AIAA 2011-3120
6th AIAA Theoretical Fluid Mechanics Conference
27 - 30 June 2011, Honolulu, Hawaii
An Experimental Investigation on the Wake Flow
Characteristics of Tandem Flapping Wings
Anand Gopa Kumar1 and Hui Hu2
Iowa State University, Ames, IA, 50014
The use of tandem wings in flapping flight is considered a unique and interesting concept
in the area of applied aerodynamics. Dragonflies using the tandem wing configuration have
been observed to be some of the most agile and maneuverable predators in the animal
kingdom. This leads us to further investigate the advantages of tandem wings and how their
application in bio-mimetics can aid in the development of future nano air vehicles (NAVs).
Using bio-inspired propulsion methods such as flapping wings, these micro-scaled unmanned
aerial vehicles (UAVs) would be operating within the Reynolds number range of insects. For
the current experimental study the wing spacing between tandem piezoelectric wings are
varied to different values with respect to the chord length of the wings. A high-resolution
Particle Image Velocimetry (PIV) system was used to quantify the time evolution of the
unsteady wake vortex structures. The measurements were performed at wing spacing values
of 0.15C, 0.5C, 1C, 1.5C and 2C between the fore-wing and the hind-wing for a chord
Reynolds number of 1,000and a Strouhal Number (St) of 0.3.
Nomenclature
A
C
CF
f
FW
h
HW
k
LEV
NAV
ReC
S
St
V


FW
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
peak-to-peak wing tip amplitude
chord length
Force Coefficient
wing-beat frequency
Fore-Wing
non dimensional plunge amplitude
Hind-Wing
reduced frequency
Leading Edge Vortex
Nano Air Vehicle
Chord Reynolds Number
Value of Spacing between the Forewing and the Hindwing
Strouhal Number
forward flight speed
relative phase difference angle between fore wing and hind wing
angle of attack
phase angle of the fore-wing during the flapping cycle
I. Introduction
B
IO inspired techniques are currently being extensively explored to solve problems which have plagued
engineering applications in recent year. Millions of years of evolution have allowed living beings to optimize
their physiology and other aspects. Insects are some of the oldest living beings on earth, they are found to operate
within Reynolds number ranges of about 10,000.
Various studies have been conducted on oscillating airfoils to understand the aerodynamic characteristics of
flapping wings over time2, 3. Most of the previous studies were focused on 2D flows in the wakes of airfoils such as
1
2
Graduate Student, Department of Aerospace Engineering, AIAA Student Member.
Associate Professor, Department of Aerospace Engineering, AIAA Associate Fellow. Emial: huhui@iastate.edu.
1
American Institute of Aeronautics and Astronautics
Copyright © 2011 by Anand Gopa Kumar and Hui Hu . Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
NACA 0012 or flat plates. By varying parameters such as the amplitudes and the flapping frequencies of the
flapping wins/airfoils, it was found that certain combinations of the parameters result in the generation of thrust. The
thrust generated by the oscillating wings/airfoils is indicated with the presence of reverse von Karman vortices
which would add momentum surfeits in the wakes of the wings/airfoils. In reality, however, the flow structures in
the wakes of flapping wings during forward flight are much more complicated than those observed in the 2D flow
cases. The flow structures such as the leading edge vortices which play a key role in the aerodynamics of flapping
flight have been observed when the experiments were carried out with fixed root 3D flow conditions4.
According to the Defense Advanced Projects Agency (DARPA), nano-air-vehicles are classified as airborne
vehicles with a wingspan of 75mm with a gross takeoff weight of 10 grams1. Insects and hummingbirds closely
relate with the takeoff weight and the wing span. These animals are found to operate with very high wing beat
frequencies usually ordering up to ranges of 100Hz. In the case of dragonflies, the wing beat frequency was found to
be between 30Hz to 100Hz and in the cases of small birds such as humming birds, the wing beat frequencies were
found to be in the order of 40Hz to 60Hz. This high wing beat frequency is attributed to maintaining an optimal
Strouhal number value during flight. Statistical studies carried out on the Strouhal number of flying and swimming
animals have revealed that most animals were found to lie within the region of 0.2 < St < 0.45. Conventional design
approaches into the development of flapping wings using mechanical flapping mechanism usually cannot be used to
generate such high amount of wing beat frequencies. The inertial forces developed by the flapping motion at high
wing beat frequencies would create structure failures on the wing during operation thereby shortening the lifespan of
the nano-air-vehicles. Another added constraint with mechanical flapping mechanism would be the sheer weight of
the gears and the motor would add to a major component of the weight of the NAV which would limit the payload
of the vehicle.
