ABSTRACT
Title of dissertation: AN INVESTIGATION OF A MAV-SCALE FLEXIBLE
FLAPPING WING IN FORWARD FLIGHT:
FLOW FIELD AND AIRLOADS EXPERIMENTS
WITH COUPLED CFD-CSD
David Benjamin Mayo
Doctor of Philosophy, 2014
Dissertation directed by: Dr. Inderjit Chopra
Department of Aerospace Engineering
Experiments were systematically executed in conjunction with a coupled com-
putational fluid dynamics (CFD) and computational structural dynamics (CSD)
aeroelastic analysis for a micro air vehicle (MAV)-scale flexible flapping-wing in
forward flight. 2-D time-resolved particle image velocimetry (PIV) and force mea-
surements were performed in a wind tunnel at a flow speed of 3 m/s. Rigid and
flexible wings were tested. The wings underwent pure flapping kinematics, held at a
fixed wing-pitch angle at the root. Chordwise velocity fields were obtained at equally
spaced spanwise sections along the wing (30% to 90% span) at two instants during
the flap cycle (mid-downstroke and mid-upstroke) for the reference Reynolds number
of 15,000. The flowfield measurements and averaged force measurements were used
for the validation of the 3-D aeroelastic model. The objectives of the combined
efforts were to understand the unsteady aerodynamic mechanisms and their relation
to force production on a flexible wing undergoing an avian-type flapping motion.
The coupled CFD-CSD analysis combined a compressible Reynolds Averaged Navier
Stokes (RANS) solver (OVERTURNS) with a multi-body structural solver (MBDyn)
to resolve the complex, highly vortical, three-dimensional flow on a flexible wing.
The coupled CFD-CSD predicted and experimental flowfields showed comparable
results. A vorticity summation approach was used to calculate the circulation of
the leading edge vortex (LEV) from both the PIV measurements and the numerical
simulations to further validate the CFD-CSD code. The time-averaged vertical and
horizontal aerodynamic forces measured from the experiment using a miniature
force balance were also used to validate the force predictions from the CFD-CSD
model. Pertaining to the flow physics, the flapping motion induces large angles of
attack along the wing span. This motion causes the outboard sections to stall during
downstroke. However, during the upstroke, the outboard sections operate at very low
or even negative angles of attack. It was seen that the dynamic twisting produced
by the flexible wing helped in decreasing the effective angle of attack (nose-down)
during the downstroke and increased the angle of attack (nose-up) for the upstroke.
This temporal and spanwise variation of wing pitch angle affected both lift and
drag, and primarily helped the wing produce positive thrust during both upstroke
and downstroke, which is not possible with a rigid wing undergoing pure flap at a
constant pitch angle. Both PIV and CFD-CSD studies showed that the LEV stayed
attached for a longer duration of the flap cycle during downstroke for the flexible
wing compared to the rigid wing, especially towards the outboard sections. Also,
during the upstroke, the LEV strength for the flexible wing was significantly higher
than that for the rigid wing. This is due to the effective change in angle of attack.
Concerning performance for the flexible wing, the optimal CZ/CX occurs at the flap
frequency 10 Hz and initial set pitch angle 12◦.
INVESTIGATION OF A MAV-SCALE
FLEXIBLE FLAPPING WING IN FORWARD FLIGHT:
FLOW FIELD AND AIRLOADS EXPERIMENTS WITH
COUPLED CFD-CSD
by
David B. Mayo
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2014
Advisory Committee:
Dr. Inderjit Chopra, Chair/Advisor
Dr. James E. Hubbard Jr.
Dr. James Baeder
Dr. Darryll J. Pines
Dr. Amr Baz
© Copyright by
David Benjamin Mayo
2014
To my wife and my parents
ii
Acknowledgments
First, I must express my heartfelt appreciation to Dr. Inderjit Chopra for
affording me the opportunity to work on a very exciting and dynamic research topic
and the use of the Micro Air Vehicle Laboratory and Alfred Gessow Rotorcraft
Center facilities. His support and leadership helped me to grow within the group
and prepared me for the many challenges that lay ahead. I would also like to thank
my committee Dr. James E. Hubbard Jr., Dr. Darryll J. Pines, and Dr. James
Baeder for their mentorship during the doctoral process. There is no finer group of
academic mentors and experts. I would like to thank the aerospace engineering staff
for their help assistance and making me feel like I was part of a family.
Special thanks to student and friends; Dr. Moble Benedict and Dr. V.T
Nagaraj for assisting with experiments, giving guidance, and providing expertise.
James Lankford has been a great friend and colleague academic. I thank him
especially for the motivating conversations, friendship, constructive criticism, and
always maintaining our “Team Flapping-Wing” spirit even when things were not
going so well. Additional thanks goes to Dr. Joseph Milluzzo, Dr. Anish Sidney, Dr.
Bharath Govindarajan, and Joseph Ramsey for their belief in me when others did not.
I would like to acknowledge my colleagues in the lab for their meticulous attention
to detail, insight, and all the help they provided throughout the experimentation
and analysis process.
Finally, I must thank my wife/best friend, Talitha Hampton-Mayo for bringing
out the best in me. Her love, encouragement, and unrelenting support served as a
iii
source of encouragement through this challenging process. I would like to thank my
parents (Jessie and Conchita Mayo) and my 6 siblings (especially my oldest brother
Dr. Jessie B. Mayo Jr. who passed away on April 16, 2013). My hope is that they
can be inspired by this milestone in my life knowing how much they have inspired
me to rise above our humble beginnings. My family’s unconditional love anchored
my self-confidence and enabled me to accomplish all that I have.
Thank you God for giving me an amazing family, friends, professors, and
opening doors that I never knew existed. You saw fit to bring me through the
violence and destruction of war and combat as a US Marine (mentally and physically
in tact). I pray that this milestone in my life can be an example to others.
Once a Marine, Always a Marine... Semper Fidelis.
iv
Table of Contents
List of Tables viii
List of Figures ix
List of Abbreviations xiv
1 Introduction 1
1.1 Motivation for Micro Air Vehicle (MAV) Development . . . . . . . . . 1
1.1.1 MAV Design Specifications . . . . . . . . . . . . . . . . . . . . 2
1.2 Fixed-Wing MAVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Rotary-wing MAVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Flapping Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 Bio-inspired Flapping MAVs . . . . . . . . . . . . . . . . . . . 19
1.4.1.1 Entomopters . . . . . . . . . . . . . . . . . . . . . . 20
1.4.1.2 Ornithopters . . . . . . . . . . . . . . . . . . . . . . 25
1.5 Challenges to the Development of MAVs . . . . . . . . . . . . . . . . 28
1.5.1 Vehicle Control/Actuation . . . . . . . . . . . . . . . . . . . . 29
1.5.2 Energy Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5.3 Propulsion and Platform Integration . . . . . . . . . . . . . . 32
1.5.4 Low Reynolds Number Effects . . . . . . . . . . . . . . . . . . 34
1.6 Unsteady Lift Enhancement Mechanisms . . . . . . . . . . . . . . . . 42
1.6.1 The Leading Edge Vortex . . . . . . . . . . . . . . . . . . . . 43
1.6.2 Other Lift Augmenting Mechanisms . . . . . . . . . . . . . . . 48
1.7 Review of Flapping Wing Experimental Studies . . . . . . . . . . . . 52
1.8 Review of Flapping Wing Numerical Studies . . . . . . . . . . . . . . 59
1.9 Need for New Experimental Data . . . . . . . . . . . . . . . . . . . . 64
1.9.1 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . 67
1.10 Research Objective and Approach . . . . . . . . . . . . . . . . . . . . 68
1.11 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . 69
v
2 Methodology: Numerical Approach and Experimental Setup 71
2.1 Numerical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.1.1 Description of Flow Solver . . . . . . . . . . . . . . . . . . . . 72
2.1.2 Description of Grid System and Simulation . . . . . . . . . . . 74
2.1.3 Grid Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . 75
2.1.4 Structural Model and Coupling . . . . . . . . . . . . . . . . . 76
2.2 Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.2.1 Flapping Mechanism and Wing Design . . . . . . . . . . . . . 79
2.2.2 Particle Image Velocimetry Setup . . . . . . . . . . . . . . . . 84
2.2.3 Wind Tunnel Specifications . . . . . . . . . . . . . . . . . . . 89
2.2.4 PIV Experiment Challenges . . . . . . . . . . . . . . . . . . . 92
2.2.5 Experimental Uncertainty . . . . . . . . . . . . . . . . . . . . 93
2.3 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.3.1 Wing Covering Material Tensile Tests . . . . . . . . . . . . . . 101
2.3.2 Wing Frequency Verification Tests . . . . . . . . . . . . . . . 106
2.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3 Comparison of Predicted and Experimental Results 109
3.1 Comparison of Structural Dynamic Solver to Experiments . . . . . . 109
3.1.1 Flexible Wing Static Loading Comparison . . . . . . . . . . . 109
3.1.2 Flexible Wing Dynamic Tests . . . . . . . . . . . . . . . . . . 110
3.1.2.1 Comparison of Flexible Wing Frame Fundamental
Frequencies . . . . . . . . . . . . . . . . . . . . . . . 110
3.1.2.2 Comparison of Flexible Wing Frame Flapping Motion115
3.1.3 Comparison of Aerodynamic Solver (CFD-CSD) and PIV Results118
3.1.3.1 Rigid and Flexible Wing Flowfield Comparison . . . 118
3.2 Comparison of Sectional LEV Strength . . . . . . . . . . . . . . . . . 138
3.2.1 Rigid Wing LEV Circulation (PIV and CFD) . . . . . . . . . 138
3.2.2 Flexible Wing LEV Circulation (PIV and CFD-CSD ) . . . . 143
3.3 Airloads Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
3.3.1 Rigid Wing Comparison of Aerodynamic Forces from Flowfield 146
3.3.2 Comparison of Predicted and Averaged Direct Force Measure-
ments for the Rigid and Flexible Wing . . . . . . . . . . . . . 149
3.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
4 Rigid and Flexible Wing Comparison (Aerodynamic Force Production) 153
4.1 Understanding Lift and Thrust Production for a Rigid Flapping Wing 154
4.1.1 Rigid Wing Force History . . . . . . . . . . . . . . . . . . . . 154
4.1.2 Analysis of the 3-D Rigid Wing FlowField over a Flap Cycle
(Q-Criterion) . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.1.3 Rigid Wing Analysis of the 3-D Flowfield Over a Flap Cycle
(Spanwise Vorticity Contours) . . . . . . . . . . . . . . . . . . 160
4.1.4 Rigid Wing 2-D Analysis of Wing (Sectional Vertical and
Horizontal Force Coefficients along the Span) . . . . . . . . . 167
vi
4.1.5 2-D Analysis of Rigid Wing (Sectional Lift and Drag Coeffi-
cients along the Span) . . . . . . . . . . . . . . . . . . . . . . 173
4.1.6 Section Summary . . . . . . . . . . . . . . . . . . . . . . . . . 177
4.2 Rigid and Flexible Wing Comparison . . . . . . . . . . . . . . . . . . 178
4.2.1 Aerodynamic Force Production . . . . . . . . . . . . . . . . . 178
4.2.2 3-D Analysis of Wing (Aerodynamic Force Production over a
Flap Cycle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.2.3 3-D Rigid and Flexible Wing Flowfield Comparison (Q-Criterion)185
4.2.4 3-D Rigid and Flexible Wing Flowfield Comparison (Spanwise
Vorticity Contours) . . . . . . . . . . . . . . . . . . . . . . . . 187
4.2.4.1 2-D Analysis of Wing (Sectional CZ and CX along
the Wing Span)) . . . . . . . . . . . . . . . . . . . . 193
4.2.4.2 2-D Analysis of Wing (Sectional Cl and Cd along the
Wing Span) . . . . . . . . . . . . . . . . . . . . . . . 197
4.2.5 Section Summary . . . . . . . . . . . . . . . . . . . . . . . . . 202
5 Concluding Remarks 204
5.1 Conclusions from Rigid Wing Analysis . . . . . . . . . . . . . . . . . 205
5.2 Conclusions from the Comparison of Rigid and Flexible Wings . . . . 208
5.3 Major Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
5.4 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . 213
5.5 Acknowledgment of Sponsors . . . . . . . . . . . . . . . . . . . . . . 215
Bibliography 216
vii
List of Tables
1.1 MAVs described by DARPA [1]. . . . . . . . . . . . . . . . . . . . . . 4
1.2 Typical parameters for wing kinematic for large hovering insects [2]. . 16
1.3 Characteristics of existing entomopter designs [3]. . . . . . . . . . . . 25
2.1 Time-resolved PIV test matrix. . . . . . . . . . . . . . . . . . . . . . 93
2.2 Tensile test results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.3 Flexible wing properties. . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.1 Comparison of flexible chordwise member natural frequencies. . . . . 115
4.1 Chart of averaged CZ and CX for flap frequency and pitch angle (rigid
wing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.2 Chart of UP, UT, V and φ along the span (rigid wing). . . . . . . . . 168
4.3 Chart of CZ and CX for flap frequency and pitch angle (flexible and
rigid (in parenthesis) wing respectively). . . . . . . . . . . . . . . . . 182
4.4 Chart of UP, UT, V and φ along the span (flexible wing). . . . . . . . 194
viii
List of Figures
1.1 Defined mission scenarios for MAVs [4,5]. . . . . . . . . . . . . . . . . 3
1.2 Fixed-wing MAVs (AeroVironment) [6]. . . . . . . . . . . . . . . . . . 7
1.3 Ducted single rotor, single rotor (with vanes), and coaxial MAVs. . . 9
1.4 MAV quad rotors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Unconventional rotating-wing MAVs (University of Maryland). . . . . 13
1.6 a) Typical hovering flight wing motion. b) Wing path for “insect”
type flyers: 1) Pronation; 2) Downstroke; 3) Supination; 4) Upstroke.
Modified from original CTA-MAST Program Report, used with per-
mission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Schematic diagram of coordinate systems and wing kinematics for
angles corresponding to Table 1.2 [7]. . . . . . . . . . . . . . . . . . . 16
1.8 Wing kinematics for various “avian” type flyers (a) albatross, fast
gate; (b) pigeon, slow gate; (c) horseshoe bat, fast gate (d) horseshoe
bat, slow gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Perspective views of avian wing movements during normal forward
flight [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.10 a) Upstroke and b) downstroke forces on a flapping wing in forward
flight [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.11 University of Toronto Mentor Entomopter. [10] . . . . . . . . . . . . . 20
1.12 Thrust Augmented Entomopter [11]. . . . . . . . . . . . . . . . . . . 21
1.13 Light-weight MAVs: Concept drawing of the Micromechanical Flying
Insect (MFI), the prototype Microbot, and 3-D printed hover prototype. 23
1.14 Flapping-wing MAVs developed at the University of Maryland, a)
Daedal and b) “64 Gram Flapper”. . . . . . . . . . . . . . . . . . . . 25
1.15 AeroVironment’s Nano Hummingbird [12]. . . . . . . . . . . . . . . . 26
1.16 Commercial Kinkade ParkHawk onithopter on UMD Morpheus Lab
test mount [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.17 MAV-scale ornithopters . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.18 Energy storage systems energy densities [14]. . . . . . . . . . . . . . . 32
1.19 Comparison of efficiency parameters for hover-capable MAV-scale
fliers [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
ix
1.20 Airfoil performance as a function of Reynolds number [16]. . . . . . . 40
1.21 Laminar separation bubble [17]. . . . . . . . . . . . . . . . . . . . . . 41
1.22 3-D conical LEV structure: a) LEV cross-section; b) three-dimensional
structure and spanwise flow (note that le is the leading edge, te is the
trailing edge, dss is the dividing stream surface) [18]. . . . . . . . . . 44
1.23 Airloads and flow structures on a 2-D airfoil during the dynamic stall
process [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.24 Illustration of wing with flow restricted by baffles, and vorticity with
overlaid velocity field (Note: Blue denotes a vortex) [20]. . . . . . . . 47
1.25 Illustration of the clap-and-fling/Weis-Fogh mechanism [21]: A) at
end of half-stroke wings moving toward each other; B) wings continue
approach to each other; C) fluid is moved out by wings; D) wings
rotation about trailing edge; E) fluid pulled into the void left by the
wings; F) LEV formation begins as wings move apart. . . . . . . . . . 49
1.26 Illustration of the wake capture mechanism [21]: (A) After translation,
wing generates vorticity at both the leading and trailing edges, (B)
Vortices induce a strong velocity field in the intervening region, (C/D)
wing comes to a halt and reverses stroke (D/E), wing translates in
the opposite directions [21]. . . . . . . . . . . . . . . . . . . . . . . . 51
1.27 Robofly oil tank test setup [22]. . . . . . . . . . . . . . . . . . . . . . 55
1.28 Passive pitch, bi-stable single-degree-of-freedom flapping mechanism [23]. 56
2.1 Wing mesh embedded in background Cartesian mesh. . . . . . . . . . 75
2.2 Variation of predicted aerodynamic force coefficients for different mesh
resolutions (k = 0.32, θ = 0◦). . . . . . . . . . . . . . . . . . . . . . . 77
2.3 Four-bar linkages and flapping mechanism. . . . . . . . . . . . . . . . 82
2.4 a) Rigid and b) flexible wing construction. . . . . . . . . . . . . . . . 83
2.5 Schematic depicting the general setup of a 2-D PIV system and image
processing methodology. . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.6 Schematic PIV experiment setup in wing tunnel test section. . . . . . 87
2.7 Actual PIV experiment setup in wing tunnel test section. . . . . . . . 88
2.8 Schematic of low speed wind tunnel. . . . . . . . . . . . . . . . . . . 90
2.9 Variation in wind tunnel turbulence with wind tunnel speed. . . . . . 91
2.10 Typical test setup for motion tracking system. . . . . . . . . . . . . . 96
2.11 Schematic of VICON test for isolated bending and torsion testing. . . 98
2.12 Large deformation of a beam under point load at free tip [24]. . . . . 99
2.13 Torsion test schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.14 Image of wing membrane material in during tensile test. . . . . . . . 104
2.15 Tensile tests for wing covering. . . . . . . . . . . . . . . . . . . . . . . 104
2.16 VICON motion tracking “shaker” test for modal analysis. . . . . . . . 107
3.1 Left side, images of static wing loading tests with VICON markers
and Right side, load deflection curves for chordwise ribs. . . . . . . . 111
3.2 Raw signal of tip (TE) displacements and Fast Fourier Transform
from motion tracking experiment. . . . . . . . . . . . . . . . . . . . . 113
x
3.3 Mode shapes for wing frame structural members. . . . . . . . . . . . 114
3.4 Comparison experiment and predicted (MBDyn) wing frame tip dis-
placements for 6 Hz flapping. . . . . . . . . . . . . . . . . . . . . . . 117
3.5 Perspective view schematic of the rotating wing setup. . . . . . . . . 119
3.6 Comparison of representative chordwise PIV and CFD vorticity con-
tours at t = T/4, (40◦ flapping amplitude, θ = 24◦, 4 Hz flapping
frequency, V∞ = 3 m/s, k = 0.32). . . . . . . . . . . . . . . . . . . . . 120
3.7 Comparison of representative chordwise PIV and CFD vorticity con-
tours at t = T/4, (40◦ flapping amplitude, θ = 12◦, 6 Hz flapping
frequency, V∞ = 3 m/s, k = 0.48). . . . . . . . . . . . . . . . . . . . . 122
3.8 Comparison of representative chordwise PIV and CFD vorticity con-
tours at t = T/4, (40◦ flapping amplitude, θ0 = 12◦, 4 Hz flapping
frequency, V∞ = 3 m/s, k = 0.32). . . . . . . . . . . . . . . . . . . . . 123
3.9 Comparison of representative chordwise PIV and CFD vorticity con-
tours at t = T/4, (40◦ flapping amplitude, θ0 = 24◦, 6 Hz flapping
frequency, V∞ = 3 m/s, k = 0.64). . . . . . . . . . . . . . . . . . . . . 124
3.10 Comparison of representative chordwise PIV and CFD vorticity con-
tours at t = T/4, (40◦ flapping amplitude, θ0 = 0◦, 8 Hz flapping
frequency, V∞ = 3 m/s, k = 0.64). . . . . . . . . . . . . . . . . . . . . 125
3.11 Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles,
rigid wing ,θ = 0◦ at 4 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).129
3.12 Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles,
rigid wing, θ = 12◦ at 6 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).131
3.13 Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles,
rigid wing, θ = 24◦ at 4 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).133
3.14 Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles,
flexible wing, θ0 = 12◦ at 4 Hz. (Note: y/b = 0.5, t = T/4, Reref =
15, 000). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
3.15 Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles,
θ0 = 24◦ at 6 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000). . . . . . 135
3.16 Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles,
flexible wing, θ = 0◦ at 8 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).137
3.17 Distribution of averaged LEV circulation, Γv along the span, rigid
wing, Ω =4 Hz, (40◦ flap amplitude, V∞ = 3 m/s) with error bars
showing standard deviation. . . . . . . . . . . . . . . . . . . . . . . . 139
3.18 Distribution of averaged LEV circulation, Γv for a variation in flap
frequency, rigid wing, y/b = 0.5 (40◦ flap amplitude, V∞ = 3 m/s) at
50% span. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
xi
3.19 Distribution of averaged LEV circulation, Γv along the span, flexible
wing, Ω =4 Hz, (40◦ flap amplitude, V∞ = 3 m/s). . . . . . . . . . . . 144
3.20 Distribution of averaged LEV circulation, Γv for a variation in flap
frequency, flexible wing, y/b = 0.5 (40◦ flap amplitude, V∞ = 3 m/s)
at 50% span. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
3.21 Schematic explaining CZ calculation. . . . . . . . . . . . . . . . . . . 148
3.22 Variation of vertical force coefficient (Cz) from rigid wing averaged
PIV and instantaneous CFD flowfield data (50% span location, 4 Hz
flapping). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3.23 Rigid and flexible wing comparison of averaged experiment and pre-
dicted vertical (FZ) and horizontal forces (FX) for various flap frequencies.151
4.1 Variation of total vertical force coefficient (CZ) and total horizontal
force coefficient (CX) from CFD data (rigid wing). . . . . . . . . . . . 156
4.2 Iso-surfaces of Q-Criterion colored with vorticity magnitude contour
at various instances of the flap cycle (rigid wing). . . . . . . . . . . . 159
4.3 Vorticity magnitude along the span at various instances of flap cycle
(rigid wing). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
4.4 Vorticity contours with overlaid velocity along the span: left side,
mid-downstroke and right side, mid-upstroke (rigid wing), 4 Hz, θ = 24◦.166
4.5 X-Vorticity magnitude along the span from CFD data (rigid wing), 4
Hz, θ = 24◦. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
4.6 Rigid wing sectional Cz and Cx, at mid-downstroke and mid-upstroke,
normalized by V∞. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
4.7 Rigid wing Cz and Cx, at mid-downstroke and mid-upstroke, normal-
ized by the resultant V. . . . . . . . . . . . . . . . . . . . . . . . . . 172
4.8 Schematics of force and velocity vectors for the airfoil cross section. . 174
4.9 Lift coefficient, Cl, and drag coefficient, Cd, along the span, at mid-
downstroke and mid-upstroke. . . . . . . . . . . . . . . . . . . . . . . 175
4.10 Rotation of the lift and drag vectors toward the wing tip. . . . . . . . 177
4.11 Rigid and flexible wing comparison of predicted vertical (FZ) and
horizontal force (FX) for single flap cycle with flap frequency of 6 Hz
and θ0 = 12◦. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
4.12 Variation of total vertical force coefficient (CZ) and total horizontal
force coefficient (CX) from coupled CFD-CSD data (flexible wing). . . 183
4.13 Rigid and flexible wing comparison of iso-surfaces of Q-Criterion
colored with vorticity magnitude at various instances of the flap cycle. 188
4.14 Superimposed rigid and flexible showing deformations, θ0 = 12◦, Ω =6
Hz, (40◦ flap amplitude, V∞ = 3 m/s). . . . . . . . . . . . . . . . . . 189
4.15 Chordwise vorticity contour with overlaid velocity field at 30%, 50%,
70%, and 90% span locations at mid-downstroke (flexible and rigid
wing). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
4.16 Chordwise vorticity contour with overlaid velocity field at 30%, 50%,
70%, and 90% span locations at mid-upstroke (flexible and rigid wing).192
xii
4.17 Sectional Cz and Cx, at mid-downstroke and mid-upstroke, 6 Hz,
θ0 = 12◦. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
4.18 Variation of geometric pitch angle along the span during the mid-
upstroke and mid-downstroke at an initial pitch angle of 12◦ for 4, 6,
8, 10 Hz flap frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . 199
4.19 Variation in geometric pitch angle at the mid-downstroke and mid-
upstroke (6 Hz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
4.20 Lift coefficient, Cl, and drag coefficient, Cd, along the span at mid-
downstroke and mid-upstroke. . . . . . . . . . . . . . . . . . . . . . . 201
xiii
Nomenclature
A Flap amplitude
Ae Effective area
AR Aspect ratio
b Wing span
c Wing chord
Cd Sectional drag coefficient
Cl Sectional lift coefficient
CX Horizontal force coefficient
CZ Vertical force coefficient
EI Bending stiffness
FM Figure of merit
FX Propulsive Force
FZ Vertical Force
GJ Torsional rigidity
J Advance ratio
k Reduced frequency, k = Ωc2V∞
M Image magnification
P Pressure
PL Power loading
r Radial dimension
rc Vortex core radius
Re Chord Reynolds number = ρV c/µ
St Struhaul number
t Time, s
T Period of flap cycle
u, v, w Flow velocity in the x, y, z directions
UP Parallel (to flap plane) component of resultant velocity
UT Normal (to flap plane) component of resultant velocity
V Resultant velocity experienced by the wing
Vr Radial velocity
Vθ Swirl velocity
V∞ Free stream velocity
x, y, z Cartesian coordinate system
xiv
Greek Symbols
α Angle of attack
δ change in specimen length
 Normal strain
Γv Vortex circulation
µ Dynamic viscosity
ω Vorticity, rad/s
Ω Frequency of flapping, rad/s
φ Flap induced angle
Ψ Phase angle in the flapping cycle
σ Normal stress
ρ Density
θ Pitch angle
xv
List of Abbreviations
CCD Charged Coupled Device
CFD Computational Fluid Dynamics
CMOS Complementary Metal Oxide Semiconductor
CSD Computational Structural Dynamics
c.g. center of gravity
DAQ Data Acquisition
DARPA Defense Advanced Research Projects Agency
DPIV Digital Particle Image Velocimetry
FFT Fast Fourier Transform
fps Frames-Per-Second
FSI Fluid Structure Interactions
FV Flow Visualization
GTOW Gross Takeoff Weight
IVP Initial Value Problem
LEV Leading Edge Vortex
MAV Micro Air Vehicle
MBDyn Multibody Dynamics
MLS Moving Least Squares
MSD Multibody System Dynamics
N-S Navier Stokes
RC Radio Controlled
Re Reynolds Number
URANS Unsteady Reynolds-Averaged Navier-Stokes
xvi
Chapter 1: Introduction
1.1 Motivation for Micro Air Vehicle (MAV) Development
Because of the continued increased use and efficacy of unmanned aircraft,
research and development of micro air vehicles (MAVs) continues for a variety
of military and civilian applications. In general, MAVs are autonomous flying
vehicles with a size constraint (typically palm-size). They are small light-weight
systems, which offer the attributes of portability, stealth, and enhanced flight agility.
Their relative size also provides the benefit of a vehicle with comparatively low
production and operational costs compared to larger scale unmanned aerial vehicles
[25–27]. These characteristics make MAVs an ideal platform for reconnaissance and
surveillance missions in confined and hazardous areas.
MAVs have both a military and civilian role. This is because hover-capable/low-
speed flight vehicles with gust tolerances can perch and observe, offer greater situa-
tional awareness for military covert scouting/reconnaissance, and search and rescue
missions inside buildings, caves or tunnels. As it pertains to civil applications,
MAVs can be useful for missions such as investigating a chemically dangerous area
or a radioactive environment, border security, law enforcement, disaster response,
1
homeland defense, pipeline patrol, etc. Figure 1.1 illustrates the mission scenarios
defined by the Defense Advanced Research Projects Agency (DARPA) and the Army
Research Lab [5]. The need for such vehicles that can handle these scenarios has
been around for decades, and today there is even more of a need for this capability
that MAVs can provide.
1.1.1 MAV Design Specifications
Most major MAV research started in 1997 when DARPA requested the devel-
opment of what was then a new type of unmanned vehicle with a size constraint [4].
The program’s intention was to spark innovation in creating a new type of small
vehicle. Initially, a 15 cm size constraint, an endurance of about an hour, and a
gross takeoff weight (GTOW) of less than 100 grams were defined for such a vehicle.
However, DARPA initiatives expanded to require a vehicle which could fit into a
cylinder 7.5 cm in diameter and up to 7.5 cm long [28]. Table 1.1 lists some other
MAV design specifications. Furthermore, DARPA defined a second, lighter class
of vehicles called “Nano-Air” (NAVs), which should have a GTOW of less than 20
grams. While the classification of “MAVs” has grown today to encompass vehicles
both smaller and larger than 15 cm, enormous scientific interest continues to drive
the development of small, autonomous MAVs.
The size constraint presents several challenges in the areas of low Reynolds
number aerodynamics, sensors and actuators, propulsive systems design, energy stor-
age, and system integration. Although these challenges are inherent to MAV design
2
(a) 1997 DARPA illustration of MAV mo-
bile immersion sensor mission scenario.
(b) 1997 DARPA illustration of Urban Op-
erations Missions scenario for MAVs.
(c) 1997 DARPA illustration of ”Over-
The-Hill Reconnaissance” mission sce-
nario for MAVs.
(d) 2014 CTA-MAST illustration of perimeter defense and building search mission
scenarios.
Figure 1.1: Defined mission scenarios for MAVs [4,5].
3
Table 1.1: MAVs described by DARPA [1].
Criteria Specification Requirements
Vehicle dimension
Weight, g (GTOW) 100
Size, m (Maximum dimension) <15.24
Performance parameters
Speed, m/s (Maximum flight speed) 15
Endurance, min (Loiter time on station) 60
Range, km (Operational range) 1–10
Altitude, m (Operational ceiling) <150
Weapons/Sensor package Payload, g, (Mission dependent) 20
Budget Cost, $ (Maximum cost) 1,500
and practical solutions will be the foundation of building successful MAV concepts,
research results reported in this dissertation are focused mainly on aerodynamics
issues.
Currently, the two main types of MAVs being developed are rotating-wing and
fixed-wing. Though these two types of types have been the most commonly examined
concepts in the quest for successful MAVs, small bio-inspired platforms such as
flapping-wings are also an option for meeting the demands of the aforementioned
mission scenarios (e.g., highly agile/maneuverable, operation in confined, obstacle-
rich urban environments, compact, and hover-capable). These types of MAVs are
described in the next section.
1.2 Fixed-Wing MAVs
MAVs of the fixed-wing variety are more technologically developed than other
MAVs. These vehicles have the advantage of being less complex than other MAVs as
there are often fewer moving parts associated with the design. These platforms also
have high cruise speeds, more range, and very good stability characteristics. Also, like
4
their large-scale high endurance counterparts (e.g., modern bombers or commercial
aircraft), they have the advantage of being relatively efficient. These types of vehicles
are often deployed on long endurance missions as they have characteristics that
are best utilized for a perimeter defense or reconnaissance type mission. However,
research continues to further improve these vehicles.
Numerous experimental and numerical studies of low-Reynolds number airfoil
and wing designs have been performed [25,29–31]. Specifically, Mueller has deter-
mined the aerodynamic characteristics of many MAV-scale low-aspect ratio wings
varying wing planform, aspect ratio, and Reynolds number in a low-speed wind
tunnel [32]. These wing model tests have proven very useful for MAV development
in that they have shown the effects of a range of wing parameters at the MAV-scale.
In the area of MAV platform testing, the University of Arizona built four MAV
wind-tunnel models to test the effects of varying wing camber [33]. It was observed
that at the MAV-scale, a low camber wing yields an optimal lift-to-drag ratio for
high-speed, and efficient flight, and highly cambered wings gave the best low-speed
performance because near stall the wings experienced only mild pitching moments
while maintaining high lift-to-drag ratios.
In the area of flexible wings, a very popular field of research, the University
of Florida used wind tunnel testing to compare flexible wings to a rigid baseline
wing [34]. Airloads, 3-D visual image correlation for deformation measurements,
and flow visualization were examined. It was observed that pitch stability could
be improved by using wing perimeter reinforced flexible wings. This resulted in
an increase in maximum lift coefficient. Both the University of Arizona and and
5
the University of Florida conducted tests on MAVs they developed. Current re-
search innovation pertaining to fixed-wing MAVs has been in the area of active
morphing. This is a technique where the wing lift distribution is controlled using
spatially distributed actuators, conformal sensors, and aeroelastic deformations of
light-weight/flexible/wing membranes to improve performance [35–38].
There have been several successful fixed-wing MAV prototypes developed
over the past two decades. Figure 1.2 shows three images from AeroVironment’s
fixed-wing MAV program. In 1998, they produced the 80 g Black Widow (see
Fig. 1.2(a)). This vehicle has a 6 inch wing span with an endurance of 30 minutes.
Later, in 2002, an endurance record of 107 minutes was established by the WASP [39].
WASP has a wing span of 33 cm and weighed 170 grams (see Fig. 1.2(b)). The
latest prototype (2006) is called WASP Block III, selected by the U.S. Air Force’s
Battlefield Air Targeting Micro Air Vehicle (BATMAV) program. Each successive
aircraft experiences an increase in aspect ratio to reduce drag and an increase in
battery size. WASP III (see Fig. 1.2(c)), has a wingspan of 72 cm and a weight
of 430 grams [6]. Other major fixed-wing MAV prototypes include the University
of Florida’s 4.5 inch “bendable-wing” MAV [34, 40, 41], the Black Kite (National
Aerospace Laboratories, India) [42], and NRL’s MITE [43].
There are some design challenges and disadvantages to the use of fixed-wing
MAVs. These platforms use low aspect ratio (AR) wings designed to maximize
wing area for a constrained wingspan. With this, there is a considerable increase
in the amount of induced drag on the vehicle. This is also the case with large-scale
airplane wings but the effects are more severe for fixed-wing MAVs. Typically, MAV
6
(a) Black Widow (AeroVironment
1998) [44].
(b) WASP Block I (AeroVironment 2002) [45].
(c) WASP Block III (AeroVironment 2006).
Figure 1.2: Fixed-wing MAVs (AeroVironment) [6].
7
fixed-wing aspect ratios are in the range of 1 < AR < 2, while large-scale endurance
UAVs have an aspect ratio of above 20. Another major disadvantage is in the
inability of these aircraft to fly at very low speeds or to hover. This is because they
must maintain a high forward velocity so that their wings can generate lift. Also,
there is a large turning radius for these vehicles. Therefore, even with the many
innovations directed at improving fixed-wing aircraft performance and endurance,
these vehicles are not well suited for missions in confined areas [46].
1.3 Rotary-wing MAVs
Currently, rotating-wing MAVs represent the majority of the vehicles being
developed at the MAV scale. This is because rotating-wing MAVs have the ability to
hover. Most micro-rotorcraft use their rotors to provide both lift and thrust, though
a ring-wing shroud can augment lift in hover. To reduce the complexity of the rotor
system, many rotary-wing MAV designs use fixed-pitch rotors and use control tabs
in the rotor downwash or incorporate multiple rotors to control the vehicle. The
main types of rotary-wing MAVs are the single main rotor, coaxial, and quadrotor
systems.
At the MAV scale, single main rotor designs with a mechanism for anti-torque
or a coaxial configuration are often used for low-speed flight (see Figs. 1.3). A single
main rotor configuration would require a tail rotor as a separate device for anti-torque.
To eliminate the need for a tail rotor and to reduce the overall size of the single rotor
design, vanes in the downwash can be used to counteract the torque. Many single
8
(a) University of Maryland, “TiShrov” [47]. (b) University of Kansas, shrouded single
rotor “XQ-138” [48].
(c) University of Maryland, Coaxial “Mi-
cor” [48,49].
Figure 1.3: Ducted single rotor, single rotor (with vanes), and coaxial MAVs.
9
main rotor concepts are basically scaled-down conventional helicopters and suffer
from comparatively lower efficiency ratings. Ducts and shrouds have been utilized to
improve aerodynamic efficiency for the coaxial design. The duct acts to accelerate
the inlet airflow and reduces tip loss effects to provide increased thrust. At the MAV
scale, the thrust gains need to exceed the duct weight. Ducts also add profile drag to
the vehicle and large pitching moment in forward flight. In general, because of their
inherent compactness, coaxial designs appear more attractive than vehicles with a
single rotor, but neither are particularly able to handle gusty environments. The
advantage of the single and coaxial designs is in the general familiarity in construction
and control of the vehicle.
Another widely researched rotary-wing concept is the quad rotor (see Fig. 1.4).
These vehicles have four rotors and offer a wide range of advantages such as good
flight stability and agility, large operational envelopes, and improved thrust-to-weight
ratios. However, disadvantages are in the area of size. Vehicle weight can be an issue
because it can be difficult to scale down the motors and the four rotors consume
more power than a vehicle with fewer rotors.
There are several unconventional rotating-wing concepts being researched (e.g.
flapping rotors, powered Samaras, and cyclocopters). Referred to as Flotors (flapping
rotors), ornicopters, or rotopters are bio-inspired designs that combine the motion of
vertically flapped wings with the rotary-wing motion of helicopters. Figure 1.5(a)
shows the micro rotor experimental test stand used to demonstrate the effects of
high frequency blade flapping on average rotor forces at the University of Maryland.
This test rig is capable of independent flapping and rotating motion [50]. Blade
10
(a) University of Maryland/Daedalus Flight Sys-
tems Micro Quad.
(b) Stanford University Mesicopter.
Figure 1.4: MAV quad rotors.
rotation and superimposed blade flapping showed improvements in both figure of
merit (FM), ratio of ideal power required to hover to actual power required, and
maximum thrust. However, one disadvantage is in increased design complexity. Also,
there are periodic inertial forces that are directly proportional to the mass of the
blades and improvements in efficiency often do not justify the increase in weight and
complexity of the system.
Another bio-inspired design, the Samara, is based on the winged seed of the
maple tree. When these seeds fall to the ground, they generate lift by auto-rotating.
An MAV concept was designed based on the same principle. To hover, a motor
driven propeller is added to maintain the rotation of the vehicle. Figure 1.5(b) shows
the University of Maryland’s Samara MAV design [51]. This vehicle is controlled by
manipulating the propeller RPM/throttle and the collective pitch. The disadvantage
of this type of MAV is that it needs a launch space, the payload (cameras, weapons,
or sensors) should not be sensitive to the rotation of the vehicle, and stabilizing the
11
vehicle can be challenging.
In a cycloidal rotor system (Ref. [52]), the span of the blades run parallel to
the axis of rotation of the rotor, i.e., a form of paddle-wheel type of concept (see
Fig. 1.5(c)). The effective disk area in this case can be defined as the product of
rotor span and rotor diameter. The pitch angle of each blade on a cyclorotor is
varied periodically such that the angle of attack is such that the blades create lift
at both the top and bottom parts of the rotational cycle. Varying in configuration
and size/weight, the cyclorotor concepts developed at the University of Maryland
have achieved efficiency values within the range of 0.42 < FM < 0.65 for range of
effective disk loadings, whereas conventional rotor systems operated at MAV scales
(when operated with the same or similar values of disk loading) achieve a somewhat
lower figure of merit of between 0.4 and 0.5 [15]. The optimized MAV-scale cycloidal
rotor could achieve a higher power loading than conventional rotor in hover.
For comparison, it cannot be overlooked that rotating-wing MAVs have lower
aerodynamic efficiency ratings and in some cases be more difficult to control compared
to their fixed-wing counterparts, especially in gusty environments. The trade-off is
that fixed-wing vehicles cannot hover. With these limitations, it is important to
consider flight vehicles, which can hover, handle gusty environments, and fly at very
low-speeds. Inspired by natural flyers, flapping-wing MAVs may present one solution.
The next section discusses some of the recent advancements in flapping wing designs.
12
(a) Flapping rotor test rig, “Flotor” [50]. (b) Robotic Samara [51].
(c) Cyclocopter MAVs [52].
Figure 1.5: Unconventional rotating-wing MAVs (University of Maryland).
13
1.4 Flapping Wings
Bio-mimetic flapping wings have received much interest because of perceived
high aerodynamic efficiencies and gust tolerance at the MAV scale [53]. In nature, the
four biological groups that have evolved for flapping flight are pterasaurs (vertebrates),
and insects (invertebrates). Vertebrate (bird and bat) wings are evolved through the
modification of an existing limb so they have muscles for control. Insect wings consist
of thin non-living membranes and rods, and they are controlled by pulling on those
rods. These wings are passive structures controlled from the wing base. These two
types of flapping motion are nearly vertical (“avian” type) and horizontal (“insect”
type) with respect to the body frame. This is not a fixed physical rule because
there are a few examples of birds and insects using both vertical and horizontal wing
motions. Nevertheless, bird-type and insect-type MAVs are often called ornithopters
and entemopters respectively. The “insect” type wing kinematics are most often
observed in hovering flight as the wings move at a very high wing beat frequency at
low Reynolds numbers.
For hover-type wing kinematics, the stages of the wing flap are the upstroke
translation, wing rotational stages, and downstroke translation (see Fig. 1.6). Here,
the leading edge of the wing is denoted by a dot on the wing section, and it is the
same during both half-strokes. These stages occur in the horizontal plane relative to
the body frame. The wing sweeps through the air at relatively large pitch angles. The
wing rotational stages occur at the end of each half-stroke and are called pronation
and supination. This is where a reversal in wing orientation occurs and the upper
14
Figure 1.6: a) Typical hovering flight wing motion. b) Wing path for “insect” type
flyers: 1) Pronation; 2) Downstroke; 3) Supination; 4) Upstroke. Modified from
original CTA-MAST Program Report, used with permission.
surface becomes the lower surface. This ensures that the wings reach positive pitch
angles on both parts of the translational motion. There can be a small amount of
stroke deviation, where the wing moves perpendicular to the stroke plane; however,
its purpose is not well understood [7].
As seen in Fig. 1.6, both wings move symmetrically, and the motion is described
using kinematic parameters like stroke amplitude, wing beat frequency, wing angle of
attack, stroke plane angle, downstroke/upstroke ratio, wing tip trajectory, and timing
for wing rotation. Typical wing parameters for large insects are shown in Table 1.2.
Typically, for most large animals, hovering flapping stroke amplitude is 120◦ to 180◦
or greater. The geometric angle of attack of hovering insects at mid-stroke is 30◦
to 45◦ [2]. In forward flight, the wing motion is more birdlike as the stroke plane
tilts forward. Figure 1.7 describes the insect wing and body movement. The body
kinematics can be represented by the body angle χ and the stroke refers to angle
15
Table 1.2: Typical parameters for wing kinematic for large hovering insects [2].
Kinematic Parameter Typical Value
Wing-beat Frequency, n 20− 40 Hz
Stroke Amplitude, Φ 120◦
Angle of Attack, α 30◦
Body Angle, χ 50◦ → 10◦ (flight speed: 0→ max)
Stroke Plane Angle, β 10◦ → 50◦ (flight speed: 0→ max)
Stroke Timing, d/u 1− 1.1
φ: position angle 
θ: elevation angle 
α: angle of attack of the wing 
β: stroke-place angle 
χ: body angle 
Figure 1.7: Schematic diagram of coordinate systems and wing kinematics for angles
corresponding to Table 1.2 [7].
formed by the maximum and minimum sweep positions. The stroke plane angle and
