48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2010, Orlando, Florida
AIAA 2010-1025
An Experimental Study of Unsteady Vortex Structures in the Wake
of a Piezoelectric Flapping Wing
Lucas Clemons1, Hirofumi Igarashi2 and Hui Hu3()
Iowa State University, Ames, Iowa, 50011
An experimental study was conducted to explore the potential applications of
compact, gearless, piezoelectric flapping wings with the wing size, stroke amplitude
and flapping frequency within the range of actual insect characteristics for the
development of novel insect-sized, flapping-wing-based Nano-Air-Vehicles (NAVs).
Unlike most of previous studies with 2-D flapping airfoil models, a fix-rooted 3-D
piezoelectric flapping wing was used in the present study with the consideration of
more practical configurations usually used in NAV designs. The experimental study
was conducted in a low-speed wing tunnel with the test parameters of chord length
of C = 12.7mm, chord Reynolds number of Re = 1,200, flapping frequency of f = 60
Hz, reduced frequency of k = 3.5, and non-dimensional flapping amplitude at
wingtip h = A/C = 1.3. The corresponding Strouhul number of the root-fixed 3-D
piezoelectric flapping wing is Str = 0.30, which is within the optimal range of 0.2 <
Str < 0.4 usually used by flying insects and swimming fishes. A digital particle image
velocimetry (PIV) system was used to achieve phased-locked and time-averaged flow
field measurements to quantify the formation and separation processes of the
Leading Edge Vortex (LEV) structures on the upper and lower surfaces of the
flapping wing in relation to the phase angle (i.e., the positions of the flapping wing)
during upstroke and down stroke flapping cycles. The evolutions of the wake vortex
structures in the chordwise cross planes at different wingspan locations of the rootfixed flapping wing were compared quantitatively to elucidate underlying physics
for better understanding of the unsteady aerodynamics of the flapping flight and to
explore/optimize design paradigms for the development of novel insect-sized,
flapping-wing-based NAVs.
I. Introduction
W
ITH the rapid progress made in micro-electromechanical system (MEMS), micro fabrication, miniaturized
power cells, remote communication, imaging and control devices, and other enabling technologies, a new
class of miniaturized aircraft known as Nano-Air-Vehicles (NAVs) is becoming possible in the not so distant future.
According to the definition given by Defense Advanced Research Projects Agency (DARPA) [1], NAVs are refers
as “airborne vehicles no larger than 7.5 cm in length, width or height, capable of performing a useful military
mission at an affordable cost and gross takeoff weight (GTOW) of less than or equal to 10 grams”. The potential of
NAVs opens up new possibilities in the formulation of various civilian and military strategies with respect to
information superiority in urban operations. It is expected that their main attributes will be low cost, low weight,
little to no logistical footprint, mission versatility, endurance, low visibility, covertness and precision. Their
distinctive flight envelope will include hovering, perching, and other high-agility maneuvers in order to perform
1
Graduate Student, Department of Aerospace Engineering.
Graduate Student, Department of Aerospace Engineering.
3
Associate Professor, Department of Aerospace Engineering, AIAA Senior Member, email: huhui@iastate.edu.
2
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American Institute of Aeronautics and Astronautics
Copyright © 2010 by Lucas Clemons , Hirofumi Igarashi and Hui Hu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
their missions. The real mission niche for these insect-size aircraft may well be in the indoor setting where there is
currently no reconnaissance asset available for various civilian and military applications.
Aerodynamic design challenges for NAVs are driven by a combination of low Reynolds number physics
(<10,000) and the requirement for a multi-functional platform structure. These challenges have already motivated
many novel approaches for NAV designs with fixed-wing, rotary wings, flapping-wings, or even designs like maple
tree seeds [2-3]. Fortunately, these challenges are similar to the aerodynamic challenges overcome with micro-airvehicle (MAVs) [4] and researchers can build upon this knowledge. However, the limited volume of space available
within the NAVs makes the aerodynamic challenges even greater than those overcome by MAVs. In general, fixedwing solutions for NAV applications are discounted because they require either high forward speed or large wings.
Although rotary-wings offer good agility and vertical-take-off-and-landing (VTOL) capability, they suffer from
wall-proximity effects, are too noisy, and usually are inefficient for low Reynolds number flight [5-6]. As
demonstrated by flying birds and insects, flapping flight is advantageous for its superior maneuverability and lifting
capability at low Reynolds numbers.