An alternative to using mechanical flapping mechanism such as motors and gears to actuate the flapping motion
of the nano-air-vehicle can be carried out with the help of piezoelectric actuators. Piezoelectric actuators are bimorph ceramics which actuate mechanically when an electric current is passed through it. Piezoelectric materials
are used in a variety of applications ranging from pressure sensing to cooling of confined spaces using piezoelectric
wings. Piezoelectric actuators have been proven to be useful in the applications of nano-air-vehicles. Properties such
as high energy density, inertness to atmospheric factors such as humidity and temperature and other chemical
inertness make them an ideal candidate for NAV applications. A working example of piezoelectric based flapping
wing NAVs is developed by the Harvard Microrobotics Lab with their microfly6, 7. In that case, a single
piezoelectric actuator is used to flap the wings and the resulting prototype was found to perform powered flight
under lab conditions.
Previous experimental studies on tandem flapping wings have been conducted as a means of understanding a
more optimal propulsion system for micro and nano air vehicles8. However, studies conducted previously on this
topic are mostly based on 2D oscillating wings. In the current study a 3D fixed root piezoelectric wing will be
subjected to experimental study similar to the studies conducted by Clemons et al9, 10 and Gopa Kumar and Hu11.
II. Experimental Setup
The experimental study was conducted in a closed-circuit low-speed wind tunnel located in the Aerospace
Engineering Department of Iowa State University. The tunnel has a test section with a 1.0 9 1.0 ft (30 9 30 cm) cross
section, and the walls of the test section are optically transparent. The tunnel has a contraction section upstream of
the test section with honeycombs, screen structures and a cooling system installed ahead of the contraction section to
provide uniform low turbulent incoming flow into the test section.
Figure 1 shows the schematic of the piezoelectric flapping wing used in the present study. The tested
piezoelectric flapping wing has a rectangular planform with a chord length 12.7 mm (i.e., C = 12.7 mm), wingspan
34 mm (i.e., b = 34 mm), and thickness 0.26 mm. A piezoelectric actuator film (~0.1 mm in thickness) was bonded
at the root of the tested wing to drive the rectangular wing in flapping motion. In the present study, the velocity of
the incoming flow was set as U = 1.0 m/s, which corresponds to a chord Reynolds number of ReC = 1,200. The
turbulence intensity of the incoming flow was found to be about 1.0%, measured by using a hotwire anemometer,
with the test model installed in the test section.
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Figure – 1: Schematic Diagram of Piezoelectric wing
Figure 2 shows the experimental setup used in the present study. A small mount unit, which includes a mount
plate and two hollowed supporting legs, was designed to fix the root of the test flapping wing in the middle of the
wind tunnel test section in order to minimize the effects of wind tunnel walls on the evolution of the vortex and flow
structures in the wake of the tandem piezoelectric flapping wings. Electric wires would go through the hollowed
supporting legs of the mount unit to connect to the piezoelectric flapping wings. A sinusoidal AC voltage, which
was supplied by using a function generator and amplified through a high-voltage amplifier, was used to drive the
piezoelectric flapping wings. The wings would be in plunging motion with the same frequency as the applied AC
voltage. The amplitude of the plunging motion was found to reach its peak value when the frequency of the applied
AC voltage matches the resonance frequency of the piezoelectric wing, which is 60 Hz for the present study. The
peak-to-peak flapping amplitude of the wingtip was found to increase linearly with the applied AC voltage. Fig. 3
shows the flapping motion of the wings in anti-phase motion with the forewing and the hindwing moving in
opposite phase with respect to each other. It should also be noted that the piezoelectric flapping wing was found to
bend along spanwise direction under dynamic conditions; however, no observable torsional mode of bending (i.e.,
no flex along chordwise direction) was found in the present study.
