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

Contents
Summary iii
Samenvatting v
Contents xii
1 Introduction 1
1.1 Motivation . 1
1.2 Literature review of present state . 2
1.3 Approach 7
1.4 Outline . 8
2 Terminology, wind tunnel models and methodologies 9
2.1 Terminology . 9
2.1.1 Characteristic (non-)dimensional numbers 9
2.1.2 Flap phase angle 10
2.1.3 Averaging methods . 10
2.1.4 Data reduction . 11
2.2 Wind tunnel model . 11
2.2.1 Model description . 11
2.2.2 Wing model derived with co-kriging . 12
2.3 Standard wind tunnel corrections for steady flow 13
2.3.1 Steady corrections closed wind tunnels 13
2.3.2 Steady corrections for open jet wind tunnels . 14
2.4 Wind tunnel measurements and FSI . 15
2.5 Particle Image Velocimetry 16
2.5.1 Principles of PIV 16
2.5.2 Phase-locked PIV 17
2.6 Methods to derive (un)steady forces . 17
2.6.1 Kutta-Joukowski’s circulatory approach . 17
2.6.2 Noca’s momentum flux equation . 18
2.6.3 Implementation of Noca’s method 20
ix2.7 Uncertainty analysis 24
3 Experimental benchmark I and numerical comparison: an aerofoil
with actuated flap 25
3.1 Problem definition . 26
3.1.1 Low turbulence tunnel . 26
3.1.2 The model and equipment . 27
3.1.3 Steady and unsteady test cases 28
3.1.4 PIV setup and apparatus . 29
3.2 Numerical model 31
3.2.1 2-D panel code . 32
3.3 Wind tunnel corrections 32
3.3.1 Wind tunnel wall corrections . 33
3.3.2 Gap correction . 37
3.4 Results 38
3.4.1 Force evaluation 38
3.4.2 Steady cases 38
3.4.3 Unsteady cases . 40
3.5 Conclusions . 45
4 Experimental benchmark II: a free plunging wing with imposed flap
oscillations 47
4.1 Problem definition . 48
4.1.1 Open jet wind tunnel . 48
4.1.2 Wind tunnel model . 49
4.1.3 Supporting structure 49
4.1.4 Structural characteristics . 50
4.1.5 Steady and unsteady test cases 52
4.2 Measurements and post-processing 54
4.2.1 Measurement devices 54
4.2.2 Force derivation 55
4.2.3 Measurement procedure and post-processing 57
4.2.4 Uncertainty analysis 58
4.2.5 PIV setup and apparatus . 59
4.2.6 Wind tunnel corrections 61
4.3 Results 61
4.3.1 Steady cases 61
4.3.2 Unsteady case: 2-D PIV 67
4.3.3 Unsteady cases . 70
4.4 Conclusions . 80
5 Comparative study of numerical models for a free plunging aerofoil
with imposed flap oscillations 83
5.1 Problem definition . 83
5.1.1 Test problem simplification 83
5.1.2 Wind tunnel corrections 84
5.2 Numerical methods . 88
x5.2.1 2-D Extended Theodorsens model 88
5.2.2 2-D panel code with structural model 89
5.2.3 2-D Unsteady Reynolds-averaged Navier Stokes solver with struc-
tural model . 90
5.2.4 Post-processing . 92
5.3 Results 92
5.3.1 Steady cases 93
5.3.2 Unsteady cases - description 98
5.3.3 Unsteady cases - subiterations 98
5.3.4 Unsteady cases - PIV test case 100
5.3.5 Unsteady cases - sensor test cases . 102
5.4 Conclusions . 112
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
List of publications 165
xiAcknowledgements 167
Curriculum Vitae 169

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