Flapping wing systems as inspired by bird and insect flight generally involve the wing completing pitching,
yawing and sweeping components of motion over a flapping cycle [7-8]. Different mechanisms such as pneumatic
and motor-driven actuators with gear systems have been widely used to mimic this complex flapping motion, but
these mechanisms often suffer from heavy weight and mechanical system complexity [8]. Piezoelectric materials
are widely used in smart structures such as sensors and actuators due to their high bandwidth, high output force,
compact size, and high power density [9]. Since only a small deflection can be expected directly from the bending
piezoelectric unimorph/bimorph, motion amplification mechanisms are usually required to achieve large deflection
amplitude. One of the most commonly-used motion amplification mechanism is a piezoelectric fan (piezofan) which
couples a piezoelectric unimorph/bimorph to an attached flexible blade and is capable of producing large deflections
especially at resonance. Piezofans were first investigated in the late 1970s [10]. In the last few years the demand for
portable electronic devices has brought interest in the use of piezofans as a compact, low power, noiseless air
cooling technology for applications such as laptop computers and DVD players [11, 12]. Since piezofans are
compact in size (i.e., ~10mm in chord length) and can generate large flapping amplitude (~25mm) at very high
flapping frequency (60Hz~110Hz), which naturally point to the potential applications of employing piezofans as
gearless flapping-wings for NAV designs [13-14]. With this in mind, we conduct the present study to try to leverage
the unique features of piezofans to explore the potential applications of piezoelectric flapping wings for the
development of novel insect-sized, flapping-wing NAVs.
It has been found that flapping airfoils/wings generate thrust at certain combinations of flapping frequency and
amplitude. While numerous investigations on flapping airfoils/wings were concentrated on pure pitching or
combined heaving and pitching motions, many studies have also been conducted on pure heaving motion. Garrick
[15] determined the propulsive efficiency of a plunging and pitching flat-plate airfoil as a function of the flapping
frequency, with the assumption of potential flow and small-amplitude oscillation. Freymuth [16], Jones et al.[17]
and Lai & Platzer [18] show that the wakes of plunging airfoils can be characterized as drag-producing, neutral, or
thrust-producing depending on the plunge frequency and amplitude. Drag-producing wakes are found to have
velocity profiles that show a momentum deficit when time averaged, typically with von Karman vortex street wake
configurations with two alternating vortex rows, clockwise above and anticlockwise below for a flow from left to
right. Vortex pairs form mushroom-like structures that are tilted upstream. Thrust producing wakes show a
momentum surfeit, or jet, superimposed on the momentum-deficit velocity profile in the time-averaged flow, such
that the thrust of the jet is greater than the inherent drag of the airfoil. The wake configuration is typically a reverse
von Karman vortex street with two rows of alternating vortices with anticlockwise above and clockwise below, so
that vortex pairs form downstream tilted mushrooms. Neutral wakes, where the thrust due to plunging balances the
inherent drag, may show multiple vortex shedding per half-cycle, and vortex pairs are not tilted.
While useful information has already been uncovered through those previous studies, much work was still
needed for a better understanding of fundamental mechanism of flapping flight for optimum aerodynamic design of
functional NAVs. For example, most of the previous studies about the evolution of the unsteady wake vortex
structures generated in flapping flight were carried out by using two-dimensional airfoils in flapping motion.
Considering more practical configurations in NAV/MAV designs with fix-rooted flapping wings, the effects of
spanwise variations in flapping amplitude and the existence of additional wingtip vortex for a fix-rooted flapping
wing on the evolution of wake vortex structures as well as the resultant aerodynamic forces (i.e., lift and thrust) have
never been explored. It should also be noted that, while the wingtip displacement observed in the flapping flight of
birds and insects was found to be on the order of wing chord length, the plunging/pitching amplitudes of the
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flapping airfoils/wings used in most of previous studies were usually quite small, i.e., less than 20% of the
airfoil/wing chord length [16-22]. The effects of the large flapping amplitude (i.e., h=A/C > 1.0) on the evolution of
the unsteady vortex structures in wakes of 3-D flapping wings are still unclear. Since mechanical-based flapping
mechanism systems, which often suffer from heavy weight and mechanical system complexity, were widely used in
previous experimental studies, the flapping frequency of the mechanical-based flapping mechanisms are usually less
than 10 Hz, which is much lower than the wing beating frequency of birds and insects, e.g. humming birds (40 ~ 60
Hz) and dragonflies (30Hz ~100Hz), which have comparable size as NAVs. Besides, the dimension of the
plunging/pitching airfoil/wing models used in most of the previous experimental studies is usually significantly
larger compared with the size definition of NAVs.
