NUMERICAL SIMULATION OF THE UNSTEADY AERODYNAMICS OF FLAPPING AIRFOILS John ...

360 Pages·2012·5.34 MB·English

School of Aerospace, Civil and Mechanical Engineering
The University of New South Wales
Australian Defence Force Academy

NUMERICAL SIMULATION OF THE UNSTEADY
AERODYNAMICS OF FLAPPING AIRFOILS

John Young

A thesis submitted for the degree of
Doctor of Philosophy

May 2005
Statement of Originality

I hereby declare that this submission is my own work and to the best of my
knowledge it contains no materials previously published or written by another
person, or substantial proportions of material which have been accepted for the
award of any other degree or diploma at UNSW or any other educational
institution, except where due acknowledgement is made in the thesis. Any
contribution made to the research by others, with whom I have worked at
UNSW or elsewhere, is explicitly acknowledged in the thesis.
I also declare that the intellectual content of this thesis is the product of my own
work, except to the extent that assistance from others in the project's design
and conception or in style, presentation and linguistic expression is
acknowledged.

John Young
May 2005
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Abstract

There is currently a great deal of interest within the aviation community in the
design of small, slow-flying but manoeuvrable uninhabited vehicles for
reconnaissance, surveillance, and search and rescue operations in urban
environments. Inspired by observation of birds, insects, fish and cetaceans,
flapping wings are being actively studied in the hope that they may provide
greater propulsive efficiencies than propellers and rotors at low Reynolds
numbers for such Micro-Air Vehicles (MAVs).
Researchers have posited the Strouhal number (combining flapping frequency,
amplitude and forward speed) as the parameter controlling flapping wing
aerodynamics in cruising flight, although there is conflicting evidence. This
thesis explores the effect of flapping frequency and amplitude on forces and
wake structures, as well as physical mechanisms leading to optimum propulsive
efficiency. Two-dimensional rigid airfoils are considered at Reynolds number
2,000 – 40,000. A compressible Navier-Stokes simulation is combined with
numerical and analytical potential flow techniques to isolate and evaluate the
effect of viscosity, leading and trailing edge vortex separation, and wake vortex
dynamics.
The wake structures of a plunging airfoil are shown to be sensitive to the
flapping frequency independent of the Strouhal number. For a given frequency,
the wake of the airfoil exhibits ‘vortex lock-in’ as the amplitude of motion is
increased, in a manner analogous to an oscillating circular cylinder. This is
caused by interaction between the flapping frequency and the ‘bluff-body’ vortex
shedding frequency apparent even for streamlined airfoils at low Reynolds
number.
The thrust and propulsive efficiency of a plunging airfoil are also shown to be
sensitive to the flapping frequency independent of Strouhal number. This
dependence is the result of vortex shedding from the leading edge, and an
interaction between the flapping frequency and the time for vortex formation,
separation and convection over the airfoil surface.
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The observed propulsive efficiency peak for a pitching and plunging airfoil is
shown to be the result of leading edge vortex shedding at low flapping
frequencies (low Strouhal numbers), and high power requirements at large
flapping amplitudes (high Strouhal numbers). The efficiency peak is governed
by flapping frequency and amplitude separately, rather than the Strouhal
number directly.
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Acknowledgements

I wish to express my sincere gratitude to a number of people who have
supported me in a variety of ways throughout the course of this thesis.
Firstly, thankyou to my supervisor Professor Joseph Lai for his gentle
encouragement, wisdom and endless patience. Thanks also to Associate
Professor Sudhir Gai and Dr John Milthorpe, for their numerous discussions of
the finer points of unsteady potential flow.
I would like to thank Professor Ismail Tuncer of the Middle East Technical
University for his provision of the Navier-Stokes code adapted within this thesis.
I would also like to acknowledge the National Facility of the Australian
Partnership for Advanced Computing (APAC) at the Australian National
University for the award of computer time under the Merit Allocation Scheme.
Thanks to my family who have always encouraged and supported me in
whatever I chose to do.
Finally to my wife Judith, without whom I could not have finished this work, you
already know how I feel.
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Table of Contents

