Influence of a cavity on the dynamical behaviour of an airfoil

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Influence of a cavity on the dynamical behaviour of an airfoil
Citation for published version (APA):
Olsman, W. F. J. (2010). Influence of a cavity on the dynamical behaviour of an airfoil. [Phd Thesis 1 (Research
TU/e / Graduation TU/e), Applied Physics and Science Education]. Technische Universiteit Eindhoven.
https://doi.org/10.6100/IR673149
DOI:
10.6100/IR673149
Document status and date:
Published: 01/01/2010
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influence of a cavity on the dynamical
behaviour of an airfoil
Copyright ' 2010 W.F.J. Olsman
Cover design by W.F.J. Olsman
Printed by Universiteitsdrukkerij TU Eindhoven, Eindhoven,
The Netherlands
A catalogue record is available from the Eindhoven University of
Technology Library
Olsman, W.F.J.
Influence of a cavity on the dynamical behaviour of an airfoil / by Willem
FrederikJurri¨enOlsman.–Eindhoven:TechnischeUniversiteitEindhoven,
2010. – Proefschrift.
ISBN: 978-90-386-2230-9
NUR: 968
Trefwoorden:caviteit/trappedvortex/dynamischgedragvleugel/vleugel
Subject headings: cavity / trapped vortex / dynamical behaviour wing /
wing
influence of a cavity on the dynamical
behaviour of an airfoil
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
rector magnificus, prof.dr.ir. C.J. van Duijn, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen
op dinsdag 25 mei 2010 om 16.00 uur
door
Willem Frederik Jurri¨en Olsman
geboren te Hilversum
Dit proefschrift is goedgekeurd door de promotoren:
prof.dr.ir. G.J.F. van Heijst
en
prof.dr.ir. A. Hirschberg
Copromotor:
dr.ir. R.R. Trieling
Part of this research has been supported by the
European project VortexCell2050 within the Sixth
Framework, under contract number AST4-CT-2005-
012139.
Contents
Contents vii
1 Introduction 1
2 Theoretical considerations 7
2.1 Oscillating object versus oscillating flow . . . . . . . . . . . 7
2.2 Linearised thin airfoil theory . . . . . . . . . . . . . . . . . 8
2.3 Effect of finite airfoil thickness . . . . . . . . . . . . . . . . 17
2.4 Apparent mass . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Wall interference effects . . . . . . . . . . . . . . . . . . . . 22
2.6 Numerical methods . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.1 Discrete vortex method . . . . . . . . . . . . . . . . 23
2.6.2 Solutions of Euler equations . . . . . . . . . . . . . . 25
2.6.3 Navier–Stokes solutions . . . . . . . . . . . . . . . . 28
3 Experimental method 33
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Experimental method . . . . . . . . . . . . . . . . . . . . . 35
3.3 Acoustics without main flow . . . . . . . . . . . . . . . . . . 39
3.3.1 Infinite duct . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.2 Acoustical validation setup . . . . . . . . . . . . . . 40
3.3.3 Finite duct . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.4 Test section with wing installed . . . . . . . . . . . . 45
3.3.5 Test section in wind tunnel without wing . . . . . . 47
3.3.6 Test section in wind tunnel with wing installed . . . 49
3.3.7 Determination of the transversal velocity . . . . . . 50
3.4 Numerical method for flow field . . . . . . . . . . . . . . . . 51
3.5 Measurements on a NACA0018 airfoil . . . . . . . . . . . . 52
vii
3.5.1 Steady flow . . . . . . . . . . . . . . . . . . . . . . . 52
3.5.2 Unsteady flow. . . . . . . . . . . . . . . . . . . . . . 53
3.5.3 Estimation of plunging velocity . . . . . . . . . . . . 55
3.5.4 Relation to plunging motion . . . . . . . . . . . . . . 56
3.5.5 Dependency of ∆C on excitation amplitude . . . . 57
pu
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4 Numerical simulation of flow without forcing 61
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Numerical method based on Euler equations . . . . . . . . . 63
4.3 Numerical method based on Navier–Stokes . . . . . . . . . 68
4.4 Experimental facility . . . . . . . . . . . . . . . . . . . . . . 71
4.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.1 NACA0018 . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.2 NACA0018 with cavity . . . . . . . . . . . . . . . . 77
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 Flow visualisation and three-dimensional flow effects 87
5.1 Water channel setup . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Cavity modes . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Three-dimensional flow effects . . . . . . . . . . . . . . . . . 93
5.3.1 Two closed end plates . . . . . . . . . . . . . . . . . 93
5.3.2 One end plate removed . . . . . . . . . . . . . . . . 95
5.3.3 External forcing . . . . . . . . . . . . . . . . . . . . 97
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6 Airfoils with cavities and applied forcing 101
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Numerical results of Navier–Stokes method . . . . . . . . . 103
6.2.1 Clean airfoil . . . . . . . . . . . . . . . . . . . . . . . 104
6.2.2 Airfoil with cavity A . . . . . . . . . . . . . . . . . . 107
6.2.3 Airfoil with cavity B . . . . . . . . . . . . . . . . . . 107
6.3 Wind tunnel experiments . . . . . . . . . . . . . . . . . . . 109
6.3.1 Steady flow . . . . . . . . . . . . . . . . . . . . . . . 109
6.3.2 Hot-wire anemometry . . . . . . . . . . . . . . . . . 112
6.3.3 Unsteady flow. . . . . . . . . . . . . . . . . . . . . . 122
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7 Conclusions 127
viii
A Geometry of NACA0018 airfoils 131
B Added mass of a flat plate 134
C K´arm´an–Trefftz airfoil 138
C.1 Quasi-steady solution . . . . . . . . . . . . . . . . . . . . . 139
C.2 Added mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
D Pressure difference without Kutta condition 141
E Lock-in method 143
F Hot-wire measurements for cavity B 145
Bibliography 153
Summary 159
Samenvatting 161
Dankwoord 163
Curriculum Vitae 165
ix