A dimensionless parameter that is widely used to quantify flapping flight is Strouhal number (Str). In addition,
reduced frequency, k, is also widely used to characterize the aerodynamic performance of flapping flight. By using
non-dimensional flapping amplitude, h, the relationship between the product of kh and the Strouhal number (Str) can
be written as kh = 2Str. Extensive previous studies with either pitching or heaving airfoils/wings have revealed that
optimum propulsion efficiency for a flapping airfoil/wing (defined as the ratio of aerodynamic/hydrodynamics
power output to mechanical power input) would be within the range of 0.2< Str <0.4. It has also been found that
natural selection is likely to tune birds and insects to fly in the range of 0.2<Str<0.4. For the present study, the peakto-peak flapping amplitude at the wingtip of the root-fixed piezoelectric flapping wing was found to be 10.0 mm
(i.e., A = 10.0 mm; h/C = 1.35). Following the work by Taylor et al.5 to use half of the peak-to-peak flapping
amplitude at wingtip to calculate the equivalent Strouhal number (Str) for a root-fixed 3-D flapping wing, the
equivalent Strouhal number (Str) for the present study was found to be 0.30 (i.e., Str = 0.30), which is well within
the optimal range of 0.2<Str <0.4 usually used by flying birds and insects as well as swimming fishes.
A digital particle image velocity (PIV) system was used in the present study to make detailed flow field
measurements to quantify the evolution of the wake vortex structures in relation to the position of the piezoelectric
wings during the upstroke and down stroke cycles. The flow was seeded with 1–5-lm oil droplets. Illumination was
provided by a double-pulsed Nd:YAG laser (NewWave Gemini 200) adjusted on the second harmonic and emitting
two pulses of 200 mJ at the wavelength of 532 nm with a repetition rate of 10 Hz. The laser beam was shaped to a
sheet by a set of mirrors, spherical, and cylindrical lenses. The thickness of the laser sheet in the measurement
region is about 1.0 mm. As shown in Fig. 2, a mirror was installed on the top of the wind tunnel to reflect the
illuminating laser sheet back to the measurement region in order to eliminate the shadow region of the piezoelectric
flapping wing for PIV measurements. A high-resolution 12-bit (1,600 9 1,200 pixel) CCD camera (PCO1600,
Cooke-Corp) was used for PIV image acquisition with the axis of the camera perpendicular to the laser sheet. The
CCD camera and the double-pulsed Nd:YAG laser were connected to a workstation (host computer) via a Digital
Delay Generator (DDG, Berkeley Nucleonics, Model 565), which controlled the timing of the laser illumination and
image acquisition.
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Figure – 2: Experimental Setup
0.6
Hindwing Motion
Forewing Motion
0.5
0.4
0.3
A/C Ratio
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
0
45
90
135 180 225 270 315 360 405 450 495 540 585 630 675 720
Phase Angle ()
Figure – 3: Wing locations at different phase averaged results
During the experiments, the sinusoidal signal supplied by the function generator to drive the piezoelectric
flapping wing was also used as the input signal to the Digital Delay Generator (DDG) to trigger the PIV system to
conduct phased-locked PIV measurements. By adding different time delays between the input sinusoidal signal and
the TTL signal output from the DDG to trigger the digital PIV system, phased-locked PIV measurements at different
phase angles (i.e., corresponding to different positions of the flapping wing) in the course of the upstroke and down
stroke flapping motion for the flapping wing were accomplished. At each pre-selected phase angle, 160 frames of
instantaneous PIV measurements were used to calculate phase-averaged flow field around the flapping wing. In
addition to phase-locked PIV measurements, time-averaged PIV measurements were also carried out by simply
disconnecting the phase-locking between the flapping motion of the flapping wing and the PIV system in order to
derive the mean flow field around the flapping wing.
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In the present study, instantaneous PIV velocity vectors were obtained from the acquired PIV images by using a
frame to frame cross-correlation technique involving successive frames of patterns of particle images in an
interrogation window 32× 32 pixels. An effective overlap of 50% of the interrogation windows was employed to
derive instantaneous velocity vectors for the PIV image processing. After the instantaneous velocity vectors (ui, vi)
were determined, instantaneous spanwise vorticity (z) could be derived. The time-averaged quantities such as mean
velocity (U, V) and ensemble-averaged spanwise vorticity (z) distributions were obtained from a cinema sequence
of 750 frames of instantaneous velocity fields in each chordwise cross planes. The uncertainty level for the
instantaneous velocity measurements is estimated to be within 2.0% of the local flow velocity and that of the
spanwise vorticity data is expected to be within 10.0% of the local vorticity.
Being the primary focus for this study is to study the effects of spacing between the forewing and the
hindwing and its effects on the wake region during flapping motion of the wings. Figure – 4 shows the various wing
spacing cases which are used in this study. As shown in the figure, the spacing between the tandem wings, S, was
varied from 0.15 chord length to 2.0 chord length of the flapping wing during the experiments. For each of these
cases, the PIV measurements are carried out at spans of 100%, 75% and 50%.