body angle vary with flight speed. The wing-beat kinematics can be described by the
position angle φ, elevation angle θ, and the feathering angle α (the angle of attack).
Unlike the “insect” wing kinematics, “avian” kinematics are associated with
flapping mostly in a vertical plane while sweeping wings forward and back. Wing
twist along the span and wing folding allow for the adjustment of the wing’s wetted
area [7]. This flapping motion is important because it generates both vertical and
propulsive forces that enable flight. Figure 1.8 shows the wing tip path for various
16
Figure 1.8: Wing kinematics for various “avian” type flyers (a) albatross, fast gate;
(b) pigeon, slow gate; (c) horseshoe bat, fast gate (d) horseshoe bat, slow gate.
birds and bats in forward flight. Typically, figure eights and ovals are the two tip
path shapes. The wing tip path can vary based on flight mode (e.g., take-off or
landing) and patterns are highly dependent on flight speed. The sequence of motions
is illustrated in Fig. 1.9.
For “avian” type flyers, variable wing pitching plays a very important role
during flight. This pitching is implemented using a very complex musculoskeletal
system [54, 55]. Figure 1.10 shows the forces generated during forward flight by a
flapping wing with positive wing camber during downstroke and upstroke. During
downstroke, the wing is always at a positive angle of attack with significant upward
inflow near the wing tip. The relative inflow tilts the lift vector forward so that it
produces thrust. This is experienced more heavily near the wing tip. The pitch
remains nose down (into the flapping direction) so the flow stays attached. This
is because nose down pitching is the primary mode for creating a positive angle of
attack during the upstroke. This positive angle of attack is achieved by creating
significant upward twist in the wing. This is necessary because the downward inflow
angle, due to the flapping motion, increases with increasing span position. If a
17
Figure 1.9: Perspective views of avian wing movements during normal forward
flight [8].
18
Figure 1.10: a) Upstroke and b) downstroke forces on a flapping wing in forward
flight [9].
positive angle of attack is achieved, the lifting force will be upwards and backward,
increasing the drag on the wing. However, if the angle of attack during upstroke is
negative, the lift vector will be negative and forward, creating thrust but also causing
negative lift. The motion of the wing tip is very important for increasing thrust and
decreasing drag, while the interior of the wing primarily produces lift. There is a
significant amount of flow near the wing tip where the flap motion is large [9, 56].
1.4.1 Bio-inspired Flapping MAVs
Observations of biological flyers in nature and systematic gust studies [57,58]
on real insects have shown high maneuverability and gust tolerance capability for
flapping wings. This is because of their ability to generate large, almost instantaneous,
control forces and moments over just a couple of wing strokes. The following section
highlights two current flapping-wing MAVs (entomopters and ornithopters).
19
Figure 1.11: University of Toronto Mentor Entomopter. [10]
1.4.1.1 Entomopters
The entomopter is a versatile insect-like robot, often with the capability of
flying and/or crawling. Though many entomopter type MAVs lack the ability to
crawl, insect-like flying has been integrated into many designs. The first entomopter
to demonstrate controlled free flight for both translation and hover was the SRI
Institute/University of Toronto Mentor (see Fig. 1.11). The four wings are arranged
in an X-configuration. This vehicle is controlled by onboard electronics that move
fins and gyros to direct the downwash. The original Mentor design was powered by
an internal combustion engine and had a 36 cm wingspan. The weight was 580 g.
This design flew for one minute and was able to achieve hover for 20 seconds. A
later version of the vehicle only weighed 440 g and used a Nickel Cadmium battery
to power a brushless motor [10].
At the University of Maryland, a hybrid, hover-capable insect-based MAV
20
concept was proposed [11]. This vehicle would be called the Thrust Augmented
Entomopter (TAE). The estimated weight would be 160 grams and the wingspan
would be 218 mm. The proposed configuration would utilize flapping wings and
a pusher propeller for thrust in forward flight. The wings would be configured for
minimum power requirements in hover, and would not flap during forward flight.
This MAV was at a concept stage and was never built. However, this concept would
be the motivation for future entomopter designs. Figure 1.12 shows the concept
drawing of this MAV design.
(a) Thrust Augmented Entomopter in Airplane Mode.
(b) Thrust Augmented Entomopter in Insect Mode.
Figure 1.12: Thrust Augmented Entomopter [11].
21
The Micromechanical Flying Insect (MFI) project was developed at the Uni-
versity of California Berkeley [59]. This vehicle was designed to mimic a blow fly,
Calliphora (see Fig. 1.13(a)). The design specifications were that the mass would be
100 mg, the wing length would be 11 mm, and the wing beat frequency would be
150 Hz. Actuation would be done by using piezo bimorphs to connect the wings to a
four-bar mechanism. This would only utilize about 10 mW of actuator power. The
outcome of this study was that this vehicle did generation the adequate lift equal to
weight (500µN) [59–63].
An offshoot of the MFI program’s research was the Harvard Microrobotic
Fly (see Fig. 1.13(b)). This was expected to produce the smallest entomopter to
demonstrate tethered flight [64]. This vehicle used only one piezoelectric actuator
and weighs 56 milligrams. The wings were rigid, but a root joint allowed feathering
in response to aerodynamic and inertial forces. The flapping and feathering strokes
were limited to 100◦ using mechanical stops. The vehicle was able to exert a vertical
force that was 3.6 times its own weight. This vehicle has demonstrated the ability to
achieve thrust equal to weight, however, only a small number of controlled flights have
been reported and the vehicle was powered from the ground. Ongoing modifications
are being made to this vehicle to create an autonomous flight-capable vehicle weighing
about 120 mg.
The use of 3-D printing technology has greatly expanded possibilities for
wing design, allowing wing shapes that mimic those of real insects or virtually any
other shape. This reduces the time of a wing design cycle to a matter of minutes.
Figure 1.13(c) shows a flapping-wing prototype produced at Cornell University. This
22
(a) UC Berkley MFI [59]. (b) Harvard University Microbot [64].
(c) 3-D printed flapping-hovering insect prototype
[3].
Figure 1.13: Light-weight MAVs: Concept drawing of the Micromechanical Flying
Insect (MFI), the prototype Microbot, and 3-D printed hover prototype.
23
research focused on developing an extremely light-weight hovering MAV using 3-D
printed wings and mechanical parts. This prototype has a mass of 3.89 grams and
has demonstrated an 85-second passively stable untethered hovering flight [3]. There
have been many hovering MAVs produced and Table 1.3 shows the characteristics
for many of these vehicles.
Figure 1.14 shows two flapping-wing MAVs developed at the University of
Maryland that have been successfully flight tested. Specifically, Fig. 1.14(a) shows the
Daedal prototype, which was developed as a collaboration between Daedalus Flight
Systems, LLC and the University of Maryland’s Autonomous Vehicle Laboratory.
This 12 gram MAV is capable of free-flight at a wing-beat frequency of 25 Hz. Each
wing’s length is 91 mm and the wing skin is made of 5µm thick Mylar sheet [65, 66].
The Daedal prototype did demonstrate both hover and free-flight; however, vehicle
flight control was limited by actuator latency. The vehicle’s endurance was only
3–4 minutes. Currently, there are plans to reduce the weight to reach a GTOW of
10 grams. Figure 1.14(b) shows the University of Maryland’s “64 Gram Flapper”
flapping MAV. The actual weight is 63.8 grams and control for this MAV was enabled
by using a wing-based control system. This vehicle has successfully demonstrated
both hover and controlled flight. However, the “64 Gram Flapper” experienced some
issues with control and over-heating.
DARPA sponsored a Nano Air Vehicle program centered around developing
an ornithopter technology demonstrator. Through this program, AeroVironment
developed a vehicle called the Hummingbird to satisfy the requirements (see Fig. 1.15).
This vehicle is arguably the most notable flapping wing MAV built to date. The
24
(a) University of Maryland Daedal [65]. (b) University of Maryland “64 Gram Flapper”
[67].
Figure 1.14: Flapping-wing MAVs developed at the University of Maryland, a)
Daedal and b) “64 Gram Flapper”.
vehicle is comparable in size to a natural hummingbird in that the mass is 19 grams
and the wingspan is 16.5 cm. The AeroVironment Hummingbird has the ability
to hover for several minutes and has a maximum forward flight speed of about 6.7
m/s [68].
Table 1.3: Characteristics of existing entomopter designs [3].
Design Year Mass (g) Span (cm) Wings Endurance (s) Features
Mentor 2002 580 36 4 >60 Gas Powered
DelFly II 2006 16.07 28 4 480 Camera, R/C
van Breugel 2007 24.2 45 8 33 Passively Stable
Microbot 2007 0.06 3 2 N/A Piezoelectric
DelFly Micro 2008 3.07 10 4 N/A Camera, R/C
NAV 2009 10 7.5 2 20 Active Wing Pitch
3-D Print 2010 3.89 14.3 4 85 3-D Print Wings
1.4.1.2 Ornithopters
Avian-based flight utilizes a nearly vertical, up-down, flapping motion. Often,
the wings are comprised of flexible membrane skins covering a musculoskeletal
system controlled by small synchronized variations of angle of incidence. Similar to
25
Figure 1.15: AeroVironment’s Nano Hummingbird [12].
fixed-wing vehicles, ornithopters cannot hover, and they require an initial airspeed
for taking off. Also, commercial ornithopters can have wing spans on the order of
one to two meters and are often much heavier than the MAV design requirements.
However, ornithopter-type MAVs have not been able to replicate the performance
of birds because of their inability to copy the morphing structures of avian wings.
Nevertheless, ornithopters do provide insight into low Reynolds number flight, and
they are used by both hobbyists and researchers.
One successful commercial ornithopter is the Kinkade model (see Fig. 1.16).
The Kinkade Parkhawk series of ornithopters has a wing span of 107 cm and weighs
about 454 grams. Flight speeds range from 2.5 m/s to 9 m/s. The total stoke
amplitude is 55◦ and experiment flap frequencies were 2-6 Hz. The wings on this
vehicle employ passive morphing behavior during flight which allows for variations
in the local bending and twisting angles. Several flight tests (using motion tracking)
26
Figure 1.16: Commercial Kinkade ParkHawk onithopter on UMD Morpheus Lab
test mount [13].
(a) Delft Technical University’s DelFly I [70]. (b) AeroVironment’s Microbat [71].
Figure 1.17: MAV-scale ornithopters .
and predictive analyses have been performed on this vehicle at the University of
Maryland’s Morpheus Laboratory [13,69]. There have been several avian-type MAVs
produced specifically for research (see Fig. 1.17).
Figure 1.17(a) show’s the DelFly ornithopter created by Delft University [70].
The vehicle’s wing beat frequency is 6 Hz; wingspan is 350 mm. The weight is 17
grams, and it can cruise at speeds of 1.8 m/s. However, the endurance is only 12
minutes. Figure 1.17(b) shows Aerovironment’s Microbat weighs about 12 grams,
which uses microelectromechanical systems (MEMS) technology. The wing span is
14 cm but like many avian-based ornithopters, this vehicle can not hover [71].
27
The flapping-wing concept generates much interest within the aerodynamics
community because of the relatively strong, unsteady, three-dimensional vortical flow
structures that are produced on small span, low aspect ratio wings. Although some
successful flapping MAVs have been produced, flapping-wing research has lagged
fixed and rotating wing research, and current flappers have lower hovering efficiency
ratings compared to rotating wing vehicles. The flapping-wing must be thoroughly
investigated from the perspective of fundamental aerodynamics. Specifically, there is
a need for greater understanding of the fundamental lift and thrust mechanisms, as
well as it requires systematic performance measurements that can be correlated with
predictions in order to develop a viable mechanism for an MAV. An understanding
of the design challenges may then allow more efficient and reliable MAVs to be
designed.
1.5 Challenges to the Development of MAVs
There are several technical barriers to producing mission capable MAVs. Dif-
ficulties in the theoretical analysis, experimentation, replication of natural wing
kinematics, and numerical simulation of the capabilities of the various competing
MAV concepts have led to a wide range of assessments and opinions of their actual
capabilities. There are also issues such as small-scale power generation and storage,
navigation and communications, and efficient propulsion and aerodynamics [14].
Conventional rotors have been scaled down for MAVs, but have suffered from consid-
erably lower aerodynamic efficiencies than those achieved at larger scales [1, 72,73].
28
The same lower efficiencies are also seen for flapping wings. Research efforts have
produced several hover-capable flapping-wing MAVs with varying performance like
the Microbot [61,64], Daedal [65], Delfly [70], and Nano Hummingbird [68]. However,
these vehicles have largely been developed with a focus on an operational vehicle
design rather than an in-depth understanding of the fundamental aerodynamics
associated with flapping MAVs. This approach has led to the development of several
MAV prototypes, but these vehicles are only capable of flight with limited payload
and in controlled environments. Challenges facing MAV development are discussed
below.
1.5.1 Vehicle Control/Actuation
Manipulation of the control surfaces is a crucial task for MAV design, especially
at the small scale. This is because actuation can define the maximum possible
performance. The two main criteria for an actuation concept are the power to weight
ratio and the technical feasibility. A further constraint in the selection of an actuator
concept for flapping MAV applications is wing beat frequency (speed of actuation).
There are two types of actuator categories: rotary and linear. Rotary type actuators
include brushed DC motors, brushless DC motors, micro internal combustion engines
(ICEs), and piezoelectric motors. Linear actuators include piezoelectric ceramic,
shape memory alloy (SMA), magnetostrictor, solenoid, and electroactive polymers.
Some of these actuation concepts are under development and have not yet matured
for MAV applications, but the most promising are electric motors and solenoids,
29
SMA wires, and piezo elements.
Electric motors and solenoids are based on the same physical principles, with
the difference being that solenoids deliver a linear motion, while motors rotate.
Electric motors and solenoids can be scaled down to 1-2 grams; however, solenoids
have a lower energy density and reaction time in comparison to electric motors.
Miniaturized electric motors do suffer from a 30% decrease in efficiency when
compared to large motors [39]. In general, the efficiency of a rotating motor with
gearing has been preferable to a linear solenoid.
SMA wires imitate natural muscles such as the ones of birds and performance
is very good within the expected range. This material can contract when heated
and expand when cooled. Some SMA actuators are commercially available for
micro-scale applications, and a theoretical analysis was conducted for the BAT-MAV
program [74]. However, the disadvantage is in the speed and fatigue life of such
actuators. This is because of the slow time associated with heat dissipation. With
this, SMA actuators are not fast enough for application in flapping MAVs [75].
Another interesting technology is piezo based actuators. These are actuators
that use piezoelectric material that responds mechanically when an electric charge is
applied. Depending on the size, they can be miniaturized to a weight of less than
1 g [76]. They can also achieve very high frequencies. The disadvantage of such
elements is the high voltage (typically greater than 100 V) needed to induce the
contraction of the material [77,78].
In summary, solenoids must have a very high strain rate but a low energy
density. SMA wires are interesting because they mimic the behavior of natural muscle,
30
but their performance is not yet suitable [14]. They do not have the bandwidth
required for high frequency flapping. They may become an option in future if the
performance is improved. Piezo elements are inadequate due to the high voltage
and small deflections. Finally, micro-scale electric motors are currently the most
suitable (light-weight and efficient) devices for the construction of a flapping wing
mechanisms and therefore often used for MAVs.
1.5.2 Energy Sources
All MAVs must draw power from a fuel source to function (e.g., to power
motors and sensors). Figure 1.18 shows that hydrogen and gasoline currently have
the highest energy density of the energy sources reviewed. Even though fossil fuels
have a higher energy density than current battery technology, the disadvantages are
a increased noise signature (internal combustion engines) and increased emissions.
The main issue is the lower efficiency (¡ 5%) of the small scale engines. The energy
sources for robotic flyers includes conventional batteries, fuel cells, ultra capacitors,
and solar cells. Most small-scale flight vehicles use batteries.
Various consumer electronics industries have driven up the power density of
batteries. Mainly driven by the cell phone industry, lithium polymer batteries are
the only commercially available technology that can satisfy the requirements of
insect-sized MAVs [79, 80]. However, the capacity of lithium polymer batteries
decreases at high discharge rates. The properties of the capacity derating depend
heavily on the battery design and manufacturing parameters. As a result, it is
31
Figure 1.18: Energy storage systems energy densities [14].
difficult to estimate battery performance without a specific battery in mind; at the
same time, it is important to consider derating because the high power requirements
of hovering MAVs inevitably translate to high battery discharge rates. The derating
relationship may be nonlinear. Promising new technologies include micro solid oxide
fuel cells [81] (where chemical fuel is transformed into electric current through an
electrochemical process), lithium batteries with silicon nanowire anodes [82], ultra
capacitors, solar cells, and lithium air batteries [83].
1.5.3 Propulsion and Platform Integration
The devices by which most MAVs are propelled are electric motors, as they
are light-weight, controllable, reliable, and efficient. Motor overheating is one disad-
vantage, though this can be mitigated by proper sizing. Small internal combustion
engines have been employed, but efficiency, noise, and system integration can be
32
problematic. Some promising alternatives include hybrid gas/electric systems [84,85]
and miniature gas turbine generators [86], but these concepts have not yet been
applied to MAVs because of the size limitations and difficulty in integrating the
propulsion system into the rest of the vehicle components.
In general, platform integration of MAV components is a very challenging
endeavor. The main consideration is to keep the vehicle weight low while maintaining
the functionality to complete a given mission. Because smaller structures and hence
stiffer components are required, MAVs tend to be very rigid unless intentionally
made flexible. One example of the incorporation of vehicle flexibility is at the
University of Florida where interstitial (overlapped) wing materials were used [40].
The multi-functionality of components becomes very important when vehicle space
is limited. Also, innovation in design becomes crucial when antennae or sensors need
to be integrated into the wings, or the power source needs to be integrated with the
fuselage structure (as examples) [87].
The sustained hover endurance goal of one hour has eluded MAV researchers
and designers, especially for flapping wings. Advancements in MEMS, improvements
in battery technology, and clever ideas for platform integration have advanced the
state of the art. However, motor efficiency and the battery specific energy and power
are not at the level to meet the endurance goals. To improve endurance, there is
an opportunity to optimize the aerodynamic design of MAVs for operation in a
low Reynolds number regime. Considering the typical missions MAVs will have to
perform, it is not difficult to conclude that these key performance parameters are
the maximum lift producing capability (Cl,max), aerodynamic efficiency (lift per unit
33
power), maneuverability (control forces per unit body inertia), and robustness to
external disturbances such as wind gusts, both in an open-loop (bare airframe) and
closed-loop sense. Both rotating- and fixed-wing MAVs are highly vulnerable to the
nonsteady aerodynamic environment, but flappers appear to stand out because the
low Reynolds number effects are often overcome by leveraging unsteady aerodynamic
effects. The next subsection contains a more in-depth discussion of low Reynolds
number issues.
1.5.4 Low Reynolds Number Effects
Flapping MAVs operate in the Reynolds number range of 104–105. In this range,
there are aerodynamic sensitivities to wing profile and overall geometry, low lift-
to-drag ratios, increased susceptibility to flow separation, increased boundary layer
thicknesses, and higher relative viscous losses [7,19]. These unfavorable aerodynamic
characteristics are seen when scaled down conventional rotors show considerably
lower aerodynamic efficiency than those achieved at larger scales [1, 72]. Reference
15 discusses the aerodynamic efficiency for various hover-capable MAVs as well as
avian and entomological flyers examined on the basis of their absolute maximum
attainable efficiency. Though various other types of hover-capable MAV designs
have also been developed, including biomimetic vehicles, most of the flapping wing
MAVs still do not exceed the hovering efficiencies that have been obtained with their
conventional counterparts in both hover and forward flight.
A comparison of the aerodynamic efficiency for many different hover-capable
34
MAVs, as well as natural fliers, was performed based on the maximum attainable
efficiency in the form of power loading [15]. The power loading, PL, of a flight
vehicle is the ratio of the thrust, T , produced by the vertically lifting aerodynamic
surfaces per unit of power, P , expended to produce thrust. To predict the absolute
minimum power required to hover, ideal flow conditions (i.e., incompressible, inviscid,
one-dimensional, and quasi-steady) are assumed. The power loading for a hovering
vehicle can be related to wing loading or rotor disk loading, T/Ae, and the figure of
merit, FM , by the following equation:
PL =
√
2ρ FM
√
T/Ae
(1.1)
In this equation, ρ is the fluid density; Ae is the effective area of the reciprocating
wing stroke plane or rotor disk; and FM is the figure of merit, a measure of efficiency
given by the ratio of actual to ideal power required.
To achieve maximum hover endurance, a special effort must be made to obtain
the best possible performance in hover, i.e., maximize power loading. For hovering
vehicles, as effective disk loading decreases, power loading increases rapidly (see
Eq. 1.1). The result is that a hover-capable vehicle must be very light and/or have a
large wingspan or rotor disk area. MAV size constraints ensure particular attention
is given to a reduction in vehicle weight through careful engineering design. In hover,
thrust equals weight, so reducing vehicle weight results in a reduced disk loading,
T/Ae. A flapping wing MAV concept that can achieve lower effective disk loadings
through a reduction in vehicle weight can, for a fixed figure of merit, also achieve
35
Figure 1.19: Comparison of efficiency parameters for hover-capable MAV-scale
fliers [15].
improved power loadings.
Figure 1.19 shows measured and computed disk/wing and power loading data
for various full-scale and small-scale hovering vehicle concepts with lines of constant
FM given by momentum theory. For small-scale and large-scale rotary-wing vehicles,
the theoretical maximum attainable levels of hovering efficiency are greater than
or comparable to those achieved by natural fliers (when compared on the basis of
equivalent wing stroke area/disk loading). However, current MAVs have generally
achieved relatively low hovering efficiencies. Currently, large-scale rotors typically
exhibit maximum figure of merit (FM) values between 0.7 and 0.8, whereas MAV-
scale rotors have FM values near 0.4–0.5 [19]. Flapping MAVs have even lower
efficiency values, FM < 0.2. As such, there is room for improvement in MAV
36
design to increase overall efficiency. To this end, an improved understanding of the
aerodynamic issues associated with flight operations at the small-scale is needed,
with special attention to performance and efficiency parameters.
A key concern today, is the fact that, even though many of these studies,
especially by Dickinson [20, 22, 88–90], shed light on the complex aerodynamics
of insect flight operating at very low Reynolds numbers (Re < 1000), it is not
very clear whether these conclusions would still hold true at MAV-scale Reynolds
numbers, which are at least an order of magnitude higher than 1,000. In that
case, the usefulness of these conclusions in formulating the design principles for an
actual flapping-wing MAV are questionable. Therefore, systematic studies need to
be performed at MAV-scale Reynolds numbers (Re > 10, 000). Also, these studies
should not be limited to understanding the fundamental physics, but they should
also be able to derive standard quantitative aerodynamic efficiency metrics (such as
thrust/power and figure of merit) for a flapping wing in hover. This would clearly
show how efficient or inefficient the flapping wing concept really is, in comparison to
other hover-capable concepts such as a conventional helicopter rotor.
One key challenge in developing efficient and robust FMAVs is overcoming
aerodynamic issues attributed to flight at Reynolds numbers on the order of 104,
such as low lift-to-drag ratios and increased susceptibility to flow separation [1, 91].
Though birds and insects have successfully adapted to such aerodynamic conditions
and fly well in the lower Reynolds number regime, these aerodynamic challenges
contribute to the low efficiency observed in MAVs [7].
Reynolds number (Re) is defined as the ratio of vehicle inertial force to viscous
37
force. Reynolds number is a non-dimensionalized parameter that can be seen in
Navier-Stokes equations. Navier-Stokes equations are the fluid flow equations and
have the following form for an incompressible fluid [17]:
∂(~u)
∂(t)
+
(
~u · ~5
)
~u = ~5p+
1
Re
~5
2
~u (1.2)
where, 5 is the spatial gradient operator normalized by some length scale (L), u is
the velocity vector normalized by some velocity scale (U), t is the time normalized
by the convective time scale (L/U), p is the pressure (normalized by the dynamic
pressure ρU2), and ρ is the fluid density. The Re is defined as:
Re =
(
ρUL
µ
)
(1.3)
Here, ρ is again the fluid density, and U is the free-stream velocity. The reference
length of the object is represented by L, which is usually chord length of a wing, and
µ is the fluid viscosity.
Flow separation and transition are highly sensitive to Reynolds number, pressure
gradient, and the disturbance environment. The aerodynamic characteristics of a
vehicle, (e.g., wing design) in turn affect the static, dynamic, and aeroelastic stability
of the entire vehicle. Therefore the management of the boundary layer for a particular
low Reynolds number vehicle design is critical.
Figures 1.20 shows the variation in airfoil section Clmax, Cdmin, and (Cl/Cd)max
as a function of Reynolds number. The general trend is that performance is greatly
reduced as the chord Reynolds number decreases below 100,000. Again, MAVs operate
38
at Reynolds numbers less than 105. This means that as vehicle control (thrusting
and lifting) surfaces are made smaller and flow velocities are reduced, these vehicles
become inherently less efficient. In the range between 1, 000 < Re < 10, 000 the
boundary layer flow is laminar and it becomes difficult to cause transition to turbulent
flow. For chord Reynolds numbers between 10,000 and 30,000, the boundary layer
is completely laminar. Experience with hand-launched glider models indicates that
when the boundary layer separates, it does not reattach.
Figure 1.20(a) shows the variation in lift coefficient Cl with Reynolds number.
This parameter is dependent on the local airfoil camber which affects the relative
angle of attack. Airfoils with large camber have high lift coefficients at small and
even negative angles of attack, but they also achieve stall at angles of attack lower
than small cambered or symmetric airfoils.
Figure 1.20(b) shows the drag coefficient (Cd) as a function of Reynolds number.
The two components of drag are the profile (form drag, skin friction and interference
drag) and induced drag (drag required to maintain lift). Induced drag increases
when the aspect ratio is decreased (specific to MAVs).
Figure 1.20(c) shows the lift-to-drag ratio for an airfoil. This is a measure of
the aerodynamic efficiency in that aerodynamic efficiency is optimal at the maximum
lift-to-drag ratio. The two factors that affect lift-to-drag ratio include wing planform
and local airfoil shape.
For Reynolds numbers < 105, wings must be designed to reduce the profile
drag by avoiding the formation of laminar separation bubbles. A laminar separation
bubble is shown in Fig. 1.21 and is caused by an adverse pressure gradient. This
39
(a) Maximum lift coefficient.
(b) Maximum drag coefficient.
(c) Maximum lift-to-drag ratio.
Figure 1.20: Airfoil performance as a function of Reynolds number [16].
40
Figure 1.21: Laminar separation bubble [17].
adverse pressure gradient is the reason the boundary layer starts to separate. The
laminar separated shear flow is unstable and transitions to a turbulent separated
shear flow. The turbulence then transports momentum from the free-stream, across
the shear layer, and down towards the surface. When the momentum transport is
sufficient, the turbulent boundary layer is considered to be reattached to the surface,
thus closing the separation bubble [19]. These bubbles become larger as the Reynolds
number decreases, usually resulting in a rapid deterioration in performance, i.e.,
substantial decrease in L/D.
Low Reynolds number airfoils will experience flow separation and stall at low
angles of attack. However, a sharpened leading edge of a thin flat (or curved arc)
airfoil acts as a boundary layer trip. This causes the flow to become turbulent once
it passes the leading edge of the airfoil. Even with these types of modifications, the
lifting performance of optimized wings are not enough to handle the abrupt change
in performance brought on at low Reynolds numbers. This is the reason that many
41
current MAVs utilize curved thin plates or membrane wings.
MAV designers are interested in the 30,000 to 70,000 Reynolds number range
because this is where many model-scale aircraft operate. In this range, it has been
seen that thick airfoils (i.e., 6% and above) can suffer from degraded performance as
a result of laminar separation [32]. Near the 50,000 Reynolds number, the free shear
layer after laminar separation does not transition to turbulent flow in time to reattach.
Thin airfoil sections (i.e., less than 6% thick) operate reasonably well at the upper end
of this regime [92]. For the Reynolds number range 70, 000 < Re < 200, 000, where
some small radio controlled airplanes also operate, laminar flow can be observed on
the wings and airfoil performance is improved.
1.6 Unsteady Lift Enhancement Mechanisms
Like helicopters, flapping wings generate a very complex aerodynamic flowfield
with large vortical structures on the wings. In general, dynamically pitching airfoils
allow for the flow to remain attached to angles of attack greater than what would
cause stall during static conditions. This is the case for both rotary- and flapping-
wing MAVs, but especially for FMAVs. This mean that the unsteady nature of the
flow can be used to enhance the lift characteristics for flapping wings. With careful
engineering, designers can bring forth the next-generation of MAVs to bridge the
gap between rotating- and fixed- wing vehicles. A key is that flapping-wing micro
air vehicles (FMAVs) must produce high maximum lift coefficients by generating
strong three-dimensional vortices on small, low aspect ratio wings.
42
Many studies have been conducted in relation to the shedding of concentrated
vorticity from the leading edge of a flapping wing as a significant source of lift
enhancement at the MAV scale. However, steady and quasi-steady aerodynamic
theory, experiments, and modeling (e.g., computational fluid dynamics or CFD) have
not yet fully explained the ability of flapping-wing flyers to generate the values of lift
needed to achieve hover and to fly forward at the observed speeds [18, 20, 22]. It has
been established that MAVs suffer from degraded performance, but biological flyers
perform well in this low Reynolds number aerodynamic environment. This is done
by leveraging several unsteady aerodynamic mechanisms to improve performance.
These mechanisms are discussed in the next two subsections.
1.6.1 The Leading Edge Vortex
The leading edge vortex (LEV) is the most significant source of lift enhancement
for a flapping wing. A LEV forms on the upper surface of the wing when flow separates
over the sharp leading edge and rolls up into a coherent vortex. The lift increase
occurs because the presence of a LEV lowers the local pressure on the upper surface
of the wing, thus increasing the overall lift. Figure 1.22 shows an illustration of a
two-dimensional cross section of the LEV, and the three-dimensional segment of
the LEV, showing the axial flow component. Here the streamlines roll up into the
vortex as it spirals towards the wing tip (spanwise direction) [18]. The spiraling flow
structure is caused by spanwise fluid transport.
Ellington was the first to examine the LEV using flow visualization on a live
43
Figure 1.22: 3-D conical LEV structure: a) LEV cross-section; b) three-dimensional
structure and spanwise flow (note that le is the leading edge, te is the trailing edge,
dss is the dividing stream surface) [18].
tethered hawkmoth at chord Reynolds numbers near 2,000 [18]. His pioneering
research also explored the flow on flapping wings at Reynolds numbers from 4,000 to
7,000 and sparked much follow-up research [18,93,94]. It was subsequently concluded
that because insects fly with wings at a high angle of attack and at low Reynolds
numbers, they must utilize the lift-enhancing effects of a LEV to produce sufficient
lift for flight [95, 96]. Experiments were continued on mechanical models to study
the LEV and it was shown that the prominent flow structure generated on these
wings was a three-dimensional LEV. The main observations were that 1) the LEV
was smaller towards the wing root and larger outboard, 2) near the wing tip, the
LEV separated and joined with the tip vortex, and 3) LEV formation resembled the
process of dynamic stall.
Dynamic stall occurs when the angle of attack of an airfoil increases rapidly,
causing a delay in the onset of flow separation and the formation of a vortex on the
upper surface of the wing [19, 97]. The vortex grows in strength before detaching
from the leading edge and convects over the wing and into the wake, resulting
44
Figure 1.23: Airloads and flow structures on a 2-D airfoil during the dynamic stall
process [19].
in overall wing stall. Figure 1.23 shows a schematic of the flow morphology and
unsteady airloads during the dynamic stall process for a two-dimensional airfoil.
The five stages indicate the various levels of flow separation, LEV growth, LEV
shedding/convection, and flow reattachment as the wing changes angle of attack [98].
Subsequent experiments have confirmed the lift-generating characteristics of
LEVs on flapping wings [18, 20, 20, 22, 89, 90, 99]. Based on these studies, it is
45
concluded that an attached LEV is the key high-lift source on a flapping wing.
While experiments on live birds and insects can be extremely challenging, the use of
mechanical models that mimic the flapping kinematics of the wings seen in nature
has allowed for further and more detailed studies of the LEV [73, 100, 101]. Such
mechanical models make it easier to systematically study the effects of variations in
Reynolds number, angle of attack, and wing aspect ratio on the behavior of the LEV.
Although most of these experiments have been conducted on rigid flapping wings,
they have provided valuable insight into the overall aerodynamic effects produced by
LEVs.
Dickinson and colleagues independently observed a stable LEV on a dynamically
scaled robotic fruitfly wing model operating in an oil tank at much lower Reynolds
numbers (Re = 100 - 1000) [20, 22, 89, 90]. Large lift and drag coefficients were
measured by the force balance at the wing root, and the magnitude of these forces
were directly related to the strength of the LEV, clearly showing that the LEV is the
leading contributor to the aerodynamic forces on a flapping wing. The important
consideration was in how flapping wings could produce such a coherent stable vortical
structure, where the flow would not separate on a steady translating 2-D wing at
such high angles of attack. Ellington postulated that this was because there is a
strong spiraling spanwise flow, which would transport vorticity from the LEV along
the wing length to the tip vortex that prevents the LEV from shedding [18,94].
Dickinson showed that at Reynolds numbers matching the flow relevant to
most insects (Re < 1, 000), flapping wings do not produce a spiraling vortex, and
the stability of the LEV was attributed to the decrease in effective angle of attack
46
Figure 1.24: Illustration of wing with flow restricted by baffles, and vorticity with
overlaid velocity field (Note: Blue denotes a vortex) [20].
because of the downward flow induced by the strong tip vortices [20]. Birch and
Dickinson further investigated the stability of the LEV on a dynamically scaled fruit
fly wing (Re = 160). To assess the effect of spanwise flow on the LEV, they applied
fences and baffles on the wing’s upper surface. This would restrict the spanwise flow.
Even after placing these baffles, the flow still did not detach from the wing. It was
stated that there must be some Reynolds number dependence pertaining to LEV
stability. Figure 1.24 show some flowfield results of the LEV and a schematic of the
wing.
Recent studies by Lentink and Dickinson indicate that the LEV is stabilized
by the ‘quasi-steady’ centripetal and Coriolis accelerations of the fluid particles close
to the wing’s surface because of the propeller-like sweep of the wing, especially when
the radius to chord ratio is low (lower Rossby number) [101]. This study also showed
that LEV stability is not dependent on Reynolds number, at least over the range
47
most relevant for insect flight (100 < Re < 14, 000). Although early analyses of
flapping wings has identified high maximum vertical force coefficients, the LEV is
not the only lift augmenting mechanism for a flapping wing.
1.6.2 Other Lift Augmenting Mechanisms
The other unsteady mechanisms for a flapping wing are 1) clap and fling,
2) rotational lift, 3) added mass, and 4) wake capture. Studies have exposed a
general understanding of the unsteady aerodynamic forces produced by flapping
wings [99,102,103].
The Weis-Fogh or clap and fling mechanism is a phenomena initiated when two
wings move close together approaching pronation or supination. This fluid dynamic
process was discovered to be prevalent for small insects [104,105]. In general, fluid
is pulled into the void left by the wings as the move away from each other. An
illustration of this phenomena is shown in Fig. 1.25. Figure 1.25(A-C) shows the clap
phase of the mechanism. Here, the leading edges of the wings come together during
wing pronation/supination until they are in close proximity and almost parallel to
one another. The fluid is pushed out by the wings. The wings then rotate about the
trailing edge, and as the wings separate, a vortex pair forms on the leading edges.
During the fling phase, shown in Fig. 1.25(F-D), the wings separate, and the fluid
rushes into the growing gap increasing the circulation. Lehmann et al. [106] examined
the lift augmentation produced by the clap-and-fling mechanism on a scaled fruit fly
wing at a chord. They compared force measurements from a single flapping-wing
48
Figure 1.25: Illustration of the clap-and-fling/Weis-Fogh mechanism [21]: A) at end
of half-stroke wings moving toward each other; B) wings continue approach to each
other; C) fluid is moved out by wings; D) wings rotation about trailing edge; E) fluid
pulled into the void left by the wings; F) LEV formation begins as wings move apart.
configuration to that of a dual flapping-wing configuration. The clap and fling
mechanism increased the lift by as much as 17% (and the LEV circulation in the fling
phase by 32%) for Reynolds number between 50–200. However, it was found that
as Reynolds number increased, lift enhancement resulting from the clap-and-fling
motion began to decrease.
A second mechanism of lift augmentation is circulation from wing rotation
(flip). This is caused by the rotation of the wings and is especially prevalent at the
end of the hovering stroke (pronation and supination). This mechanism is caused
by Kramer’s effect, which is closely related to delay/dynamic stall [19, 21]. The
wing goes through a large rotation at a very high angular rate towards the end of
49
the stroke. The mechanism of circulation generated by rotation is similar to the
Magnus effect. Though this effect cannot be applied directly to the flat surface of a
flapping wing, where the establishment of the Kutta condition is necessary [17], this
mechanism is enhanced when the wings are flexible (favorable deformation) [107].
The third mechanism is wake capture (also called wing-wake-interaction),
caused by the reciprocating nature of the wing flapping. Figure 1.26 shows a
schematic of the wake capture phenomena. This happens immediately after stroke-
reversal (see Fig. 1.26(AF)). At the ends of the stroke (pronation and supination),
the wing reverses direction, the incoming free-stream velocity may also be increased
by the induced effects of the incoming shed wake or wakes (see Fig. 1.26(C-D)). It
is even possible for a flapping wing to come into contact with a shed LEV at the
beginning of its half-stroke (see Fig. 1.26(E-F)). Therefore, a better understanding of
this interaction may lead to a MAV with more highly optimized wing kinematics that
could take advantage of this mechanism of lift production. Work done by Dickinson
et al. [22] shows that lift enhancement could be achieved for their flapping-wing
mechanism. Confirmation that the enhanced lift force due to wake capture was
shown by observing that the lift peak continued even after the wing motion was
terminated. This showed that the shed wake was the energy source for lift generation.
It was also shown that lift increases from the wake capture mechanism are dependent
on the wing kinematics at the end of each half-stroke.
Finally, there are added or “virtual” mass effects. As the wing accelerates
(because of the rotational and translational motion), it encounters a reaction force due
to the inertia of the accelerated fluid [104,108,109]. This reactive, non-circulatory
50
Figure 1.26: Illustration of the wake capture mechanism [21]: (A) After translation,
wing generates vorticity at both the leading and trailing edges, (B) Vortices induce
a strong velocity field in the intervening region, (C/D) wing comes to a halt and
reverses stroke (D/E), wing translates in the opposite directions [21].
force falls outside standard circulation based steady-state analysis, but can be
modeled by additional mass. Concerning MAVs, Ansari et al. [108] noted that
flapping wings cause high accelerations and rapid stroke reversals making forces
significant even though the mass of the wing may be small. In general the inertia
of the flapping wing is increased by the mass of the accelerated fluid [104,106,110].
Because added mass forces typically occur at the same time as the circulatory forces,
it is usually difficult to measure them in isolation [110]. The added mass force is
often modeled in quasi-steady terms, using a time-invariant added-mass coefficient,
and any time dependence is implicit due to the time course of wing acceleration [88].
In general, all unsteady phenomena, except the LEV, persist for only a short
duration during the wing stroke and also depend on the timing of rotation. Therefore,
they do not contribute much to the time-averaged wing forces. Also, very high
rotational lift because of wing rotation was only observed at very low Reynolds