In the present study, an experimental study was conducted to explore the potential applications of a compact,
gearless, piezoelectric flapping wing with the wing size, stroke amplitude and flapping frequency within the range of
actual insect characteristics for the development of novel insect-sized, flapping-wing-based Nano-Air-Vehicles
(NAVs). Unlike most of previous studies with 2-D flapping airfoil models, a fix-rooted 3-D piezoelectric flapping
wing was used in the present study with the considering of more practical configurations usually used in NAV
designs. The experimental study was conducted in a low-speed wing tunnel with the test parameters of chord length
of C = 12.7mm, chord Reynolds number of Re = 1,200, flapping frequency of f = 60 Hz, reduced frequency of k =
3.5, and non-dimensional flapping amplitude at wingtip h = A/C = 1.35. The corresponding Strouhul number (Str) of
the 3-D piezoelectric flapping wing is 0.30, which is within the optimal range of 0.2 < Str < 0.4 usually used by
flying insects and swimming fishes [23-24]. A digital particle image velocimetry (PIV) system was used to achieve
phased-locked and time-averaged flow field measurements to quantify the formation and separation process of the
Leading Edge Vortex (LEV) structures on the upper and lower surfaces of the flapping wing in relation to the phase
angle (i.e., the positions of the flapping wing) during upstroke and down stroke flapping motions. The evolutions of
the wake vortex structures in the chordwise cross planes at different wingspan locations of the root-fixed 3-D
flapping wings were compared quantitatively in order to elucidate underlying physics for better understanding of the
unsteady aerodynamics of the flapping flight and to explore/optimize design paradigms for the development of novel
insect-sized, flapping-wing-based NAVs.
II. Experimental Setup and Studied Wings
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 × 1.0 ft (30 × 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.
Piezoelectric material
A
Span length = 34 mm
(a). Side view
Piezoelectric material
c =12.7mm
(b). global view
Fig. 1: The studied piezoelectric flapping wing
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American Institute of Aeronautics and Astronautics
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 the chord length 12.7mm (i.e., c=12.7mm), wingspan
34mm (i.e. b=34mm), and thickness 0.26mm. In the present study, the velocity of the incoming flow was set as U∞
= 1.40 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 hot-wire anemometer.
Fig. 2: Experimental set up for PIV measurements
25
20
y=0.105*x
Measurement data
20
Sine wave fit
Measurement data
15
Wingtip Displacement (mm)
Peak-to-peak flapping amplitude at Wingtip(mm)
Figure 2 shows the experimental setup used in the present study. The test piezoelectric flapping wing was
installed in the middle of the wind tunnel test section. 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 wing.
The piezoelectric wing 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. As shown in
Figure 3, the peak-to-peak flapping amplitude of the wingtip was found to increase linearly with the applied AC
voltage.
15
10
5
10
5
0
-5
-10
0
0
40
80
120
160
200
-15
0
90
Applied AC Voltage (V)
Fig 3: Flapping amplitude vs. applied AC voltage
180
270
Phase Angle (deg.)
Fig4: Wingtip position over one flapping period.
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360
As revealed in Koochesfahani [22], for a given flapping frequency and amplitude, a variety of complex wake
vortex structures can be generated by simply changing the shape of the wave-form of the flapping motion. An
experiment was conducted in the present study to measure the wave-form of the plunging trajectory for the wingtip
as the piezoelectric wing is driven by a sinusoidal AC voltage. Figure 4 shows the wingtip displacements over one
period of the plunging motion. It can be seen clearly that the plunging motion of the piezoelectric flapping wing is
sinusoidal when it is driven by a sinusoidal AC voltage.
A digital PIV system was used in the present study to make detailed flow velocity field measurements to
quantify the formation and separation processes of Leading Edge Vortex (LEV) structures on the upper and lower
surface of the piezoelectric flapping wing in relation to the position of the wing during the up stroke and down
stroke cycles as well as the evolution of the unsteady vortex structures in the wake of the piezoelectric flapping wing.