Figure – 4: Wing Spacing Values for the Current Study
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III. Results and Discussion
Figure – 5 shows the result from the case where the wing spacing between the forewing and the hindwing is
0.15C. This wing spacing is closely related to the spacing observed in insects like the dragonfly. The results shown
in the figures below are shown at different phase angles of the forewing at a wing span of 100%.
– LEV being formed
before downstroke
+ LEV Shedding
into the hindwing
Fully formed + LEV
during upstroke
(a) FW = 0o
(b) FW = 90o
+ Vortex Trajectories
Previous –LEV
shed into wake
+ LEV transferred
to the hindwing
+ LEV transferred
to the hindwing
- Vortex Trajectories
(d) FW = 270o
(c) FW = 180o
Figure – 5: Phase Averaged Results for 0.15C Wing Spacing in Anti-Phase Flapping at 100% Span
The results shown in figure – 5 from (a) to (d) show the vortex shedding patterns in the wake region of the
tandem wings. The dashed red line shows the shedding path of the positive vorticity (+ z) being shed in to the
wake, on the other hand the blue dashed and dotted line shows the path traveled by the negative vorticity (- z). As
the forewing continues with its cycle, a clear positive leading edge vortex (LEV) formation can be observed in the
case of FW = 0o where a fully formed LEV is clearly visible. This positive LEV is later transferred into the influence
of the hindwing in at the FW = 180o and subsequently shed into the wake region as the cycle of the wing ends. A
fresh negative LEV once again being formed at the leading edge of the forewing and is visible just before the downstroke of the forewing at FW = 90o.
Flow-field measurements obtained at the wingspan region of 75% are shown in figure – 6. The results obtained
show a different set of vortex patterns being shed into the wake region from the flapping motion of the wing.
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(a)FW = 0o
(b)FW = 90o
(d)FW = 270o
(c)FW = 180o
Figure – 6: Phase Averaged Results for 0.15C Wing Spacing in Anti-Phase Flapping at 75% Span
A primary change from the vortex patterns observed in the results shown in figure – 5 in comparison to these
results is the presence of a reverse von Karman vortex street in the wake region of the flow field. A primary finding
in Clemons et al9, 10 was that at 100% the wing tip vortex generated by the flapping piezoelectric wing generates a
low velocity jet region along the neutral axis of the wing due to the presence of a wing tip vortex. Though in this
case, an anomaly is found from that conclusion with the presence of a hindwing in the flow-field, this anomaly will
be discussed in detail at a later part of this section. The vortex shedding pattern shown in the results from this span
location indicate the presence of alternating vortex streets being shed into the wake region. The pairing of vortices of
opposite magnitude is less obvious in this case with the majority of the vorticity being focused in the von Karman
vortex street along neutral axis of the wings. Phenomena such as evolution of the leading edge vortices due to the
wing stroke is also visible further in this case as a continuation of the results shown in 100% span. This once again
emphasizes the 3D nature of the vortex structure generated by the flapping motion of a fixed-root wing.
Figure – 7 shows the further data taken for the same case where the measurement plane is placed at the span of
50%. The results obtained from this case show that the vortex structures are only obtained along the neutral axis of
the wings with 50% being a zone where a very minimal amount of amplitude is exhibited during the flapping cycle
of the fixed-root wing. The resulting low h = A/C value imparts minimal to no momentum into the wake region of
the flow-field thereby exhibiting only the presence of drag in the wake region indicated by the presence of the von
Karman vortex street. Previous studies along the span-wise direction of the flapping wings have shown a similar
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trend of the presence of a momentum deficit in the wake region at such a location farther away from the wingtips9,
.
10
(a)FW = 0o
(b)FW = 90o
(d)FW = 270o
(c)FW = 180o
Figure – 7: Phase Averaged Results for 0.15C Wing Spacing in Anti-Phase Flapping at 50% Span
The flow-field measurements shown in this span-wise location once again show the evolution of the leading
edge vortex which is generated during the flapping motion of the wing. The results obtained in the span-wise
location of the wing also indicate that the leading edge vortex size also decreases as the measurement plane reaches
closer to the root of the wing.
The above mentioned results were obtained by obtaining the eight phase averaged results at each of the spanwise locations. On the other hand figure – 8 shows the time averaged results obtained at each of these three spanwise locations with an average of 750 images for each result.