51
numbers (Re < 1000) and is not of much consequence for flapping-wing MAVs that
operate above that range. Therefore, for flapping wing studies, which are geared
towards MAV development, the strength and stability of the LEV should be the focus
because the LEV does contribute the most to the time-averaged forces independent
of the small variations in wing kinematics.
1.7 Review of Flapping Wing Experimental Studies
While many studies of the unsteady aerodynamics of pitching and plunging air-
foils predate interest in flapping wing aerodynamics [111–113], the flows produced by
insects and birds (and biomimetic mechanisms) have presented many new challenges
in the areas of flow measurement and simulation. In the early 1900s, Knoller and
Betz were the first to identify that positive propulsive thrust is produced due to pure
plunging motion of a wing in freestream. This is because the wing motion results in a
change in the effective angle of attack during the up-stroke and downstroke [114,115].
As mentioned previously, later work (e.g., References 20,89) has shown that a strong
LEV forms on such a wing and likely contributes to lift production, but there is still
a need for additional research on flapping wings to understand how they produce lift.
There have been several studies conducted on live insects and birds [116,117].
Mainly, PIV and flow visualization have been used to analyze the flowfield on live
insect and bird flapping-wings. Bomphery et al. [118] used two-dimensional PIV
to examine the velocity fields produced on a tethered hawkmoth. They performed
PIV at several locations in the wing stroke and compiled these results into a time-
52
resolved history of the flowfield. PIV measurements were taken of the flowfield of a
free-flying hummingbird by Warrick et al. [119]. They examined the complex wake
structure as well as how the shed vortices evolved and diffused into the far-field
wake. Concerning wing flexibility, Wang et al. showed that dragonflies improved
their aerodynamic efficiency by producing chordwise camber, thereby significantly
enhancing the thrust [120].
Other research on biological flyers has come from the zoology and biology
community and has focused on the wing behavior. For example, it was stated that
hover-capable birds and insects (e.g., hummingbirds and bumble bees) flap at wing
beat frequencies on the order of 30 to 90 Hz [121]. It was shown that the wing
motion throughout the stroke is generally in the horizontal plane. Larger flyers such
as song birds, eagles, and condors (wing beat frequencies 3 – 20 Hz) [121] often
flap their wings mostly in the vertical plane while changing their wing planform to
accommodate different flight modes. Over the flap cycle, dynamic twist (temporal
change in twist) is utilized to vary the angle of attack along with the flapping motion.
Later, it was discovered that large changes in wing pitch angle are necessary to
produce lift for hover. Many of the lift enhancement techniques discussed earlier
(e.g., leading edge vortices, Weis-Fogh mechanism, and rotational circulation) used
to increase thrust production over the stroke [99,102,103,122] were discovered by
observing natural flyers. However, measurements on live animals are extremely
challenging because specimens can vary from test to test, fatigue of the specimen
can be an issue, and it is not possible to perform direct power measurements on live
animals. These issues contribute doubt to the reported efficiency levels of biological
53
flappers. Therefore, researchers have turned to (often simplified) mechanical models
that mimic the flapping behavior.
The inherently three-dimensional nature of the flow structure, and the overall
dependence of the flow on the wing kinematics, geometry, and wing-wake interactions,
make a simplified experiment useful for understanding the flow physics. The reason
for many of the simplified flapping mechanism is because it is difficult to reproduce
small scale, complex reciprocating motions at high flapping frequencies. There have
been many simplified rigid revolving wing models used to mimic various aspects of
the wing stroke, especially the translational part of the stroke [101,123–128]. These
efforts have typically focused on a simplified wing model (e.g., a rigid flat plate)
and kinematics (e.g., pitching, plunging, translating, rotating) in an attempt to
identify the flow structures that produce lift, and shed light on the wing geometry
and kinematics that most efficiently produce these structures. One such model is
Dickinson’s robofly (see Fig. 1.27) [22]. This flapper was designed to model the
kinematics of a fruit fly by flapping in mineral oil at Reynolds numbers O(100). Both
wings were capable of rotational motion about three axes and were controlled by six
stepper motors for force sensors and digital particle image velocimetry measurements.
The main focus was on rigid wings.
Revolving-wing experiments in oil and water tanks do aid in gaining a better
understanding of the vortical structures produced on flapping wings. However, the
major technical barrier for such experiments is the contamination of the inertial force
with the measured aerodynamic forces. The inertial force could be much larger than
the aerodynamic forces. Therefore, experiments conducted for the same kinematics in
54
Figure 1.27: Robofly oil tank test setup [22].
air as well as in inertial can be performed so that the vacuum forces can be separated
from the total forces. This allows for the isolation of the aerodynamic forces [129].
Even though this may sound conceptually straightforward, implementing such a
technique and obtaining accurate aerodynamic data is quite challenging because the
inertial forces could be much larger than aerodynamic forces, especially in the plane
of flapping. Therefore, developing a good experimental procedure for inertial force
subtraction is useful. This is the primary reason why experiments should be carried
out in air, even though experiments may be executed more easily in a higher density
medium such as water or oil.
Many notable flapping wing studies have been conducted in air at the University
of Maryland on a biomimetic flapping-wing device [73,100]. This device was operated
at a mean chord Reynolds number of about 15,500 and is shown in Fig. 1.28. This
device was capable of single-degree-of-freedom flapping. Averaged air loads were
55
Figure 1.28: Passive pitch, bi-stable single-degree-of-freedom flapping mechanism [23].
measured using a load cell with piezo-resistive strain gauges. There were two key
observations. The inertial loads constituted the major portion of the total loads
acting on the wings tested and the propulsive thrust decreased at higher frequencies.
Flow visualization and PIV experiments showed that there was a continual formation,
convection and shedding process of the non-stable LEV, with several LEVs formed
on the upper surface of the wing during a single wing stroke [73].
Force and power measurements performed on dynamically scaled insect-wing
models have revealed some of the key physical phenomena contributing to the large
aerodynamic forces on insect wings [20, 22, 89, 90, 101]. Birch and Dickinson used
PIV to quantify the flow around the wing throughout the entire wing stroke of a
dynamically scaled fruit fly wing in an oil tank [89]. More recently, Hart et al. [130]
experimentally measured the instantaneous lift and drag of a pitching and plunging
small aspect ratio rigid wing. This study included PIV measurements of the flowfield
at one spanwise location (a very sparse data set). Here, it was shown that MAV-scale
56
flapping wings, which generally have a very low aspect ratio, experience significant
3-D effects that play an important role in maintaining flight. Though this study
does not explain the flow physics in much detail, the data is still useful for CFD
validation. Yuan et al. [131] conducted root based flapping experiments on a rigid
wing that mimicked avian wing flight kinematics. The focus was on obtaining
instantaneous force measurements over a flap cycle. Rigid-wing experiments such as
those performed by Yuan et al. are useful as valuable insight can be gained regarding
the fundamental flow physics [128,132]. However, in nature, the wings of birds and
insects are very light-weight and highly flexible. Rigid flapping wings do not mimic
the aeroelastic effects inherent to the wing motions seen in nature or those produced
by flight-capable MAVs [133]. For experiments, mechanical models make it easier to
systematically study the effects of variations in Reynolds number, angle of attack,
and wing aspect ratio on the behavior of the LEV. A detailed understanding of the
unsteady, and three-dimensional aerodynamics and their complex interaction on the
flexible wing and the flow is critical to understanding flapping MAV performance.
Some flowfield and airloads experiments on flexible wings have been conducted
in hover [134–136], but very few studies have been carried out on flexible flapping
wings in forward flight. There have been even fewer experiments performed in
the lower Reynolds number regime on flexible flapping wings for both hover and
forward flight. Tanaka et al. showed using experiments, hoverfly based wings (at
the insect scale) could exploit intrinsic compliance, but a rigid wing could be more
suitable for producing large lift [137]. For this study, there was no flowfield analysis,
no forward flight cases, no analysis on the effect of wing flexibility on drag, and
57
no modeling component. Ho et al. and Heathcote conducted rigid and flexible
flapping wing wind tunnel experiments [138–140]. The main parameters varied
were flap frequency and freestream velocity. While flexibility along leading edge
leads to deteriorating lift performance, flexibility near the trailing edge actually
improves propulsive thrust [138]. Heathcote performed one of the few aeroelastic
experimental studies for forward flight conditions. Force and flowfield measurements
were made on a heaving rectangular wing (AR = 6) in a water tunnel at Reynolds
numbers between 10,000–30,000 [139]. Only the spanwise flexibility (highly flexible,
moderately flexible, and rigid) was varied and the wings were stiff in the chordwise
direction. The conclusion of this study was that a limited degree of flexibility was
very advantageous, for a wing with intermediate flexibility, propulsive thrust was
increased by 50%, and for the highly flexible wing, propulsive thrust was reduced.
This experiment has been used for validation in many studies because it is one of
the very few studies involving structurally characterized flexible wings.
Malhan et al. [141] also carried out experiments on flexible flapping wings in air
and showed that wing flexibility plays an important role in aerodynamic performance.
More recently, Malhan et al. validated computational fluid dynamics (CFD) with
average force measurements for a MAV-scale flapping wing in forward flight [142].
However, detailed flowfield studies were not performed to analyze the flow state along
the wing during the stroke. It was highlighted that it would be useful to conduct
flowfield experiments where the unsteady phenomena occur, especially during the
dynamic process. Vortex shedding was caused by the flapping wing motion, but the
cause of the dynamic stall conditions is not always clear.
58
Though valuable insight can be gained into the fundamental flow physics of
flapping wings [128], most of the flow experiments have utilized rigid wings, which do
not mimic the aeroelastic effects inherent to the wing motions seen in nature or those
produced by flight-capable MAVs [133]. Even with the limited number of MAV-scale
experiments on flexible wings in forward flight, it is too time consuming to test
every parameter variation. Therefore this is an area that needs more exploration.
Detailed flowfield experiments are extremely challenging at the small scale and some
attempts have been made at overcoming those challenges. However, the approach
should be to analyze the flowfield with airloads for various wing types so that
forces can be placed in the context of what is happening in the flowfield. The low
number of previous studies underscores the need for more experiments (flowfield and
force measurements) in conjunction with computational fluid/structural dynamics
simulations that account for the complex unsteady aerodynamic effects of the flapping
wing problem. Validation of modeling efforts using experimental data will serve to
provide confidence in determining the effects of combinations of Reynolds number
and flapping frequency resulting in high effective angles of attack incurred during a
flexible wing’s motion. The next section contains a discussion of the modeling efforts
in the area of flapping wings.
1.8 Review of Flapping Wing Numerical Studies
A detailed understanding of the complex, unsteady, and three-dimensional
aerodynamics and the complex interaction is critical to an understanding of flapping
59
MAV performance; however, the governing equations that describe these processes
are non-linear and are challenging to resolve analytically. Attempts to model
such unsteady loads produced on flapping wings in forward flight using classical
aerodynamic analysis have been marginally successful. A few attempts have been
made at estimating the forces produced on a flapping wing theoretically. Minotti
worked to estimate these forces generate by a flapping wing by using empirical
coefficients [143]. The assumptions were that the flow was two-dimensional and
inviscid. The model correlated relatively well with experiment, but real flowfield
conditions are far more difficult for numerical solvers to handle. This can be
attributed to difficulties in modeling the highly nonlinear unsteady aerodynamic
effects produced by flow separation, shedding of concentrated vorticity, and wing-
kinematics associated with forward flight [56,144,145]. Because of this, few analytical
and numerical studies have been carried out on flapping wings in forward flight
using complex non-linear calculations. There have been various attempts at building
semi-empirical extensions based on classical theories; however, issues with modeling
turbulence and the implementation of moving, overlapped grids present challenges
that require more empirical data [120,146–149].
Using modified strip theory, DeLaurier developed an aerodynamic model for
large aspect ratio flapping wings in forward flight [150]. This model included
the effects of the mean camber, skin friction drag, and sectional mean angle of
attack. Partial leading edge suction, stall behavior, and vortex-wake effects were also
addressed. Many of the assumptions were based on the fact that the wing’s aspect
ratio is assumed large enough that the flow over each wing section is essentially
60
chordwise. This model was used to calculate average propulsive thrust and vertical
forces, power required, and propulsive efficiency of a flapping wing in steady level
flight. However, this model does not hold for low aspect ratio wings (the MAV scale).
Later, Singh produced an unsteady rigid-wing model to analyze insect wing
aerodynamics in hover [151]. This model was based on the indicial function and
was specifically modified to handle translation and rotational circulation based on
thin airfoil theory. The induced flow velocity was determined using only momentum
considerations (disk theory). Thin airfoil theory addresses the non-circulatory forces
and the Wagner function is used to account for the starting vortex produced during
both the rotational and translational circulation. The leading edge vortex was
determined by using Polhamaus leading edge suction analogy for delta wings at
high angles of attack [152]. The Kussner function is used to address the shed wake
and tip vortex effects. It was assumed that the inflow was uniform. This model
was validated against the Robofly oil tank data at very low frequencies [22]. From
this model, there was a significant difference in the experiment and predictions at
pronation and supination.
Computational analyses of flapping wings conducted by Lui and Kawachi,
examining the aerodynamic characteristics of the hawkmoth and fruit fly wing
shapes, focusing on the spanwise flow inside the core of the LEV [153]. Evaluation
of the characteristics of the LEV showed that the fruit fly wing shape maintained a
stable LEV throughout its translational motion, whereas for the hawkmoth wing, the
LEV was shed as the wing decelerated during the downstroke of the wing motion [41].
These studies were only conducted in hovering flight. Sun et al. computationally
61
examined the aerodynamics of various insects, including the fruit fly in hover and
in forward flight, reporting calculations of power requirements and effects of wing
kinematics [148, 149]. While these studies assessed flight dynamics, a potential
simplified model was used and the analysis was limited by the 2-D linear form of the
equations of motion.
Using CFD models to understand the rigid flapping-wing flowfield [148,153,154]
has thus far provided only limited additional physical insight. This is mainly because
of the difficulties in modeling turbulence and in preserving the three-dimensional
wake vorticity to relatively old ages in terms of wing flapping cycles. These studies
underscore the need for computational fluid dynamics and structural dynamics
simulations that account for the complex unsteady aeroelastic effects of flexible
flapping wings. Well-validated simulations using experimental data, both flowfield
and force measurements, are also necessary. In the literature, much of the research
has focused on experimentation or computational analysis of rigid flapping wings
rather than more realistic flexible flapping wings. This is because adding aeroelastic
wing deformation produced by aerodynamic and inertial loading throughout the
flapping cycle adds a level of complexity. Real flapping MAV wings are highly
anisotropic with varying levels of chordwise and spanwise flexibility. In order to
generate sufficient forces, the wings operate at high flap frequencies and significant
flap and pitch amplitudes. It has been shown that wing flexibility does improve its
flight performance and modeling this aspect is important.
Only a few aeroelastic solvers for flapping wings have been produced. The
extreme wing flexibility and low wing weight cause large non-linear deformations.
62
Therefore, it is very important to model these flexible wings accurately, with non-
linearities in both the structures and fluids. Newman presents research in the area
of linear membrane aerodynamics and solution methods [155]. However, Thwaites
was the first to analyze the nonlinear equation associated with the aerodynamics
of the wing membrane [156]. This two-dimensional sail theory enabled a variety of
experimental, theoretical, and numerical approaches to membrane aerodynamics.
Later, researchers expanded the analysis to include viscosity effects, nonlinearities,
and three dimensionality.
A tethered moth was simulated by Smith et al. [157] using an unsteady aero-
dynamic panel and finite element methods. This study highlighted the importance
of including the wake in the unsteady analysis of flexible wings. The method used a
combination of beam and membrane elements. However, the model did not address
the separation at the leading edge. As a result, there was not good correlation of
forces when compared to experiments.
Singh also developed an aeroelastic model [151]. At the University of Maryland
an in-house structural solver was coupled to an unsteady aerodynamic solver. The
structural solver was based on linear finite element plate analysis. It was validated
with prior research on rotating plates and in-house experiments. This analysis
was used to simulate experiments of flexible isotropic plates undergoing insect
kinematics in hover but only small flap amplitudes and low wing angles of attack
were examined. The main conclusion from this study was that aerodynamic loads
cannot be neglected while computing the wing response. Kim et al. [158] also used
modified strip theory [150] in their model. This model addresses the issues associated
63
with dynamic stall effects at high angles of attack. A reduced multi-body dynamics
model for a rectangular wing was used to account for structural flexibility. This
simulation was validated with experiments at low flapping frequencies.
Malhan et al. validated CFD with average force measurements for a flapping
wing in forward flight [142, 145, 159]. However, detailed flowfield studies were not
performed to analyze the flow state along the wing, especially for regions where
unsteady flow phenomena such as vortex shedding or stall occur. During the dynamic
process of the flapping wing motion where these conditions are more prevalent, the
cause is not always clear. Therefore, flowfield validation is necessary to determine
the effects of combinations of Reynolds number and flap frequency resulting in high
effective angles of attack incurred during the wing motion.
Though much computational work has given insight into the flapping wing phe-
nomena [140,160], much of this work is limited by a 2-D flow environment, simplistic
aerodynamic modeling (based on unsteady lifting line airfoil theory, unsteady panel
methods), simplistic structural models (based on linear/non-linear beam models,
linear plate/membrane models), or all of the above. Also, many of the simulation
results have not been validated against experiments.
1.9 Need for New Experimental Data
Some technological advances in micro manufacturing have illuminated the
intricacies of natural wing kinematics and have shown that the wing motion can
be reproduced on bio-mimetic vehicles. However, there is a dearth of experimental
64
data on flexible wings in forward flight. This is because the goal of most of the
previous studies was to understand only the aerodynamics of flapping wings and,
therefore, utilized rigid wings with prescribed kinematics. However, all the biological
wings and even the expected MAV wings are flexible and undergo large deflections
while flapping, due to aerodynamic and inertial forces. Even though the rigid wing
experiments could help understand the aerodynamics, a realistic flapping wing should
be analyzed as a coupled aeroelastic problem. Thus, these studies need to be extended
to flexible wings.
Specifically, most of the previous experiments were conducted using dynamically
scaled mechanical wing models flapping in water or oil at extremely low frequencies
(< 0.5 Hz) [20,22,88–90,101]. Such an approach was followed because the Reynolds
number of a natural flyer or even an MAV could be matched at very low frequencies
in a high density medium such as water or oil. This could greatly reduce the inertial
force contamination of the measured fluid dynamic forces (eliminating the need
for inertial force subtraction) and would also reduce the structural loads on the
flapping mechanism. Also, in most of these experiments, each degree of freedom
in the wing kinematics was actuated by independent servo motors and not using a
continuously rotating motor with a linkage mechanism. Therefore, another reason
for performing these low frequency experiments in water or oil is because of the
fact that these servo motors do not have the bandwidth to generate the required
wing kinematics in air at high frequencies. Even though this approach is more
convenient and even more accurate, than high frequency experiments in air, this
would limit such studies to rigid wings. These low frequency motions can simulate
65
high levels of fluid dynamic forces (and match the Reynolds number) owing to the
higher density of oil and water (almost 800 times higher than air), the inertial forces
would be several orders of magnitude smaller than the fluid dynamic forces. This is
because the inertial forces are proportional to the square of frequency. For a realistic
flexible wing flapping in air, the inertial forces have a stronger contribution than
aerodynamic forces. Therefore, in order to produce similar deflections on a flexible
wing, along with matching the Reynolds number and the reduced frequency, it is also
important to match the ratio of aerodynamic to inertial forces in these dynamically
scaled experiments, which is not feasible if the experiments are carried out at such
ultra-low frequencies in oil or water tanks. A flexible wing must be tested in air
at high frequencies to understand flapping wing aerodynamics. This has yet to be
done in much of the literature and only a small number of flight viable flight capable
flapping MAVs have been produced.
Although a few flight-capable flapping vehicles of varying performance levels
have been produced, there are still minimal experimental measurements, especially in
the area of flowfield measurements. For most of these studies, there has not been any
structural characterization of the wings. Currently, there is a need for experimental
data on structurally characterized flexible, light-weight wings. Of particular interest,
for both avian and insect flapping flight, is the creation and manipulation of flow
unsteadiness when these wings are simultaneously pitched (feathering) and flapped at
a particular wing beat frequency during the reciprocating motion. These parameters
become very important for understanding the flow physics on the realistic flapping
wings.
66
1.9.1 Chapter Summary
This chapter contains a discussion of the motivation and background for
MAVs. Advancements in MAV design, experiment techniques, and computational
efforts are highlighted along with many challenges associated with developing MAVs.
Specifically, low Reynolds number effects and the flowfield inherent to MAVs were also
described. In this flow regime, there are lower maximum lift coefficients, increased
boundary layer thickness, increased shear drag, and lower max L/D compared to
conventional aircraft. Details of the complexity of the aerodynamic environment are
explored in the areas of flowfield unsteadiness, wing-wake interaction, shed vortices,
flow separation, and dynamic stall. Three dimensional effects are enhanced by
the increased influence of root/tip vortices. These characteristics underscore the
challenges associated with analyzing and producing efficient MAVs.
In the area of experiment, the concerns associated with complex wing kinematics
and the difficulties in making measurements on small low aspect-ratio wings with
complex geometry/structural designs origins was presented. With modeling, the 3-D
unsteady low Reynolds number flow invalidates the 2-D assumptions. In general,
many reduced order models and methods become difficult to justify, especially when
large non-linear deflections are the norm. In general, there is a dearth of research in
the area of structurally well characterized flexible, light-weight flapping wings. The
literature lacks detailed experimentation and analysis of how the flowfield affects
force production mechanisms, especially in the context of biologically-inspired flexible
flapping wing MAVs in forward flight.
67
This chapter is concluded with the research objectives and an outline of the
dissertation.
1.10 Research Objective and Approach
The goal of this study was to assess the lift and drag of a flexible MAV-scale
flapping wing and associate them with the flowfield response. In-house motion
tracking, flowfield, and airloads experiments were executed in an open-circuit wind
tunnel on rigid and flexible flapping wings. The flexible wings were structurally
characterized by performing experimental testing and these structural properties and
test data were used to compare with an aeroelastic solver. The primary focus was to
examine the dynamics of a flapping flexible wing and to understand the contribution
of flapping kinematics along with wing deflections (primarily dynamic twist) to the
vertical and horizontal aerodynamic forces during a flap cycle.
The objectives of this research are listed below:
1. Design and characterize the structural parameters of a flexible wing
2. Develop effective flow diagnostic techniques to permit high-fidelity measure-
ments in the flowfield of a bio-mimetic flapping wing
3. Analyze flowfield in forward flight conditions (flexible and rigid wings)
4. Evaluate flight parameters in forward flight conditions
5. Apply aeroelastic model to study the flowfield response to wing flexibility
68
1.11 Organization of the Dissertation
In the present work, the temporal evolution of the flow features associated with
rigid and flexible flapping wings in forward flight were quantified and the predictive
capability of a computational flow solver coupled with a structural analysis tool was
compared using flowfield measurements (using PIV) and direct force measurements.
Rigid wing experiments are used as a baseline. Force and PIV experiments are
performed using pure flapping kinematics.
Due to the torsional compliance of the wing, a spanwise variation in pitch angle
(twist) was produced, in addition to the temporal variation (dynamic twisting). The
parameters defining the wing kinematics are wing beat frequency and root pitch
angle variations, which were examined systematically. Pertinent flowfield results are
presented with experimental and computational aerodynamic forces. Specifically,
analysis of the LEV, downstream wake, and airloads associated with the wing are
examined using the CFD-CSD model and experiment results.
Utilizing non-intrusive flow and force measurement techniques along with an
aeroelastic solver to understand the influence of wing flexibility on force production
and the flow physics of a flapping wing MAV in forward flight,
• Chapter 1 contains information about the motivation for MAV development
and highlights the pertinent past research contributions.
• Chapter 2 describes the research methodology and approach. Specifically, the
areas of discussion are the experimental and analytical methods.
69
• Chapter 3 shows a validation/comparison of the aerodynamic and structural
solver with experiments.
• Chapter 4 contains the findings related to the flapping wing fundamental flow
physics.
• Chapter 5 summarizes the key conclusions from this work.
• Chapter 6 presents the major contributions of this dissertation research con-
ducted at the University of Maryland and suggests potential follow-up research.
70
Chapter 2: Methodology: Numerical Approach and Experi-
mental Setup
This chapter contains a discussion of the approach and methodology associ-
ated with the numerical aeroelastic solver used in conjunction with particle image
velocimetry, force measurements (airloads analysis), and motion tracking (for struc-
tural properties). Wind tunnel specifications, experiment challenges, and experiment
uncertainty are also presented.
2.1 Numerical Approach
An in-house CFD solver, OVERTURNS, is used to model the aerodynamics of a
flapping wing. This solver is a Reynolds Averaged Navier Stokes Solver and has been
used extensively for rotary wing applications, but has been extended to low Reynolds
number flapping wing flows. The focus is to simulate the flowfield of flapping wing
MAVs. However, only one wing is modeled in this study and its surface can be
treated as a solid wall. The aerodynamic solver is coupled to a multibody dynamics
solver to model the structural dynamics. The numerical solution algorithms are
described in this section. The flow domain that is being studied is initially identified
71
and the details of the mesh system, aerodynamic solver, structural solver, and the
connectivity approach are discussed.
2.1.1 Description of Flow Solver
The 3-D fluid dynamics of the flapping wing were computed using a compressible,
structured, overset Reynolds Averaged Navier-Stokes (RANS) solver, OVERTURNS
[49]. This overset structured mesh solver utilizes the diagonal form of the implicit
approximate factorization method developed by Pulliam and Chaussee [161] with
second-order accuracy in time. The advantage of using an overset structured grid is
that different grids can be generated independent of each other and can be placed
in the region of interest without any distortion [49]. Due to these advantages, the
current work employs overset meshes. To calculate the inviscid terms, a third-order
Monotone Upstream-Centered Scheme for Conservation Laws [162] with Roe flux
difference splitting [163] and Korens limiter [164] is used. A second-order central
differencing method is implemented in order to calculate the viscous terms of the
compressible RANS equations. Given the relatively low Mach numbers of the flapping
wing cases, a time accurate, low-Mach pre-conditioning dual time-stepping scheme
described by Buelow et al. [165] and Pandya et al. [166] is applied. The low-Mach
preconditioning not only improves the convergence of the simulations, but also the
solution accuracy [49]. The Spalart-Allmaras [167] turbulence model is employed for
closure of the RANS equations. The equation is given by:
∂ν¯
∂t
+ V · (∇ν¯) =
1
σ
[∇ · ((ν¯ + ν)∇ν¯ + cb2(∇ν)
2] + cb1S¯ν¯ − cw1fw
[ ν¯
d
]2
(2.1)
72
These equations relate the Reynolds stresses to the mean strain. The constants
in this equation are cb1 = 0.1355, cb2 = 0.622, cw1 =
cb1
κ +
1+cb2
σ , κ = 0.41, σ =
2
3 ,
and cw2 = 0.3, cw3 = 2.0. The turbulent eddy viscosity, νt, is obtained by solving
this partial differential equation for a related variable, where the two quantities are
related by νt = ν¯fv1. Here, fv1 is a function of ν¯ and the molecular viscosity, ν. The
equation for fv1 is
fv1 =
χ3
χ3 + c3v1
(2.2)
with χ = ν¯ν , cv1 = 7.1, fv2 = 1 −
χ
1+χfv1
, fw = g
[
1+c6w3
g6+c6w3
]1/6
. In the equation,
g = r + cw2(r6 − r) and r = min( ν¯S¯κ2d2 , 10.0). S¯ is equal to S +
ν¯
κ2d2fv2 and S is |ω|.
The distance from the wall is d, and V is the mean flow velocity [167].
Closure for all variables is provided by loosely coupling the Navier-Stokes
equations and obtaining the turbulent eddy viscosity. From this, the shear stress
in the moment and energy equations can be evaluated. The turbulence model has
the advantages of ease of implementation, computational efficiency, and numerical
stability. An implicit hole cutting method developed by Lee [168], and further refined
by Lakshminarayan [49], is employed to find the connectivity information between
the overset meshes used in the simulations.
Previous studies [169–171] suggest that a Large-Eddy Simulation (LES) may
more accurately predict the highly vortical and separated flow present in low-Reynolds
number MAV-scale CFD problems. However, in comparison to RANS, the LES
approach would yield a penalty of higher computational costs and increased grid
73
refinement. Validation of the current solver against the LES results shown by
Gordnier et al. showed good agreement [171]. Therefore, RANS was used for all the
simulation results presented in this work.
2.1.2 Description of Grid System and Simulation
An avian wing has very complex wing motions that are a combination of
flapping, pitching, and wing folding/bending. The two main degrees of freedom,
flapping and pitching, are considered for this study. The wing planform used
during simulation was based on the rectangular, low-aspect ratio wing used during
experimentation. In the computational model, the wing has an aspect ratio of 1.67
and a flat-plate cross section consisting of a thickness-to-chord ratio of 1.0%. In the
simulation, the wing is offset from the flapping axis by 0.33 chords to account for the
20% root cutout in the experimental setup. An overset system of meshes, consisting
of a C-O type airfoil mesh for wing and Cartesian background mesh is used for
the computation. The wing mesh has 307×161×75 grid points in the wrap-around,
spanwise and normal directions, respectively. To better capture the shed wake and
vorticity at these locations, points were more tightly grouped toward the leading
edge, trailing edge, wing root, and wing tip. All simulations were run using at least
6 sub-iterations per time-step to minimize linearization errors with farfield boundary
conditions being implemented 20 chord lengths away from the wing surface. When
the grid has been generated and grid motions are prescribed, the flowfield properties
at each grid point within the overset mesh system can be obtained by solving the
74
Figure 2.1: Wing mesh embedded in background Cartesian mesh.
conservation laws of physics for fluid flow. An example of the CFD grid can be seen
in Fig. 2.1.
2.1.3 Grid Sensitivity Study
A grid sensitivity study was executed for the rigid wing simulation. All
computational grid sensitivity simulations were carried out on the flat plate airfoil
described in the previous section. In order to determine the appropriate simulation
grid size, a single flapping wing case with second-order spatial discretization was
performed on three different C-O meshes. The nominal mesh consisted of 267×141×85
nodes in the wrap-around, spanwise and normal directions. A coarse mesh and fine
mesh consisted, respectively, of 133×113×65 and 397×169×105 in the wrap-around,
spanwise and normal directions. Each mesh was used to simulate the 4 Hz flapping
75
case at a pitch angle of 0◦. A total of 1440 time-steps per cycle were carried out
for a duration of 4 flap cycles. Figure 2.2 shows a comparison of the predicted
aerodynamic force coefficients for the three grids tested during the 4th flap cycle.
It can be seen that the aerodynamic coefficient values obtained from the coarse,
nominal, and fine meshes show similar agreement. Note that the results from the
coarse mesh show greater oscillations in the vertical force time-history near instances
of peak aerodynamic force production. This is because the coarse mesh does not have
enough nodes to completely resolve the leading edge vortex formed. Consequently
the nominal mesh was used to obtain all the results discussed in the subsequent
sections to resolve the flow features without increasing computation time.
2.1.4 Structural Model and Coupling
The structural analysis portion of the numerical simulations was conducted
using MBDyn, which is an open-source general purpose multibody software developed
at Politecnico di Milano [172, 173]. MBDyn integrates the equations of motion
temporally for a constrained mechanical systems (in this case for flapping wing).
The equations associated with the linear and angular motion of a set of independent
rigid bodies (Newton-Euler equations) are explicitly constrained by a set of algebraic
equations. These equations express the kinematic constraints between the bodies.
Modifications were made to enable the use of non-linear 2-D structural elements
(shells) and allow for generic Fluid-Structure Interaction functionality. This solver’s
implementation of non-linear beam elements, in conjunction with the newly added
76
(a) Vertical lift coefficient, CZ.
(b) Horizontal lift coefficient, CX.
Figure 2.2: Variation of predicted aerodynamic force coefficients for different mesh
resolutions (k = 0.32, θ = 0◦).
77
non-linear shell elements [174], gives it the capability to accurately model the large,
non-linear deflections and complex structural dynamics of highly flexible wings [141].
The structural analysis is based on the direct integration in time of an Initial Value
Problem that describes the dynamics of a set of arbitrarily interconnected bodies.
Compliant connectivity is realized in the form of non-linear finite elements, using
the aforementioned beam and shell elements, while the kinematic constraints are
modeled by algebraic relationships enforced using Lagrange multipliers.
In order to facilitate the data exchange between the CFD solver (OVERTURNS)
and the CSD solver (MBDyn), a Python computational framework was implemented.
This coupling algorithm allows for the exchange of structural deformations (kinematic
mapping from the CSD to the CFD solver) and aerodynamic loads (from the CFD
to the CSD solver) at the fluid-structure interface (i.e., the wing surface). Tight-
coupling is used for the data exchange, meaning that information is passed during
each sub-iteration of the non-linear problem solution procedure for a given time step.
However, in an effort to reduce computational cost, it is relaxed as soon as it is
allowed by the relative compliance of the coupled problem. While coupling of the
two solvers was done using both a first order and staggered second order accurate
approach, which satisfies the discrete geometric conservation law, it was observed
that both approaches gave similar results. It should be noted that the domains and
meshes of the two solvers are non-conformal. These incompatible domains were
mapped via an original scheme that preserves the work exchanged between the
structural and the aerodynamic domains. This mapping is based on a Moving Least
Squares fitting of the discretization of the interface between the two domains using a
78
compact support that consists of Radial Basis Functions. The full simulation results
were compared to flowfield and force experiment data.
2.2 Experimentation
This section contains a discussion of flapping wing mechanism design, rigid
and flexible wing designs, and the high-speed flow measurement techniques and
force measurements. The main experiment technique for measuring the flow was
time-resolved digital particle image velocimetry (DPIV). PIV was used to acquire
velocity fields, and the components of vertical (lift) and propulsive or drag force were
measured using a force transducer. These flow interrogation techniques allowed for
the quantification of the unsteady mechanisms.
2.2.1 Flapping Mechanism and Wing Design
A flapping mechanism was used to provide the required flapping kinematics to
the wing (see Fig. 2.3(a)). A schematic of the four-bar linkages is shown in Fig. 2.3(b).
The link AD is the driving link and BC is connected to the wing. If the link AD
rotates by θ, the driven link rotates by φ (wing flap angle) which is calculated as
follows:
x = L2 cos θ − L1 (2.3)
y = L2 sin θ (2.4)
79
φ = tan−1
y
x
− cos−1
L24 + x
2 + y2 − L23
2L4
√
x2 + y2
(2.5)
For the mechanism, the lengths of the links were chosen to closely replicate
sinusoidal motion. The baseline linkage lengths were L1 = 0.42 cm, L2 = 5.52 cm,
L3 = 6.41 cm, and L4 = 1.6 cm. The wing would be attached to L4. Flapping
kinematics were designed to be close to harmonic for the flapping amplitude of 40◦.
The four-bar was driven by a flywheel attached to the shaft of a motor.
A 260-W outrunner motor manufactured by MODEL MOTORS (Czech Repub-
lic; AXI 2217) was used to rotate the flywheel. A 3:1 planetary gear box was used to
provide the required torque. A potentiometer was used to measure the instantaneous
angular position of the wing as it flaps. The flapping frequency was measured
from the 1/rev signal obtained using a Hall switch and was verified using a digital
laser tachometer, stroboscope, and the PIV system timing hub. The flapping-wing
mechanism is fixed to the bottom of the wind tunnel such that the flow is parallel to
the wing plane when the angle of attack is zero. A wing attachment was designed
such that the wing can be set at any desired geometric angle of attack. Only pure
flap tests were executed (no active wing pitching). This means that the wing is held
fixed at the root and is flapped at a set initial pitch angle. As the wing flaps, there
is a spanwise variation in pitch at one instant of time for the flexible wing, so the
wing sections rotate by different amounts along the span due to torsion flexibility.
Also, the spanwise twist varies as a function of time. This is referred to as dynamic
twisting and is caused by the inertial and aerodynamic forces acting on the wing
80
during flapping.
Rigid wings were fabricated using unidirectional carbon rods, which are 1.5 mm
in diameter as shown in Fig. 2.4(a). High-speed videos of these wings while flapping
showed that there was no discernible deformation. These wings had a rectangular
planform with a span of 12.7 cm and a chord of 7.62 cm with a 20% (3.05 cm) root
cutout. For PIV experiments, a thin layer of matte black paint was used to reduce
reflections. The wing mass was 8.2 grams.
Similar to the rigid wings, torsionally flexible wings were also fabricated using
unidirectional carbon rods, which are 1.5 mm in diameter as shown in Fig. 2.4(b).
The chordwise ribs (Root, Mid, Tip) were constructed from unidirectional single
layered carbon fiber strips. These wings also had a rectangular planform with a span
of 12.7 cm and a chord of 7.62 cm with a 20% (3.05 cm) root cutout. The wings were
rigidly attached to the four-bar mechanism at the root tab. For PIV experiments,
the wings were covered with heat resistant film to prevent laser burn, and a thin
layer of matte black paint was used to reduce reflections. The wing mass was 6.47
grams.
A six-component balance was used to measure the flapping loads. This load
cell, the ATI Nano 17, weighs less than 10 grams and was attached to the root of the
wing to measure the loads acting on the wing directly without any interference from
the inertial loads generated by the rest of the mechanism. The first natural frequency
of this balance is 7200 Hz. The force transducer was connected to a National
Instruments (Austin, TX) USB DAQ device (NI USB-6251). Raw data from the
sensors were transmitted to a computer using a software called LabVIEW. These
81
(a) Flapping mechanism.
(b) Four-bar linkages.
Figure 2.3: Four-bar linkages and flapping mechanism.
82
(a) Rigid wing.
Leading edge spar 
Ro
ot r
ib 
Mid
 rib
 