The flow was seeded with 1~5 μm 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 to eliminate the shadow region of the piezoelectric flapping wing for PIV measurements. A high resolution
12-bit (1376 x 1040 pixel) CCD camera (SensiCam-QE, CookeCorp) 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.
During the experiments, the sinusoidal wave signals supplied by the function generator, which was used to drive
the piezoelectric flapping wing through a high-voltage amplifier, was also used as the input signal to the DDG to trig
the PIV system to achieve phased-locked PIV measurements. By adding different time delays between the input
sinusoidal wave signal and the TTL output signal from the DDG to trig the PIV system, the 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 of the piezoelectric flapping wing were accomplished. At each preselected phase angle, 160 frames of instantaneous PIV measurements were used to calculate averaged phase-locaked
flow field around the piezoelectric flapping wing. In addition to phase-locked PIV measurements, time-averaged
PIV measurements were also conducted by disabling the phase-locking between the flapping motion of the
piezoelectric flapping wing and the PIV system in order to derive the time-averaged flow field around the
piezoelectric flapping wing. 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 (ωz) could be derived. The time-averaged quantities such as mean
velocity ( U , V ), ensemble-averaged spanwise vorticity (ωz) distributions were obtained from a cinema sequence of
500 frames of instantaneous velocity fields in each studied chordwise cross planes. The measurement uncertainty
level for the instantaneous velocity vectors is estimated to be within 2.0%.
III. Experimental Results and Discussions
A non-dimensional parameter that is widely used to describe the wing kinematics of flying birds and insects is
the Strouhal number, Str = f A / U ∞ , which divides flapping frequency ( f ) and stroke amplitude (A) by the forward
flying speed U ∞ the flight speed. In addition, reduced frequency, k = 2π f c / U ∞ , where c is the airfoil/wing chord
length, was also widely used to characterize the flight performance of many flying animals ranging in size from
small insects to albatrosses and kestrels. Since the production of flapping frequency, f, and chord length, c, is a
measure of the wing flapping velocity, hence reduced frequency, k, is a measure of the flapping velocity relative to
the flying speed. By using non-dimensional flapping amplitude, h = A / c , the relationship between the product kh
and the Strouhal number (Str) can be written as kh = 2π Str . It has been found that natural selection is likely to tune
birds and insects to fly in the range of 0.2 < Str < 0.4 for high propulsive efficiency. For example, Taylor et al. [24]
analyzed the flapping frequencies and amplitudes of 42 species of birds, bats, and insects in cruise flight and found
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American Institute of Aeronautics and Astronautics
that the flying animals operate within a narrow range of Strouhal number with 0.2 < Str < 0.4. Similar results were
also found to be true for dolphins, sharks, bony fish and other swimming fishes [23].
For the present study, the incoming flow velocity or forward flight speed is U∞ = 1.40 m/s, the chord length of
the piezoelectric flapping wing is c = 12.7mm. The flapping frequency of the piezoelectric flapping wing is f =
60Hz. The peak-to-peak flapping amplitude of the piezoelectric flapping wing at middle wingspan was found to be
A = 6.90 mm. Following the work of Taylor et al. [24] to use the peak-to-peak flapping amplitude at middle
wingspan to calculate the equivalent Strouhal number (Str) for the fix-rooted 3-D piezoelectric flapping wing, the
equivalent Strouhal number (Str) was found to be 0.30, i.e., Str = 0.30, which is within the optimal range of 0.2 <
Str < 0.4 usually used by flying birds and insects and swimming fishes.
4
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
4
Y/C
2
Y/C
2
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
0
0
-2
-2
0
2
4
6
8
0
2
X/C
(a). Wing at the upmost position, down stroke starts
4
4
6
8
X/C
(b.) Wing at the neutral position, during down stroke
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
4
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
2
Y/C
Y/C
2
0
0
-2
-2
0
2
4
6
8
0
2
(d). Wing at the neutral position, during upstroke
4
6
8
X/C
X/C
(c). Wing at the bottom most position, up stroke starts
Fig. 5: Phase-locked PIV measurement results in the chordwise cross plane at 50% wingspan.