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The current results obtained from the phase
averaged have shown vortex shedding trajectories
in the wake region consistently for both the
positive and negative vortices. In the previous
results, the paths of these trajectories were marked
with the color of the line indicating the orientation
of the vortex street. When those trajectories are
superimposed on the time average results showing
the direction in which the high speed jets are
oriented. In the phase averaged results, the wake
region shows a pattern of vortex pairs of opposite
magnitude being shed into the wake region. On
observing the normalized mean velocity field, it is
clearly evident that the presence of such a vortex
pair imparts a high speed jet in the wake region.
This phenomenon is clearly visible in the 100%
span case.
A von Karman vortex street which was seen in
the 75% span results. Once the trajectories of the
positive and negative vortices are tracked, the
region where the von Karman vortex is formed
manifests itself as a low speed region along the
wake. Along with the high speed jet, this small low
speed region is present along the neutral axis of the
measurement plane.
Further at the span-wise location of 50% of the
total span, the only significant presence which was
mentioned earlier is the presence of the von
Karman vortex. The same region shown in the
phase averaged cases once again shows the
presence of a low speed region in the wake. No
significant amount of momentum is being imparted
into the flow at this measurement plane. Apart
from the low speed region, the rest of the
measurement plane is equal to the free-stream flow
velocity.
+ Vortex Trajectories
High Speed Jets
- Vortex Trajectories
(a) 100% Span
High Speed Jets
Low Speed Region
(b) 75% Span
The next set of results that will be discussed in
this section is the flow-field measurements of the
same wing spacing of 0.15C with the wings in inphase flapping motion. In this case, the forewing
and the hindwing perform their oscillatory cycle in
the same direction. Figure – 9 shows the flow-field
measurements obtained at the 100% span region.
Low Speed Region
The wake structures formed in this case show a
different pattern in contrast to the anti-phase results
obtained before. Though the vortex shedding
(c) 50% Span
pattern is very much identical to that of the antiFigure – 8 Time Averaged Results Obtained for
phase results, the clear indication of the transfer of
0.15C at anti-Phase Flapping
the leading edge vortex from the forewing to the
hindwing is visible. Being in almost similar phase angles relative to each other, the effect of interaction between the
forewing and the hindwing is not too evident in this case.
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– LEV being formed
before downstroke
+ LEV Shedding
into the hindwing
Fully formed + LEV
during upstroke
(a) FW = 0o
(b) FW = 90o
+ Vortex Trajectories
Previous +LEV
shed into wake
+ LEV formed during
upstroke
- LEV transferred to
the hindwing
- Vortex Trajectories
(d) FW = 270o
(c) FW = 180o
Figure – 9: Phase Averaged Results for 0.15C Wing Spacing in-Phase Flapping at 100% Span
A greater inclination is given to conclude that the forewing and the hindwing in this case would act as a single
entity due to their low relative phase angle (). The vortex shedding pattern though similar in structure, is lower in
magnitude in comparison to the anti-phase flapping case.
Figure – 10 shows the results obtained for the same in-phase flapping case with flow-field measurements at 75%
span. The results shown in this measurement plane ones again presents itself as a wake structure quiet similar to that
of the anti-phase flapping condition with a prominent von Karman vortex street being formed along the neutral axis
of the measurement plane. The single prominent vortex streets of opposite magnitudes envelop the von Karman
vortex street in this case also though the angle of the vortex street is a lot shallower than that of the anti-phase
flapping case. The LEV evolution in this case is a lot more prominently visible in the 75% span with the suction of
the LEV from the forewing being taken carried on to the hindwing before it is shed into the wake region. The results
obtained at 50% span in the in-phase flapping exhibit a similar trend as the previous anti-phase with only a von
Karman vortex being shed into the wake region by the tandem wings. This decrease in the thrust with low h value in
at the mid span of the wing is predicted from all the previous studies conducted using the piezoelectric flapping
wings.
The time averaged results obtained from the in-phase flapping results are shown in figure – 11. Once again for
each of the time averaged cases, the trajectory of the prominent vortex streets are marked from the phase averaged
results.
