue dots) and photogrammetry measurements (red dots) of the 3-D wing geometry are shown in Figure 2.1a. The 3-D wing model resulting from co-kriging of the CMM and photogrammetry data is shown in Figure 2.1b. Source: Boon et al. [2012]

2.3 Standard wind tunnel corrections for steady flow

The flow around an object in the wind tunnel is influenced by the presence of walls or jet flow in case of an open jet tunnel. This is well known and amongst oth-ers Garner et al. [1966] and Krynytzky et al. [1998] presented overviews of classical wind tunnel corrections for both closed wind tunnels and open test section wind tun-nels. Corrections can be split into three main contributions: lift interference (due to upwash/downwash and streamwise velocity perturbations), solid blockage and wake blockage. In case of open jet tunnels not much is known about wake blockage and it is considered to be negligible, see Krynytzky et al. [1998]. In this section the wind tun-nel corrections for a closed wind tuntun-nel and for an open jet wind tuntun-nel are discussed that are used in this research. Both approaches are valid for steady flows. Since for unsteady flows the wind tunnel influences are more case specific, unsteady wind tunnel corrections are treated for each problem separately in the relevant chapters.

2.3.1 Steady corrections closed wind tunnels

For steady flows Havelock [1938] presented a set of relations for the 2-D lift interference correction for a centrally positioned wind tunnel model. The relations correct the angle of attack and the lift and moment coefficients as follows:

∆α = πc 2 96βh2(cl,t+ 4cm,t)− 7π3_c4_c l,t 30720β3_h4, ∆cl= cl,t −π 2 48 _c βh 2 + 7π 4 3072 _c βh 4! , ∆cm= cl,t +π 2 192 c βh 2 − 7π 4 15360 c βh 4! . (2.8)

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In these equations the subscript t denotes a tunnel recorded value, h is the tunnel height, c the chord and β the Prandtl-Glauert compressibility factor given by

β =p1− M2_, _(2.9)

where M is the Mach number. The solid blockage and wake blockage can be corrected using correction formulations presented by Krynytzky et al. [1998]. For solid blockage and wake blockage the interferences can be determined using

ǫsb= π 6 A β3_h2, ǫwb= cd 4β2 c h, (2.10)

where the solid blockage is indicated by the subscript sb and the wake blockage by wb. In the solid blockage relation A is the effective cross-sectional area of the model, the other variables are according to the previous definitions. These relations can be used to apply a linear correction to amongst others the flow velocity and the Reynolds number:

u = ut(1 + ǫsb+ ǫwb),

Re = Ret(1 + (1− 0.7M2t)(ǫsb+ ǫwb).

(2.11) The presented corrections are applied in numerical simulations. The steady balance measurements in the closed wind tunnel, see Chapter 3, are corrected by embedded correction models in the wind tunnel control systems, as presented in A. These cor-rection formulations differ from the corcor-rections presented here, but the underlying principles are similar. Furthermore, a quick check using both correction methods on steady balance measurements in the closed wind tunnel learned that the corrected results are very similar.

2.3.2 Steady corrections for open jet wind tunnels

The open jet wind tunnel corrections are taken from work presented by Brooks et al. [1984]. The wind tunnel corrections are valid for an aerofoil in a steady, open jet flow and given by the relations:

α = αt− √ 3σ π cl,t− 2σ πcl,t− σ π4cm,t, cl = cl,t, cd= cd,t+ −3σ_πcl,t cl,t, cm= cm,t−σ 2cl,t, (2.12)

where the tunnel blockage factor σ is a parameter based on the wind tunnel geometry: σ = π 2 48 c h 2 . (2.13)

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In the equations the subscript t again denotes the measured quantity in the wind tunnel, h is the wind tunnel height and c the wing chord. These corrections are used in the various numerical simulations of the aeroelastic experiment to take into account the wind tunnel influences.

2.4 Wind tunnel measurements and FSI

The wind tunnel corrections presented in the former section are an example of widely accepted and used correction methods by the community. Drawback is that the cor-rections are intrinsically valid for steady measurements. For unsteady measurements corrections are less straightforward and an assessment of each problem can be done to quantify the influence of the wind tunnel on the measured unsteady quantities. This influence will be a combination of level shifts, similar to steady flows, and time delays. In this work two different wind tunnels are used and for each of these tunnels an investigation is done on the wind tunnel corrections. This will be presented more in depth including results in Section 3.3 for a closed wind tunnel and in Sections 4.2.6 and 5.1.2 for an open jet wind tunnel.