Tip
 rib
 
5 in 
3 in 
(b) Flexible wing.
Figure 2.4: a) Rigid and b) flexible wing construction.
83
voltages were later post-processed with the ATI-supplied calibration matrices to
generate the observed forces and moments. Since instantaneous force measurements
would include significant inertial forces, only the time-averaged force measurements
were used for validating the analysis.
2.2.2 Particle Image Velocimetry Setup
PIV is a measurement technique that is non-intrusive and gives a planar velocity
field within a desired region of interest. This technique is especially useful for MAV
applications where the scale of the flow is such that hot wire anemometers or wing
pressure taps are not feasible. In general, uniformly dispersed tracer particles are
introduced to the fluid medium to track the flow. The three main components
of the digital PIV system are the high repetition pulsed laser (with optics), PIV
camera, and data acquisition system (including a sychronizer). The laser produces a
planar laser light sheet. Particles within the region of interest are illuminated by
the laser sheet. The digital camera is orthogonal to the light sheet. The camera is
uniformly focused over the region of interest. The seeded flowfield is then illuminated
twice within a small pulse separation time, ∆t = t2 − t1, which is on the order of
microseconds. The camera is then digitally synchronized with the laser to capture
two successive images (frame A and frame B). After a time series of image pairs is
obtained, the raw data is hyper-streamed to a processing computer.
For the selected pulse separation time, each image pair contains the pixel
displacement of the particles in that region of interest. During processing, the images
84
are divided into smaller interrogation windows. A cross-correlation technique is used
to match the intensities of the particles between the two frames within each small
window, and then computes the magnitude and direction of the pixel displacement
(∆x,∆y) [175]. This process was performed utilizing a Fast Fourier Transform (FFT)
algorithm in the frequency domain [176]. A deformation grid algorithm is used to
improve particle correlation [177]. Once the pixel displacement was found, the local
velocity could be calculated using the equation
{
U
V
}
=
1
M∆t
{
∆x
∆y
}
(2.6)
where M is the image magnification. The image magnification is calculated within
the PIV software from a master image with a calibration plate placed in the laser
plane to calibrate the ratio of pixels to millimeters. The cross-correlation process
was then repeated for all interrogation windows within the image, the outcome being
a planar velocity field. The interrogation windows were sized so there were at least
5-10 seed particles within each and the particles moved only about one quarter of
the window length. One of the assumption associated with the PIV cross-correlation
technique is that the particles within each interrogation window translate linearly
between image pairs. With this in mind, the interrogation window size, as well as
the value of ∆t, was chosen to best resolve the relatively steep velocity gradients
induced by the flapping wing. The PIV system was acquired from LaVision Inc and
Fig. 2.5 outlines the PIV process methodology.
85
Figure 2.5: Schematic depicting the general setup of a 2-D PIV system and image
processing methodology.
A schematic of the PIV test setup is shown in Fig. 2.6. A low-speed, open-
circuit/closed-section wind tunnel was used to conduct the experiments. The test
section cross sectional dimensions are 20 in × 28 in, and the tunnel’s maximum
speed was 100 mph. At the tunnel inlet, the flow was seeded using a six-jet atomizer
allowing for sub-micron sized tracer particles (<0.2 µm) to be introduced into the
wind tunnel inlet. Bis (2-ethylhexyl) sebacate was used as the seeding fluid. PIV
images were acquired in chordwise planes for the span locations y/b = [0.3 0.4 0.5 0.6
0.7 0.8 0.9] using the time-resolved measurement system. A double-pulsed high-speed
laser illuminated the seeding particles (Litron LDY304 Nd:YLF laser, wavelength
of 527 nm with 30 mJ/pulse at 1 kHz rep-rate). Two mirrors were used to redirect
portions of the laser sheet back towards the flapping wing to reduce the shadow cast
86
Figure 2.6: Schematic PIV experiment setup in wing tunnel test section.
by the wing. A high-speed camera (Phantom V311, 4MPx, 3,250 fps) was positioned
above the test section and oriented downward to view the wing through a circular
acrylic window. The actual tunnel test section is shown in Fig. 2.7 and the camera
view is from the top of the wind tunnel. The flapping mechanism was mounted
vertically from the bottom of the test section with the wing cantilevered. To avoid
any obstruction to the flow, the flapping mechanism was installed outside the test
section with only the wing exposed to the flow. The wing pitching mechanism was
located at the root, permitting an unobstructed field of view for the camera. PIV
experiments were conducted with the wing flapping at the pitch angles θ0 = 0◦− 24◦
in increments of 3◦, for 0, 4, 6, 8, and 10 Hz for a freestream velocity of V∞ = 3 m/s.
The PIV images contained the pixel displacement of the seed particles for
the selected pulse separation time. The seeding density was adjusted to provide
at least 10 particles in each interrogation window [178]. The raw PIV images were
87
Figure 2.7: Actual PIV experiment setup in wing tunnel test section.
then divided into smaller 48-by-48 pixel interrogation windows (with a 50% overlap)
and a deformation grid correlation method was used for processing [177]. A cross-
correlation FFT based procedure was used to match the intensities of the particles
between the two images within each small window, providing the magnitude and
direction of the pixel displacements [179]. This was carried out with interrogation
windows of size 24-by-24 for better resolution of the higher velocity gradients within
the flow. Spurious vectors in the results were determined using a Gaussian peak
method with a signal-to-noise ratio of 1.3. The data was sent through a local vector
validation process by examining a neighboring set of 3-by-3 vectors using a universal
median test. Vectors identified as spurious were then removed. PIV data (e.g.,
50 image pairs corresponding to the downstroke and upstroke respectively) were
phase-averaged from each experimental case.
Concerning alignment, great care was taken such that the PIV camera was
88
oriented at the center of the wind tunnel test section and the camera viewing plane
was perpendicular to the wing span at the mid-stroke location. A PIV mask of the
static wing was created within the frame. This mask was used as an indicator of
the wing chord at mid-downstroke and mid-upstroke during flapping. Time-resolved
PIV data was acquired during the wing flapping motion at 1300 frames per second
and only the image pairs that fit the custom mask (produced when the wing was
static) were used to represent the mid-upstroke and mid-downstroke positions.
2.2.3 Wind Tunnel Specifications
The wind tunnel experiments were performed using an open circuit, low-
turbulence wind tunnel located at the University of Maryland (schematic shown in
Fig. 2.8). The main components of the wind tunnel are the screen, nozzle (contraction
section), test section, diffuser, and the fan. Downstream of the test section is a
diffuser that slows the flow as it approaches the impeller. The impeller is driven
by a variable speed electric motor. The tunnel inlet is where seed particles were
passed through a honeycomb structure, which aided in removing much of the larger
turbulence and eddies that would enter the test section. The wind’s exit was released
into the open air. DPIV was used to measure the background turbulence within the
wind tunnel at the center of the tunnel at a height of 10 in (tunnel center), 5 in,
and 2 in from the tunnel floor of the test section. An interrogation window size of 2
in×2 in was utilized to quantify the freestream fluctuations. Ten seconds of data
was obtained at a ∆t of 50µs. Though the target freestream velocity was 3 m/s,
89
Figure 2.8: Schematic of low speed wind tunnel.
the tunnel velocity was set at 1, 3, 6, 9, and 23 m/s. The turbulence intensity in
the test section has been determined by dividing the standard deviation of the wind
tunnel speed by the average freestream velocity [180]. Figure 2.9 shows the percent
turbulence for various locations in the wind tunnel with varying tunnel speed. The
higher levels of turbulence were seen at a height of 2 in, which is close to the tunnel
wall. Close to the wall, as the tunnel speed is increased, the turbulence increases as
well (due to wall effects). The wind tunnel fluctuations remained below 2% in all
cases. A Fast Fourier Transform was applied to the freestream velocity, V∞, data
and there was no discernible frequency peak. Additionally, the velocity fluctuation
signal magnitude was extremely low. Also, the low intensity of the fluctuations was
such that it did not have any effects on the flow structures because wing flap speeds
and flow feature velocities were several orders of magnitude greater than the tunnel
fluctuations. Therefore, tunnel fluctuations are negligible.
The two main parameters associated with flapping flight are the reduced
frequency and Strouhaul number. The reduced frequency is a measure of flow
90
Figure 2.9: Variation in wind tunnel turbulence with wind tunnel speed.
unsteadiness. It is the ratio between forward velocity and flapping velocity. This is
expressed in an equation as follows:
k =
Ωc
2V∞
(2.7)
where Ω is the flapping frequency, c is the wing chord, and V∞ is the freestream
velocity. Flow is considered unsteady if k > 0, but can generally be considered
quasi-steady for a reduced frequency 0 < k < 0.03, where unsteady effects are not
significant [7]. For 0.03 < k < 0.1, flow can be considered moderately unsteady, and
beyond k = 0.1, flow is considered fully unsteady. Reduced frequency is typically
between 1 and 10 for small insects [7]. The reduced frequencies, k, for this study
corresponding to flap frequencies, Ω, are 0, 0.32, 0.48, 0.64 and 0.80 respectively.
91
Strouhal number describes the oscillating flow mechanism and is also utilized to
characterize flapping in forward flight. Strouhal is related to reduced frequency by
St =
kA
pic
(2.8)
where A is the flap amplitude. This data set is applicable to low Reynolds number
flyers where the Strouhal number is within the range of 0.2 < St < 0.4 [181].
Conversely, the advance ratio is given by
J =
V∞
2piΩA
(2.9)
At first glance, this dimensionless parameter may appear to be the inverse of the
reduced frequency. Ho et al. claimed that this parameter accounts for the three-
dimensional nature of the flow [138], where the breakpoint between quasi-steady and
unsteady flow occurs when J = 1. For J > 1, the flow can be considered quasi-steady
while J < 1 corresponds to unsteady flow regimes. Most insects operate in this
unsteady regime. This experiment set explores the set of advance ratios J = [2.4317,
1.6207, 1.2154, 0.9722]. The main experiment parameters for this dissertation are
listed in Table 2.1.
2.2.4 PIV Experiment Challenges
Many of the challenges in performing PIV measurements on flapping wings
resides in the ability to view the flow associated with 3-D unsteady low Reynolds
number aerodynamic phenomena occurring on a small low aspect ratio wing under-
92
Table 2.1: Time-resolved PIV test matrix.
Freestream, V∞ 3 m/s
Reference Reynolds number, Re 15,000
Flap amplitude ±40◦
Span location 30% – 90%
Initial Pitch Angle, θ0 0◦ – 24◦, ∆θ = 3◦
Flap frequency, Hz 0, 4, 6, 8, 10
Reduced frequency, k 0, 0.32, 0.48, 0.64, 0.80
Strouhal number, St 0, 0.13, 0.2, 0.26, 0.33
going large non-linear deformations with complex wing kinematics. Specifically, it is
difficult to acquire the optimum laser placement because every wing position and
phase angle gives at least some surface reflections from the wing. These spurious
reflections can, in some cases, obscure the flow features or otherwise limit the ability
to track the flow features in time because they exist for a very short duration of time.
Wing masking and background image subtraction were found to be useful techniques
for removing unwanted reflections before processing the PIV images. In particular,
intense reflections from the wing planform made the cross-correlations near the wing
surface extremely difficult. These reflections were slightly reduced by the appropriate
selection of camera aperture setting and laser intensity level. Masking was used
to remove areas in the region of interest that were not desired for processing and
background subtraction involved generating a composite minimum intensity image,
which was then subtracted from each individual PIV image.
2.2.5 Experimental Uncertainty
The preset wing angle of attack and spanwise position are accurate to within
0.25◦ and 1 mm respectively. Again, the flapping frequency was verified using a digital
93
laser tachometer, a stroboscope, and the PIV system timing hub. The two main
sources of error associated with DPIV are the mean bias error (bias) and root-mean-
square (RMS) error (RMS) where the total error (tot) is equal to the sum of bias
and RMS. The fundamental source of bias and RMS error is the implementation of
cross correlation. Other contributors include the sub-pixel accuracy of the correlation
peak-finding scheme and noise within the particle images themselves. Both the
mean-bias and RMS errors have been found to be on the order of 0.1 pixel for cross
correlation and the error associated with particle image pattern matching are an
order of magnitude less than those of cross correlation [182]. For the current PIV
setup, bias = −0.01 due to image pixel loss. The RMS error, produced from the
calibration, was kept below -0.3 pixels. Therefore, the total error associated with
the PIV measurements is tot = −0.04 pixels. Based on an average displacement of 6
pixels, the estimated uncertainty of the measured velocity is 0.667%. There is also
a confidence level associated with the motion tracking measurements. Given the
size of the retro-reflective markers (3.5 mm in diameter) and the relative proximity
of the motion capture camera system to the flapping wing or wing frame, it was
estimated that the error in the spatial tracking of the markers was roughly 2.8% of
the measured displacements.
With the PIV experiments, the LEV and trailing edge vortices were imaged
at strategic instances during the wing stroke. This was compared to the predicted
flowfield, which produced the LEV formation, convection, and shedding. Force
measurements quantified the effect of the LEV on the lift and drag. The results
obtained contributes to the understanding of flapping-wing flow physics. From these
94
experiments, needed data is added for the low Reynolds number realm. The next
section contains a discussion of how the structural properties for the flexible wing
were characterized.
2.3 Structural Properties
Characterization of the flexible wing frame structural properties was primarily
conducted using the VICON motion tracking system. Tensile tests were used to
obtain the properties for the wing covering. In-house VICON motion tracking
experiments (static and dynamic) were done to generate more data for the structural
model validation.
The VICON system allows for the tracking of an object in three-dimensional
space. This is done by applying retro-reflective reference markers to a surface and
placing high-speed infrared cameras in various positions and orientations around the
object. The camera system then tracks the markers in space and time by utilizing
triangulation methods. The camera system must be placed such that at least two
of the cameras can view each marker throughout the duration of the experiment.
A VICON camera system has an operable capture frame rate in the range of 20 to
2000 frames-per-second (fps) depending on the hardware platform, camera choice,
and number of cameras being used. For this study, four cameras were strategically
placed around the test area at different heights and angles to track the markers. Half
sphere retro-reflective markers were placed on the wing. Each marker’s diameter was
millimeters. Figure 2.10 shows the VICON test setup and the camera placements.
95
Figure 2.10: Typical test setup for motion tracking system.
During motion tracking experiments, it is very important to ensure that the infrared
cameras have an unobstructed views of the markers. The total mass of each marker
was 0.02 g. After the raw data were captured, marker reconstruction and processing
provided the complete displacement of the wing components during static tests and
the time-history of the three-dimensional location of each marker during dynamic
tests.
The structural properties of each of the wing’s members were obtained experi-
mentally, and then they were used to build a structural model in the Multi-Body
Dynamics solver. Bending and torsion tests were carried out for the chordwise ribs
and the leading edge spar. Loads were added to simulate bending and torsion and the
wing member deflections were measured using four infrared cameras. The bending
and torsion stiffness properties (EI and GJ) were then obtained from these results.
Fig. 2.11 shows the marker placement and setup. The determination of the bending
96
and torsion stiffness parameters in this work are based on Euler Bernoulli Beam
theory.
Figure 2.11(a) shows a schematic of the marker and representative load place-
ment to measure the bending of the tip member. The retro-reflective markers are
shown on the schematic and were placed at the leading edge, midpoint, and tip of the
member. To calculate the bending stiffness from the measured, nonlinear deflections,
an equation for bending is given using a homotopy analysis method with explicit
formulas for calculating large deflections of a beam [24].
A schematic of the large deformation of a cantilever beam under point load at
the free tip is shown in Fig. 2.12. The bending equation of a uniform cross-section
beam with large deformation is expressed as follows:
ds
dθ
=
P
EI
(l1 − x), θ(0), θ
′(l) = 0 (2.10)
where the arc-coordinate of the neutral axis is s, the horizontal coordinate from the
fixed end is x, the beam length is l, the point load at the free tip is P . The bending
stiffness is EI, the rotation of cross-section of the beam is θ, and the horizontal
distance between the two ends is l1. For the cantilevered member, the axial elongation
is smaller than the deflection at the tip.
Differentiating the equation with respect to s and then using the dimensionless
variables ξ = s/l, the equation 2.10 becomes
θ′′ + α cos θ θ(0), θ′(1) = 0 (2.11)
97
(a) Isolated bending.
(b) Isolated torsion.
Figure 2.11: Schematic of VICON test for isolated bending and torsion testing.
98
Figure 2.12: Large deformation of a beam under point load at free tip [24].
where α = Pl
2
EI . The rotation angle of the cross-section at the tip is θB = θ(1), and
the exact vertical displacement of the free tip is given by the equation
fB = l − 2[E(µ)− E(φ, µ)]
√
EI
P
(2.12)
where E(µ) and E(φ, µ) are the elliptic integrals of the second kind shown below:
µ =
√
1 + sin θB
2
φ = arcsin
(
1
√
2µ
)
(2.13)
With this, the dimensionless vertical displacement at the free tip is shown below
fB
l
= 1−
2
√
α
[E(µ)− E(φ, µ)] (2.14)
Additionally,
l1
l
=
√
2EI
P l2
sin θB =
√
2 sin θB
α
(2.15)
The dimensionless horizontal displacement of the free tip is expressed by the following
99
equation:
δB
l
=
l − l1
l
= 1−
√
2 sin θB
α
(2.16)
If there are large deflections,
√
α = K(µ)−F (φ, µ) where K(µ) and F (φ, µ) are
the elliptic integrals of the first kind. The solution is obtained using the homotopy
analysis method where for large deflections,
θB =
α
2
f(α)
g(α)
(2.17)
and
f(α) =1 + 3.98575× 10−2α2 − 5.41174× 10−2α4 + 5.72575× 10−3α6
+ 3.79533× 10−4α8 − 8.87896× 10−6α10 + 2.63041× 10−8α12
− 1.51429× 10−11α14 − 2.29142× 10−15α16
− 3.45006× 10−21α18 − 7.00678× 10−28α20
(2.18)
g(α) =1 + 0.131524α2 − 5.99231× 10−2α4 + 2.34466× 10−3α6
+ 9.90299× 10−4α8 − 1.37001× 10−5α10 + 3.44172× 10−8α12
− 1.45098× 10−11α14 − 2.26721× 10−15α16
− 3.50731× 10−21α18 − 7.00678× 10−28α20
(2.19)
100
This analysis was used to predict the bending stiffness, EI, for each flexible wing
member from the measured deflection data.
Figure 2.11(b) shows a schematic of the test setup of a single rib with the load
applied on the wing frame for a purely torsional loading. To increase the moment
arm, a carbon beam is put on the tip. One load is applied from the top with a pulley
while the other hangs freely. To be sure that the load applied is not creating bending,
in addition to torsion, the vertical displacement of the beam tip was measured to
ensure minimal deflection. Specifically, the vertical displacement of Marker 3 was
verified to ensure that Markers 4 and 5 received the same load. Using this method,
the shear center is the beam center (Marker 3). The torsion angle is obtained by
using the displacement of the ends of the carbon rod.
Figure 2.13 shows a schematic of a beam/rib in torsion where θ is the angle
of twist, T is the applied torque, L is the length of the beam, J is the moment of
inertia, and G is the modulus of rigidity. The assumption is that GJ is constant.
The torsion equation is given below.
θ′ =
T (x)
GJ
(2.20)
2.3.1 Wing Covering Material Tensile Tests
An important area of materials mechanics is the behavior of deformable bodies,
especially the details of how a material will behave under load. Tensile and compres-
sion experiments allow for the determination of these properties. With tensile tests,
101
Figure 2.13: Torsion test schematic.
a load is applied along the longitudinal axis of a test specimen. The specimen will
stretch along this axis, and the amount of elongation can be measured. Loads and
deformations may be converted to stresses and strains by
σ =
P
A
 =
δ
L
(2.21)
where σ, is normal stress on a plane perpendicular to the longitudinal axis of the
specimen, P is the applied load, A is the cross sectional area,  is the normal strain
in the longitudinal direction, δ is the change in the specimen length, and L is the
original length.
The stress-strain curve gives a direct indication of the material properties. The
initial portion of the stress-strain diagram for most materials is a straight line. For
the initial portion of the diagram, the stress (σ) is directly proportional to the strain
. Therefore, the slope of the straight-line portion is the (Elastic Modulus or Young’s
Modulus) and is given by the following:
E =
σ