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– LEV being formed
before downstroke
+ LEV Shedding
into the hindwing
Fully formed + LEV
during upstroke
(a) FW = 0o
(b) FW = 90o
+ Vortex Trajectories
Previous +LEV shed into wake
+ LEV formed during
upstroke
- LEV transferred to
the hindwing
- Vortex Trajectories
(d) FW = 270o
(c) FW = 180o
Figure – 10: Phase Averaged Results for 0.15C Wing Spacing in Anti-Phase Flapping at 75% Span
With the time averaged results, the velocity field generated by the presence of vortex pairs is once again shown
in this case also. The vortex street shown in figure – 9 which are found to direct a primary vortex away from the
neutral axis is a different pattern which is formed in the in-phase flapping case. A secondary vortex of an opposite
magnitude is present along with the single primary vortex street which whose trajectory in figure – 9 and figure –
11. This vortex is ignored as the magnitude of vorticity is very low for this case, as a result, the velocity magnitude
in the wake region is found to be significantly lower than compared to the anti-phase flapping. This is primarily
caused due to the in-phase flapping motion of the forewing and hindwing due to which they both act as a single
larger wing. In comparison the anti-phase wake profile which generates a much higher forewing – hindwing
interaction thereby generating a higher amount of thrust.
Further in the case of the span at 75%, the results provide a different set of velocity patterns. The overlay of
vortex trajectories indicate the presence of a strong velocity jet at the immediate wake region of the hindwing as
illustrated in figure – 11(b). This increase in the velocity is attributed to close interaction of vortices of higher
magnitudes with each other. This strong velocity jet is further bifurcated into jets which are directed to the upper and
lower directions as it further moves down the wake. This bifurcation of the velocity jet would lead to a low speed
region just between the two jets in the region where the von Karman vortex street was observed.
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Figure – 11 (c) shows the time averaged results
obtained at the 50% span measurement plane. The
velocity profiles obtained at this location is once again
similar to that to the other 50% span results obtained
from anti-phase flapping. Though the wake region
shows the presence of a momentum deficit, the effect
of the strong jet formed at the trailing edge of the
hindwing as seen in the 75% span results is still
visible in this case. A small high speed region
generated close to X/C = 2 thereby indicative that the
jet formed in that region extends further down the
span of the tandem wings.
In order to understand the effects of the phase
angle difference, and its impact on the wake region of
the flow-field, the wake profile at X/C = 6 is obtained.
This velocity profile is extracted for all the span-wise
measurement cases for both the in-phase and antiphase flapping conditions.
Figure – 12 shows the normalized wake profiles
for both the both the anti-phase and in-phase flapping
conditions. The wake profile shown in the both inphase and anti-phase cases, at all the span-wise
measurement planes mentioned earlier. For the antiphase flapping case, the wake profile show a greater
amount of momentum surfeit being added into the
wake region of the flow field. In comparison to the
results obtained by Clemons et al9, 10, the wing tip
vortex was found to provide a detrimental amount of
momentum imparted into the flow at the measurement
plane at 100% span while a higher amount of
momentum is added to the wake region at 75% span.
However in this case, the wing spacing between the
forewing and the hindwing is so minimal the
interaction between the two wings negates the effect
of wing tip vortices in the flow-field in both the cases.
A momentum deficit is noticed in all three of the cases
along the chord-wise direction along the neutral axis
of the flow field. The results however indicate that a
higher amount of momentum is imparted at the wing
tip of both the in-phase and anti-phase. This is
indicative that the influence of the wing tip vortex is
minimized by a big factor with the presence of a
hindwing which would severely influence the
properties of the flow structures in the wake region. In
both the in-phase and anti-phase flapping, the
momentum surfeit at the wingspan is found to be the
highest followed by the 75% span location with the
lowest amount of momentum imparted by the mid
span of the wings. Though this anomalous trend is
observed at cases with lower wing spacing values, at
higher wing spacing values a higher amount of
momentum surfeit is shown at the 75% span is clearly
visible thereby consistent with the observations noted
by Clemons et al.