Statement of Originality ....................................................................................i
Abstract.............................................................................................................ii
Acknowledgements.........................................................................................iv
Table of Contents..............................................................................................v
List of Figures...................................................................................................x
List of Tables.................................................................................................xxv
Nomenclature.............................................................................................xxviii
Chapter 1 Introduction .....................................................................................1
1.1 General Introduction.............................................................................1
1.2 Geometry and Kinematics of Airfoil Motion...........................................5
1.3 Objectives.............................................................................................7
1.4 Outline of the Thesis.............................................................................7
Chapter 2 Literature Review.............................................................................9
2.1 Aerodynamics of Thrust Production and Wake Evolution.....................9
2.1.1 Vortex Wake Signatures of Thrust and Drag.................................9
2.1.2 Trailing Edge Separation and the Unsteady Kutta Condition.......13
2.1.3 Leading Edge Suction, Separation and Vortex Shedding............15
2.2 Strouhal Number as the Fundamental Aerodynamic Parameter? ......16
2.2.1 Frequency Selection in Nature....................................................16
2.2.2 Experimental, Analytical and Computational Studies..................17
2.3 Analysis and Computation Methods...................................................22
2.3.1 Two-Dimensional Flat-Plate Small-Amplitude Potential Flow
Analyses....................................................................................................22
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2.3.2 Three-Dimensional Linearised Potential Flow Analyses..............24
2.3.3 Two- and Three-Dimensional Panel Methods .............................24
2.3.4 Navier-Stokes Methods...............................................................25
2.4 Parameter Selection in this Thesis.....................................................26
Chapter 3 Linearised Flat-Plate Potential-Flow Analysis............................28
3.1 Introduction.........................................................................................28
3.2 Airfoil Motion.......................................................................................29
3.3 Parametric Expressions for Airfoil Forces and Wake Strength...........30
3.3.1 Lift................................................................................................30
3.3.2 Moment .......................................................................................32
3.3.3 Thrust..........................................................................................35
3.3.4 Power..........................................................................................39
3.3.5 Propulsive Efficiency ...................................................................41
3.3.6 Wake Vorticity..............................................................................42
3.4 Region of Validity of the Garrick Analysis...........................................45
3.4.1 Wake Integration Assumptions....................................................45
3.4.2 Lift and Thrust Formulation Assumptions....................................45
3.4.3 Summary.....................................................................................46
Chapter 4 Code Development and Validation...............................................47
4.1 Unsteady Panel Method (UPM) Code Development ..........................47
4.1.1 Basic Code Development............................................................47
4.1.2 Wake Evolution Models...............................................................53
4.1.3 Vortex Wake Evolution (VWE) Code...........................................54
4.2 UPM Code Validation.........................................................................54
4.2.1 Force Comparison.......................................................................54
4.2.2 Wake Shape Comparison............................................................56
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4.2.3 Panel and Time Step Refinement Study......................................58
4.3 Navier-Stokes (NS) Code Development.............................................63
4.3.1 Basic Code Algorithm and Modifications.....................................63
4.3.2 Additional Modifications...............................................................66
4.4 NS Code Grid Generation...................................................................67
4.4.1 Introduction..................................................................................67
4.4.2 Hyperbolic Grid Generation.........................................................67
4.5 NS Code Validation............................................................................76
4.5.1 General Issues............................................................................76
4.5.2 Quantitative Validation – Force Measurement.............................87
4.5.3 Grid Refinement..........................................................................91
4.5.4 Quantitative Validation – Frequency Measurement.....................91
4.5.5 Qualitative Validation – Wake Structures ....................................93
4.6 Summary............................................................................................96
Chapter 5 Plunging Airfoil Wake Structures.................................................97
5.1 Introduction.........................................................................................97
5.2 Karman and Reverse Karman Vortex Streets.....................................98
5.3 Dependence of Wake Structure on Plunging Parameters................104
5.3.1 Predictions based on Linearised Analysis.................................104
5.3.2 Predictions of the UPM Code....................................................113
5.3.3 Experimental Observation of Wake Structures..........................121
5.3.4 Navier-Stokes (NS) Solver Wake Structures.............................128
5.4 Multiple Vortex Pair Shedding Modes and Vortex Lock-In................140
5.5 Effect of Turbulence Modelling and Numerical Viscosity in the NS
Calculations.................................................................................................151
5.6 Summary..........................................................................................153
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Chapter 6 Plunging Airfoil Aerodynamic Forces.......................................155
6.1 Introduction.......................................................................................155
6.2 Effect of Wake Roll-up on Aerodynamic Forces...............................156
6.3 Estimation of Thrust from Wake Velocity Profiles.............................166
6.4 Dependence of Aerodynamic Forces on Plunging Parameters........169
6.4.1 Effect of Free-Stream Mach Number on NS Results.................178
6.5 Leading Edge Shedding and Frequency Dependence.....................185
6.6 Summary..........................................................................................200
Chapter 7 Strouhal Number Characterisation of Combined Pitching and
Plunging Motion............................................................................................203
7.1 Introduction.......................................................................................203
7.2 Navier-Stokes Comparison with Experimental Motion Cases...........204
7.2.1 Summary of Case 1 to Case 4 Results......................................219
7.3 Analysis of the Computational Results.............................................221
7.3.1 Effect of Angle of Attack and Wake Dynamics ..........................221
7.3.2 Effect of Viscous Forces............................................................229
7.3.3 Effect of Leading and Trailing Edge Separation........................233
7.3.4 Origin of the Efficiency Peak .....................................................252
7.3.5 Summary of Numerical vs Experimental Comparison...............277
7.4 Strouhal Number as the Governing Parameter?...............................278
7.5 Phase Angle Optimisation................................................................282
7.6 Summary..........................................................................................286
Chapter 8 Conclusions and Recommendations.........................................289
8.1 Conclusions......................................................................................289
8.2 Recommendations for Future Work..................................................293
References.....................................................................................................295
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Publications from This Research.................................................................306
Journal Articles........................................................................................306
Refereed Conference Papers..................................................................306
Conference Papers..................................................................................306
Appendix A Unsteady Panel Method (UPM) Code User Instructions.......307
Source Files................................................................................................307
Compilation.................................................................................................307
Execution.....................................................................................................307
Control File..................................................................................................307
Output Files.................................................................................................310
Data Processing..........................................................................................311
Execution Times..........................................................................................311
Appendix B Navier-Stokes (NS) Code User Instructions ..........................312
Source Files................................................................................................312
Compilation.................................................................................................312
Execution.....................................................................................................312
Control File..................................................................................................312
Input Files....................................................................................................316
Output Files.................................................................................................316
Example Run Procedure.............................................................................318
Data Processing..........................................................................................318
Execution Times..........................................................................................319
Parallelisation..............................................................................................319
Appendix C UPM Code Refinement Study..................................................320
Appendix D Combined Pitching and Plunging NS Simulations................327

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