NUMERICAL SIMULATION OF THE FLOW OVER FLAPPING AIRFOILS IN PROPULSION AND

217 Pages·2013·4.13 MB·English

School of Engineering and Information Technology
The University of New South Wales
Australian Defence Force Academy

NUMERICAL SIMULATION OF THE FLOW OVER
FLAPPING AIRFOILS IN PROPULSION AND
POWER EXTRACTION REGIMES

Muhammad Arif Ashraf

A thesis submitted for the degree of
Doctor of Philosophy

August 2010

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.

Muhammad Arif Ashraf
August 2010
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Abstract

Inspired by the natural flying and swimming creatures, the application of
flapping wings has attracted a great deal of attention from the scientific
community in recent years. On one hand, flapping wings are expected to
replace conventional rotor systems to build Micro and Nano Aerial Vehicles
(MAVs and NAVs) operating at low Reynolds number while on the other hand
they are also being investigated for the role of power generation in conjunction
with conventional rotary wind turbines.
For the development of MAVs/NAVs and understanding of unsteady
aerodynamics, the current thesis fills the gaps in the current state of the flapping
wing aerodynamics research. Firstly, at Reynolds number Re = 20000, the
effect of large amplitude motions on the plunging airfoil propulsion is
investigated with both two-dimensional (2D) and three-dimensional (3D) Navier-
Stokes (NS) simulations. For a given plunging frequency, it is shown that
increasing the amplitude of plunging airfoil motion causes the flow to be chaotic.
From 3D simulations, it is shown that the chaotic force generation is not an
artefact of 2D assumption.
Secondly, the effect of airfoil shape (thickness and camber) variation on thrust
and efficiency of a flapping airfoil at Reynolds number 200, 2000, 20000 and
2 × 106 is assessed with 2D NS and Unsteady Panel Method (UPM)
simulations. It is found that for different Reynolds numbers, there exists an
optimum thickness of symmetric airfoil section for maximum thrust and
propulsive efficiency. The role of leading edge vortices is shown to be key to the
observed performance variation. It is also shown that varying camber does not
provide any benefit in terms of thrust or propulsive efficiency.
Flapping airfoils can also be exploited to function as power generators, NS
simulations are performed to study different configurations of flapping airfoils as
power generators which include single and two foils in tandem arrangement
with prescribed sinusoidal and non-sinusoidal flapping motions at Re = 20000.
Also, a numerical strategy is developed to model a fully flow-driven flapping foil
power generator by utilising the aero-elastic response to the lift and moment
acting on it. It is found that non-sinusoidal motion produces around 20% more
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power than the sinusoidal counterpart and the fully flow-driven simulation
results show the practicality of flapping wing power generators.