(2.22)
102
Tensile tests were performed to obtain the modulus of the wing covering. A
hydraulic materials testing system (MTS) was used. Three layered rectangular
specimens were clamped at each end and placed in the tensile test machine. The
sample was then stretched so that the force and displacement could be measured
using the MTS DAQ and a 100 lbf load cell. A 4th order Butterworth low pass
filter with a cutoff frequency of 50 Hz was applied to the raw data to eliminate all
high frequency noise sources. The test samples included a 10-layer Mylar membrane,
a 10-layer heat resistant material, and a 5-layer heat resistant material. Table 2.2
shows data from the tests. Of particular interest is the stress and strain in the elastic
region as it was not expected that the aerodynamic forces would exceed the yield
stress of the material.
The two wing cover materials were Mylar and a heat resistant material. Fig-
ure 2.15 shows representative data from the tensile tests. Figure 2.15(a) shows raw
and filtered force and displacement data for the heat resistant material in the elastic
region. Here, the stress applied to the 10-layer heat resistant material sample is
proportional to the strain and the material will return to its original shape when
unloaded. Figure 2.15(b) shows the results of 5 separate tests for the 5-layered heat
resistant material. The five specimens were identical and were each stretched to
different maximum (0.05–0.30 in) to observe the elastic limit, which is the stress
that can be applied without resulting in permanent deformation when unlaoded. It
is seen that the 5-layer heat resistant sample does return to the original shape up to
a yield stress of 3,250 lbfs2 ( = 0.02).
The structural properties of each of the flexible wing members was obtained
103
Figure 2.14: Image of wing membrane material in during tensile test.
(a) Unfiltered and filtered load and displacement
for 10 layer heat resistant wing covering .
(b) Stress and strain 5 layer heat resistant wing
covering.
Figure 2.15: Tensile tests for wing covering.
104
Table 2.2: Tensile test results.
Test specimen Thickness (in) Length (in) Width (in) Weight (g/in) E (lbf/in2)
Mylar-10 0.0105 4.863 1.532 0.2504 1.1889e+4
Heat Resistant-5 0.012 7.113 1.047 0.2531 1.6429e+5
Heat Resistant-10 0.025 7.41 1.072 0.5647 1.6168e+5
Table 2.3: Flexible wing properties.
Member Properties
Wing chord (m) 0.0762
Wing span (m) 0.127
Leading edge spar, GJ (N/m2) 6.1 ×10−3
Leading edge spar, EI (N/m2) 2.4 ×10−2
Root rib, EI (N/m2) 4.92 ×10−4
Mid rib, EI (N/m2) 2.4 ×10−4
Tip rib, EI (N/m2) 2.1 ×10−4
Root Rib, GJ (N/m2) 2.05 ×10−4
Mid Rib, GJ (N/m2) 4.86 ×10−5
Tip Rib, GJ (N/m2) 2.02 ×10−4
Membrane, E (N/m2) 5.02 ×109
Membrane, ν 0.45
experimentally. Bending and torsion tests were carried out for the chorwise ribs
and the leading edge spar. Loads were added to simulate bending and torsion and
a motion tracking system was used to measure the deflections. The bending and
torsion stiffness properties (EI and GJ) were then obtained from these results. The
modulus of elasticity was determined for the wing covering using tensile tests. The
geometric and structural properties of the flexible wing are shown in Table 2.3. These
properties were used as inputs to the MBDyn structural model.
With these structural component details, a complete MBDyn structural model
was used. The spar and ribs were modeled as beam elements and the wing covering
was modeled as 2-D shell element. The VICON system was used for shaker frequency
experiments.
105
2.3.2 Wing Frequency Verification Tests
The predicted natural frequency of each wing member was verified through
modal tests using a “shaker”. A shaker is a device that excites an object or structure.
The shaker device was a LDS V101 Permanent Magnet Shaker produced by Bruel
and Kjaer Inc. This shaker model is capable of achieving an 8.9 N (2 lbf) peak sine
thrust. The continuous peak-to-peak displacement is 2.5 mm and the frequency
range is 5–12,000 Hz. The shaker was controlled using a Hewlet-Packard Agilent
8656B RF Signal Generator. The shaker was fixed to the leading edge at the root
rib, mid rib, and tip rib of the flapping wing frame. A swept sine signal was used
as the input for normal mode testing. The result was compared to the prediction
values. Shaker tests also allowed for the determination of the mass for each structural
member (see section 3.1.1). Figure 2.16 shows the attachment of the wing to the
shaker for the modal experiments.
2.4 Chapter Summary
This chapter contains a discussion of the numerical and experimental methods
utilized in this study. The aeroelastic solver is a coupled OVERTURNS/MBDyn
solver modified for low Reynolds number flows, and the details were discussed. Details
of the flapping-wing test rig, the PIV system, force measurement technique, wind
tunnel, and motion tracking setups are provided. The PIV was used to acquire
velocity field measurements in several planes along the wing span. Several challenges
associated with performing flow measurements on a flapping-wing MAV were also
106
(a) Root rib mounted.
(b) Mid rib mounted. (c) Tip rib mounted.
Figure 2.16: VICON motion tracking “shaker” test for modal analysis.
107
described. The VICON motion tracking system allowed for the measurement of the
wing structural properties and wing kinematics. Finally, the methods for determining
the structural properties of the flexible wing were presented.
108
Chapter 3: Comparison of Predicted and Experimental Re-
sults
This chapter provides a comparison of the simulation results with the experiment
results. First, the structural solver was validated and then the flowfield. Flow features
produced from the experiment and the simulation of the flapping wing for various flap
frequencies and pitch angles are compared using PIV and CFD-CSD respectively for
rigid and flexible cases. Force measurements are also used for simulation comparison.
Of particular interest in the present study is a comparison of the formation and
convection of the LEV and its effects on the unsteady aerodynamic forces produced
on the wing.
3.1 Comparison of Structural Dynamic Solver to Experiments
3.1.1 Flexible Wing Static Loading Comparison
Static structural tests were performed on each wing frame member and the
whole wing (covering included). VICON markers were placed along the root, mid,
and tip ribs (3 span locations). Loads were placed at tips of the members. Figure 3.1
shows representative images of the covered wing, wing loading, and VICON markers
109
(Left column: Figs. 3.1(a), 3.1(c), and 3.1(e)) along with deflection results for the
chordwise ribs (Right column: Figs. 3.1(b), 3.1(d), and 3.1(f)). The left column
contains the predicted (MBDyn) results for comparison to the experiment deflections.
When comparing the results, it is seen that there is good correlation (predicted
within < 5% difference compared to measured values). The analysis discussed in
section 2.3 for large bending deflections was used to assess the EI for the various
flexible wing members.
3.1.2 Flexible Wing Dynamic Tests
3.1.2.1 Comparison of Flexible Wing Frame Fundamental Frequencies
For further comparison of the flexible wing simulation to the experiment, the
natural (fundamental) frequency of the wing frame was obtained by exciting the wing
frame from the root tab. The shaker was given a 15 second sinusoidal ramp to 50
Hz while VICON data was taken for 20 seconds. The displacements of the markers
located at the trailing edges of the root, mid, and tip members were measured using
the motion tracking system.
Figure 3.2 shows the raw signal of the tip displacements and the corresponding
Fast Fourier Transform (FFT) to assess the signal for the shaker tests. The FFT
is used to convert the time/space data to the frequency domain. The left column
(Figs. 3.2(a), 3.2(c), and 3.2(e)) shows the raw displacements from the trailing edge
root, mid, and tip ribs. Several clear peaks in the displacement are observed from
the raw signal. These are the instances in time where the resonant frequencies of the
110
Wing 
Root rib 
loading 
(a) Root spar load.
2 4 6 8 10 -25 
-20 
-15 
-10 
-5 
0 
Root Rib 
Experiment (VICON) 
Predicted (MBDyn) 
Mid Rib 
Tip Rib 
Loading, g 
Dis
pla
ce
me
nt,
 m
m 
(b) Load at trailing edge of root rib.
Wing 
Mid rib 
loading 
(c) Mid spar load.
2 4 6 8 10 -30 
-25 
-20 
-15 
-10 
-5 
0 
Root Rib  
Mid Rib 
Tip Rib 
Loading, g 
Di
sp
lac
em
en
t, m
m 
(d) Load at trailing edge of mid rib.
Wing 
 Tip rib 
loading 
(e) Tip spar load.
2 4 6 8 10 -50 
-40 
-30 
-20 
-10 
0 Root Rib  
Mid Rib 
Tip Rib 
Loading, g 
Dis
pla
ce
me
nt,
 m
m 
(f) Load at trailing edge of tip rib.
Figure 3.1: Left side, images of static wing loading tests with VICON markers and
Right side, load deflection curves for chordwise ribs.
111
frame members occur. Figure 3.2(b) shows that the frequency at which the peak
signal occurs at about 30 Hz for the tip displacements of the root spar. In Fig. 3.2(d)
and 3.2(f) show FFT signal peaks at about 16.5, 23.5 and 31 Hz. There are several
peaks observed in the tip displacement signal because the frame is a coupled system.
The shaker test for the frame was modeled using the MBDyn solver. The frequency
content of the frame is compared to the predicted results and displayed in Table 3.1.
The predicted natural frequencies were calculated by computing the eigenvectors
and eigenvalues within the structural solver. In comparing the natural frequency
content, the percent difference in the predicted natural frequencies and the measured
remained between 1.05% and 7.93%.
The resonant frequencies gives a great deal of information about the charac-
teristics of a system (e.g., mode of vibration is characterized by a modal frequency
and a mode shape). Figure 3.3 shows the mode shapes for the wing frame structural
members. For the first mode of the root spar (Fig. 3.3(a)), it is seen that the
deflection of the root rib does not have a significant effect on the tip and the middle
ribs. However, the middle rib has an effect on the tip spar (see Fig. 3.3(b)). This
oscillatory coupling of the individual degrees of freedom is also seen as the tip rib
affects the leading edge spar and the middle rib (see Fig. 3.3(c)). Because each
wing member is interconnected by the wing covering, the natural frequency is not
approached when the wing is flapping for the current tests (¡10 Hz).
112
0 5 10 15 20−6
−4
−2
0
2
4
6
Time,s
Displ
acem
ent, m
m
(a) Root spar displacement.
0 10 20 30 40 500
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Frequency (Hz)
|Y(f)|
(b) Root spar FFT.
0 5 10 15 20−6
−4
−2
0
2
4
6
Time,s
Displ
acem
ent, m
m
(c) Mid spar displacement.
0 10 20 30 40 500
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Frequency (Hz)
|Y(f)|
(d) Mid spar FFT.
0 5 10 15 20−6
−4
−2
0
2
4
6
Time,s
Displ
acem
ent, m
m
(e) Tip spar displacement.
0 10 20 30 40 500
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Frequency (Hz)
|Y(f)|
(f) Tip spar FFT.
Figure 3.2: Raw signal of tip (TE) displacements and Fast Fourier Transform from
motion tracking experiment.
113
(a) Root spar mode shape.
(b) Mid spar mode shape.
(c) Tip spar mode shape.
Figure 3.3: Mode shapes for wing frame structural members.
114
Table 3.1: Comparison of flexible chordwise member natural frequencies.
Structural Member Experiment ωn Predicted ωn
Root Rib 31.18 Hz 32.01 Hz
Middle Rib 23.97 Hz 22.07 Hz
Tip Rib 16.89 Hz 17.07 Hz
3.1.2.2 Comparison of Flexible Wing Frame Flapping Motion
The VICON system was used to compare experiment and predicted results for
the complex kinematics of the flexible wing frame throughout the entire stroke. Again,
the tip displacements were tracked using the VICON system and simulations were
conducted using MBDyn. Figure 3.4 shows a representative result from the dynamic
tests. It is seen that the upstroke and downstroke are the same magnitude, resulting
in a “symmetric” kinematic profile. It is seen that the experiment and simulation
are periodic; however, there is some higher frequency content in the experiment
that is not accounted for in the simulation. For the VICON data, the tip motion is
not purely sinusoidal because of the inertial effects of the wing components. This
difference in the kinematics is caused by inertial effects. To account for aerodynamic
damping in the simulation, Rayleigh damping was used within the simulation to
account for damping within the system.
Rayleigh damping is an empirical means to account for damping, and was
applied to the wing frame simulations. This damping is associated with linear theory,
and is used for isolating each mode [183]. This proportional damping is a widely
used approach to model dissipative forces in complex structures and it has been
used in various dynamic problems. The proportional damping model expresses the
115
damping matrix as a linear combination of the mass and stiffness matrices.
C = α1M + β1K (3.1)
where α1 and β1 are real scalars. With Raleigh’s proportional damping, the modal
damping factors have a special form:
α1 + β1ω
2
i = 2ωiξi (3.2)
where resonant frequencies, ωi, are obtained through modal analysis, and ξi are
damping ratios. Rearranging gives this equation results in the following expression:
ξi =
α1
2ωi
+
β1ωi
2
(3.3)
Assigning values to α1 and β1, allows for the filtering or retention of the higher mode
effects. For this study, β1 was set to 1.0e−4 and the higher harmonic term α1 is
set to zero because no tests were performed to achieve the coefficients. Figure 3.4
shows a comparison of the motion tracking experiment and predicted (MBDyn) wing
frame tip displacements. The flap frequency for this test was 6 Hz. Even with this
simplification, the flap characteristics are captured in that the sinusoidal nature of
the wing flapping motion, the flapping phase, and the flap amplitude are comparable.
This worked well for the comparison, and the inertial effects seen when the frame
was flapping were further damped when the wing covering was present.
116
0 0.2 0.4 0.6 0.8 1−200
−150
−100
−50
0
50
100
150
200
Time (sec)
Dis
pla
cem
ent
 (mm
)
 
 TipMidRoot
(a) Motion capture experiment tip displacements.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -200 
-150 
-100 
-50 
0 
50 
100 
150 
200 
Time (sec) 
D
is
pl
ac
em
en
t (
m
m
) 
  
  
(b) Predicted tip motion.
Figure 3.4: Comparison experiment and predicted (MBDyn) wing frame tip displace-
ments for 6 Hz flapping.
117
3.1.3 Comparison of Aerodynamic Solver (CFD-CSD) and PIV Re-
sults
3.1.3.1 Rigid and Flexible Wing Flowfield Comparison
To visualize the flow, the vorticity field, ~ω = ~∇× ~V , was acquired by computing
the velocity gradients of the PIV velocity field using a second order accurate Least
Squares differencing method. The Least Squares method was chosen to reduce
measurement uncertainty from the PIV [179]. For the contours presented, the
wing is at the middle of the downstroke, t = T/4 (mid-downstroke), and the free
stream velocity is 3 m/s from left to right. The masked wing in the PIV is shown
as black squares. Every 5th and 20th vector has been plotted for the PIV and
CFD, respectively. The pitch angles and reduced frequencies presented were chosen
to highlight the similarities and differences for comparison of the simulation and
experiment at low and high pitch angles and flap frequencies.
To define the wing kinematics, Fig. 3.5 shows a perspective view of the wing
rotation and the wing’s nomenclature. The solid wing represents an initial time
within the wing half stroke and the translucent wing represents the wing at a later
instant in time within that same half stroke. The stroke angle is given as the angle
Ψ and is defined as the angle through which the wing rotates. The pitch angle, θ, is
defined as the angle of incidence of the wing, b is the distance from the rotational
axis to the wing tip, y/b is the non-dimension distance along the span, and c is the
chord.
118
20% 
Tip Midspan 
Span locations 
Root 
Rotational  
axis 
θ	

y 
x 
z 
Ψ
c 
b
Figure 3.5: Perspective view schematic of the rotating wing setup.
Figures 3.6(a), 3.6(b), and 3.7(a) and 3.7(b) show representative rigid wing
PIV and CFD results (vorticity contours) for span locations of y/b = [0.3 – 0.9],
at t = T/4, mid-downstroke. Here, the salient aerodynamic features in the flow
on the flapping wing can be seen at the different chordwise locations, including
the leading-edge vortex (LEV), the trailing edge vortex, and small eddies from a
turbulent shear layer. Here the blue regions denote locations of increased (positive)
vorticity.
For the θ = 24◦ (at 4 Hz) and θ = 12◦ (at 6 Hz) cases, a leading edge vortex
has formed at all span locations. The reduced frequencies, k, are 0.32 and 0.48
respectively. In Figs. 3.6(a) and 3.7(a), this LEV can be seen as tightly structured
near the wing root but greatly expands until approximately y/b = 0.6 which is when
the LEV starts to diffuse for the PIV. For the CFD, the LEV grows in size along
the chord also out to the y/b = 0.6 span location; however, the size of the LEV
is decreased past that point out toward the wing tip (see Figs. 3.6(b) and 3.7(b)).
119
(a) PIV, θ = 24◦, Ω = 4 Hz
(b) CFD, θ = 24◦, Ω = 4 Hz
Figure 3.6: Comparison of representative chordwise PIV and CFD vorticity contours
at t = T/4, (40◦ flapping amplitude, θ = 24◦, 4 Hz flapping frequency, V∞ = 3 m/s,
k = 0.32).
120
Note that an increase in flap frequency results in an increase in vorticity magnitude.
There are some differences seen in the 3-D vorticity flowfields, e.g., the vorticity near
the tip appears to be more diffused for PIV (an effect of averaging). Also, the CFD
dpes not capture the same shed vorticity near the wing tip. This is because the
prediction is not capturing the exact same behavior caused by the interraction of the
LEV and the tip vortex. Therefore, velocity profiles will be presented to quantify
the differences. Overall, there is a qualitative correlation between CFD and PIV
for all the span locations and many of the flow features seen in the PIV measured
flowfield are captured in the CFD-predicted results. Note that an increase in flap
frequency, results in an increase in vorticity magnitude.
For θ0 = 12◦ (4 Hz), 24◦ (6 Hz), and 0◦ (8 Hz) cases, again a LEV is formed at
all span locations (Figs. 3.8 to 3.10). In Figs. 3.8(a) and 3.9(a), this LEV can be seen
as tightly structured near the wing root, but greatly expands until approximately
y/b = 0.6 and then the LEV starts to diffuse and move further away from the wing’s
surface for the PIV. For the coupled CFD-CSD predictions, the LEV grows in size
along the chord also out to the y/b = 0.6 span location; however, the size of the LEV
is decreased past that point out toward the wing tip (see 3.8(b) and 3.9(b)). There
is a good correlation between coupled CFD-CSD and PIV for all the span locations
and many of the flow features seen in the PIV measured flowfield are captured in the
predicted results. Figures 3.9(a) and 3.9(b) show an increase in flap frequency results
in an increase in vorticity magnitude. Though there is good agreement, the coupled
CFD-CSD is not capturing the same levels of shedding compared to the experiment
at y/b > 0.5. Figures 3.10(a) and 3.10(b) show the wing undergoing large amounts of
121
(a) PIV, θ = 12◦, Ω = 6 Hz
(b) CFD, θ = 12◦, Ω = 6 Hz
Figure 3.7: Comparison of representative chordwise PIV and CFD vorticity contours
at t = T/4, (40◦ flapping amplitude, θ = 12◦, 6 Hz flapping frequency, V∞ = 3 m/s,
k = 0.48).
122
(a) PIV, θ0 = 12◦, Ω = 4 Hz
(b) CFD, θ0 = 12◦, Ω = 4 Hz
Figure 3.8: Comparison of representative chordwise PIV and CFD vorticity contours
at t = T/4, (40◦ flapping amplitude, θ0 = 12◦, 4 Hz flapping frequency, V∞ = 3 m/s,
k = 0.32).
123
(a) PIV, θ0 = 24◦, Ω = 6 Hz
(b) CFD, θ0 = 24◦, Ω = 6 Hz
Figure 3.9: Comparison of representative chordwise PIV and CFD vorticity contours
at t = T/4, (40◦ flapping amplitude, θ0 = 24◦, 6 Hz flapping frequency, V∞ = 3 m/s,
k = 0.64).
124
(a) PIV, θ0 = 0◦, Ω = 8 Hz
(b) CFD, θ0 = 0◦, Ω = 8 Hz
Figure 3.10: Comparison of representative chordwise PIV and CFD vorticity contours
at t = T/4, (40◦ flapping amplitude, θ0 = 0◦, 8 Hz flapping frequency, V∞ = 3 m/s,
k = 0.64).
125
flexibility during the downstroke. The reduction in angle of attack, caused by wing
flexibility, results in a smaller LEV formed on the wing’s upper surface. The next
section contains details about the vorticity contours and normalized velocity profiles
for both the CFD and PIV (rigid and flexible wing) at the 50% span location.
For the rigid and flexible wing, downstream velocity cuts (i.e., vertical sectional
cuts) were taken along the Z-direction at the X/c = 1.1, 1.5, and 2 (X/c = 0 is the
leading edge) to give a quantitative comparison of the CFD and PIV wakes. The
downstream velocity cuts have been denoted by the letters A, B, C and A’, B’, C’ for
the PIV and CFD respectively. The vertical velocity cuts in the wake are 2 chords
in length. The velocity cuts show good agreement and the shear layer is captured by
the simulation; however, there are slight differences when comparing the shear layer
angle and size of the shed vortices.
Furthermore, a swirl velocity, Vθ, profile was taken through the LEV for a
quantitative comparison at the LEV structure. The center of the vortex was located
using the λ1-function. The LEV structure required a more precise definition of the
vortex core, so the non-local vortex detection scheme of Graftieaux et al. [184] was
employed. This function was used to locate and quantify the rotation rate of local
swirl regions. The λ1-function is given by
λ1(P ) =
1
N
∑
S
sin(θM)
where N is the number of points inside a two-dimensional area S centered around
point P . The angle θM is formed by the position vector from P to M and the velocity
126
vector at point M . The value of λ1 can range from -1 to 1. |λ1| = 1 when the point P
is at the center of an ideal vortex. Note that the value of λ1 depends on the direction
of the velocity field, not its magnitude. The center of a vortex is taken to be the local
maximum of |λ1|, and the vortex core is the region within the |λ1| ≥ 0.6 contour.
Swirl velocity profiles were generated along a diagonal cut through the vortex core.
The diagonal dashed line (parallel to the wing) shows the velocity cut through the
LEV. The vortex center is denoted by a white dot. A specified number, n, of equally
spaced points along the cut (n = 200) were assigned to the line. Along this cut, the
u and w velocities corresponding to points along x and z in the velocity field were
obtained. Because PIV yields a planar grid of velocity vectors, not all points on the
diagonal fall on a node in the velocity field grid. If a point n on the line did not
fall on a grid node, the u and w velocity components were interpolated based on
the neighboring vectors. To calculate the swirl velocity, the u and w velocity values
(from the Cartesian grid) on the diagonal were converted to polar coordinates to
give the radial (Vr) and tangential (Vθ) velocities of the vortex. Each swirl velocity
profile is a plot of Vθ (normalized by V∞) as a function of position along the diagonal
cut. The upper left of the diagonal dashed line corresponds to the bottom of the
velocity profile.The vortex is analyzed by determining the core radius, rc, defined as
the radial distance from the location where Vθ is a maximum to the center of the
vortex, determined from the swirl velocity profiles.
Figures 3.11(a) and 3.11(b) show the vorticity fields with overlaid velocity for
the CFD and PIV results. Here, the wing is in its mid-downstroke position and
the focus is on the mid-span plane. The wing is at 0◦ and the flap frequency is
127
4 Hz. The vorticity gives the structure of the vortex. It is seen that the velocity
magnitude is very similar; however, vortex structure is different. Both the averaged
PIV and instantaneous CFD vorticity fields show the LEV as a tight concentration
of vorticity near the leading edge encompassing about 25% of the chord. There is
a small amount of opposite sign vorticity, which shows as red within the LEV for
the predicted result. The shear layer appears as more diffused for the PIV. This is
a result of averaging and the turbulence model used for the simulation, which was
developed for higher Reynolds number flows. Even with these considerations, the
velocity fields are quite similar for the PIV and CFD in that the LEV and smaller
trailing edge vortices form for both. The LEV is bound to the wing’s upper surface.
Figures 3.11(c) and (d) shows the downstream horizontal velocity component profile
at three different downstream locations. A reduction in velocity behind the wing
is representative of a wing that is producing drag via a decrement in momentum.
The normalized u velocity just behind the wing at 1.1 chord length is about half the
freestream velocity. In Fig. 3.11(e), which compares the instantaneous normalized
vortex swirl velocities (Vθ/V∞) as a function of nondimensional radial distance from
the vortex center (rc/c), it is seen that the vortex from CFD and PIV are of similar
size and magnitude. Here the vortex size is about 0.23 chord lengths as determined
from the peak to peak distance in the swirl velocity profiles. In general, the velocity
fields show very good agreement as seen by the velocity profiles.
In Fig. 3.12, the leading edge vortex centers (determined by λ1-function) are
the centers of the velocity cuts through the vortex. Here, the wing pitch angle is 12◦
and the locations of the leading edge vortex centers for the measurement and CFD
128
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
D
A B C
(a) PIV vorticity contour with overlaid velocity
field.
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1 A’ B’ C’
D’
(b) CFD vorticity contour with overlaid velocity
field.
−3 −2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
l Z−c
oordi
nate,
 in ch
ords
Normalized streamwise velocity, U/Voo 
 
A − 1.1 chordB − 1.5 chordC − 2.0 chord
(c) PIV downstream U/V∞ velocity distribution.
−3 −2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
lized
 Z−co
ordin
ate, i
n cho
rds
Nondimensionalized streamwise velocity, U/Voo 
 
A’ − 1.1 chordB’ − 1.5 chordC’ − 2.0 chord
(d) CFD downstream U/V∞ velocity distribu-
tion.
−3 −2 −1 0 1 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
Norm
alize
d Vo
rtex R
adius
, r/ch
ord
Normalized Vortex Swirl Velocity, (Vθ/U) 
 
D − PIVD’ − CFD
(e) PIV and CFD normalized LEV swirl velocity
profiles.
Figure 3.11: Velocity vectors and vorticity field with overlaid velocity profile cuts, for
corresponding normalized downstream and swirl velocity profiles, rigid wing ,θ = 0◦
at 4 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).
129
are close in proximity (about 5% difference in straight line distance from the leading
edge). Here the LEV is bound to the wing’s surface. Though the recirculation region
near the leading edge is not well predicted in the CFD, and the trailing edge vortices
have a different size and trajectory. Also, the trend line for the velocity profiles and
magnitude of the flow are similar. There are some differences in comparison that
are highlighted by the vorticity contours (e.g. vortex structure); however, the peak
swirl velocity and the core radius of the LEV for the PIV and CFD are comparable,
as shown in the 6 Hz, 12◦ case. It is seen that the trajectories of the vortices shed
from the trailing edge have a different trajectory. It can be seen in Figs. 3.12(c)
and 3.12(d) that profiles C and C’ do not match. This is because the C profiles cut
through a significant region of vorticity present in the downstream wing wake. The
trailing edge vortex present in the wing wake of the PIV image was not appropriately
captured in the CFD simulation. The magnitudes of the velocity deficit are similar
up to about 1.5 chord lengths behind the leading edge. Nevertheless, the leading
edge vortex and shed trailing edge vortices are predicted with similar values for
vorticity, and velocity magnitude. Figure 3.12(e) shows that the LEV encompasses
almost half of the wing’s upper surface; however, the swirl velocity profiles do not
quite have the same magnitudes. The higher flap frequency does produce stronger
vortices with higher swirl velocities.
Figure 3.13 shows the lowest tested flap frequency, 4 Hz, but the highest
geometric pitch angle, θ = 24◦. When the wing is in the mid-downstroke position,
the vortex has diffused, and flow separation is observed on much of the upper wing’s
surface. The remnants of the LEV are present; however, the circulation is not bound
130
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
D
A B C
(a) PIV vorticity contour with overlaid velocity
field.
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
D’
A’ B’ C’
(b) CFD vorticity contour with overlaid velocity
field.
−3 −2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
l Z−c
oordi
nate,
 in ch
ords
Normalized streamwise velocity, U/Voo 
 
A − 1.1 chordB − 1.5 chordC − 2.0 chord
(c) PIV downstream U/V∞ velocity distribution.
−3 −2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
lized
 Z−co
ordin
ate, i
n cho
rds
Nondimensionalized streamwise velocity, U/Voo 
 
A’ − 1.1 chordB’ − 1.5 chordC’ − 2 chord
(d) CFD downstream U/V∞ velocity distribu-
tion.
−3 −2 −1 0 1 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
Norm
alize
d Vo
rtex R
adius
, r/ch
ord
Normalized Vortex Swirl Velocity, (Vθ/Voo) 
 
