Numerical simulation of dynamic stall for heaving airfoils using adaptive mesh techniques [Elektronische Ressource] / Wided Medjroubi. Betreuer: Joachim Peinke

Numerical simulation of dynamic stall for heaving airfoils using adaptive mesh techniques [Elektronische Ressource] / Wided Medjroubi. Betreuer: Joachim Peinke

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Numerical Simulation of Dynamic Stall for HeavingAirfoils Using Adaptive Mesh TechniquesWided MedjroubiVon der Fakultat fur Physikder Carl von Ossietzky Universitat Oldenburgzur Erlangung des Grades und Titels einesDoktors der NaturwissenschaftenDr. rer. nat.angenommene Dissertationvon Frau Wided Medjroubigeboren am 11.10.1979 in Constantine, AlgerienGutachter: Prof. Dr. Joachim PeinkeZweitgutachter: Prof. Dr. Alexander RauhTag der Disputation: 01 Juli 2011iiiWhat makes me myself rather than anyone else is the very fact that I am poisedbetween two countries, two or three languages, and several cultural traditions. It isprecisely this that defines my identity. Would I exist more authentically if I cut off apart of myself - Amin MaaloufivInhaltsverzeichnisList of Tables xvAbstract xvi1 Introduction 11.1 Turbulence and unsteadiness . . . . . . . . . . . . . . . . . . . . . 11.2 Unsteady ows over airfoils . . . . . . . . . . . . . . . . . . . . . 51.3 Dynamic Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.1 Aerodynamics of Stall . . . . . . . . . . . . . . . . . . . . 61.3.2 Literature Review on Dynamic Stall. . . . . . . . . . . . . 71.4 Heaving Airfoils Wakes . . . . . . . . . . . . . . . . . . . . . . . . 111.4.1 Aerodynamics of Heaving Airfoils . . . . . . . . . . . . . . 121.4.2 Literature Review on Heaving Airfoils. . . . . . . . . . . . 141.4.3 Thrust Generation by Heaving . . . . . . . . . . . 211.

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Numerical Simulation of Dynamic Stall for Heaving
Airfoils Using Adaptive Mesh Techniques
Wided Medjroubi
Von der Fakultat fur Physik
der Carl von Ossietzky Universitat Oldenburg
zur Erlangung des Grades und Titels eines
Doktors der Naturwissenschaften
Dr. rer. nat.
angenommene Dissertation
von Frau Wided Medjroubi
geboren am 11.10.1979 in Constantine, AlgerienGutachter: Prof. Dr. Joachim Peinke
Zweitgutachter: Prof. Dr. Alexander Rauh
Tag der Disputation: 01 Juli 2011iii
What makes me myself rather than anyone else is the very fact that I am poised
between two countries, two or three languages, and several cultural traditions. It is
precisely this that defines my identity. Would I exist more authentically if I cut off a
part of myself - Amin MaaloufivInhaltsverzeichnis
List of Tables xv
Abstract xvi
1 Introduction 1
1.1 Turbulence and unsteadiness . . . . . . . . . . . . . . . . . . . . . 1
1.2 Unsteady ows over airfoils . . . . . . . . . . . . . . . . . . . . . 5
1.3 Dynamic Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Aerodynamics of Stall . . . . . . . . . . . . . . . . . . . . 6
1.3.2 Literature Review on Dynamic Stall. . . . . . . . . . . . . 7
1.4 Heaving Airfoils Wakes . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.1 Aerodynamics of Heaving Airfoils . . . . . . . . . . . . . . 12
1.4.2 Literature Review on Heaving Airfoils. . . . . . . . . . . . 14
1.4.3 Thrust Generation by Heaving . . . . . . . . . . . 21
1.5 Frequency regimes in forced airfoil wakes . . . . . . . . . . . . . . 21
1.6 Direct Numerical Simulations (DNS) - High Order Simulations . . 23
1.7 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.8 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Spectral /hp Finite Element Method 34
2.1 Introduction to Computational Fluid Dynamics (CFD) . . . . . . 35
2.2 Intro to Spectral /hp Element Methods . . . . . . . . . . . 39
2.3 Framework of the weighted residuals and the Galerkin formulations 40
2.4 Spectral /hp Element Discretization in two Dimensions . . . . . . 42
2.5 Spectral/hpt in three dimensions . . . . . . 54
2.6 Time Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.7 Airfoil motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3 Validation 63
3.1 Flow over a motionless cylinder . . . . . . . . . . . . . . . . . . . 64
3.2 Flow over a airfoil . . . . . . . . . . . . . . . . . . . . 70
3.2.1 = 0 and Re = 500 . . . . . . . . . . . . . . . . . . . . . 70
3.2.2 = 10 and Re = 500 . . . . . . . . . . . . . . . . . . . . 70vi INHALTSVERZEICHNIS
3.2.3 = 20 and Re = 800 . . . . . . . . . . . . . . . . . . . . 76
3.3 Flow over a heaving airfoil . . . . . . . . . . . . . . . . . . . . . . 76
3.3.1 Wake validation . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3.2 Forces v . . . . . . . . . . . . . . . . . . . . . . . 82
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 High-orderNumericalSimulationsOfTheFlowAroundAHeav-
ing Airfoil 90
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.2 The numerical method . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3 Simulations for a motionless airfoil . . . . . . . . . . . . . . . . . 103
4.3.1 Fixed airfoil at = 12 . . . . . . . . . . . . . . . . . . . 103
4.3.2 Fixed at = 20 . . . . . . . . . . . . . . . . . . . . 107
4.4 Simulations for a heaving airfoil . . . . . . . . . . . . . . . . . . . 109
4.4.1 Heaving airfoil at = 12 . . . . . . . . . . . . . . . . . . 109
4.4.2 Heaving at = 20 . . . . . . . . . . . . . . . . . . 116
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5 PlungingAirfoilWakesclassificationUsingSpectral/hpElement
Method 125
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.2 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.1 Constant amplitude transition . . . . . . . . . . . . . . . . 128
5.3.2t frequency . . . . . . . . . . . . . . . . 131
5.3.3 Wake structures classication . . . . . . . . . . . . . . . . 132
5.3.4 The multiple-vortices-per-half cycle mode . . . . . . . . . . 137
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6 Frequency Selection in Plunging Airfoil Wakes Using a High-
Order Method 143
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.2 The Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . 147
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.3.1 Unforced airfoil wakes . . . . . . . . . . . . . . . . . . . . 154
6.3.2 Forced airfoil wakes . . . . . . . . . . . . . . . . . . . . . . 155
6.3.3 Frequency regimes classications - a frequency pattern . . 163
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7 Conclusions and Outlook 174
7.1 Synopsis of motivation and results . . . . . . . . . . . . . . . . . . 174
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177INHALTSVERZEICHNIS vii
Danksagung 179
Lebenslauf 180
Erkl¨arung 182
Publikationsliste 183