Fig. 5 to Fig. 7 shows the phase-locked PIV measurement results in the chordwise cross planes passing 50%
wingspan, 75% wingspan and 100% wingspan (i.e., wingtip) of the root-fixed 3-D piezoelectric flapping wing,
respectively. For the phase-locked PIV measurements shown in the figures, the positions of the piezoelectric
flapping wing were at its upmost position (i.e., at the end of up strokes or beginning of down strokes), neutral
position during down strokes, bottom most position (i.e., at the end of down strokes or the beginning of down
strokes), and the neutral position during up strokes, respectively. In the figures, the uniform incoming velocity U∞
was subtracted from the measured flow velocity vectors in order to reveal the unsteady vortex structures induced by
the flapping motion more clearly.
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The phase-locked PIV measurement results in the chordwise cross planes at different wingspan locations
revealed very similar scenario about the formation and separation processes of the leading edge vortex (LEV)
structures on the lower and upper surfaces of the root-fixed piezoelectric flapping wing. It can be seen clearly that,
when the piezoelectric flapping wing was at its upmost position to begin a down stroke, while a large positive
(counter-clockwise) LEV structure generated on the wing lower surface during the previous upstroke cycle was
found to begin to separate from the leading edge of the flapping wing, a new negative (clockwise) LEV was found to
form on the upper surface of the piezoelectric flapping wing. During the down stroke of the flapping motion, while
the separated positive LEV on the lower surface was found to be stretched and pushed downstream to approach the
trailing edge of the wing, the negative LEV structure newly formed on the upper surface of the flapping wing was
found to grow up rapidly. As the wing passing the neutral position during the down stroke of the flapping motion,
while the negative LEV formed on the upper surface of the flapping wing became much larger and stronger, the
majority portion of the separated positive LEV on the wing lower surface was found to be at the downstream of the
wing trailing edge with the rear tip of the separated positive LEV structure attached to the trailing edge of the
piezoelectric flapping wing. The negative LEV on the upper surface was found to stay attached to the leading edge
firmly during the entire down stroke of the flapping motion, and became so big that it covered almost entire upper
surface of the flapping wing when the wing reaches its bottom most position at the end of the down stroke of the
flapping motion.
4
U∞
<ωZ>*C/U ∞
4
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
<ωZ>*C/U ∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
Y/C
2
Y/C
2
U∞
0
0
-2
-2
0
2
4
6
8
0
2
X/C
(a). Wing at the upmost position, down stroke starts
4
U∞
4
6
8
X/C
(b.) Wing at the neutral position, during down stroke
<ωZ>*C/U ∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
4
2
U∞
<ωZ>*C/U ∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
Y/C
Y/C
2
0
0
-2
-2
0
2
4
6
8
X/C
(d). Wing at the neutral position, during upstroke
0
2
4
6
X/C
8
(c). Wing at the bottom most position, up stroke starts
Fig. 6: Phase-locked PIV measurement results in the chordwise cross plane at 75% wingspan.
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American Institute of Aeronautics and Astronautics
As the next upstroke starts, while the separated positive LEV formed on the lower surface of the flapping wing from
the previous up stroke was found to separate completely from the trailing edge of the piezoelectric flapping wing and
became a wake vortex moving further downstream, a new positive LEV was found to form near the leading edge on the
lower surface of the flapping wing. During upstroke of the flapping cycles, similar as the positive LEV formed on the
lower surface of the flapping wing in the course of the previous down stroke of the flapping cycle, the negative LEV
formed on the upper surface of the flapping wing during the previous down stroke would separate from the leading edge
and was pushed downstream to approach the trailing edge of the flapping wing. The positive LEV newly formed on the
lower surface of the piezoelectric flapping wing was found to stay attached firmly to the leading edge of the wing while
becoming bigger and stronger. At the end of the up stroke of the flapping circle, the separated negative LEV on the upper
surface would be shed from the trailing edge of the wing as a wake vortex, while the positive LEV formed on the lower
surface become so big to cover almost the entire lower surface. The process described above would repeat again as
another round of the down stroke of the flapping circle starts. As a result, positive (clockwise) and negative (counterclockewise) vortex structures were found to shed alternatively in the wake region downstream of the piezoelectric
flapping wing.