D − PIVD’ − CFD
(e) PIV and CFD normalized LEV swirl velocity
profiles.
Figure 3.12: Velocity vectors and vorticity field with overlaid velocity profile cuts, for
corresponding normalized downstream and swirl velocity profiles, rigid wing, θ = 12◦
at 6 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).
131
to the wing’s surface. The trends in the downstream wake are very similar. However,
the velocity deficit is under predicted, and the swirl velocity profiles are dissimilar
(see Figs 3.13(b) and 3.13(c)). The variation in the predicted and the measured swirl
velocity profiles is a result of the unsteady nature of the vortex. Though the swirling
flows near the leading edge are similar, the vortex identification method (determined
by λ1-function) has assessed the vortex center of the predicted result to be about
0.25 chord lengths further away from that of the PIV result. There is also far less
opposite sign vorticity within the experiment results. The predicted and measured
flow fields are similar, however; the nature of the flow at this point is such that the
flow features are more aperiodic, which accounts for the difference in the profiles.
In general, the flow solver predicted the overall flow features. At higher angles
of attack, the flow on the wing’s upper surface becomes more aperiodic. This is the
reason some of the flow details are not shown in the averaged flowfields. However,
the general trends are reflected by the CFD analysis. These results serve as a
comparison between CFD predictions, and experimental measurements show very
good agreement when the LEV is attached. Next, the flexible wing results will be
discussed.
Figures 3.15(a) and 3.15(b) show the vorticity contours for the flexible wing at
6 Hz, for θ0 = 24◦, in the mid-downstroke position. The mid-span location is shown.
Figure 3.15(e) compares the instantaneous normalized vortex swirl velocities (Vθ/V∞)
as a function of nondimensional radial distance from the vortex center (rc/c); it
is seen that the vortex from coupled CFD-CSD and PIV are of similar size and
magnitude.
132
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
D
A B C
(a) PIV vorticity contour with overlaid velocity
field.
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
D’
A’ B’ C’
(b) CFD vorticity contour with overlaid velocity
field.
−3 −2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
l Z−c
oordi
nate,
 in ch
ords
Normalized streamwise velocity, U/Voo 
 
A − 1.1 chordB − 1.5 chordC − 2.0 chord
(c) PIV downstream U/V∞ velocity distribution.
−3 −2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
lized
 Z−co
ordin
ate, i
n cho
rds
Nondimensionalized streamwise velocity, U/Voo 
 
A’ − 1.1 chordB’ − 1.5 chordC’ − 2.0 chord
(d) CFD downstream U/V∞ velocity distribu-
tion.
−3 −2 −1 0 1 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
Norm
alize
d Vo
rtex R
adius
, r/ch
ord
Normalized Vortex Swirl Velocity, (Vθ/U) 
 
D − PIVD’ − CFD
(e) PIV and CFD normalized LEV swirl velocity
profiles.
Figure 3.13: Velocity vectors and vorticity field with overlaid velocity profile cuts, for
corresponding normalized downstream and swirl velocity profiles, rigid wing, θ = 24◦
at 4 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).
133
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
A B C
D
(a) PIV vorticity contour with overlaid velocity
field.
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
D’
C’B’A’
(b) CFD vorticity contour with overlaid velocity
field.
−2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
l Z−c
oordi
nate,
 in ch
ords
Normalized streamwise velocity, U/Voo 
 
A − 1.1 chordB − 2.0 chordC − 3.0 chord
(c) PIV downstream U/V∞ velocity distribution.
−2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
lized
 Z−co
ordin
ate, i
n cho
rds
Nondimensionalized streamwise velocity, U/Voo 
 
A’ − 1.1 chordB’ − 2.0 chordC’ − 3.0 chord
(d) CFD downstream U/V∞ velocity distribu-
tion.
−4 −2 0 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
Norm
alize
d Vo
rtex R
adius
, r c/ch
ord
Normalized Vortex Swirl Velocity, (Vθ/Voo) 
 
D − PIVD’ − CFD−CSD
(e) PIV and CFD normalized LEV swirl velocity
profiles.
Figure 3.14: Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles, flexible wing,
θ0 = 12◦ at 4 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).
134
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
A B C
D
(a) PIV vorticity contour with overlaid velocity
field.
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
D’
A’ C’B’
(b) CFD vorticity contour with overlaid velocity
field.
−2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
l Z−c
oordi
nate,
 in ch
ords
Normalized streamwise velocity, U/Voo 
 
A − 1.1 chordB − 2.0 chordC − 3.0 chord
(c) PIV downstream U/V∞ velocity distribution.
−2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
lized
 Z−co
ordin
ate, i
n cho
rds
Nondimensionalized streamwise velocity, U/Voo 
 
A’ − 1.1 chordB’ − 2.0 chordC’ − 3.0 chord
(d) CFD downstream U/V∞ velocity distribu-
tion.
−4 −2 0 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
Norm
alize
d Vo
rtex R
adius
, r c/ch
ord
Normalized Vortex Swirl Velocity, (Vθ/Voo) 
 
D − PIVD’ − CFD−CSD
(e) PIV and CFD normalized LEV swirl velocity
profiles.
Figure 3.15: Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles, θ0 = 24◦ at 6
Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).
135
Figure 3.16 shows a comparison of the PIV experiment and CFD-CSD solver
flexible wing results for the 8 Hz flapping case when the wing’s initial pitch angle
was set to 0◦. Here, the wing is at the mid-downstroke position and the y/b = 0.5
span location is shown. The CFD-CSD solver is slightly under-predicting the wing
deflection in that the wing angles are about −18◦ and −15◦ for the experiment and
prediction, respectively. This slight difference in wing angle is likely caused by a
nonuniformity in the wing material near the trailing edge of the wing as exhibited by
the sharp change in wing angle at about the mid-chord location (see Fig. 3.16(a)).
Nevertheless, the concentration of vorticity at the wing’s leading edge are comparable
in size for both the experiment and the CFD-CSD prediction. In the downstream
wake, the shear layer at the trailing edge for the PIV and the CFD-CSD have a
similar trend in length and diffusion characteristics, but they are at slightly different
angles. This is reflected in the downstream velocity profiles shown Figs 3.16(c) and
3.16(d). For the CFD-CSD, the profile A’ cuts through the beginning of the trailing
edge shear layer, while the profile A intersects the shear layer further downstream.
Figure 3.16(e) shows the swirl velocity profiles for the PIV and CFD-CSD velocity
fields. The location of the vortex center is predicted and the vortex structures are
similar, however, there are some discrepancies in the prediction of the flow ahead of
the wing’s leading edge. In general, the trends is predicted.
Because the LEV is a continuous vortex filament, chordwise sections of the LEV
do give insight into its behavior. In general, during wing flapping, the vortex goes
through a periodic growth, convection, and dissipation process. If this vortex could
remain coherent and attached (bound), perhaps lift could be improved during the
136
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
A B C
D
(a) PIV vorticity contour with overlaid velocity
field.
Normalized X−coordinate, x/c
Norm
alize
d Z−c
oordi
nate,
 z/c
 
 
−0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
C’B’A’
D’
(b) CFD vorticity contour with overlaid velocity
field.
−2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
l Z−c
oordi
nate,
 in ch
ords
Normalized streamwise velocity, U/Voo 
 
A − 1.1 chordB − 2.0 chordC − 3.0 chord
(c) PIV downstream U/V∞ velocity distribution.
−2 −1 0 1 2−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nond
imen
siona
lized
 Z−co
ordin
ate, i
n cho
rds
Nondimensionalized streamwise velocity, U/Voo 
 
A’ − 1.1 chordB’ − 2.0 chordC’ − 3.0 chord
(d) CFD downstream U/V∞ velocity distribu-
tion.
−4 −2 0 2−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
Norm
alize
d Vo
rtex R
adius
, r c/ch
ord
Normalized Vortex Swirl Velocity, (Vθ/Voo) 
 
D − PIVD’ − CFD−CSD
(e) PIV and CFD normalized LEV swirl velocity
profiles.
Figure 3.16: Velocity vectors and vorticity field with overlaid velocity profile cuts,
for corresponding normalized downstream and swirl velocity profiles, flexible wing,
θ = 0◦ at 8 Hz. (Note: y/b = 0.5, t = T/4, Reref = 15, 000).
137
flap cycle. One reason for the persistence of an LEV is the stretching of the vortex
as it convects over the wing’s surface; however, the change in effective angle of attack
may also be a cause. The vortex strength is related to its persistence. In general,
the effects of the vortical structures are observed in the experiment measurement
(velocity profiles) and the coupled CFD-CSD is predicting the overall flow features
and the general trends. There are some limitations, such as slight differences in
the trailing edge vortices, but the limitations associated with the predictive model
are not so significant that insight could not be gained from this analysis. These
comparisons between coupled CFD-CSD predictions and experimental measurements
provide confidence in the CFD-CSD results when the LEV is coherent. However,
to further improve the understanding of the flow physics and the capability of the
modeling tool, the LEV strength based on the CFD-CSD analysis and PIV flowfields
are compared.
3.2 Comparison of Sectional LEV Strength
LEV circulation, which is related to the lift, is quantified for the predicted and
experimental results. This was done for both the rigid and flexible wing.
3.2.1 Rigid Wing LEV Circulation (PIV and CFD)
The velocity field of both the CFD and PIV were used to estimate the strength
of the LEV for comparison. The process involves choosing a suitable integration
contour (i.e., around the LEV in this case) and numerically evaluating the closed-
138
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Nondimensional span location, y/b
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 Avg. Instantaneous PIV − θ = 0oInstantaneous CFD − θ = 0o
(a) θ0 = 0◦
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Nondimensional span location, y/b
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 Avg. Instantaneous PIV − θ = 12oInstantaneous CFD − θ = 12o
(b) θ0 = 12◦
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Nondimensional span location, y/b
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 Avg. Instantaneous PIV − θ = 24oInstantaneous CFD − θ = 24o
(c) θ0 = 24◦
Figure 3.17: Distribution of averaged LEV circulation, Γv along the span, rigid
wing, Ω =4 Hz, (40◦ flap amplitude, V∞ = 3 m/s) with error bars showing standard
deviation. 139
loop velocity integral. This loop must completely enclose the LEV, but without
intersecting any other extraneous circulation. The equation for circulation is given
below as
Γv = −
∫
~V · ~ds = −
∫ ∫
(∇× ~V ) · ~dS (3.4)
where ~V is the velocity vector, ~ds is the directed line segment at a point on a
predefined contour, ∇× ~V is the vorticity, and ~dS is the area enclosed by a curve [17].
For this analysis, a vorticity threshold was set (−400 < ω < 400) so that low
magnitude extraneous vorticity would not be included in the integration contour
that was used to enclose the LEV. Next the vorticity field is scanned in order to
locate pockets of vorticity of a certain size (3 × 3 grid square) within that threshold.
These regions are then stored as grid locations. Line contours are drawn around
these concentrations of vorticity so that an area integral can be assessed to obtain
the circulation for the vortices in the PIV experiment (with error bars) and those
generated by CFD.
Figures 3.17(a), 3.17(b), and 3.17(c) show the phase-averaged spanwise distribu-
tion of LEV circulation over the wing for pitch angles of 0◦, 12◦, and 24◦ respectively
for the PIV and CFD. The flap frequency here is 4 Hz. LEV size and strength does
vary at different span locations along the wing. This is because an increase in vorticity
would also mean that there is an increase in net circulation around the wing, thereby
causing increased lift when the LEV is present. The measured peak in the circulation
was observed to occur between the y/b = 0.6 and 0.7 span locations with a rapid
140
decrease in circulation toward the wing tip and root. The low values of circulation
near the wing root and tip arose because of the high flap-induced velocities there and
also because the flow at these locations is partially separated. Even though the CFD
simulation is able to predict the circulation of the inboard sections with sufficient
accuracy there is some over-prediction in the outboard sections. The difference in
the predicted and measured values for the outboard section at θ0 = 12◦ is largely
due to the simulation’s inability to accurately resolve the flow when the tip vortex
interacts with the LEV. In general, circulation is under-predicted further outboard
for this case when there is significant mixing. There is an over-prediction along the
span when the wing is at 24◦. This is because the flow is fully separated and difficult
to resolve, although there is less of an effect from the tip vortex.
Figure 3.18 shows the distribution of LEV strength for a variation in flap
frequency for the y/b = 0.5 span location. The pitch angles are θ0 = 0◦, 12◦, and
24◦. Here the general trend is an increase in circulation as the wing flap frequency
is increased. There is very good agreement in LEV strength value at the 0◦ pitch
angles and lower frequencies. However, as the flap frequency is increased along with
pitch angle there is less agreement between the measurements and the simulation.
The effect of the tip vortex is more prevalent at higher frequencies making it difficult
to resolve because of mixing with the LEV, especially at high reduced frequencies.
This is an exacerbation of the effect of the interaction of the tip vortex with the LEV
caused by the higher frequency flapping.
141
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Flap frequency, Hz
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 PIV ExpCFD
(a) θ0 = 0◦
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Flap frequency, Hz
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 
PIV ExpCFD
(b) θ0 = 12◦
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Flap frequency, Hz
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 
PIV ExpCFD
(c) θ0 = 24◦
Figure 3.18: Distribution of averaged LEV circulation, Γv for a variation in flap
frequency, rigid wing, y/b = 0.5 (40◦ flap amplitude, V∞ = 3 m/s) at 50% span.
142
3.2.2 Flexible Wing LEV Circulation (PIV and CFD-CSD )
The velocity field of both the coupled CFD-CSD solver and PIV were used to
estimate the strength of the LEV for comparison. The circulation was also calculated
in the manner explained previously in that line contours were drawn around the
concentrations of vorticity so that an area integral can be assessed to obtain the
circulation for the vortices in the PIV experiment and those generated by the coupled
CFD-CSD solver.
Figures 3.19(a), 3.19(b), and 3.19(c) show the spanwise distribution of LEV
circulation over the wing for pitch angles of 0◦, 12◦, and 24◦ respectively for the
flexible wing case. Again, the flap frequency here is 4 Hz. The measured peak in
the circulation was observed to occur between the y/b = 0.5 and 0.7 span locations
with a rapid decrease in circulation toward the wing tip and root. The low values of
circulation near the wing root and tip arise because of the high induced velocities
there and also because the flow at these locations is partially separated. Even though
the coupled CFD-CSD simulation is able to predict the circulation of the inboard
sections with sufficient accuracy, there is some over-prediction in the outboard
sections.
Figure 3.20 shows the distribution of LEV strength for a variation in flap
frequency for the y/b = 0.5 span location. The pitch angles are θ0 = 0◦, 12◦, and
24◦. The general trend is an increase in circulation as the wing flap frequency is
increased. There is a very good agreement of LEV strength value at the 0◦ pitch
angles and lower frequencies.
143
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Nondimensional span location, y/b
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 PIV − θ = 0oCFD − θ = 0o
(a) θ0 = 0◦
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Nondimensional span location, y/b
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 PIV − θ = 12oCFD − θ = 12o
(b) θ0 = 12◦
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Nondimensional span location, y/b
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 PIV − θ = 24oCFD − θ = 24o
(c) θ0 = 24◦
Figure 3.19: Distribution of averaged LEV circulation, Γv along the span, flexible
wing, Ω =4 Hz, (40◦ flap amplitude, V∞ = 3 m/s).
144
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Flap frequency, Hz
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 PIV − θ = 0oCFD − θ = 0o
(a) θ0 = 0◦
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Flap frequency, Hz
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 PIV − θ = 12oCFD − θ = 12o
(b) θ0 = 12◦
0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Flap frequency, Hz
LEV
 Circ
ulati
on, (Γ
LEV
),   m
2  s−
1
 
 
PIV − θ = 24oCFD − θ = 24o
(c) θ0 = 24◦
Figure 3.20: Distribution of averaged LEV circulation, Γv for a variation in flap
frequency, flexible wing, y/b = 0.5 (40◦ flap amplitude, V∞ = 3 m/s) at 50% span.
145
LEV size and strength does vary at different span locations along the wing.
This is because an increase in vorticity indicates that there is an increase in net
circulation around the wing, thereby causing increased lift when the LEV is present.
When the LEV is shed, the vorticity becomes less concentrated and diffused rather
rapidly when the LEV starts to detach. This effect is most pronounced further
outboard on the wing.
3.3 Airloads Comparison
3.3.1 Rigid Wing Comparison of Aerodynamic Forces from Flowfield
Along with the flowfield, it is also important to validate the instantaneous
forces predicted by CFD with test data. However, discerning the instantaneous
aerodynamic force component on a flapping wing is a challenging task. This is
because the total force is dominated by the inertial force component especially in the
vertical direction (along Z-axis). Therefore, an attempt was made to calculate the
vertical force (Fz) from the measured flowfield. A conventional method for obtaining
lift from velocity field is by numerically calculating the circulation using a line integral
along a closed contour enclosing the airfoil [17]. The size of the integration contour
around the airfoil is increased until the circulation converges to a steady value. Even
though such a method could work for the steady attached flows, its applicability
is limited for highly unsteady, vortex-dominated separated flows, similar to those
observed for flapping wings in the present study. In most of the present test cases, the
control volume-based method did not converge to a unique value and, hence, could
146
not be used with sufficient confidence. Therefore, a different method was developed,
which utilizes a rectangular control volume around the airfoil (ABCD) as shown in
Fig. 3.21. This method requires the use of a momentum-based approach to calculate
the vertical force acting on the airfoil. As shown in Fig. 3.21, the moving fluid exerts
pressure and shear forces on the wing, which creates a resultant aerodynamic force
per unit span, given by R. In turn, by Newton’s third law, the body exerts equal and
opposite pressure and shear forces (−R) on the flow. This effect would manifest itself
in the flowfield around the airfoil. This method is implemented using the integral
form of the momentum equation given below
∂
∂t
∫∫∫
ρ~V dv +
∫∫
(ρ~V · ~dS)~V = −
∫∫
p ~dS − ~R (3.5)
The force acting on the airfoil (~R) can be calculated as follows:
~R = −
∂
∂t
∫∫∫
ρ~V dv −
∫∫
(ρ~V · ~dS)~V −
∫∫
p ~dS (3.6)
The first term on the right hand side of equation 3.6 is the acceleration of the
fluid in the control volume and the second term is the momentum flux across the
boundary of the control volume. These two terms can be calculated from the PIV
measured flowfield. However, the third term (
∫∫
p ~dS) cannot be obtained from the
velocity field. One approach would be to consider a control volume much bigger than
the airfoil so that the pressure along the boundary is the ambient pressure (P∞) and
the surface integral would average to zero. However, a practical window size used in
147
Figure 3.21: Schematic explaining CZ calculation.
a PIV measurement would not be large enough to compute this. Note that the PIV
window size is 2 chords × 3.5 chords. Therefore, a hybrid approach is used in the
present study where the pressure along the box sides was obtained from CFD. Also
note that since the pressure always acts normal to the sides, only the pressure along
sides AB and CD contributes to the vertical force (Fz). An alternative experimental
approach to obtain pressure could be to use an array of pressure transducers on
the ceiling and floor of the wind tunnel test section. Another method could be to
compute the pressure from the PIV-measured velocity data, which is a very active
area of research.
The vertical force coefficient (Cz) obtained from the rigid wing PIV measured
flowfield using the present method is compared with Cz obtained from CFD in
148
0 2 4 6 8 10
0
1
2
3
4
Flapping frequency (Hz)
Ve
rtic
al 
for
ce
 co
eff
icie
nt,
 C Z
 
 
0 deg (PIV)
12 deg (PIV)
24 deg (PIV)
0 deg (CFD)
12 deg (CFD)
24 deg (CFD)
Wing pitch
angle
Figure 3.22: Variation of vertical force coefficient (Cz) from rigid wing averaged PIV
and instantaneous CFD flowfield data (50% span location, 4 Hz flapping).
Fig. 3.22. This is for the 4 Hz case and data was used for the 50% span location
(mid-downstroke). As shown in this figure, there is generally good agreement between
the PIV and CFD for a wide range of pitch angles and flapping frequencies. This
further validates the CFD analysis and also the present method of calculating forces.
3.3.2 Comparison of Predicted and Averaged Direct Force Measure-
ments for the Rigid and Flexible Wing
Along with the flowfield comparison, it is important to compare the forces
predicted by CFD-CSD with test data. These direct force measurement experiments
were performed with the flapping mechanism instrumented with a force transducer
at the root. The wing frequency was varied for three pitch angles (θ = 0◦, 12◦, and
24◦). The flap amplitude was 40◦ and the wind tunnel speed was 3 m/s. Figure 3.23
149
shows the results for the averaged forces.
Figures 3.23(a) and 3.23(b) show the resulting variation of average FZ and
FX for the rigid wing. Here, 0◦ pitch flapping generates a propulsive force. This
is a very important observation and will be examined in subsequent chapters. The
production of this positive aerodynamic force in the chordwise direction (propulsive
force) is called the Knoller-Betz effect [114]. For the θ0 = 0◦ pitch angle, the FZ force
is symmetric for the up-stroke and down-stroke, and thereby the average vertical
force is nearly zero. As the pitch angle is increased, the propulsive force is decreased
and the wing begins to produce more drag. As the pitch angle is increased, the FZ
force increases and the FX force goes further negative. Although pure flapping of
this rigid wing is not a practical solution for real MAV-scale forward flight, these
results provide insight into the effects of flapping on the wing. The flow solver results
correlate well with the averaged force measurements.
Figures 3.23(c) and 3.23(d) show the resulting variation of average FZ and FX
with flapping frequency for flexible wings. It can be observed that the wing with
root pitch angle of 0◦ produced almost zero FZ and 9.5 grams of FX at 10 Hz. There
is some propulsive force generated at the zero pitch angle (similar to the rigid wing).
On increasing the root pitch angle, the vertical force increases, but the propulsive
force reduces. For the case with θ0 = 24◦, FZ of 12 grams and FX of 5 grams was
generated at 10 Hz.
In general, the horizontal force is improved by adding wing flexibility. The
details for why this is the case will be discussed next in Chapters 4 and 5. As the
pitch angle is increased, the FZ force increases and the FX force decreases. There
150
4 5 6 7 8 9 10−2
0
2
4
6
8
10
12
14
Frequency, Hz
Verti
cal fo
rce, F
Z (g)
 
 Exp − θ = 0oCFD − θ = 0oExp − θ = 12oCFD − θ = 12oExp − θ = 24oCFD − θ = 24o
(a) Rigid wing variation of FZ.
4 5 6 7 8 9 10−4
−2
0
2
4
6
8
10
Frequency, Hz
Horiz
ontal
 force
, F X (g
)
 
 
Exp − θ = 0oCFD − θ = 0o
Exp − θ = 12o
CFD − θ = 12o
Exp − θ = 24oCFD − θ = 24o
(b) Rigid wing variation of FX.
4 5 6 7 8 9 10−2
0
2
4
6
8
10
12
14
Frequency, Hz
Verti
cal fo
rce, F
Z (g)
 
 Exp − θ = 0oCFD − θ = 0oExp − θ = 12oCFD − θ = 12oExp − θ = 24oCFD − θ = 24o
(c) Flexible wing variation of FZ.
4 5 6 7 8 9 10−4
−2
0
2
4
6
8
10
Frequency, Hz
Horiz
ontal
 force
, F X (g
)
 
 
Exp − θ = 0oCFD − θ = 0oExp − θ = 12oCFD − θ = 12oExp − θ = 24oCFD − θ = 24o
(d) Flexible wing variation of FX.
Figure 3.23: Rigid and flexible wing comparison of averaged experiment and predicted
vertical (FZ) and horizontal forces (FX) for various flap frequencies.
is good agreement between averaged force measurements and CFD-CSD predicted
result for a wide range of pitch angles and flapping frequencies. This does somewhat
validate the CFD-CSD analysis for large wing deflections with highly unsteady and
separated flows.
3.4 Chapter Summary
The multibody dynamics solver was used to model the structure of a MAV
flexible flapping wing. Cantilevered wing members were tested in both bending and
151
torsion to obtain the structural properties. Validation of the shell model was executed
using static load experiments and analysis on the full wing. The capability of MBDyn
to model plate structures with large deformations was successfully demonstrated. In-
house experiments were also conducted to measure the deflections of the wing using
a VICON system during flapping. Shaker tests were also performed to acquire the
wing member natural frequencies for comparison to predicted values, and satisfactory
correlation was obtained. The coupled aerodynamic and structural model were also
compared to experimental results with satisfactory correlation.
Once the 3-D CFD-CSD model was systematically compared with experiments,
the model was used to understand the physics of lift and thrust production on a
flapping wing in forward flight. The model was used for this instead of experiments
because PIV measurements were only conducted at two instants during the flap cycle
(mid-downstroke and mid-upstroke). Also, the computational analysis can provide
more information such as the temporal and spatial variation of wing forces, which
are very important for understanding the physics.
152
Chapter 4: Rigid and Flexible Wing Comparison (Aerody-
namic Force Production)
In the previous chapter, the results from the 3-D CFD-CSD analysis were
compared systematically with the results from the PIV and force transducer wind
tunnel experiments. In this chapter, the results of the computational analysis are
utilized to better understand the flow physics about a flapping wing in forward
flight and, more importantly, the influence of flexibility on the production of lift (FZ)
and propulsive thrust (FX). The numerical analysis was used because it was more
appropriate than using the experimental results since the PIV measurements were
taken at only two points within the flap cycle (mid-downstroke and mid-upstroke).
Additionally, the computational analysis is capable of providing more detailed
information with respect to the spatial and temporal variations in the aerodynamic
forces over the course of a flap cycle. It should be stated that throughout this study,
the structural characteristics of the wing were kept constant with the goal being to
compare the results of a structurally characterized flexible wing to those of a rigid
wing.
153
4.1 Understanding Lift and Thrust Production for a Rigid Flapping
Wing
4.1.1 Rigid Wing Force History
It is important to understand the variation in forces over the flap cycle. Fig-
ure 4.1 shows the variation in vertical force coefficient (CZ) and horizontal force or
propulsive thrust coefficient (CX) of the flapping wing over the course of one flap
cycle for the different combinations of flap frequency and pitch angle for the rigid
wing.
Note that, for (CX), a positive value indicates drag force while a negative value
indicates propulsive thrust force. The flap frequencies tested during the experiments
and numerical simulations (0 Hz, 4 Hz, 6 Hz, 8 Hz, and 10 Hz) correspond to reduced
frequencies (k) of 0, 0.32, 0.48, 0.64 and 0.798 respectively. Figures 4.1(a) and 4.1(b)
show the variation of CZ and (CX), respectively, over one flap cycle for a pitch angle
of 0◦ and flapping frequencies of 0, 4, 6, 8 and 10 Hz. From Fig. 4.1(a) it can be seen
that for the static case (0 Hz), as expected CZ is almost zero, but as the flapping
frequency is increased the instantaneous CZ is also increased because of the increase
in angle of attack induced due to flapping and also due to the higher resultant
velocity experienced by the wing. For the 0◦ pitch angle, the upward force during the
downstroke is almost exactly the same as the downward force during the upstroke,
producing almost zero net vertical force over a flap cycle. However, as shown in
Fig. 4.1(b), the wing produces positive propulsive thrust (negative (CX)) during
154
both upstroke and downstroke and the magnitude of thrust increases with flapping
frequency. As the pitch angle is increased (12◦ and 24◦), as shown in Figs. 4.1(c)
and 4.1(e), there is an asymmetry in the variation of CZ over the flap cycle. A larger
magnitude positive CZ is produced during the downstroke in comparison to the
negative CZ in upstroke resulting in a net positive vertical force. Also, there is an
increase in the mean of CZ over the flap cycle with increased pitch angle. However,
as shown in Figs. 4.1(d) and 4.1(f), CX follows the opposite trend because as the
pitch angle is increased, the mean (CX) becomes more positive indicating that the
wing is producing more drag than thrust. Also, for all the frequencies examined, the
average propulsive thrust was always negative (positive (CX)) for 12◦ and 24◦ pitch
angles. This is because the wing produces positive (CX) during the downstroke, the
magnitude of which is much higher than the negative (CX) during the upstroke. In
essence, for the cases with a non-zero pitch angle, in a majority of cases the positive
vertical force and negative thrust force is produced during the downstroke of the
flap cycle. Conversely, the negative vertical force and positive thrust is produced
during the upstroke of the flap cycle. Table 4.1 provides a list of the averaged (CZ)
and (CX) force coefficients over the duration of one flap cycle for the flap frequencies
and pitch angles tested.
Table 4.1: Chart of averaged CZ and CX for flap frequency and pitch angle (rigid
wing)
4 Hz 6 Hz 8 Hz 10 Hz
θ CZ CX CZ CX CZ CX CZ CX
0◦ -0.02 0.00 0.01 -0.01 -0.01 -0.04 -0.02 -0.07
12◦ 0.53 0.12 0.66 0.13 0.80 0.14 0.54 0.04
24◦ 0.89 0.40 1.09 0.47 1.19 0.50 0.94 0.35
155
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−6
−4−2
02
46
Flap Cycle (t/T)V
ertical 
Force 
Coeffic
ient (C Z)
 
 0Hz4Hz6Hz8Hz10Hz
Downstroke
Upstroke
(a) CZ, θ = 0◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−0.2
−0.15−0.1
−0.050
0.050.1
0.150.2
Flap Cycle (t/T)Ho
rizonta
l Force
 Coeffic
ient (C X)
 
 0Hz4Hz6Hz8Hz10Hz
Downstroke
Upstroke
(b) CX, θ = 0◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−6
−4−2
02
46
Flap Cycle (t/T)V
ertical 
Force 
Coeffic
ient (C Z)
 
 0Hz4Hz6Hz8Hz10Hz
Downstroke
Upstroke
(c) CZ, θ = 12◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−2
−1
0
1
2
3
Flap Cycle (t/T)Ho
rizonta
l Force
 Coeffic
ient (C X)
 
 0Hz4Hz6Hz8Hz10Hz
Downstroke
Upstroke
(d) CX, θ = 12◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−6
−4−2
02
46
Flap Cycle (t/T)V
ertical 
Force 
Coeffic
ient (C Z)
 
 0Hz4Hz6Hz8Hz10Hz
Downstroke
Upstroke
(e) CZ, θ = 24◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−2
−1
0
1
2
3
Flap Cycle (t/T)Ho
rizonta
l Force
 Coeffic
ient (C X)
 