(a) 100% Span
(b) 75% Span
(c ) 50% Span
Figure – 11: Time Averaged Results for 0.15C
In-Phase Flapping
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3
3
50% Span
75% Span
100% Span
2
1
Y/C
1
Y/C
50% Span
75% Span
100% Span
2
0
0
-1
-1
-2
-2
-3
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
-3
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
U/U
U/U
(a) Anti – Phase Flapping Wake Profile
(b) In – Phase Flapping Wake Profile
Figure – 12: Span-wise Wake Profile at X/C = 6 for In-Phase and Anti-Phase Flapping for 0.15C
– LEV being formed
before downstroke
+ LEV Shedding
into the hindwing
Fully formed + LEV
during upstroke
(a) FW = 0o
+ LEV Direct
Shedding
- LEV Direct
Shedding
(b) FW = 90o
+ Vortex Trajectories
Previous –LEV
shed into wake
+ LEV transferred
to the hindwing
- Vortex Trajectories
(d) FW = 270o
(c) FW = 180o
Figure – 13: Phase Averaged Results for a Wing Spacing of S = 2C in Anti-Phase Flapping at 100% Span
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– LEV being formed
before downstroke
Fully formed + LEV
during upstroke
(a) FW = 0o
+ LEV Direct
Shedding
- LEV Direct
Shedding
(b) FW = 90o
+ Vortex Trajectories
Previous –LEV
shed into wake
+ LEV transferred
to the hindwing
- Vortex Trajectories
(d) FW = 270o
(c) FW = 180o
Figure – 14: Phase Averaged Results for a Wing Spacing of S = 2C in In-Phase Flapping at 100% Span
To illustrate the flow structures observed at a higher wing spacing value, figure – 13 shows the flow-field
measurements carried out when the wing spacing value is a 2C. In this case, the wing spacing is significantly further
apart from the results shown previously where S = 0.15C. Both the in-phase and anti-phase flapping cases show a
much more complex set of vortices being shed into the wake region by the flapping motion of the wings. A
prominent phenomenon which is observed due to the larger wing spacing between the forewing and the hindwing is
the direct shedding of the vortex structures from the forewing into the wake region of the flow field. The vortex
streets shed in this manner is independent of any kind of interaction with the hindwing in the tandem configuration.
This additional vortex street causes the much more complex wake profile which is observed in this case, a gradual
increase in the complexity of the wake structure is observed with increase in the spacing between the forewing and
the hindwing. The time averaged results are for the case where S = 2C for both anti-phase and in-phase flapping is
shown in figure – 15 at varying spans of the measurement plane.
The results shown in figure – 15 indicate a wider momentum thickness being imparted into the wake region with
the presence of two flapping at a higher distance from each other. This could lead us to conclude that with a higher
amount of wing spacing between the forewing and the hindwing leads to the individual wings starting to act like
individual wings. This causes the wake structure to be extremely complex as illustrated by the votex trajectories
superimposed on each of the time averaged and phase averaged results shown in figures – 13, 14 and 15. Similar to
the previous case where S = 0.15, a von Karman vortex street is observed from the point where the measurement
plane is at 75% and is indicated once again by the low speed region.
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(a) 100% Span Anti-Phase Flapping
(a) 100% Span In-Phase Flapping
(b) 75% Span Anti-Phase Flapping
(b) 75% Span In-Phase Flapping
(c) 50% Span Anti-Phase Flapping
(c) 50% Span In-Phase Flapping
Figure – 15: Time Averaged Velocity Profiles at Varying Spanwise Locations for In-Phase and Anti-Phase
Flapping case for S = 2C
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In-order to obtain a much more accurate way of qualitatively explaining the momentum imparted into the flow
field of 2D oscillating airfoils, Bohl and Koochesfahani12 have developed an equation based on the momentum flux
equation which is commonly used. Equation 1 depicts the means of finding the force coefficient CF for a given plane
in the wake region.
(1)
Where  is obtained by using the equation
(2)
For the experimental results obtained in the current study, for all the wing spacing cases were used to calculate
the force coefficient values at a chord-wise wake location of X/C = 6. The results obtained for the from the
calculation of the force coefficient are shown in figure – 16.
Figure – 16: CF Values Obtained at Various Wing Spacing Cases for In-Phase and Anti-Phase flapping
Though the results obtained from equation 1are ideally used for the calculation of the force coefficients of 2D
wake regions, it can still be applied in the current measurement plane. An accurate measurement of the thrust
imparted by the fixed – root flapping wing cannot be obtained accuratelythrough non – contact flow measurement
techniques such as PIV. This is due to the existence of a large out of plane velocity vector component which cannot
be captured by 2D PIV techniques. The equation shown by Bohl and Koochesfahani can however give a trend of the
force coefficient which would be obtained at various wing spacing cases. Figure – 16 shows an upward trend in the
thrust generated by the tandem wing configuration during in-phase and anti-phase flapping. This increase in the CF
value can be observed from the case where S = 0.5C all the way till S = 1.5C this upward trend by both the in-phase
and anti-phase flapping results can be explained by the interaction of the forewing and the hindwing during flapping
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flight. For the case where S = 0.15C, the wings tend to act as a single entity irrespective of the relative phase
difference of the forewing and hindwing. On the other hand, the case where S = 2C, the forewing and the hindwing
act as independent entities thereby the interference of both the wings and the resultant influence on the wake region
is minimal. In cases such as S = 0.5C the suction of the LEV shed by the forewing into the influence of the hindwing
has been observed in the current study as well as previous experimental studies conducted by the authors11.
