Computer analysis of wing design for general aviation aircraft

329 Pages·2017·6.1 MB·English

Loughborough University
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Computer analysis of wing
design for general aviation
aircraft
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by the/an author.
Additional Information:
• AMastersDissertation,submittedinpartialfulfilmentoftherequirements
of the award of Master of Science of Loughborough University.
Metadata Record: https://dspace.lboro.ac.uk/2134/16174
Publisher: (cid:13)c Michael Papadakis
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Please cite the published version.
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COMPUTER ANALYSIS OF WING DESIGN
FOR GENERAL AVIATION AIRCRAFT
BY
MICHAEL PAPADAKIS
A Thesis
submitted in partial fulfilment of
the requirements for the award of
the degree of Master of Science
of the Loughborough University of Technology
January, 1981.
Supervisors: F.G. MACCABEE, .. Eng.,A.F.R.Ae.S.
M,~Sc.,D.C.Ae :.J~'
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Department of Transport Technology
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K.S. PEAT,'B.Sc.,Ph.D.
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Department of.Engineering Mathematics --"
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SUMMARY
The calculation of the two dimensional viscous incompressible flow about
single and multielement aerofoil sections is considered.
A panel method, based on vorticity and source distributions is used for
the calculation of the potential flow. Once the velocity distribution is
known, integral boundary layer methods are employed to predict the viscous
effects. A wake model has also been developed for the calculation of the wake
behind the aerofoil system.
The solution is iterative. At the end of each iteration the velocities
on the aerofoil are corrected for viscosity and wake effects; the wake position
is also relaxed, before the next iteration starts.
The mathematical model of the flow, together with the computer program
written to test the model are described here in detail. The numerical results
obtained using the computer program are found to be in good agreement with
both experimental data and exact solutions.
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,
,
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ACKNOWLEDGE~1ENTS
The author wishes to acknowledge the co-operation and
assistance he has received from many quarters; in particular
he is indebted to his supervisors, Dr. Peat and Mr. Maccabee
for their help and advice during the course of this research.
The author also wishes to thank Mr. Tony Cross and
Mr. David Butter, of British Aerospace, for their technical
advice and Dr. Shanehchi who helped with the computer program.
Finally for the work of typing thanks are due to
Miss Judy Briers •
..
2
CONTENTS
PAGE
SUMMARY 1
2
ACKNOWLEDGEMENTS
3
CONTENTS
8
LIST OF FIGURES
11
LIST OF SYMBOLS
INTRODUCTION 15
Section 1: MODELLING OF THE AIR FLOW - A GENERAL DISCUSSION
1.1 Introduction 19
1.2 Models to Describe the Air and Some of its Properties 19
1.3 Potential Flow 23.
1.4 Methods for Solving for the Flow Around an Aerofoil 26
1.4.1 Conformal Mapping 26
26
1.4.2 Singularities
Section 2: THE HISTORY AND DEVELOPMENT OF TWO-DIMENSIONAL POTENTIAL
FLOW METHODS
2.1 Introduction 28
2.2 The Problem of Calculating Wing Lift 28
2.3 The Early Stages 29
2.4 Development of the First Methods 30
33
2.5 Modern Methods
2.6 Concluding Remarks 38
Section 3: SURFACE SINGULARITY MODEL FOR THE CALCULATION OF THE
POTENTIAL FLOW ABOUT THICK AEROFOIL SECTIONS
41
3.1 Introduction
3.2 Linear Vorticity Panel Method 42
3.2.1 Model Description 42
42
3.2.2 Equations
3.3 Symmetrical Linear Vortex and Constant Source
Surface Singularity Model
3.3.1 Basic Considerations 43
45
3.3.2 Theoretical Basis
3.3.3 Numerical Solution Procedure 46
3.3.4 Velocity Equations 46
..
3
PAGE
Section 4: VISCOUS FLOW - A GENERAL DISCUSSION
4.1 Introduction 50
4.2 Genesis of the Boundary Layer Concept 50
4.3 Viscous Flow Model 52
4.4 Viscous Flow Representation 54
4.5 Aerofoil Surface Velocity Equations 56
Section 5: LAMINAR BOUNDARY LAYER
5.1 Introduction 59
5.2 Thwaites Method 59
5.3 CurIe's Method 61
5.3.1 Equations 62
5.3.2 Calculation Procedure 62
5.3.3 Laminar Separation 63
Section 6: BOUNDARY LAYER TRANSITION
6.1 Introduction 67
6.2 Crab tree Criterion 67
6.3 Michel's Method 68
6.4 Granville's Method 68
6.4.1 Instability Prediction 69
6.4.2 Transition Prediction 69
Section 7: SHORT BUBBLE ANALYSIS
7.1 Introduction 72
7.2 Short Bubble Model of Shear Layer 73
7.2.1 Laminar Part of Shear Layer 74
7.2.2 Turbulent Part of Shear Layer 75
7.2.3 Bubble Length ~t Bursting 76
7.3 Method of Solution 77
Section 8: TURBULENT BOUNDARY LAYER
8.1 Introduction 80
8.2 Head's Entrainment Method 80
81
8.2.1 Equations
8.2.2 Method of Calculation 81
8.3 The Method of Head and Patel 82
83
8.3.1 Equations
83
8.3.2 Method of Calculation
84
8.4 Initial Values
8.5 Turbulen.t Boundary Layer Separation
8.5.1 Head's Criterion 85
8.5.2 Epplers Method 85
86
8.6 toncluding Remarks
4
PAGE
Section 9: WAKE ANALYSIS
9'.1 Introduction 92
9.2 Potential Flow Wake Model 92
9.3 Wake Singularity Sheet 93
9.4 Velocity Equations 94
9.5 Wake Viscous Flow Analysis 95
9.5.1 Equations 95
9.5.2 Initial Conditions ' 97
9.5.3 Calculation Procedure 97
9.6 Calculation of Wake Singularities 97
9.7 Wake Relaxation 98
9.8 End of Potential Core 100
9.9 Aerofoil Velocities 101
Section 10: CONFLUENT BOUNDARY LAYER
10.1 Introduction 107
10.2 General Considerations 107
10.2.1 Main Assumptions 108
10.3 Model Description 108
10.4 Equations for the Calculation of Main Region 1 and 2 110
10.4.1 Coles Velocity Profile 110
10.4.2 Main Region 1 111
10.4.3 Main Region 2 115
10.5 Initial Conditions 117
10.5.1 Main Region 1 is Preceded by a Core Region 117
10.5.2 Main Region 2 Not Preceded by Core 118
10.5.3 Main Region 2 119
10.6 Calculation Procedure 119
10.7 Boundary Layer Parameters
~' Conf1ue~t
10.7.1 Thickness 0 119
4
10.7.2 Displacement: Thickness 0 * 120
10.7.3 Momentum Thickness e 120
10.7.4 Skin Friction 120
10.7.5 Separation 121
10.8 Further Comments 121
Section 11: SEPARATED FLOW MODEL
11.1 Introduction 125
11.2 Flow Separation 125
11.3 Separation Flow Model, 127
11.3.1 Basic Considerations and Assumptions , 127
11.3.2 Approximations for the Free Shear Layer 129
11.3.3 . Theoretical Basis 130
11.3.4 Method of Solution 130
11.4 .. Concluding Remarks 132
5