 0Hz4Hz6Hz8Hz10Hz
Downstroke
Upstroke
(f) CX, θ = 24◦.
Figure 4.1: Variation of total vertical force coefficient (CZ) and total horizontal force
coefficient (CX) from CFD data (rigid wing).
156
4.1.2 Analysis of the 3-D Rigid Wing FlowField over a Flap Cycle
(Q-Criterion)
In order to gain a deeper understanding of the cause behind these trends,
it is important to investigate the three-dimensional flow across the wing through
the course of one flap cycle. Throughout the rest of this section, the figures and
tables will focus on one case with a flap frequency of 4 Hz and a pitch angle of 24◦.
To visualize the vortical flow across the wing, the second invariant of the velocity
gradient tensor (Q-criterion) of the flowfield is calculated. Physically it represents
the influence of pure shear to that of pure rotation on a given fluid element and
can be used to determine the presence of coherent vortical structures within the
flowfield [185]. Figure 4.2 shows iso-surfaces of the second invariant of the velocity
gradient tensor, (Q-criterion), colored with a magnitude of vorticity contour at
various intervals of the flap cycle for this case.
Figures 4.2(a) and 4.2(b) represent the initial stages of the downstroke portion
of the flap cycle where t = 0 and t = T/8 respectively. It is here that the initial
formation of the leading edge, root and tip vortices upon the upper surface of
the wing can be seen. Note that in Fig. 4.2(b), along the bottom surface, there
is spanwise vorticity forming from the root to the tip of the wing. In Fig. 4.2(c)
(t = T/4, mid-downstroke) and Fig. 4.2(d) (t = 3T/8) when the wing is undergoing
the second half of the downstroke, there is a large accumulation of vortical structures
on the wing’s upper surface that has begun to encompass much of the wing chord.
Figures 4.2(e) and 4.2(f) show the flowfield at t = T/2 and t = 5T/8, respectively
157
and depict the end of the downstroke and the beginning of the wing’s upstroke.
Globally, there is a noticeable decrease in the vortices about the wing’s upper surface.
The amount of vorticity present has become smaller in magnitude and less coherent
in comparison to that at t = T/4. This is due to the change in flow direction
around the root and tip associated with the change in flap direction. Figure 4.2(g)
characterizes the mid-upstroke of the flap cycle. Notice that vortical structures are
now beginning to form on the underside of the wing and there are significantly fewer
vortical structures present in comparison to the mid-downstroke position (Fig. 4.2(c)).
The reason for this is the lower angles of attack experienced by the wing during the
upstroke. Lastly, Fig. 4.2(h) shows the latter half of the upstroke portion of the flap
cycle. There is a clear formation of a vortex core at the wing tip as the majority
of the vorticity has developed on the bottom surface of the wing. For the duration
of the upstroke, while there was a clear formation of a tip vortex, the root vortex
remained less coherent, suggesting that the difference between the high pressure and
the low pressure side is small at the wing root compared to the tip.
The plots of Q-Criterion over time in Figs. 4.2 provide a global view of how
the 3-D flow around the wing was evolving over the course of a single flap cycle. In
this case, the Q-criterion allows for a qualitative examination of where vorticity was
being generated and showed how this vorticity migrated within the flowfield. The
Q-Criterion does show the overall complexity of the flow and the evolution of the
flow structures. However, the iso-surface plots are not able to give a clear view of
the vortical flow at different locations of the flapping wing so that it could be related
to the forces produced by the wing.
158
(a) t = 0/T . (b) t = T/8.
(c) t = T/4. (d) t = 3T/8.
(e) t = T/2. (f) t = 5T/8.
(g) t = 3T/4. (h) t = 7T/8.
Figure 4.2: Iso-surfaces of Q-Criterion colored with vorticity magnitude contour at
various instances of the flap cycle (rigid wing).
159
4.1.3 Rigid Wing Analysis of the 3-D Flowfield Over a Flap Cycle
(Spanwise Vorticity Contours)
In order to provide a clear view of the change in the flowfield over the wing
through the duration of a flap cycle, Fig. 4.3 illustrates the vorticity magnitude at
specific spanwise locations along the wing. Within each figure, the chordwise sections
shown, from root to tip, correspond to the 30%, 50%, 70%, and 90% spanwise
locations respectively. In each image the root is on the left and the tip of the wing is
on the right.
In Fig. 4.3(a), as the wing initiates the downstroke of the flap cycle (t = 0),
the initial formation of the LEV at the various spanwise locations is observed. In
Fig. 4.3(b) (t = T/8), there is a significant growth in the size of the LEV along
the span as the wing begins to progress through the downstroke. At the 30% span
location, the LEV is still attached to the upper surface of the airfoil. However, on the
more outboard sections of the wing, portions of the LEV are beginning to separate
from the wing. This is due to an increase in the vertical component of velocity along
the span induced by flapping motion of the wing. This increase in vertical velocity
leads to an increase in the local angle of attack and resultant velocity from root to
tip. Figure 4.3(c) represents the mid-downstroke (t = T/4) and is the point during
the flap cycle where the largest magnitudes of resultant velocity and angle of attack
occur. At this time, there is a high level of vorticity and separated flow on the upper
surface of the wing creating a large region of low pressure. The highest value of
vorticity and flow separation takes place at the mid-downstroke and explains the
160
peaks in the magnitude of the CZ and CX in Figs. 4.1(e) and 4.1(f) respectively.
In Fig. 4.3(d) (t = 3T/8), there is still a significant region of separated, vortical
flow on the topside of the wing. However, from Figs. 4.1(e) and 4.1(f), we notice a
decrease in the magnitude of the aerodynamic force generated by the wing. This
is because the wing is decelerating as it approaches the end of the downstroke and
the magnitudes of the local angles of attack and resultant velocities along the span
begin to decrease.
At t = T/2, shown in Fig. 4.3(e), the wing has completed the downstroke
portion of the flap cycle and is now beginning the upstroke. A moderate level of
separated flow is present along the entire wing span, but the extent and magnitude
has noticeably decreased between Fig. 4.3(e) (t = T/2) and Fig. 4.3(d) (t = 3T/8).
This is because at the beginning of the upstroke, the velocity due to the wing’s
motion is essentially zero and the magnitude of the resultant velocity is equal to
the free-stream velocity. In Fig. 4.3(f), as the wing begins to progress through
the upstroke, there is a shift in the direction of the resultant velocity vector that
results in a decrease in the local angle of attack along the span. There is also a
significant decrease in the magnitude of vorticity across the wing’s upper surface,
and a slight amount of vorticity is beginning to form on the bottom surface of
the wing. The differences in vorticity about the upper and lower surfaces result
in the near zero values for CZ and CX seen at t = 5T/8 as shown in Figs. 4.1(e)
and 4.1(f). At the mid-upstroke (t = 3T/4), the resultant velocity vector is again
at its maximum magnitude along the span but is acting slightly downward due to
the negative component of the vertical velocity vector. From Fig. 4.3(g), it can be
161
seen that on the inboard portion of the wing, much of the vorticity is located on
the topside of the wing because of the positive angle of attack, but going outboard,
a majority of the vorticity is located on the underside of the wing owing to the
negative angle of attack induced by flapping. Therefore, the flapping motion causes
a change in sign of the angle of attack and hence a change in direction of the lift
force from root to tip. This is responsible for the small peak in negative vertical
force (negative CZ) and positive propulsive thrust (negative CX) at that instance in
the flap cycle (refer to Figs. 4.1(e) and 4.1(f)). Lastly, in Fig. 4.3(h), the magnitude
of the resultant velocity vector has decreased and there is little to no separation
along the wing span as it begins to decelerate. While the level of vorticity present is
low in comparison to the other instances of the flap cycle, the majority is located on
the wings upper surface and is responsible for the low magnitude of positive vertical
force (positive CZ) and negative propulsive thrust (negative CX) at t = 7T/8. It is
interesting to note that in Fig. 4.3(h), toward the tip, the vorticity is concentrated
on the bottom surface of the airfoil, but toward the root on the upper surface. This
again implies a difference in the sign of the local angle attack along the wing span
even during this instance of the upstroke.
To explain the changes in the flowfield over the rigid wing at particular instances
of the flap cycle, Fig. 4.4 shows the vorticity contours at specific spanwise locations
along the wing. The chordwise sections shown correspond to the 30%, 50%, 70%,
and 90% spanwise locations respectively. Figures 4.4(a), 4.4(c), 4.4(e) and 4.4(g)
show the vorticity at the mid-downstroke (t = T/4), and Figs. 4.4(b), 4.4(d), 4.4(f)
and 4.4(h) correspond to the mid-upstroke (t = 3T/4). The mid-downstroke and
162
(a) t = 0/T . (b) t = T/8.
(c) t = T/4. (d) t = 3T/8.
(e) t = T/2. (f) t = 5T/8.
(g) t = 3T/4. (h) t = 7T/8.
Figure 4.3: Vorticity magnitude along the span at various instances of flap cycle
(rigid wing).
163
mid-upstroke are highlighted because at these moments in the flap cycle, the wing is
subject to the highest instantaneous local resultant velocities, and it exhibits peaks
in aerodynamic force production.
During mid-downstroke a majority of the vorticity is concentrated on the upper
surface of the wing. At the 30% span location (Fig. 4.4(a)) there is a noticeable
formation of vorticity present at the leading edge of the wing. Near the wing root the
LEV remains attached to the wing surface, but begins to separate toward the wing
tip. In Fig. 4.4(c) and 4.4(e) it can be clearly seen that outboard of the 50% span
location, the LEV has detached from the wing’s upper surface and shed. At the 90%
span location (Fig. 4.4(g)), the flow becomes significantly chaotic due to tip effects
which cause the leading edge vortex to break down and separate. At the mid-upstroke
(t = 3T/4), the resultant velocity vector is again at its maximum magnitude along the
span but is acting slightly downward due to the negative component of the vertical
velocity vector. It can be seen that on the inboard portion of the wing (Fig. 4.4(b)),
much of the vorticity is located on the upper surface of the wing because of the
positive angle of attack. At the 50% span location (Fig. 4.4(d)), there is almost no
vorticity present on the wing surface due to the near zero local induced angle of
attack at that section of the wing. Outboard on the wing, (Figs. 4.4(f) and 4.4(h)),
a majority of the vorticity is located on the lower surface of the wing because of the
negative angle of attack induced by flapping. Therefore, the flapping motion causes a
change in sign of the effective angle of attack and hence a change in direction of the
lift force from root to tip. This is responsible for the small peak in negative vertical
force (negative CZ) and positive propulsive thrust (negative CX) at that instance in
164
the flap cycle.
To analyze the degree of three-dimensionality present in the flow, Figs. 4.5(a)
and 4.5(b) show chordwise cuts along the length of the wing at the 20% chord location
from the LE, during the mid-downstroke (t = T/4) and mid-upstroke (t = 3T/4) of
the flap cycle respectively. Here, a qualitative representation of the vorticity and
fluid flow along the wing’s span is presented.
In Figs. 4.5(a) and 4.5(b), there is a concentration of vorticity at the wing root
and tip due to the presence of the root and tip vortices. As expected, the tip vortex
is of greater size and magnitude in comparison to the root vortex. Consequently,
toward the wing root and wing tip, there was a high magnitude of spanwise velocity
on the order of the freestream velocity. However, the magnitude of spanwise velocity
at locations further from the root and tip is significantly less. At these spanwise
locations, the direction of the velocity vector can be assumed to lie in the 2-D
chordwise plane. Also, from the vorticity contours at mid-downstroke, (shown in
Fig. 4.5(a)) it can be inferred that both the root and tip of the wing (and therefore
every spanwise section of the wing) are at a positive angle of attack because the root
and tip vortices have opposite sign vorticity. This is because the flow is leaking from
the lower side to the upper side of the wing at both root and tip. However, at the
mid-upstroke (Fig. 4.5(b)) the vorticity has the same sense for both root and tip
vortices because the angle of attack is positive at the root and negative at the tip.
Thus far, the variation of CZ and CX of the entire wing over the course of
one flap cycle (shown in Fig. 4.1) was explained using the flowfield around the
wing (Figs. 4.2, 4.3, 4.4, and 4.5). It has also been shown that the flow on the
165
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(a) Mid-downstroke, 30% span.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(b) Mid-upstroke, 30% span.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(c) Mid-downstroke, 50% span.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(d) Mid-upstroke, 50% span.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(e) Mid-downstroke, 70% span.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(f) Mid-upstroke, 70% span.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(g) Mid-downstroke, 90% span.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, 
z/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(h) Mid-upstroke, 90% span.
Figure 4.4: Vorticity contours with overlaid velocity along the span: left side,
mid-downstroke and right side, mid-upstroke (rigid wing), 4 Hz, θ = 24◦.
166
(a) X Vorticity, Mid-Downstroke. (b) X Vorticity, Mid-Upstroke.
Figure 4.5: X-Vorticity magnitude along the span from CFD data (rigid wing), 4 Hz,
θ = 24◦.
flapping wing is predominantly 2-D except at the wing root and tip. Therefore,
in the following section, the vertical and propulsive thrust forces produced by the
flapping wing are investigated further using the computed force coefficients at various
spanwise sections of the wing. Note that, even though these are 2-D force coefficients,
they are obtained from the full 3-D analysis of the flapping wing and hence would
include the 3-D effects as well. The following analysis and results will be focused on
the mid-downstroke (t = T/4) and mid-upstroke (t = 3T/4) because it is at these
instances where the peaks in the magnitude of CZ and CX occur during a flap cycle.
4.1.4 Rigid Wing 2-D Analysis of Wing (Sectional Vertical and Hori-
zontal Force Coefficients along the Span)
To illustrate the variation in the sectional aerodynamic force along the wing,
Figures 4.6 shows the variation in the 2-D sectional values of Cz and Cx along the
span for both the mid-downstroke and mid-upstroke respectively for the same case
(24◦ pitch angle and 4 Hz flapping frequency).
In Figs. 4.6(a) and 4.6(b), it is interesting to point out that the sectional values
167
Table 4.2: Chart of UP, UT, V and φ along the span (rigid wing).
Span, y/b 0.30 0.40 0.50 0.60 0.70 0.80 0.90
UP, (m/s) 0.80 1.07 1.34 1.604 1.872 2.139 2.407
UT, (m/s) 3.00 3.00 3.00 3.00 3.00 3.00 3.00
V, (m/s) 3.10 3.185 3.284 3.402 3.536 3.685 3.846
φ, (deg) 14.971 19.622 24.021 28.138 31.961 35.491 38.736
of Cz and Cx are large in magnitude, especially toward the tip of the wing. Note
the forces shown in the aforementioned figures were non-dimensionalized by the
freestream velocity (V∞).
Due to the flapping kinematics of the wing, there is a significant vertical velocity
component perpendicular to the freestream direction. Thus the resultant velocity
experienced at a spanwise section of the wing is defined as:
~V = ~Vwind + ~Vflapping =
√
U2P + U
2
T (4.1)
Here, UP is the velocity parallel to flap plane and UT is the velocity component
normal to flap plane. The relative inflow angle (or induced angle of attack) is
φ = tan−1
(
UP
UT
)
.
Table 4.2 presents the values of UP, UT, V and φ for the 4 Hz flapping case at
the mid-downstroke. Here it is shown that the resultant velocity is significantly higher
than V∞ and the flap induced velocity φ is as high as 40◦ near the tip (significantly
beyond the static stall angle).
Figure 4.7 shows the spanwise distribution of Cz and Cx along the span, non-
dimensionalized by the calculated resultant velocity, V , at the corresponding spanwise
locations, for the 4 Hz flapping case. Note that the magnitude of the force coefficient
168
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−1
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Nondimensional Span Location, y/b
Vert
ical 
Forc
e Co
effic
ient,
 C z
 
Mid DownstrokeMid Upstroke
(a) Vertical force coefficient, Cz, θ = 24◦.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.5
0
0.5
1
1.5
2
Nondimesional Span Location, y/b
Hor
izon
tal F
orce
 Coe
fficie
nt, C
x
 
Mid DownstrokeMid Upstroke
(b) Horizontal force coefficient, Cx, θ = 24◦.
Figure 4.6: Rigid wing sectional Cz and Cx, at mid-downstroke and mid-upstroke,
normalized by V∞.
169
values has now decreased considerably, especially toward the tip of the wing where
the flap induced velocity is higher. It can be seen that the values of Cz and Cx along
the span during the downstroke are both positive, resulting in the wing producing
positive lift and negative propulsive thrust (such as drag) along the entirety of
the wing span. However, that same trend is not seen in the upstroke. During the
upstroke, a change in the direction of the Cz and Cx force along the span occurs.
Closer to the root, the wing is producing a positive lifting force (positive Cz) and a
drag producing force (positive Cx). However, in the outboard section (y/b > 0.45),
there is a shift, and the wing is producing a negative lifting force (negative Cz) and
a positive propulsive thrust (negative Cx).
The main difference between Fig. 4.6 and Fig. 4.7 is the magnitude of the values
for Cz and Cx. Normalization by the freestream velocity causes a higher lift coefficient
value (compared to the resultant velocity) because the induced velocity caused by
the flapping motion is not taken into account. In the literature, the calculation of
the aerodynamic forces acting on a flapping wing has been an issue. Previous studies
have made assumptions about the flowfield attempting to estimate the angle of attack.
Usherwood and Ellington [186,187] assumed a “triangular” downwash distribution
to estimate the angle of attack, where the downwash was assumed to vary linearly
with the span. Birch and Dickinson [89] calculated an angle of attack using the
velocity vectors that were acquired using PIV, where they assumed that the mean
orientation of the flow vectors near the lower surface of the wing represented the
freestream velocity. In the current study, the forces are normalized by the resultant
velocity, the angle of attack is determined by Eqn. 4.2, and for clarity, the lift and
170
drag coefficients are decomposed into vertical and horizontal force coefficients.
The flowfields in Figs. 4.3(c), 4.3(g), and 4.4, which represent the vorticity
present during the mid-downstroke and mid-upstroke respectively, can be used to
provide some information pertaining to the changes seen in the sectional aerodynamic
coefficients along the span. In Fig. 4.3(c), mid-downstroke, much of the vorticity is
close to the upper surface of the wing creating an increase in Cz and Cx. After the
50% span location (Fig. 4.4(c)), there is a reduction in both Cz and Cx due to the
leading edge vortex becoming detached and shedding downsteam. This decreasing
trend in the magnitude of Cz and Cx continues until approximately the 70% span
location (4.4(e)) where the tip vortex begins to have a more significant influence over
the flow. The tip vortex generates a region of low pressure near the tip resulting in
the slight increase in lift and drag seen at the 80% and 90% span locations.
For the mid-upstroke, there is a more linear, decreasing trend in the vertical
and horizontal force coefficients from root to tip. From Fig. 4.3(g), at the 30% span
location (see Fig. 4.4(b)), most of the vorticity is concentrated on the wings upper
surface resulting in a net positive vertical force (positive Cz) and a net drag force
(positive Cx). Near the 50% span location (e.g., Fig. 4.4(d)), the direction of net
vertical and horizontal force switches due to changes in the angle of attack across
the span. Figure 4.4(h) shows the 90% span location where all of the vortical flow
is along the underside of the wing resulting in a peak in the magnitude of negative
lifting force (negative Cz) and positive propulsive thrust (negative Cx) along the
span.
To explain the change in direction of the vertical and horizontal forces, it is
171
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.5
0
0.5
1
1.5
2
2.5
3
Nondimensional Span Location, y/b
Ver
tica
l Fo
rce
 Co
effi
cien
t, C
z
 
Mid Downstroke
Mid Upstroke
(a) Vertical force coefficient, Cz, θ = 24◦.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Nondimensional Span Location, y/b
Ho
rizo
nta
l Fo
rce
 Co
effi
cien
t, C
x
 
Mid Downstroke
Mid Upstroke
(b) Horizontal force coefficient, Cx, θ = 24◦.
Figure 4.7: Rigid wing Cz and Cx, at mid-downstroke and mid-upstroke, normalized
by the resultant V.
172
important to look at the local angle of attack, α, at the various spanwise sections.
From equation 4.2, α is defined as:
α = θ + φ (4.2)
Equation 4.2 shows that α is a function of the pitch angle, θ, and the flap induced
angle, φ. During the upstroke, φ is negative and smaller in magnitude than θ toward
the root and greater than θ toward the tip. This results in a positive α at the wing
root and negative α at the wing tip, thus explaining the difference in the direction of
aerodynamic force along the wing span and the sign difference in Cz and Cx about
the downstroke and upstroke as a whole.
4.1.5 2-D Analysis of Rigid Wing (Sectional Lift and Drag Coefficients
along the Span)
The presence of the flap induced velocity, UP, is responsible for a change in the
local α along the span and is also thought to be a factor in the increase of the force
coefficients. The vertical velocity component, UP, not only changes the magnitude
and direction of the resultant velocity vector, but also the lift and drag force vectors.
For static wing cases, where α is solely based on the pitch angle of the wing, (i.e.,
φ = 0), the magnitudes and directions of Cz and Cx correspond directly to those of Cl
and Cd respectively. However, for a flapping wing, φ is non-zero and the magnitudes
and directions of Cz and Cx are not the same as Cl and Cd. Figure 4.8 illustrates
the difference in the magnitude and direction of the vectors for Fz, Fx, lift and drag.
173
(a) Downstroke. (b) Upstroke.
Figure 4.8: Schematics of force and velocity vectors for the airfoil cross section.
From the schematics in Figs. 4.8(a) and 4.8(b), Cz and Cx can be expressed as
a function of Cl and Cd using the following equations:
Cz = Cl cos(φ) + Cd sin(φ) (4.3)
Cx = −Cl sin(φ) + Cd cos(φ) (4.4)
In equations 4.3 and 4.4, the magnitudes of Cz and Cx only depend on the magnitudes
of Cl and Cd and φ. The magnitude of Cl and Cd are governed by the local α at a
given spanwise section.
Figure 4.9 shows a plot of Cl and Cd along the span for the mid-downstroke
and mid-upstroke at a pitch angle of 24◦. In Fig. 4.9, a positive or negative angle of
attack corresponds to a positive or negative value of Cl. In contrast, the value of Cd is
always positive, regardless of the sign of α. For the case where θ is equal to 24◦, near
the wing root, where the resultant velocity is approximately equal to the freestream
value, the magnitudes of Cl and Cd for the mid-downstroke and mid-upstroke are
not comparable to the static wing case at 24◦. The flowfield analysis presented
174
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.5
0.1
0.7
1.3
1.9
2.5
Nondimensional Span Location, y/b
Lift
 an
d D
rag
 Co
effi
cie
nts
, C
l & 
 C d
 
 
Cl, downstroke
Cl, upstroke
Cd, downstroke
Cd, upstroke
−11.5°−7.9°
−4.1°−0.1°4.4°
43.6°
48.0°
52.1° 55.9°
59.5° 62.7°
−14.7°
α = 38.9°
α = 9.0°
Figure 4.9: Lift coefficient, Cl, and drag coefficient, Cd, along the span, at mid-
downstroke and mid-upstroke.
before indicated a dynamic stall type of phenomena on the wing due to the unsteady
variation of angle of attack at very high reduced frequency. This could be the reason
for the delayed stall and unusually high Cl values. Additionally, these large values of
Cl and Cd cannot be predicted using a simple quasi-steady analysis. Note that during
the mid-downstroke of the flap cycle, the value of Cl never exceeds a value of about
2.4. However, when comparing the maximum values of Cz for the aforementioned
case (Fig. 4.6(a)) it can be seen that the maximum sectional value is approximately
3. This is because of the contribution of Cd to Cz resulting from the large induced
angle (φ). As shown in Figs. 4.10(a) and 4.10(b), as the magnitude of φ increases
toward the wing tip, there is a rotation of the resultant velocity vector (V ) by the
same angle φ, upward during downstroke and downward during upstroke. In turn,
175
the lift and drag vectors also rotate by the same angle. Therefore, the magnitudes
of Cz and Cx at any span location would depend not only on the magnitudes of lift
and drag but also their direction (given by φ) as given by equations 4.3 and 4.4.
In Fig. 4.10(a), a schematic of the rotation of the wing lift and drag vectors,
the magnitude of φ increases toward the wing tip at the mid-downstroke and results
in an increase in the local angle of attack from root to tip. This causes the lift vector
to tilt forward and drag vector to tilt upward while moving from root to tip. This
would cause the lift to contribute more towards propulsive thrust, while the drag
would contribute to positive vertical force and produce less negative thrust in the
outboard sections. From Fig. 4.9 the magnitude of Cl decreases toward the wing tip;
however, in Fig. 4.7(a) there is an increase in the magnitude of Cz from the 30% to
50% span locations. This increase in Cz is due to the combination of the vertical
component of the lift force as well as a vertical component of the drag force causing
a net increase in Cz greater than the magnitude of the Cl alone.
From Fig. 4.10(b), the variation in φ along the span during the upstroke causes
the lift vector to act primarily downward and slightly forward as one goes closer to
the wing tip. This rotation of the lift vector results in part of the lift force acting to
propel the wing forward (positive propulsive force) as well as pull the wing down
(negative vertical force). From Fig. 4.9, it can be seen that the value of Cd during the
upstroke remains relatively constant, but the magnitude of the lift vector increases
from approximately the 50% span location to the wing tip. This results in a larger
component of force acting in the negative x-direction as opposed to the positive
x-direction creating a net propulsive thrust (negative Cx).
176
(a) Downstroke. (b) Upstroke.
Figure 4.10: Rotation of the lift and drag vectors toward the wing tip.
4.1.6 Section Summary
In this section, a combination of 3-D and spanwise 2-D flowfield, along with
instantaneous force coefficient values were used to understand the underlying physics
behind a wing undergoing pure flapping kinematics at a fixed pitch angle. A key
insight gained from this analysis on rigid, low-aspect ratio wings undergoing pure flap
kinematics is that much of the positive vertical force and drag is produced during
the downstroke portion of the flap cycle while a majority of the propulsive thrust
and negative vertical force is generated during the upstroke portion of the flap cycle.
The vertical and propulsive thrust distribution on a flapping wing depends on the
magnitude and direction of the lift and drag along the wing span. Significantly large
lift and drag coefficients and stall delay to very high angles of attack (much higher
than the static stall value) were observed along the span of the wing because of
the unsteady angle of attack variation at very high reduced frequency leading to a
dynamic stall type of phenomena.
It was also concluded that pure flap kinematics without active wing pitching
177
would not be able to produce both positive vertical force and propulsive thrust for
a flapping wing, thus rendering it impractical for a flapping MAV design; however,
to improve the net propulsive thrust of a rigid wing configuration, a negative pitch
angle should be utilized during the downstroke and a positive pitch angle during
the upstroke. Additionally, to improve the net positive lift, there needs to be an
asymmetry in the pitch variation between the upstroke and downstroke. Further
improvement in the efficiency of force production would require varying the pitch
angle of the wing sections along the span along with the temporal variation (or
dynamic twist). This is because different spanwise sections are subjected to different
local angles of attack over time, and adjusting the pitch angle along the span would
give more control over the angle of attack at which different spanwise sections operate.
This could be achieved using a torsionally flexible wing with a suitable spanwise
flexibility distribution with the chordwise c.g. behind the elastic axis. If the flexibility
and mass distribution are properly tailored, the inertial and aerodynamic forces
acting on the wing can be utilized to passively twist the wing without the need for
any additional pitching actuator. The next section, Section 4.2, contains a discussion
of the comparison of the rigid and flexible wing results.
4.2 Rigid and Flexible Wing Comparison
4.2.1 Aerodynamic Force Production
In the previous section, the results from the 3-D CFD model were systematically
analyzed. In this section, the results of the coupled CFD-CSD numerical solver will
178
be utilized to better understand the flow physics about a flapping wing in forward
flight. Specifically, the influence of flexibility on the production of lift (FZ) and
propulsive thrust (FX) will be presented. Throughout this study, the structural
characteristics of the wing were kept constant with the goal being to compare the
results of a structurally characterized flexible wing to those of a rigid wing.
Figure 4.11 shows the variation in the vertical force coefficient (CZ) and the
horizontal force coefficient (CX) over the course of one flap cycle for the case with a
flap frequency of 6 Hz and a pitch angle of 12◦. Figures 4.11(a) and 4.11(b) also show
the time-averaged CZ and CX values during the flap cycle. Note that a positive value
for CX represents a drag producing force while a negative value for CX represents
a propulsive thrust producing force. For concurrent rigid wing tests [132], it was
observed that a majority of the positive vertical force production occurs during the
downstroke of the flap cycle while a majority of the propulsive thrust production
occurs during the upstroke. This behavior can clearly be seen in Fig. 4.11(a) and
4.11(b). A flexible wing also exhibits similar behavior with regard to vertical force
production. Due to a positive geometric pitch angle, there is asymmetry in the force
production between the downstroke and upstroke. The asymmetry in vertical force
production results in an average CZ of approximately 0.66 for both the rigid and
flexible wings.
In contrast, in Fig. 4.11(b), there is a significant difference in the net horizontal
force produced between the rigid and flexible wings. During the upstroke of the rigid
wing (t/T > 0.5), as stated earlier, a majority of the propulsive thrust is produced,
and this remains true for the flexible wing also. However, unlike the rigid wing
179
case, the drag force generated is relatively low for a majority of the downstroke
of the flexible wing (1 < t/T < T/2). The slight amount of drag producing force
generated is of a significantly lower magnitude than that of the rigid wing during the
downstroke. When comparing the net horizontal force production over a complete
flap cycle, the net CX is 0.13 for the rigid wing and -0.19 for the flexible wing clearly
showing a large propulsive thrust for the flexible wing.
From the rigid wing analysis, it was determined that the use of rigid wings
undergoing pure flap kinematics in MAV designs would not be practical because they
are not able to simultaneously produce a significant net lifting and net propulsive
force during a flap cycle. However, from Fig. 4.11, introducing flexibility allows for the
wing to produce both a net lifting force and net propulsive force over one flap cycle.
These findings are motivation to further explore the aerodynamic force production
on a flexible wing and, more importantly, how flexibility influences the flow around
the wing and the mechanisms responsible for aerodynamic force production.
4.2.2 3-D Analysis of Wing (Aerodynamic Force Production over a
Flap Cycle)
To gain an understanding of how flexibility influences the performance of
a flapping wing in forward flight, it is important to analyze the production of
aerodynamic forces over time. Figure 4.12 shows the variation in vertical force
coefficient (CZ) and horizontal force coefficient (CX) over the course of one flap cycle
for the flap frequencies and pitch angles tested during experimentation. Again, note
180
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−4
−3
−2
−1
0
1
2
3
4
5
6
Flap Cycle (t/T)
Ver
tica
l Fo
rce
 Co
effi
cien
t (C Z
)
 
 FlexibleFlexible: Mean CZ
RigidRigid: Mean CZ
Downstroke
Upstroke
(a) Variation of CZ.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−1
−0.5
0
0.5
1
1.5
Flap Cycle (t/T)
Ho
rizo
nta
l Fo
rce
 Co
effi
cien
t (C X
)
 
 FlexibleFlexible: Mean CX
RigidRigid: Mean CX
Downstroke
Upstroke
(b) Variation of CX.
Figure 4.11: Rigid and flexible wing comparison of predicted vertical (FZ) and
horizontal force (FX) for single flap cycle with flap frequency of 6 Hz and θ0 = 12◦.
181
Table 4.3: Chart of CZ and CX for flap frequency and pitch angle (flexible and rigid
(in parenthesis) wing respectively).
4 Hz 6 Hz 8 Hz 10 Hz
θ0 CZ CX CZ CX CZ CX CZ CX
0◦ 0.01 (-0.02) -0.09 (0.00) 0.00 (0.01) -0.32 (-0.01) 0.01 (-0.01) -0.82 (-0.04) 0.02 (-0.02) -1.69 (-0.07)
12◦ 0.53 (0.53) -0.02 (0.12) 0.70 (0.66) -0.19 (0.13) 1.03 (0.80) -0.63 (0.14) 1.42 (0.54) -1.43 (0.04)
24◦ 0.89 (0.89) 0.22 (0.40) 1.25 (1.09) 0.19 (0.47) 1.74 (1.19) -0.12 (0.50) 2.50 (0.94) -0.91 (0.35)
that a positive CX value represents a drag producing force and a negative CX value
represents a propulsive thrust producing force. Figures 4.12(a) and 4.12(b) show the
change in CZ and CX, respectively, for an initial pitch angle of 0◦ at flap frequencies
of 4, 6, 8, and 10 Hz. In Fig. 4.12(a), it can be seen that as the flapping frequency is
increased, there is an increase in the magnitude of the instantaneous CZ. This is due
to an increase in the resultant velocity and induced angle of attack about the wing
caused by the flapping kinematics. The positive lifting force generated during the
downstroke of the wing is nearly identical to the downward vertical force generated
during the upstroke of the wing, resulting in a net vertical force near zero. However,
in Fig. 4.12(b), the wing is generating propulsive thrust, (negative CX), throughout
almost the entire flap cycle. The magnitude of the peak instantaneous CX value
increases with frequency and the variation of instantaneous CX is nearly symmetrical
about the upstroke and downstroke.
For the cases where the initial pitch angle is increased (12◦ and 24◦), there
is an asymmetry between the downstroke and upstroke resulting in a difference in
the aerodynamic force production over a flap cycle. In Figs. 4.12(c) and 4.12(e),
the magnitude of the positive CZ generated during the downstroke is larger than
the magnitude of the negative CZ generated during the upstroke. This creates a net
182
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−10
−5
0
5
10
Flap Cycle (t/T)
Verti
cal F
orce 
Coef
ficien
t (C Z)
 
 4Hz6Hz8Hz10Hz
(a) CZ, θ0 = 0◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−4
−3
−2
−1
0
1
Flap Cycle (t/T)
Horiz
ontal
 Forc
e Co
efficie
nt (C X
)
 
 4Hz6Hz8Hz10Hz
(b) CX, θ0 = 0◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−10
−5
0
5
10
Flap Cycle (t/T)
Verti
cal F
orce 
Coef
ficien
t (C Z)
 
 4Hz6Hz8Hz10Hz
(c) CZ, θ0 = 12◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−4
−3
−2
−1
0
1
Flap Cycle (t/T)
Horiz
ontal
 Forc
e Co
efficie
nt (C X
)
 
 4Hz6Hz8Hz10Hz
(d) CX, θ0 = 12◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−10
−5
0
5
10
Flap Cycle (t/T)
Verti
cal F
orce 
Coef
ficien
t (C Z)
 
 4Hz6Hz8Hz10Hz
(e) CZ, θ0 = 24◦.
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1−4
−3
−2
−1
0
1
Flap Cycle (t/T)
Horiz
ontal
 Forc
e Co
efficie
nt (C X
)
 
