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Unsteady Aerodynamic Forces on NACA 0015 Airfoil in Harmonic Translatory Motion
Gaunaa, Mac
Publication date:
2002
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Citation (APA):
Gaunaa, M. (2002). Unsteady Aerodynamic Forces on NACA 0015 Airfoil in Harmonic Translatory Motion.
MEK-FM-PHD, No. 2002-02

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MEK-FM-2002-02
Unsteady Aerodynamic Forces on NACA
0015 Airfoil in Harmonic Translatory
Motion
by
Mac Gaunaa
Dissertation submitted to Technical University of Denmark in partial fulfillment of
the requirements for the degree of Doctor of Philosophy in Mechanical Engineering
Fluid Mechanics
Department of Mechanical Engineering
Technical University of Denmark
April, 2002
Fluid Mechanics
Department of Mechanical Engineering
Building 403
Technical University of Denmark
DK-2800 Lyngby, Denmark
Copyright (cid:1)c Mac Gaunaa, 2002
Printed in Denmark by DTU-Tryk, Lyngby
MEK-FM-2002-02 / ISBN 87-7475-258-8
This thesis has been typeset using LATEX2e.
Preface
This dissertation is submitted in partial fulfillment of the requirements for the Ph.D.
degree. The dissertation is based on the experimental, theoretical and numerical
work carried out during the period from August 1998 to December 2001 at the Fluid
Mechanics Section at the Department of Mechanical Engineering, Technical University
of Denmark. The work has been carried out under the guidance of Professor Poul
Scheel Larsen, to whom I would like to express my deepest gratitude for inspiring
supervision.
I also wish to thank Associate Professor Jens Nørkær Sørensen for valuable inputs,
and Andreas G Jensen, Danish Maritime Institute, for fruitful discussions on the art
of experimental work.
For fruitful discussions and insights Martin O.L. Hansen and Niels Sørensen are
thanked.
Finally, I would like to thank Mia for her love and patience with me during the course
of my study.
It is acknowledged that the experimental setup was financed by the Danish Technical
Research Council, through the Research Frame Program on Computational Hydrody-
namics.
Technical University of Denmark
Copenhagen, April 2002
Mac Gaunaa

Abstract
The unsteady two-dimensional aerodynamic forces acting on a NACA 0015 airfoil un-
dergoing harmonic translatory motions have been investigated experimentally and the-
oretically/numerically.
The focus of the experimental investigations was to determine the factors that
influence the aerodynamic damping of harmonic translatory motion. Specifically, mea-
surements of unsteady pressure distributions were undertaken at a range of incidences,
movement directions, amplitudes and reduced frequencies matching real life conditions
for the flap and lead-lag motion of wind turbine rotors.
From the experimental results it was seen that the maximum negative aerodynamic
damping take place at moderate stall at an incidence of about 15o, at a movement
direction close to the chordwise direction, and that the aerodynamic damping at 150
and 20o for the stalling cases decreases as the reduced frequency is decreased. The
dependance on the amplitude of the motion was weak.
Up to three distinctively different stall modes occurring in both steady and unsteady
experiments at incidences 15o ≤ α ≤ 20o was observed. Both the mean and dynamic
characteristics was found to differ from mode to mode.
As a part of the theoretical work an unsteady panel code was implemented. This
code was used to investigate the differences in the dynamic response of an airfoil un-
dergoing heaving motion and pitching motion.
Another application of the panel code was to compute the effect of the imposition of
wind tunnel walls on the dynamic response of the airfoil. From these results dynamic
tunnel corrections was derived.
Adifferentpartofthetheoreticalworkconcernedthedevelopmentofanewheuristic
stall model, which can be considered an ‘interpolation’ between quasi-stationary theory
and unsteady potential theory. Comparison with the experimental results shows very
goodagreementintheattachedcases, butthenewmodelfailstoreproducethefeatures
of the moderately and deeply stalled flows due to the assumption of similarity between
the dynamics in the attached and stalling cases.
Comparison of results obtained with a Navier-Stokes solver showed excellent agree-
ment with the experimental data for incidences up to 8o. Fully turbulent flow was
assumed in the Navier-Stokes simulations. The differences between the results for inci-
dences 12o and above were caused by too late predicted onset of stall in the simulations,
and that the Navier-Stokes solver predicted a strong effect from vortex shedding at in-
cidence 20o, which was not found in the experiments.
The overall features of the aerodynamic damping was captured correctly for incidences
up to 15o. The discrepancies at 20o was caused by the strong vortex dynamics in the
predictions.