4
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
4
2
Y/C
Y/C
2
0
0
-2
-2
0
2
4
6
0
8
2
4
(a).Wing at the upmost position, down stroke starts
4
6
8
X/C
X/C
(b). Wing at the neutral position, during down stroke
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
4
<ωZ>*C/U ∞
U∞
-4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50
2
Y/C
Y/C
2
0
0
-2
-2
0
2
4
6
8
0
2
X/C
4
6
8
X/C
(c). Wing at the bottom most position, up stroke starts
(d). Wing at the neutral position, during up stroke
Fig. 7: phase-locked PIV measurement results in the chordwise cross plane at wingtip.
While the scenarios of the formation and separation of the positive (clockwise) and negative (counterclockewise) LEV structures on the lower and upper surface of the piezoelectric flapping wing were found to be very
similar in the cross planes at different wingspan locations, the evolutions of the wake vortex structures after they
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American Institute of Aeronautics and Astronautics
shed from the trailing edge of the 3-D piezoelectric flapping wing were found to vary significantly in the different
cross planes at different wingspan locations.
As shown clearly in Fig. 5, after shedding alternatively from the trailing edge of the piezoelectric flapping wing,
the separated LEV structures in the cross plane at 50% wingspan of the piezoelectric wing were found to form wake
vortex structures with highly concentrated cores. Since the shedding process of the positive (counter-clockwise)
separated LEV vortices occurred at the end of upstrokes, while the shedding of the negative (clockwise) vortices at
the end of the down strokes, the initial positions of the positive (counter-clockwise) vortex cores were found to be
above those of the negative (clockwise) vortex cores. Induced by the flapping motion of the piezoelectric flapping
wing, the positive (counter-clockwise) vortex cores were found to move downward, while the negative (clockwise)
vortex cores moving upward as they shed from the trailing edge of the flapping wing. The trajectories of the
negative (clockwise) and positive (counter-clockwise) wake vortex cores were found to cross over at the
downstream location of X/C ≈ 2.5. At further downstream, the concentrated wake vortices were found to align them
nicely in two parallel rows with the clockwise (i.e., negative) vortex cores above and anti-clockwise (i.e., positive)
vortex cores below, which is a typical von Karman vortex street wake configuration for the incoming flow from left
to right. According to Jones et al. [17], such von Karman vortex street wake configuration would indicate that the
wake flow at 50% wingspan of the root-fixed 3-D piezoelectric flapping wing would be drag-producing. It would
cause momentum deficits in the streamwise velocity profiles downstream the flapping wing in the time-averaged
flow field, which was confirmed from the time-averaged PIV measurements given in Fig. 9.
In comparison with those in the cross plane at 50% wingspan, the evolution of the wake vortex structures in the
cross plane at 75% wingspan (Fig. 6) were found to become much more complicated. Corresponding to the larger
flapping amplitude (A = 11.2mm), the wake vortex structures in this cross plane were found to be stretched more
seriously as they shed from the trailing edge of the piezoelectric flapping wing. As a result, the wake vortex
structures were found to have much longer braids, instead of becoming highly concentrated wake vortices as those
observed in the cross plane at 50% wingspan. Since the shedding process of the positive (counter-clockwise)
vortices occurred at the end of the upstrokes, while the negative (clockwise) vortices at the end of the down strokes,
the initial positions of the positive (counter-clockwise) wake vortices were found to be slightly above those of the
negative (clockwise) wake vortices in the near wake region (X/C<3.5). Induced by the flapping motion of the
piezoelectric flapping wing, the cores of the negative (clockwise) wake vortices were found to move upward, while
those of the positive (counter-clockwise) wake vortices moving downward, as they travelling downstream. The
trajectories of the negative (clockwise) and positive (counter-clockwise) wake vortex cores were found to cross over
each other at the downstream location of X/C ≈ 3.5. Right before the crossing over of the trajectories of the negative
(clockwise) and positive (counter-clockwise) vortex cores, the stretched wake vortex structures were found to break
down with the braids of the wake vortex structures separated from their cores to form additional two rows of wake
vortex structures. As a result, four rows of wake vortex structures with alternative rotation direction were found in
the further downstream region in this cross plane. It can also be seen clearly that, corresponding to the formation of
the four rows of the wake vortices, the wake flow in this cross plane was found to bifurcate into two jet-like flows.
Such bifurcation phenomena were never observed or reported in previous experimental studies with 2-D flapping
airfoils/wings. For each jet-like wake flow after the bifurcation, a row of clockwise (i.e., negative) wake vortices
were found to be above the anti-clockwise (i.e., positive) wake vortices. According to Jones et al [17], such wake
vortex configuration was called reversed von Karman vortex street configure for the incoming flow from left to right.