 4Hz6Hz8Hz10Hz
(f) CX, θ0 = 24◦.
Figure 4.12: Variation of total vertical force coefficient (CZ) and total horizontal
force coefficient (CX) from coupled CFD-CSD data (flexible wing).
183
positive lifting force over the course of a flap cycle, which increases in magnitude
with increased pitch angle. In Figs. 4.12(d) and 4.12(f), the increase in pitch angle
generates an asymmetry in horizontal force generation between the downstroke and
upstroke not seen in the 0◦ pitch angle cases. For the 12◦ pitch angle cases shown in
Fig. 4.12(d), the peak magnitude of CX during the downstroke is significantly less
than that seen during the upstroke. However, for a majority of the downstroke, the
wing is thrust producing throughout all the flap frequencies shown except for the two
lowest flapping frequency cases. At the 4 Hz and 6 Hz flapping frequency, the wing is
producing a drag force, (positive CX), through the entire downstroke and generates
thrust during the upstroke. In Fig. 4.12(f), which presents the 24◦ pitch angle cases,
the asymmetry in thrust production between the upstroke and downstroke is even
more significant. For all but the 10 Hz flapping frequency, the wing is producing
drag during the downstroke and producing thrust during the upstroke. However,
these cases, except for the 4 Hz and 6 Hz flapping frequencies, still produce a net
negative CX (i.e., propulsive thrust producing) force over the duration of a flap cycle.
Table 4.3 provides a list of the calculated net CZ and CX values over a flap cycle
for different of flap frequencies and pitch angles presented in Fig. 4.12. Note that
for each case within Table 4.3, the time-averaged coefficient value for the flexible
wing is listed first, followed by the time-averaged coefficient value for the rigid wing
in parentheses. From Table 4.3, it is clear that a majority of the flap frequencies
and pitch angles tested for the flexible wing generated both net lifting force and
propulsive thrust.
One way to assess the performance of the wing is to analyze the lift-to-drag
184
ratio (L/D). Lift-to-drag ratio is a measure of aerodynamic efficiency of the wing.
Conventionally, lift-to-drag ratio is the amount of lifting force generated by a wing,
or vehicle, divided by the drag force. In this case CZ and CX can be used in replace of
lifting force and drag force. However, for this particular flapping wing configuration,
L/D can be positive or negative depending on whether the wing is producing drag or
propulsive force. The optimal CZ/CX value would need to be negative and close to
-1 implying that the configuration is simultaneously producing similar magnitudes of
lift and propulsive thrust. From Table 4.3, this occurs at the 10 Hz, 12◦ case which
yields a CZ/CX value of -0.993. However, this is an approximation from observing
the current data set. Applying an optimization module to the simulation would
give a more exact value for the combination of flap frequency and pitch angle for
obtaining both high lift and propulsive force during flight.
4.2.3 3-D Rigid and Flexible Wing Flowfield Comparison (Q-Criterion)
Unlike the rigid wing analysis, flexible wings operating at particular flapping
frequencies and initial pitch angles are able to produce a net positive lifting force
and a net propulsive thrust over a flap cycle. It is important to investigate the
three dimensional flowfield around the flexible wing in order to acquire a deeper
understanding of what is causing the trends seen in Fig. 4.12. Throughout the rest of
this section, the case of a wing subjected to a flap frequency of 6 Hz and initial pitch
angle of 12◦ will be highlighted. Figure 4.13 shows iso-surfaces of the second invariant
of the velocity gradient tensor, (Q-Criterion), for both the rigid and flexible wings
185
at specific instances of the flap cycle. Note that Figs. 4.13(a) and 4.13(c) represent
iso-surfaces of Q-criterion for the flexible wing while Figures 4.13(b) and 4.13(d) are
representative of those for the rigid wing. The wing root is on the left on each image
and the wing tip is toward the right.
Figures 4.13(a) and 4.13(b) depict the mid-downstroke of the wing (t = T/4).
This is the point in the flap cycle where there is a peak in the magnitude of
instantaneous lifting force. There is a significant formation of vortical structures
about the top surface of the wing near the leading edge with both root and tip
vortices also forming on the top surface of the wing. At this point, the flexible wing
has noticeably deformed with the wing pitch angle along the span having decreased
in comparison to the rigid wing. While the rigid wing is showing larger leading
edge vortices in comparison to the flexible wing, the vortical structures begin to
break down towards the wing root and tip as seen in Fig. 4.13(b). At the more
outboard sections of the wing, the leading edge and tip vortices are beginning to
detach and move downstream. However, in Fig. 4.13(a), the vortical structures at
the leading edge, while smaller in magnitude, are more coherent and extend slightly
greater across the wing span before breaking down. The root and tip vortices are of
a slightly smaller size and appear to be closer in proximity to the wing’s surface.
Figures 4.13(c) and 4.13(d) illustrate the vortical flow about the wing during
the mid-upstroke. This case was chosen because there is a peak in propulsive thrust
production by both the rigid and flexible wings. Due to the change in flap direction,
with regard to the downstroke, a majority of the formation of vortical structures is
occurring on the underside of the wing. This suggests that during the upstroke of
186
the wing, the angle of attack along the wing span has become negative. Both the tip
and root vortices have begun to form on the underside of the wing suggesting that
the high pressure side of the wing is now on the wing’s upper surface. The flexible
wing has deformed creating an increase in the geometric pitch angle along the span
in comparison to that of the rigid wing. While both wings exhibit a relatively large
volume of incoherent vortical structures in the immediate wake of the wing, the rigid
wing shows a slightly higher amount in comparison to the flexible wing.
The Q-Criterion plots of the flexible and rigid wings in Figs. 4.13(a)–4.13(d)
provide a means of qualitatively comparing the three dimensional flow about the
wing at points in the flap cycle, which display peak aerodynamic force production.
It is seen that the introduction of flexibility was globally affecting the fluid flow and
evolution of vorticity across the wing over time. However, plots of the iso-surface of
Q-Criterion do not allow one to easily distinguish the difference in the formation of
vortical structures at various locations along the span because it is difficult to relate
the deformations seen along the span of the flexible wing to the flowfield. Therefore,
chordwise slices of the flowfield (vorticity contours) are analyzed.
4.2.4 3-D Rigid and Flexible Wing Flowfield Comparison (Spanwise
Vorticity Contours)
Figures 4.14(a) and 4.14(b) show the superimposed wing shapes at the mid-
downstroke and mid-upstroke respectively. The wing shape of the rigid wing is colored
blue while the flexible wing is colored gray. In Figure 4.14(a) for the mid-downstroke,
187
(a) t = T/4, downstroke flexible. (b) t = T/4, downstroke rigid.
(c) t = 3T/4, upstroke flexible. (d) t = 3T/4, upstroke rigid.
Figure 4.13: Rigid and flexible wing comparison of iso-surfaces of Q-Criterion colored
with vorticity magnitude at various instances of the flap cycle.
188
(a) Mid-downstroke. (b) Mid-upstroke.
Figure 4.14: Superimposed rigid and flexible showing deformations, θ0 = 12◦, Ω =6
Hz, (40◦ flap amplitude, V∞ = 3 m/s).
it can be seen that the pitch angle along the span of the flexible wing is significantly
different than that of the rigid wing. The difference in pitch angle can be seen to
increase along the span with the local pitch angle on the flexible wing decreasing
and even becoming negative from root to tip. Conversely, in Figure 4.14(b) for the
mid-upstroke, the difference in pitch angle between the flexible and rigid wing is less
severe but still shows an increasing trend along the span with the magnitude of the
local pitch angle increasing from root to tip.
Figures 4.15 and 4.16 illustrate the vorticity contours, with overlaid velocity
field, at various spanwise locations along the wing. These images more clearly
display the formation of vortical flow over the wing and provide a means to better
understand what role flexibility plays in enhancing the aerodynamic performance
of a flapping wing. Note that in each contour, the chord-wise sections correspond
to the 30%, 50%, 70%, and 90% span locations from wing root to wing tip. Fig-
ures 4.15(a), 4.15(c), 4.15(e), and 4.15(g) represent spanwise vorticity contours for the
189
flexible wing while Figures 4.15(b), 4.15(d), 4.15(f), and 4.15(h) are representative
of those for the rigid wing in the downstroke. The same can be said about the
corresponding contours in Fig. 4.16 for the upstroke.
The contours shown in Fig. 4.15 correspond to the mid-downstroke (t =
T/4). This is the point in the flap cycle where the wing is subject to the highest
instantaneous local resultant velocities and induced angles of attack. For both the
rigid and flexible wings, a majority of the vorticity is concentrated on the topside of
the wing. For the flexible wing, at the 30% span location (Figs. 4.15(a) and 4.15(b))
there is a noticeably lower magnitude of vorticity present in comparison to the same
span location on the rigid wing. This because while both sections are experiencing
the same local resultant velocity, the deformation of the flexible wing has caused the
pitch angle to decrease and consequently, lower the magnitude of the local angle of
attack relative to that of the rigid wing.
Comparing the accumulation of vorticity across the span of the rigid and flexible
wings: for the rigid wing, the concentration of vorticity present is remarkably larger
than that of the flexible wing for the 50% span location. However, outboard of the
50% span, the leading edge vortex along the rigid wing has begun to separate and
shed. On the other hand, the leading edge vortex about the flexible wing remains
attached further along the wing span until the 90% span location. At this point, the
presence of the tip effects causes the leading edge vortex to breakdown and separate.
Figure 4.16 shows the spanwise vorticity magnitude during the mid-upstroke
of the flap cycle (t = 3T/4). Note that from Fig. 4.11, it is at this instance during
the flap cycle that both the flexible and rigid wings generate the peak instantaneous
190
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(a) 30% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(b) 30% span, rigid.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(c) 50% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(d) 50% span, rigid.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(e) 70% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(f) 70% span, rigid.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(g) 90% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−0.6
−0.4−0.2
00.2
0.40.6
0.81
(h) 90% span, rigid.
Figure 4.15: Chordwise vorticity contour with overlaid velocity field at 30%, 50%,
70%, and 90% span locations at mid-downstroke (flexible and rigid wing).
191
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(a) 30% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
(b) 30% span, rigid.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(c) 50% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
(d) 50% span, rigid.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(e) 70% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
(f) 70% span, rigid.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8−0.6
−0.4−0.2
00.2
0.40.6
(g) 90% span, flexible.
Normalized X−coordinate, x/c
Norma
lized Z
−coord
inate, z
/c
 
 
−0.5 0 0.5 1 1.5 2−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
(h) 90% span, rigid.
Figure 4.16: Chordwise vorticity contour with overlaid velocity field at 30%, 50%,
70%, and 90% span locations at mid-upstroke (flexible and rigid wing).
192
propulsive thrust and negative lifting force. For both wings, toward the wing root,
there is nearly zero vorticity present because the magnitude of the local induced
angle of attack is relatively small (< 10◦). Further outboard along the span, the
concentration of vorticity along the underside of the wing increases due to an increase
in the magnitudes of the local resultant velocity and local induced angle of attack.
At the 70% and 90% span locations, the flexible wing exhibits a slightly smaller
amount of vorticity about the leading edge in comparison to the rigid wing.
At the outboard sections of the rigid wing, there is a slight amount of flow
separation present, particularly in Fig. 4.16(f). However, the leading edge vortices on
the flexible wing remain attached across the span. This is because the deformation
of the flexible wing along the wing span causes an increase in the local pitch angle
resulting in a decrease of the magnitude of the local induced angle of attack. The
decrease in the local induced angle of attack helps to mitigate detachment but still
allows for the formation of a substantial leading edge vortex.
4.2.4.1 2-D Analysis of Wing (Sectional CZ and CX along the Wing Span))
Until this point, the focus was on comparing the flowfield of the flexible wing
to that of the rigid wing to better understand how introducing flexibility changes
the fluid flow about the flapping wing. Qualitatively, it is seen that flexibility and
wing deformations cause a change in pitch angle along the span, the formation and
location of vorticity along the span including its magnitude is affected. In this section,
the variation in the sectional aerodynamic coefficients along the wing span will be
investigated at the mid-downstroke (t = T/4) and mid-upstroke (t = 3T/4) as these
193
Table 4.4: Chart of UP, UT, V and φ along the span (flexible wing).
Span, y/b 0.30 0.40 0.50 0.60 0.70 0.80 0.90
UP, (m/s) 1.20 1.60 2.01 2.41 2.81 3.21 3.61
UT, (m/s) 3.00 3.00 3.00 3.00 3.00 3.00 3.00
V, (m/s) 3.23 3.40 3.61 3.85 4.11 4.39 4.69
φ, (deg) 21.86 28.14 33.76 38.74 43.10 46.93 50.27
are the instances where the peaks in magnitude of Cz and Cx occur.
Figures 4.17(a) and 4.17(b) depict the variation of sectional Cz and Cx, respec-
tively, along the span for both the flexible and rigid wings at the mid-downstroke and
mid-upstroke. It should be noted that prior to this section, the vertical and horizontal
forces produced by the entire wing were non-dimensionalized by the free-stream ve-
locity (V∞). However, at the mid-downstroke and mid-upstroke, the velocity induced
by the flapping kinematics is at its largest magnitude and contributes significantly
to the resultant velocity at a particular spanwise section of the wing. Thus, the
sectional aerodynamic coefficients presented are normalized using equation 4.1
For reference, Table 4.4 contains the values corresponding to the magnitude of UT ,
UP , V and the flap induced angle φ at the various spanwise locations analyzed for a
flap frequency of 6 Hz.
From Table 4.4, toward the wing root, the influence of the flap induced velocity
on the local resultant velocity is relatively small causing only a 7% increase in its
magnitude. However, toward the wing tip the flap induced velocity is much higher
resulting in an over 50% increase in the magnitude of the resultant velocity in
comparison to the free-stream velocity. Given the significant difference between the
calculated resultant velocity and free-stream velocity, it is important to consider the
194
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−2
−1
0
1
2
3
4
Nondimensional Span Location, y/b
Ver
tica
l Fo
rce
 Co
effi
cien
t, C
z
 
 
Mid−Downstroke: Flexible
Mid−Upstroke: Flexible
Mid−Downstroke: Rigid
Mid−Upstroke: Rigid
(a) Vertical force coefficient, Cz.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Nondimensional Span Location, y/b
Ho
rizo
nta
l Fo
rce
 Co
effi
cien
t, C
x
 
 
Mid−Downstroke: Flexible
Mid−Upstroke: Flexible
Mid−Downstroke: Rigid
Mid−Upstroke: Rigid
(b) Horizontal force coefficient, Cx.
Figure 4.17: Sectional Cz and Cx, at mid-downstroke and mid-upstroke, 6 Hz,
θ0 = 12◦.
195
induced flap velocity when calculating the sectional force coefficients.
Shown in Fig. 4.17(a), during the mid-downstroke, the value of CZ along the
wing span is consistently positive for both the flexible and rigid wings, corresponding
to the wings producing a positive CZ at that point in the flap cycle. Also, the
magnitude of CZ along the span during the mid-downstroke is noticeably greater
toward the wing root. Note that when normalized by the local resultant velocity, the
value of sectional CZ of the flexible wing along the span during the mid-downstroke
is relatively constant at approximately 2.5 until the 70% span location. Further
outboard of the 70% span location, it is thought that the tip vortex has a more
significant effect and influences the aerodynamic force produced in that region.
Conversely, during the mid-upstroke, the value of sectional CZ along the span is
consistently negative for the rigid and flexible wing, resulting in the wing producing
a negative instantaneous CZ at that point in the flap cycle. Also, the rigid wing
consistently produces a negative sectional lifting force of greater magnitude than the
flexible. For the flexible wing, unlike during the mid-downstroke, the magnitude of
negative CZ is increasing along the span. This increase in magnitude continues until
the 70% span location where again, the tip vortex is said to begin having a more
significant influence over the aerodynamic force produced.
In Fig. 4.17(b), during the mid-downstroke of the flexible wing, the sign of the
sectional CX value changes from positive to negative after the 50% span location.
However, for the rigid wing, the value of CX is consistently positive and is of a
much higher magnitude. This shows that the rigid wing is producing a significant
amount of drag along the span, but on the flexible wing, the more inboard sections
196
are producing small drag forces while those sections toward the wing tip generate
propulsive thrust.
These findings suggest that for the flexible wing, there is a change in the
direction of the sectional resultant force vector along the wing span. The sum of
the propulsive thrust generated by the outboard wing sections is slightly greater
than the total drag force generated by the inboard wing sections resulting in an
instantaneous, net propulsive thrust force produced at the mid-downstroke. During
the mid-upstroke of the flap cycle, both wings are thrust producing (negative CX)
along the entirety of the span. Toward the wing root, the sectional CX is of like
magnitudes, but moving along the span, the flexible wing produces a notably greater
amount of sectional propulsive thrust. For the flexible wing, similar to the trend
of sectional CX during the mid-downstroke, the magnitude of CX increases along
the span until approximately the 70% span location. After this point, there is a
slight deviation from this trend and a decrease in the magnitude of sectional CX due
to the presence of the tip vortex. During the upstroke, the flexible wing produces
significantly higher propulsive thrust compared to the rigid wing in the outboard
sections.
4.2.4.2 2-D Analysis of Wing (Sectional Cl and Cd along the Wing Span)
To explain the change in magnitude and direction of the vertical and horizontal
forces along the wing span, it is important to discuss the flap induced velocity, UP, at
the various span locations. The vertical velocity component influences the magnitude
of the resultant velocity vector, V , as well as the flap induced angle, φ. Consequently,
197
UP has an effect on the local angle of attack and the direction of the lift and drag
force vectors.
Using the classical definitions of lift and drag, the lift force vector is perpendic-
ular to the resultant velocity while the drag force vector is parallel to the incoming
resultant vector. For a static wing where the wing is not flapping, φ = 0 and the lift
and drag force vectors, respectively, coincide with the vertical and horizontal forces.
However, if the wing is undergoing flapping kinematics, (i.e., φ 6= 0), the vertical and
horizontal forces do not coincide with the lift and drag forces, and can be described
again by Equations 4.3, 4.4, and 4.2.
Note that for the flexible wing, at a given time instance, the values of θ and φ
vary considerably along the wing span. The value of φ is mainly dependent on the
prescribed flapping kinematics of the wing and can easily be calculated analytically.
However, the value of θ is influenced by the wing flexibility and mass distribution as
well as the inertial and aerodynamic loads acting on the wing.
Figure 4.18 shows the variation of geometric pitch angle along the span during
the mid-upstroke and mid-downstroke at an initial pitch angle of 12◦ for all the flap
frequencies tested. We see that as the flapping frequency is increased, the change in
magnitude of the pitch angle is significantly increased in comparison to the initial
pitch angle of 12◦. During the downstroke of the wing, the direction of inertial loads
acting on the wing creates a nose-down wing twist. However, the opposite occurs
during the upstroke and the geometric pitch angle increases along the span due to a
nose-up wing twist. Note that the observed twist variation along the span was not
linear.
198
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−25
−20
−15
−10
−5
0
5
10
15
20
Nondimensional Span Location, y/b
Pitc
h A
ngl
e (°)
 
 
4Hz, downstroke
4Hz, upstroke
6Hz, downstroke
6Hz, upstroke
8Hz, downstroke
8Hz, upstroke
10Hz, downstroke
10Hz, upstroke
Figure 4.18: Variation of geometric pitch angle along the span during the mid-
upstroke and mid-downstroke at an initial pitch angle of 12◦ for 4, 6, 8, 10 Hz flap
frequencies.
Figure 4.19 shows the change in geometric pitch angle at the mid-downstroke
and mid-upstroke for the 6 Hz flapping frequency cases. At this frequency, the wing
begins to experience significant aerodynamic and inertial loads causing a large degree
of deflection along the wing span. For all the cases, there is a significant difference
in the magnitude and direction of geometric twist between the mid-downstroke and
mid-upstroke. Also, while the geometric twist is nearly symmetrical for the 0◦ initial
pitch angle case, as expected, the 12◦ and 24◦ root pitch cases exhibit an asymmetry
in the change in wing twist between the mid-downstroke and mid-upstroke.
Figure 4.20 shows the plot of Cl and Cd at the mid-downstroke and mid-upstroke
along the span of the flexible wing. First, it should be noted that the sign of the angle
of attack, (positive or negative), is indicative of a positive or negative lift coefficient.
The value of the drag coefficient is always positive, regardless of the sign of the angle
199
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−15
−10
−5
0
5
10
15
Nondimensional Span Location, y/b
Pitc
h A
ngl
e (°)
 
 
0°, downstroke
0°, upstroke
12°, downstroke
12°, upstroke
24°, downstroke
24°, upstroke
Figure 4.19: Variation in geometric pitch angle at the mid-downstroke and mid-
upstroke (6 Hz).
of attack. Second, the magnitudes of Cd and, more importantly, Cl are significantly
different from those one would expect in comparison to a static wing operating at
a high angle of attack. This is due, in part, to the unsteady effects generated by
the flapping kinematics of the wing, and it would not be possible to predict these
unsteady values for the aerodynamic coefficients using a basic quasi-steady analysis.
However, the inclusion of non-constant translation, rotation and acceleration could
improve the predictive capability of such a quasi-steady model in comparison to our
results.
In Fig. 4.20, from the curves representing the mid-downstroke, notice that
the magnitude of Cl is greater than the magnitude of Cd except at the 90% span
location. This becomes an important fact when explaining the flexible wing’s ability
to produce thrust during both the upstroke and downstroke. Toward the wing root,
200
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−2
−1.1
−0.2
0.7
1.6
2.5
r/R
C l, 
C d
 
 
Cl, downstrokeCl, upstrokeCd, downstrokeCd, upstroke
Figure 4.20: Lift coefficient, Cl, and drag coefficient, Cd, along the span at mid-
downstroke and mid-upstroke.
the magnitude of the vertical force coefficient in Fig. 4.17(a) during the downstroke
is slightly greater than the value of Cl in Fig. 4.20. Due to the presence of a positive
induced flap angle, a component of the drag force is directed in the positive vertical
direction enhancing the lifting force. However, the component of Cl directed in the
negative x-direction is smaller in magnitude than the component of Cd directed in
the positive x-direction, resulting in a drag producing sectional force.
However, toward the wing tip where the magnitude of φ is increased, the
rotation of the resultant velocity vector is also increased. The change in the rotation
of the resultant velocity vector rotates the direction of the lift and drag vectors. This
causes the lift vector to contribute more toward propulsive thrust and the drag vector
to contribute more toward vertical lifting force. At this point, the component of Cl
directed in the negative x-direction is greater than the component of Cd directed in
201
the positive x-direction. This results in the simultaneous production of propulsive
thrust and lifting force.
4.2.5 Section Summary
A combination of 3-D and 2-D flowfield analysis, in conjunction with spanwise
sectional force analysis, was used to further understand the underlying physics behind
a flexible flapping wing undergoing pure flap kinematics at a given initial pitch angle.
One of the key insights gained is that unlike a rigid flapping wing in pure flap, a
flexible wing is capable of producing substantial net positive lifting force and net
propulsive thrust over the course of a flap cycle. Similar to a rigid wing, a majority
of the positive vertical force is generated during the downstroke of the flap cycle,
and downward vertical force is produced during the upstroke. However, for a flexible
wing, propulsive thrust is generated during both the downstroke and upstroke with
a majority of the propulsive thrust being generated during the upstroke.
The enhanced aerodynamic force production of the flexible wing can be at-
tributed its ability to dynamically twist while flapping. During flapping, the inertial
and aerodynamic loads passively deform the wing creating a nose-down blade twist
during the downstroke and a nose-up blade twist during the upstroke. The spatial
and temporal variations of the pitch angle produces a more favorable local induced
angle of attack along the span. It was seen that for the flexible wing, the decrease
in the magnitude of the local induced angle of attack allows the LEV to remain
attached to the wing surface further along the wing span. A rigid wing with constant
202
pitch along the span undergoing pure flap kinematics does not allow for control
of the local induced angle of attack and exhibits decreased aerodynamic efficiency,
especially toward the wing tip. For the flexible wing, the optimal CZ/CX occurs at
the 10 Hz, 12◦.
The vertical lift and propulsive thrust along the wing span is largely influenced
by the magnitude and direction of the sectional lift and drag vectors. The presence
of unsteady effects allowed for the development of significantly large lift and drag
coefficients. The large magnitudes of the induced angles of attack along the wing
span lead to a dynamic stall type of phenomena, contributing to the increase in lift
and drag coefficient.
203
Chapter 5: Concluding Remarks
Systematic experimental and computational analyses were conducted to un-
derstand the flow physics and force production on rigid and flexible flapping wings
in forward flight. The experimental study involved detailed flowfield measurements
using PIV and direct force measurements. The computational study was performed
using a coupled CFD-CSD based aeroelastic analysis. This included a RANS solver
coupled to a large deflection geometrically exact structural model (using MBDyn).
Avian-based fixed-pitch flap wing kinematics were implemented on a rectangular flex-
ible wing in a wind tunnel at a wind speed of 3 m/s. Time-resolved planar PIV and
time-averaged force measurements were used to validate the 3-D coupled CFD-CSD
results. Time-averaged PIV flowfield results at mid-downstroke, LEV circulation,
and total force measurements were compared to the coupled CFD-CSD showing
good agreement. With an understanding of the limitations of the computational
model, analyses of the wing at various instances in the flap cycle were presented to
describe the flow physics that govern the lift and propulsive force production.
204
5.1 Conclusions from Rigid Wing Analysis
Pure flap tests were carried out on a rigid wing. From force measurements,
it was observed that with a root pitch angle, θ = 0◦, positive propulsive force (FX)
was generated. However, the average force in vertical direction (FZ) was zero for
V∞ = 3m/s. On increasing the root pitch angle, FZ increased but FX became
negative.
Upon analyzing the flowfield, the following specific conclusions are drawn from
the rigid wing study:
1. The PIV on the rigid wing showed that the LEV was observed to develop
mostly in phase along the span of the wing, peaking in strength between the
y/b = 0.5 and 0.6 span locations and decreasing quickly in strength at the root
and tip of the wing. The root and tip of the wing were shown to trail dominant
vortices into the wake. Estimated using PIV, the LEV size and strength does
vary at different span locations along the wing. This is because an increase in
vorticity would also mean that there is an increase in net circulation around
the wing, thereby causing increased lift when the LEV is present. When the
LEV is shed, the vorticity becomes less concentrated and, the LEV diffused
rapidly, especially further outboard on the wing.
2. CFD simulation results resolved the flow features present for the rigid flapping
wing, particularly at the inboard section for low flap frequencies and low
pitch angles. However, aperiodicity further outboard at higher frequencies and
205
high pitch angles decreases simulation accuracy. With this, the turbulence,
convection, and dissipation parameters for vortex behavior can be modified to
more closely reflect vortex strength and trajectory at higher angles of attack
and flap frequencies. Overall, CFD results showed good agreement with the
experimental data.
3. Flow over the rigid wing was highly susceptible to changes in the flap-induced
angle resulting from the flapping motion and variations in reduced frequency,
which manifested in the predicted airloads. It is observed that during the wing
stroke, the wing does experience stall conditions when the effective angle of
attack is very high. However, at the stall angles, Cl, and Cd were significantly
higher than the static values, indicating a dynamic stall type of phenomena. It
is important to note that for the LEV, the behavior (e.g., formation, residency
time, shedding and downstream convection) forms the core problem of dynamic
stall. As this vortex convects away from the wing surface, it does alter the
chordwise pressure distribution, and it produces transient forces fundamentally
different from those in static stall.
4. Based on the computational analysis, the spanwise flow component was not
significant except near the wing tip, and therefore, most of the vertical force
and propulsive thrust produced could be explained using the magnitude and
direction of the sectional lift and drag forces acting on the wing. This was was
because of the tip vortex and its interaction with the LEV.
5. Most of the upward vertical force was produced during the downstroke and
206
positive propulsive thrust during the upstroke for the pure flap wing kinematics
used. This shows the need for appropriate temporal and spanwise pitch
modulation of the wing along with flapping to produce positive vertical force
and propulsive thrust during the entire flap cycle. Temporal and spatial pitch
modulation could keep the vortex attached while maintaining a propulsive
force.
It was seen that both positive propulsive and vertical forces are required to
optimized forward flight; therefore, pure flap of a rigid wing may not be a viable
configuration. With this, the effects of wing flexibility were investigated to understand
its effect on those parameters and the flowfleid.
207
5.2 Conclusions from the Comparison of Rigid and Flexible Wings
From the rigid wing test, it was seen that the achievement of the best efficiency
from a wing, both temporal and spanwise variations of pitch angle are required.
Therefore, experiments and analyses were performed for a realistic (highly anisotropic
with different flexibilities in the spanwise and chordwise directions) flapping wing.
The conclusions from the rigid and flexible wing comparison are summarized:
1. The PIV showed that for the flexible wing, the LEV remains attached to
the wing up to the mid-downstroke inboard region; however, it sheds further
outboard, especially at higher flap frequency and higher angle of attack. The
LEV was observed to peak in strength between the 50% and 70% span locations
and develop mostly in-phase along the span of the wing. The LEV decreases
in sectional strength moving from mid-span toward the root or toward the tip
of the wing. The root and tip of the wing were also observed to trail small
vortices into the wake, with the portion of the LEV near the root/tip detaching
more quickly in the stroke than further inboard.
2. The downstream wake and LEV swirl velocity profile shows a comparable result
for both the coupled CFD-CSD and PIV, which shows that the salient features
(LEV, trailing edge vortices, root vortex, tip vortex) of the flow are captured
by the CFD-CSD methodology.
3. The effects of wing flexibility are shown in LEV size and strength at the different
span locations along the wing, which is reflected comparably in the coupled
208
CFD-CSD and PIV results. In both cases, there is an increase in vorticity while
the wing is in its downstroke causing an increase in net circulation around the
wing, thereby increasing lift when the LEV is present. When the LEV is shed,
the vorticity becomes less concentrated, and it diffuses rapidly as seen further
outboard on the wing.
4. Coupled CFD-CSD simulation results resolved the flow features present for the
flapping wing. However, flow separation further outboard at higher frequencies
and high initial pitch angles decreased simulation accuracy. With this, modifi-
cations to the turbulence model can be made to more accurately predict the
convection and dissipation of the vortices, particularly further away from the
airfoil surface. It would be expected that the predicted solution would more
closely reflect the vortex strength and trajectory seen in the experiment at
higher angles of attack and flap frequencies. Overall, the computational results
showed good agreement with the experimental data.
5. For both rigid and flexible wings, the flow over the wing was highly susceptible
to changes in induced angle of attack. This was a direct result of increasing
the flapping frequency (increased reduced frequency). Throughout the wing
stroke, highly vortical flow was generated by the wing, and stall conditions
were observed at high effective angles of attack. However, at the observed stall
angles, Cl, and Cd were significantly higher than the expected values for a
static wing under the same conditions. This indicates that the flapping motion
creates a dynamic stall type phenomena where increased lift is observed.
209
6. Wing flexibility increased the aerodynamic performance in comparison to a
rigid wing. Flexibility, more specifically caused dynamic twisting, allowing
for temporal and spatial variations in the geometric pitch angle throughout
the flap cycle. The variations in pitch angle decreased the magnitude of the
induced local angle of attack along the span. In comparison to a rigid wing,
the LEV of the flexible wing remained attached over more of the wing span
resulting in enhanced aerodynamic force production.
7. Unlike rigid wings undergoing pure flap kinematics at a fixed pitch, flexible
wings are capable of simultaneously producing positive lifting force and positive
propulsive thrust over a given flap cycle. For the flexible wing, the optimal
CZ/CX occurs at the 10 Hz, 12◦. This highlights that the inclusion of dynamic
twist provides a means of passive temporal and spanwise pitch modulation in a
flapping wing MAV design. In order to further improve aerodynamic efficiency,
it is necessary to aeroelastically tailor the wing to create a more optimal twist
distribution along the wing span throughout the flap cycle.
There are several benefits to using a flexible wing. In general, the flexible
wing mechanism is less complex and lighter. Also, by employing dynamic twisting,
better pitch angles are obtained for the wing. This leads to greater forces at all
spanwise sections as compared rigid wings. Finally, the flexible wing itself is also
much lighter than the rigid wing. These results show the beneficial effects of the
appropriate amount of wing flexibility. A well tailored flexible wing may be a suitable
configuration for use on an MAV.
210
5.3 Major Contributions
The main contribution of the current work was to extend the limited body of
work on 3-D flapping wings using experiments and an aeroelastic solver to study the
performance and flow physics of realistic flexible flapping wing MAVs. The major
components of the study are the flowfield experiment, airloads measurements, wing
characterization, and the coupled aeroelastic solver. To this end, experiments on
realistic flexible wings were executed to determine the physics behind generating
vertical and propulsive forces in forward flight. The wings were then structurally
characterized to generate a comprehensive data set, currently unavailable in literature,
which can be used for the validation of aeroelastic analyses. Also, this experimental
data set was used to compare with the predictive results.
The major contributions of this work are:
1. An experimental forward flight data was acquired for a set of structurally
well-characterized, flexible, lightweight flapping MAV wings. Flow diagnostic
techniques were developed to permit high-fidelity measurements of the flowfield.
Airloads were also measured for comparison with the aeroelastic solver.
2. This work quantified and identified the vortex strength for the rigid and flexible
wing undergoing passive wing deformation. Also, the wing motion and the
aeroelastic deformations of a flexible flapping-wing MAV are quantified. It was
demonstrated that forward flight performance can be improved, simultaneously
producing positive lifting force and positive propulsive thrust over a given flap
211
cycle, by aeroelastically tailoring flexible wings.
3. Flowfield characteristics are correlated to airloads adding to a lacking body of
work at the low Re scale (i.e., flow visualization, PIV, characterization of wing
properties, analysis of deflections, natural frequencies, airloads). Refinement
and validation of comprehensive CFD-CSD analysis capable of simulating
realistic anisotropic wings undergoing large non-linear deformations were carried
out systematically.
The tactical impact is that the insights gained through experimental data and
analysis can reduce the amount of time and effort spent on experimental trial and
error platform development which translates to aerodynamic improvements of MAVs
that will be used to keep military and rescue personnel safe.
212
5.4 Suggestions for Future Work
This dissertation is a step towards the development of a fully autonomous,
hover-capable flapping wing micro air vehicle. While this research coverers techniques
for experimentation and analysis, there are several approaches along which further
research can be carried out.
1. More time averaged experimental studies can be conducted, especially in the
area of PIV measurements of the spanwise flow (stereoscopic measurements).
Targeted variations in Reynolds numbers, aspect ratio, wing planform, and
different wing kinematics can be tested. The present study only utilized
a limited selection of wing coverings (wing membrane materials) for wing
construction; however, more advanced light-weight materials can also be used
on the wings. Also assessment of the tip vortex could be used to quantify the
lift and drag coefficients to the development of the the tip vortex and LEV.
Future work can be expanded with the analysis of the vortex to include a larger
range of conditions for LEV evolution and local Reynolds number effects. Also,
the amount of wing flexibility is important; however, this analysis only assessed
the performance with one set of wing properties. Future studies can explore
the point of diminishing returns as it pertains to wing bending and torsional
stiffness.
2. Most vortex models have been tested for higher Reynolds numbers; however, a
low Reynolds number vortex model would be useful for MAV analysis in the
213
future. LEV analysis can continue to characterize its structure and breakdown
toward developing a new applied vortex model. Currently, the value in this
work is that it offers a mode for flowfield comparison between the PIV and
CFD-CSD analysis. In lieu of pressure and force measurements, which are
difficult to execute at MAV scale, the assumptions made in the control volume
method for estimating the horizontal forces from the flow field are valid.
However, estimating the forces from an unsteady flowfield is an “active area of
research” and the control volume method should be explored in more detail
with comparison to direct force measurements.
3. To reduce the number of experiments and simulations time, an optimization
module can be added to the simulation. Optimization would allow for the
maximizing or minimizing of a system by systematically choosing input values
from within an allowed set and computing the value of the function. This would
aid in better understanding design trade-offs and would aid in finding an optimal
aerodynamic design point without more experimentation and simulation cost.
The simulation can be expanded to model an entire vehicle.
4. The present work only investigated simplified wing kinematics, avian-type wing
kinematics in pure flap. It would be useful to also expand the analysis to
more complex avian wing kinematics (e.g., active asymmetric pitching) as well
as hover wing kinematics. MAVs are very susceptible to wind gusts so gust
tolerance analysis using stability derivatives would be helpful in determining
the agility and maneuverability of a vehicle.
214
5.5 Acknowledgment of Sponsors
This work was supported, in part, by the Army Collaborative Technology
Alliance (CTA) for the Micro Autonomous Systems and Technology (MAST) program
Contract No. W911NF-08-2-0004 with Mr. Chris Kroninger (ARL-VTD) as technical
monitor and by the L-3 Communications Graduate Research Fellowship. The author
would also like to acknowledge with thanks the support of the NACME Alfred P.
Sloan Foundation Graduate Research Scholarship, the American Helicopter Society’s
Vertical Flight Fellowship, and Aerospace Corporation Graduate Fellowship Awards.
215
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