Synopsis
De instationære to-dimensionelle aerodynamiske kræfter p˚a et NACA 0015 vingeprofil
som udfører harmoniske translatoriske bevægelser er blevet undersøgt eksperimentelt
og teoretiskt/numeriskt.
I de eksperimentelle undersøgelser har fokus været p˚a at bestemme de faktorer som
influerer p˚a den aerodynamiske dæmpning af harmoniske translatoriske bevægelser.
M˚alinger af instationære trykfordelinger er blevet udført for en række indfaldsvinkler,
bevægelsesretninger, amplituder og reducerede frekvenser for værdier som svarer til
typiskt forekommende for en vindmøllerotors flap- og kantvise svingninger.
Fradeeksperimentelleresultaters˚as,atdenmaksimale,negativeaerodynamiskedæmp-
ning forekommer ved moderat afløst strømning ved cirka 15o indfaldsvinkel, med en
bevægelsesretining tæt p˚a den kantvise retning, og at den aerodynamiske dæmpning
for de afløste strømninger ved indfaldsviklerne 15o og 20o aftager for aftagende reduc-
eret frekvens. Afhængigheden af amplituden af bevægelsen viste sig at være svag.
Der blev observeret op til tre forskellige afløsningsniveauer for b˚ade stationære og in-
stationære eksperimenter for indfaldsvinkler i omr˚adet 15o ≤ α ≤ 20o. B˚ade middel- og
dynamiske karakteristika for de aerodynamiske kræfter afviger fra tilsvarende størrelser
for de andre afløsningsniveauer.
Som en del af de teoretiske undersøgelser blev der implementeret en instationær
panel kode. Denne blev brugt til at undersøge forskellen i den dynamiske respons af et
vingeprofil under translatorisk og roterende bevægelse.
I en anden applikation af panel koden, blev den anvendt til at beregne effekten af
vindtunnel vægge p˚a det dynamiske respons af vingeprofilet. Disse resultater dannede
basis for udledningen af dynamiske vindtunnelkorrektioner.
Enandendelafdeteoretiskeundersøgelseromhandledeudviklingenafennyheuris-
tisk stall model. Den nye stall model kan opfattes som en ‘interpolation’ mellem kva-
sistationær teori og instationær potential teori. Sammenligning med eksperimentelle
resultater viste for de ikke-afløste strømninger en god overensstemmelse, hvorimod
modellen ikke kunne reproducere de dynamiske karakteristika for de moderate eller
massivt afløste strømninger p˚a grund af antagelsen om lighed mellem strømnings dy-
namikken i den afløste og den ikke-afløste strømning.
Sammenligninger af resultater beregnet med en Navier-Stokes kode viste meget
god overensstemmelse med de eksperimentelle data for indfaldsvinkler op til α = 8o.
Navier-Stokes beregningerne antog en fuldt turbulent strømning. Forskellen mellem
resultaterne for indfaldsvinkler fra 12o og derover skyldes at den beregnede strømning
afløser senere end den m˚alte, og at Navier-Stokes beregningerne viste en kraftig effekt
fra hvirvelafkastning ved indfaldsvinklen 20o, som ikke forekom i de eksperimentelle
resultater.
viii
De overordnede karakteristika for den aerodynamiske dæmpning blev beregnet kor-
rekt for indfaldsvinkler op til 15o. Uoverensstemmelserne ved 20o skyldes den kraftige
hvirveldynamik i de beregnede resultater.
Contents
1 Introduction 1
1.1 Objectives of the present work . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Outline of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Experiments 5
2.1 Previous studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Experimental targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Design considerations . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Test rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Data processing and analysis . . . . . . . . . . . . . . . . . . . . . . . . 12
2.6 Measurement accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6.1 Pressure measuring system . . . . . . . . . . . . . . . . . . . . . 16
2.6.2 Angle of attack . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6.3 Acceleration of pressure transducers . . . . . . . . . . . . . . . . 16
2.6.4 Wind tunnel corrections . . . . . . . . . . . . . . . . . . . . . . 17
2.6.5 Statistical Uncertainty . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 Multiple stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.8.1 Determination of distinct stall modes . . . . . . . . . . . . . . . 23
2.8.2 Stationary airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.8.3 1 DOF translatory oscillatory motion . . . . . . . . . . . . . . . 32
3 Theoretical Models 43
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Analytic Unsteady Potential Theory . . . . . . . . . . . . . . . . . . . 45
3.2.1 Normal Force and Moment . . . . . . . . . . . . . . . . . . . . . 46
3.2.2 Tangential Force . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.3 Lift and Drag Forces . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.4 Oscillatory Motion . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3 Quasi-steady Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 New Stall Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5 Panel Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5.1 Singularity Elements . . . . . . . . . . . . . . . . . . . . . . . . 68