For fluid-structure interaction wind tunnel experiments the influence of the wind tunnel is not only visible in the forces, but also in the structural responses. Depend-ing on the reduced frequency or unsteadiness level, mainly quantitative level shifts are expected or a combination of quantity level shifts and phase changes. In the numerical modelling this means that the wind tunnel influences must be modelled as well to capture the correct flow and structure states. Two possible options are: 1) full modelling of the setup including wind tunnel, or 2) a modelling of wind tunnel corrections on the forces used to compute the new structure state.

The second approach is based on a correction procedure that can be summarised as follows for a certain (subiteration within a) time step, starting with the structural state:

1. Update the structure state. Structural displacements and velocities are com-puted for aerodynamic loading in the open jet or closed wind tunnel.

2. Update the flow state in freestream conditions for the structural state (in the open jet or closed tunnel) computed in step 1.

3. Determine the free stream aerodynamic loads on the structure using the flow state computed in step 2.

4. Correct the calculated aerodynamic loads using wind tunnel corrections and pass these open jet or closed tunnel loads to the structural solver. Proceed to step 1.

The solution consists of the corrected aerodynamic loads and the structure state. In case the flow state is first treated instead of the structure state, the approach is similar with the difference one starts at point 2 and ends with 1 each time level or subiteration.

The drawback of this second correction approach is that there is an inconsistency in the calculation of the flow state for freestream conditions, since it uses displacements

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that are based on wind tunnel conditions. For displacements with a considerable in-fluence on the effective angle of attack (several degrees) and/or flow conditions outside the linear part of the lift curve, this used approach is likely to cause non-negligible errors. However, for the flow and structure states considered in this work this method can be used without any significant error due to this mentioned inconsistency.

2.5 Particle Image Velocimetry

Steady or unsteady loads on a submerged structure can be deduced from velocity fields. In this thesis the velocity fields originate from particle image velocimetry (PIV). In this section a short description is given about PIV and the recording of the PIV images.

2.5.1 Principles of PIV

Particle image velocimetry (PIV) is a measurement technique based on images of scattered light from tracer particles submerged in a fluid flow. The measurement technique is extensively described in literature, see e.g. Westerweel [1997], Raffel et al. [2007]. PIV is considered to be a non-intrusive measurement technique and can be applied to a 2-D plane or a 3-D area. For 2-D measurements a laser combined with optics is used to illuminate a thin planar area where the tracer particles pass through. With one or more cameras the tracer particle locations are recorded and the velocity field is reconstructed from two consecutive images by post-processing. The post-processing is based on cross-correlation for individual, small image regions called interrogation windows. The resolution of the resulting velocity field depends on this subdivision of the images in interrogation windows.

When two cameras are used to observe a specific 2-D area, the out-of-plane velocity component can also be reconstructed (stereoscopic PIV). For 3-D tomo-PIV laser with optics illuminate a 3-D area observed by multiple cameras. Following the work of Elsinga et al. [2006] from the recordings a 3-D flow field can be reconstructed using optical tomography. In this work planar PIV is applied in the experiments. Only a few stereoscopic PIV images are recorded for flow three-dimensionality checks.

The area which is captured with the camera(s) is called the field of view (FOV). In the ideal case the FOV covers the flow domain of interest, which means that one camera setup suffices. In case the FOV is smaller than the region of interest, cameras must observe different parts of the flow domain. This can be accomplished in one or multiple experimental runs.

In case the PIV images are recorded using multiple camera/laser setups also the experimental repeatability must be assured. For the various runs the flow properties (viz. undisturbed velocity, temperature, density, pressure) might differ slightly. Small variations in the undisturbed flow velocity for the various runs can be dealt with by making each velocity field non-dimensional using the corresponding undisturbed velo-city. After combining the various velocity fields into one velocity field for each phase angle, the resulting velocity field is dimensionalised using the average undisturbed velocity.

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2.5.2 Phase-locked PIV

For periodical flows PIV can be applied in a phase-locked approach. This is convenient when e.g. the frequency of the periodical flow pattern is too large to capture the full cycle with the desired temporal resolution with the PIV system or when the flow field cannot be captured with the available camera(s) at once. For phase-locked measurements a fixed reference signal is needed for timing and using user specified time delays with respect to this trigger signal the full cycle can be resolved with a desired temporal resolution. It is evident that phase-locked PIV is only allowed when the periodicity of the flow is guaranteed.