IV. Concluding Remarks
From the current study conducted on the flowfield measurements of piezoelectric wings it can be concluded that
the wake structures generated is severely influenced by the spacing between the forewing and the hindwing. The
wake structures obtained at each of the cases are influenced by the presence of the hindwing. By varying the spacing
between the forewing and the hindwing, the effects of the presence of the hindwing can be controlled. Results
obtained at cases where the S value is too less (such as 0.15C) and where the S value is too high (such as 2C), the
wings begin to act as either a single entity or two separate wings operating independent of each other. With the
experimental cases conducted at a St = 0.3 the vortex structures in the wake region would be similar to that of
insects or micro air vehicles operating under Strouhal number conditions. Further research is needed into the force
coefficient measurements at the wake region of the PIV flow fields, though currently a trend is established on the
effects of the wing spacing and its effect on the thrust generated by the tandem wings.
V. Acknowledgements
The authors would like to acknowledge the efforts by Mr. Sean Anderson in the experimental procedure and data
gathering. The authors would like to thank Mr. Bill Rickard of Iowa State University for his contributions to
building the wind tunnel models for the current experiment. The support of National Science Foundation CAREER
program under the award number CTS – 0545918 is also gratefully acknowledged.
VI. References
1
Defense Advanced Research Projects Agency Fact Sheet, “DARPA Nano Air Vehicle Program,” December
2008.
2
Anderson, J. M., Streintlien, K., Barrett, D.S., Triantafyllou, M. S., “Oscillating Foils of High Propulsive
Efficiency,” Journal of Fluid Mechanics, Vol. 360, 1998, pp. 41-72.
3
Koochesfahani, M. M., “Vortical Patterns in the Wake of an Oscillating Airfoil”, AIAA Journal, Vol. 27, No. 9,
pp. 1200 – 1205.
4
Ellington, C. P., van den Berg, E., Willmott, A.P., Thomas, A. L.R., “Leadingedge vortices in insect flight,”
Nature, Vol. 384, 1996, pp. 19 – 26.
5
Taylor, G. K., Nudds, R. L., Thomas, A. L. R., “Flying and Swimming Animals Cruise at a Strouhal Number
Tuned for High Power Efficiency,” Nature, Vol. 425, 2003, pp. 707 – 711.
6
Wood, R. J., “The First Takeoff of a Biologically Inspired At-Scale Robotic Insect”, IEEE Transactions on
Robotics, Vol. 24, No. 2, April 2008, pp. 341 – 347.
7
Robert wood paper 2
8
Warkentin, J., DeLaurier, J., “Experimental Aerodynamic Study of Tandem Flapping Membrane Wings,”
Journal of Aircraft, Vol.44, No.5, 1653 – 1661, September – October 2007.
9
Clemons, L., Igarashi, H., Hu, H., “An Experimental Study of Unsteady Vortex Structures in the Wake of a
Piezoelectric Flapping Wing,” AIAA-2010-1025, 48th Aerospace Sciences Meeting including the New Horizons
Forum and Aerospace Exposition, Orlando, FL, Jan. 4 – 7, 2010.
10
Hu, H., Clemons, L., Igarashi, H., “An Experimental Study of the Unsteady Vortex Structures in the Wake of a
Root-fixed Flapping Wing,” Experiments in Fluids, DOI: 10.1007/s00348-011-1052-z, February 19, 2011.
11
Gopa Kumar, A., Hu, H., “Flow Structures in the Wakes of Tandem Piezoelectric Flapping Wings,” AIAA2010-4939. 28th AIAA Applied Aerodynamics Conference, Chicago, Illinois, USA, 28 June – 1 July 2010.
12
Bohl, D. G., Koochesfahani, M. M., “MTV Messurements of the Vortical Field in the Wake of an Airfoil
Oscillating at High Reduced Frequency,” Journal of Fluis Mechanics, Vol. 620, 2009, pp. 63 – 88.
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