It suggests that wake flow in this cross plane would be a thrust producing, which would result in momentum surfeits
(i.e., thrust generation) in the transverse profiles of the time-averaged streamwise velocity in the wake of the
piezoelectric flapping wing. The momentum surfeits in the time-averaged streamwise velocity profiles downstream
the piezoelectric flapping wing were confirmed from the time-averaged PIV measurement results shown in Fig. 9.
As shown in Fig. 7, the behavior of the wake vortex structures in the cross plane passing the wingtip were found
to become much more involved due to the existence of additional wingtip vortex structures. The negative (clockwise)
vortices shed at the end of the upstroke and the positive (counter-clockwise) vortices shed at the end of the down
stroke were found to be stretched even more severely. After they shed from the trailing edge of the piezoelectric
flapping wing, instead of forming concentrated vortices as those in the cross planes at 50% or 75% wingspan
locations, the wake vortex structures in the cross plane passing the wingtip were found to be elongated significantly
and broke down into smaller and weaker vortex structures rapidly. After broken down, the smaller and weaker wake
vortex structures were found to align them in six rows as they travelling downstream. For each pair of the wake
vortex rows, clockwise (i.e., negative) wake vortices were found to be above the anti-clockwise (i.e., positive)
vortices, i.e., typical a reversed von Karman vortex street configuration. It suggests that wake in the cross plane
passing the wingtip would also be thrust producing. The smaller and weaker wake vortex structures were found to be
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American Institute of Aeronautics and Astronautics
Y/C
Y/C
Y/C
dissipated rapidly and eventually vanished at further downstream. Similar as that observed in the cross plane at 75%
wingspan, bifurcation of the wake flow was also found to in this cross plane, which occurred at the downstream
region of X/C>2.0.
Figure 8 shows the time-averaged PIV
measurements in the three cross planes at 50%, 75%
U/U ∞
4
0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20
and 100% wingspan. It can be seen clearly that, in
the cross plane at 50% wingspan, the wake flow in
the downstream region of the piezoelectric flapping
wing was found to have a small region of high-speed
2
flow (i.e. the region with local streamwise flow
velocity greater than the incoming flow, U∞) right
downstream the trailing edge of the flapping wing,
0
followed by a long low-speed flow region with the
local streamwise flow velocity being smaller than
the incoming flow velocity, U∞ . Such a wake flow
-2
pattern suggests that the wake flow in the cross
plane at 50% wingspan would be mainly drag
producing.
0
2
4
6
8
As shown in Fig. 8(b), the wake flow in the near
X/C
region downstream the piezoelectric flapping wing
(a). Cross plane at 50% wingspan
in the cross plane at the 75% wingspan was featured
U/U ∞
by a high-speed jet-like flow with its streamwise
4
0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20
flow velocity much greater than the incoming flow
velocity U∞ . The jet-like wake flow was found to
bifurcate into two jets further downstream in the
2
region of X/C>4.0 (i.e., in the region after the
crossing over of the trajectories of the positive and
negative wake vortex cores revealed from the phaselocked PIV measurements). After the bifurcation, a
0
low-speed region was found to fill in the gap
between the two high-speed jet-like flows at further
downstream.
-2
The high-speed jet-like flow in the near wake
downstream the piezoelectric flapping wing was
found to become much wider in the cross plane
0
2
4
6
8
X/C
passing the wingtip (Fig. 8(c)) corresponding to the
larger flapping amplitude at wingtip. The bifurcation
(b). Cross plane at 75% wingspan
of the jet-like wake flow was found to take place
U/U ∞
much upstream (i.e. at the downstream locations of
4
0.80 0.84 0.88 0.92 0.96 1.00 1.04 1.08 1.12 1.16 1.20
X/C ≈ 2.5) compared with that in the cross plane at
75% wingspan. Corresponding with the six rows of
wake vortex structures described above, the wake
2
flow was found to be separated into three jet-like
flow streams with two low-speed regions filling in
the space between the jet-like wake flow streams.