2.6 Methods to derive (un)steady forces

Steady and unsteady load determination from velocity fields can be accomplished using various methods. A basic method to determine the lift force is by application of Kutta-Joukowski’s theorem for inviscid, incompressible flows. Alternatively forces can be derived from an evaluation of the momentum equation, whereby the pressure can be derived from the velocity fields as discussed by amongst others Unal et al. [1997], Gurka et al. [1999], Liu and Katz [2006], van Oudheusden et al. [2006]. Noca et al. [1999] developed a method to determine forces which is also based on the momentum equation applied to a control volume, with the difference that the pressure is eliminated from the equations and only velocity derivatives need to be evaluated. For solely drag determination, a wake survey approach can be applied on the velocity fields, as laid down by Jones [1936]. In the following paragraphs the used methods in this thesis, Kutta-Joukowski’s theorem and Noca’s method, are addressed.

2.6.1 Kutta-Joukowski’s circulatory approach

For inviscid, incompressible (un)steady flow the lift of a thin aerofoil can be determ-ined using Kutta-Joukowski’s method, see Katz and Plotkin [2001]. The lift can be written as a combination of the instantaneous circulation bounding the aerofoil Γ(t) (first term, equivalent to the steady-state circulation) and a time dependent con-tribution dealing with pressure changes due to the acceleration of the fluid (second term): L(t) = ρu(t)Γ(t) + ρ I c 0 ∂ ∂tΓ(x, t)dx, (2.14)

where x is the chordwise distance and the circulation Γ is given by Γ(t) = Z Z S (∇ × ~u) · ˆndS = I C ~u· ~dl. (2.15)

According to Kelvin’s theorem a change in bound circulation leads to vortex shedding in the wake of equal, opposite strength. This implies that for steady flow the location of the contour C is not important, as long as it surrounds the aerofoil. For unsteady flow, vorticity is shed in the wake and the location of the contour C in the wake determines the extent of time history or delay in the captured circulation. Hereby

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the contour C must intersect the wake more or less perpendicular with respect to the direction of convection. The time delay equals the time it takes for particles to travel from the aerofoil’s trailing edge to contour C in the wake. An exact determination of the time delay from experimental data is not always straightforward.

Since all unsteady lift forces are expected to be periodic, it is chosen to not de-termine the phase and use Relation (2.14) for steady flow in this work by neglecting the second term. Only the lift variation and mean value are considered. The occurring time delay will not be regarded. Furthermore, the disregard of viscosity introduces a small offset with respect to determined forces including viscosity effects (e.g. balance measurements).

2.6.2 Noca’s momentum flux equation

Noca’s method allows for the determination of (un)steady loads acting on a submerged object from the velocity field and its derivatives in space and time. The formulation is a rewritten version of the Navier Stokes momentum equation and is valid for in-compressible flows (∇ · u = 0). A complete description can be found in the work of Noca et al. [1999]. The final relation in tensor form is given by Equation (2.16) and the corresponding contours and sign conventions can be found in Figure 2.2, where a sample domain of integration is given.

F ρ = I S(t) ˆ n_{· γ}fluxdS− I Sb(t) ˆ n_{· ((u − u}s)u) dS− d dt I Sb(t) ˆ n_{· (ux) dS.} (2.16) In Equation (2.16) all bold printed variables are tensors and _{N is the dimension of} the problem. In this research planar PIV is used and consequently_{N = 2. The term} γfluxis a short notation for

γflux= 1 2u 2_I − uu − 1 N − 1u(x∧ ω) + 1 N − 1ω(x∧ u) − 1 N − 1 x_·∂u ∂t I_{− x}∂u ∂t + (N − 1) ∂u ∂tx + 1 N − 1[x· (∇ · T)I − x(∇ · T)] + T. (2.17)

As can be seen in Equation (2.16) the force F is composed of a surface integral along a finite contour S(t) enclosing the object(s) of interest and two surface integrals along the circumference of the object(s), denoted by Sb(t). Steady and unsteady loads predicted with Noca’s method are for incompressible flows in theory indifferent to the location of the body enclosing contour. The strength of the relation is that only the velocity field u, its time derivatives ∂u

∂t and the spatial variable x are needed. Also the spatial derivatives of the velocity field must be known to compute the vorticity ω and the viscous stress tensor T, for which a Newtonian fluid assumption is used. Other variables present in Equations (2.16) and (2.17) are: the normal vector ˆn and the body wall velocity us in tensor form.

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