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Acknowledgements

I would like to express my sincere gratitude to all the people who have
supported me throughout the course of this thesis work.
I am deeply thankful to my supervisors Dr. John Young and Professor Joseph
Lai for their constant support, guidance, wisdom and endless patience. Thanks
also to Dr. Tapabrata Ray for useful discussions regarding this research.
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 all the friends and staff at SEIT.
Thanks to my family who have always encouraged and supported me through
out my academic journey specifically to my parents who have put aside their
comforts for the sake of my better education.
Finally to my wife Amna Suri, without her support I would not be able to finish
my thesis.
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Table of Contents
Statement of Originality....................................................................................i
Acknowledgements.........................................................................................iv
Table of Contents .............................................................................................v
List of Figures................................................................................................viii
List of Tables.................................................................................................xvii
Nomenclature.................................................................................................xix
Chapter 1 Introduction.....................................................................................1
1.1 General Introduction.............................................................................1
1.1.1 Flapping Wings in Propulsion........................................................1
1.1.2 Flapping Wings in Power Extraction..............................................3
1.2 Objectives.............................................................................................6
1.3 Thesis Outline.......................................................................................8
Chapter 2 Literature Review ..........................................................................10
2.1 Introduction.........................................................................................10
2.1.1 Equations and Parameters of Flapping Wing Dynamics .............10
2.2 Aerodynamics of Thrust Production and Power Extraction using
Flapping Foils................................................................................................14
2.2.1 Wake Vortex Signature ...............................................................14
2.2.2 Unsteady Mechanisms Found in Natural flyers...........................17
2.2.3 Effect of Flapping Wing Kinematics.............................................19
2.2.4 Effect of Airfoil Shape and Reynolds number..............................28
2.2.5 Effect of Airfoil/Wing Flexibility....................................................30
2.2.6 Power Extraction.........................................................................30
2.3 Analytical and Computation Methods.................................................34
2.4 Range of Selected Parameters...........................................................36
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Chapter 3 Large Amplitude Plunging Airfoil Propulsion.............................38
3.1 Introduction.........................................................................................38
3.2 Numerical Method ..............................................................................40
3.2.1 Solver..........................................................................................40
3.2.2 Grid..............................................................................................42
3.2.3 Grid and Time step Refinement...................................................43
3.2.4 Validation with Experimental Results...........................................47
3.3 Effect of Large Amplitude Plunging, 2D Results.................................51
3.3.1 Time Series Analysis...................................................................51
3.3.2 Vortex Dynamics Discussion.......................................................56
3.4 Verification of Chaos with 3D Results.................................................62
3.5 Summary............................................................................................72
Chapter 4 Reynolds Number and Airfoil Shape Effects on Flapping Airfoil
Propulsion.......................................................................................................73
4.1 Introduction.........................................................................................73
4.2 Numerical Method ..............................................................................78
4.3 Effect of Airfoil thickness and Reynolds number.................................85
4.3.1 Re = 200, Plunging Airfoil............................................................91
4.3.2 Re = 2000 and 20000, Plunging Airfoil........................................95
4.3.3 Re = 2 × 106, Plunging Airfoil.......................................................99
4.3.4 Re = 200, 20000 and 2 × 106, Combined Motion.......................102
4.4 Effect of Airfoil Camber.....................................................................108
4.5 Summary..........................................................................................113
Chapter 5 Power Extraction through Flapping Airfoils .............................115
5.1 Introduction.......................................................................................115
5.2 Laboratory Scale Flapping Wing Power Generators.........................116
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5.2 Numerical Method............................................................................120
5.2.1 Navier-Stokes Flow Solver........................................................120
5.2.2 Grid Independence and Time step Refinement:........................122
5.2.3 Validation...................................................................................126
5.2.4 Numerical Modelling of Fully Flow-driven Generator.................130
5.3 Results and Discussion....................................................................135
5.3.1 Single Foil Prescribed Sinusoidal Motion..................................135
5.3.2 Single Foil Prescribed Non-Sinusoidal Motion...........................144
5.3.3 Tandem Foils Prescribed Sinusoidal Motion.............................152
5.3.4 Tandem Foils Prescribed Non-Sinusoidal Motion......................156
5.3.5 Comparison of Prescribed Motion Cases..................................160
5.3.6 Fully Flow-Driven Generator......................................................162
5.4 Summary..........................................................................................170
Chapter 6 Conclusions and Recommendations ........................................173
6.1 Conclusions......................................................................................173
6.2 Future Recommendations................................................................178
References....................................................................................................180
Publications from this research..................................................................188
Journal Articles............................................................................................188
Refereed Conference Papers......................................................................188
Conference Papers.....................................................................................189
Appendix FLUENT CFD SOLVER................................................................190
A.1 Flow Solver Settings.........................................................................190
A.2 User Defined Functions....................................................................191
Plunge Only Using Source Term.............................................................191
Sinusoidal Combined Pitch and Plunge with Source Term......................193
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List of Figures
Figure 2.1. Airfoil undergoing (a) pure plunging, (b) pure pitching and (c)
combined pitching and plunging motions...................................................11
Figure 2.2. Drag producing wake vortices downstream of a stationary
airfoil at an angle of attack.........................................................................16
Figure 2.3. Thrust producing wake vortices downstream of a flapping
airfoil..........................................................................................................16
Figure 3.1. C-topology grid for the plunging NACA0012 airfoil. ........................41
Figure 3.2. (a) Close-up view of 2D grid (b) span for 3D computations of
plunging NACA0012 airfoil.........................................................................43
Figure 3.3. Velocity vector field near trailing edge for a plunging
NACA0012 airfoil at k = 1.0, h = 0.25 and Re = 20000..............................43
Figure 3.4. Time history of C of flow over plunging 2D NACA0012 airfoil
T
at k = 1.0, h = 0.25 for different mesh resolutions......................................45
Figure 3.5. Vorticity contours of flow over plunging 2D NACA0012 airfoil at
k = 1.0, h = 0.25 (a) 251 x 101, (b) 901 x 101 and (c) 901 x 201 at the
end of the upstroke....................................................................................45
Figure 3.6. (a) Time history and (b) close-up of C of flow over plunging 2D
T
NACA0012 airfoil at k = 1.0, h = 0.25 for different time steps with 901
x 101 grid...................................................................................................46
Figure 3.7. Vorticity contours of flow over plunging 2D NACA0012 airfoil at
k = 1.0, h = 0.25 (a) 400, (b) 800 and (c) 1600 time steps per cycle at
t/T = 0.4.....................................................................................................46
Figure 3.8. Time history of C of flow over plunging 2D NACA0012 airfoil
T
at k = 1.0, h = 1.5 for different time steps with 901 x 101 grid....................47
Figure 3.9. (a) Time-averaged thrust coefficient and (b) efficiency against
kh for a plunging NACA0012 airfoil............................................................50
Figure 3.10. Variation of time-averaged thrust coefficient plunge amplitude
of a NACA0012 plunging airfoil at k = 1.0 and Re = 20000. ......................52
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