0
In order to reveal the variations of the
characteristics of the wake flow of the fixed 3-D
piezoelectric flapping wing in the cross planes at at
different wingspan locations more quantitatively, the
-2
transverse profiles of the time-averaged streamwise
flow velocity at four typical downstream locations
are shown in Fig. 9. As shown clearly in Fig. 9(a),
0
2
4
6
8
X/C
the time-averaged streamwise velocity profiles in all
(c). Cross plane at wingtip
the three studied chordwise cross planes were found
Fig. 8: Time-averaged PIV measurement results
to be have quite similar pattern, i.e., jet-like profiles
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American Institute of Aeronautics and Astronautics
with momentum surfeits were found in the near wake downstream the flapping wing. Compared with that at 50%
wingspan, the peak of the jet-like streamwise velocity profile at 75% wingspan was found to be much higher at the
downstream location of X/D=2.0 (i.e., one chord length downstream the wing trailing edge). Corresponding the
larger flapping amplitude at the wingtip, the high-speed jet-like wake was found to be much greater in the cross
plane at the wingtip. The time-averaged streamwise velocity profiles in the cross plane at 50% wingspan at further
downstream locations show obvious momentum deficits, which confirmed the drag producing nature of the wake
flow in the cross plane at 50% wingspan. The momentum surfeits observed from the streamwise velocity profiles at
75% wingspan and 100% wingspan also reveals the thrust producing nature of the wake flow in the cross planes. It
should also be noted that, despite the largest flapping amplitude at wingtip, the momentum surfeits in the cross plane
at 75% wingspan were found to be much greater than those in the cross plane passing the wingtip. It indicates that
more thrusts would be generated at 75% wingspan rather than at wingtip. The effects of additional wingtip vortices
for the present root-fixed 3-D flapping wing were believed to be responsible for the smaller thrust generation at the
wingtip compared with that at 75% wingspan. The bifurcation of the wake flow was also revealed quantitatively
from the time-averaged streamwise velocity profiles in the cross planes passing 75% wingspan and wingtip as
multiple high-speed velocity peaks were found in the profiles.
1.8
1.5
50% wingspan
75% wingspan
100% wingspan
1.7
1.6
1.3
1.5
U/U∞
1.4
U/U∞
50% wingspan
75% wingspan
100% wingspan
1.4
1.3
1.2
1.2
1.1
1.1
1.0
1.0
0.9
0.9
0.8
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
0.8
-3.5
3.5
-2.5
-1.5
-0.5
Y/C
(a). X/C=2.0
2.5
3.5
1.5
50% wingspan
75% wingspan
100% wingspan
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
0.9
0.9
0.8
0.8
-2.5
-1.5
-0.5
0.5
1.5
2.5
50% wingspan
75% wingspan
100% wingspan
1.4
U/U∞
U/U∞
1.5
(b). X/C=4.0
1.5
0.7
-3.5
0.5
Y/C
3.5
0.7
-3.5
-2.5
-1.5
Y/C
-0.5
0.5
1.5
2.5
3.5
Y/C
(c). X/C=6.0
(d). X/C=8.0
Fig. 10: The time-averaged streamwise velocity profiles in the wake region
Concluding Remarks
An experimental investigation was conducted to explore the potential applications of compact, gearless,
piezoelectric flapping wings with the wing size, stroke amplitude and flapping frequency within the range of actual
insect characteristics for the development of novel insect-sized Nano-Air-Vehicles (NAVs). Unlike most of previous
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American Institute of Aeronautics and Astronautics
studies with 2-D flapping airfoils, a fix-rooted 3-D flapping wing was used in the present study with the
consideration of more practical configurations in NAV designs. The experimental study was conducted in a lowspeed wing tunnel with the test parameters of chord Reynolds number of Re = 1,200, reduced frequency of k = 3.5,
and non-dimensional flapping amplitude at wingtip h = A/C = 1.3. The corresponding Strouhul number of the rootfixed 3-D piezoelectric flapping wing is Str = 0.30, which is within the optimal range of 0.2 < Str < 0.4 usually used
by flying insects and swimming fishes. A digital particle image velocimetry (PIV) system was used to achieve
phased-locked and time-averaged flow field measurements to quantify the formation of shedding process of the
Leading Edge Vortex (LEV) structures on the upper and lower surfaces of the 3-D piezoelectric flapping wing in
relation to the positions of the flapping wing during upstroke and down stroke motions. The evolutions of the wake
vortex structures in the cross planes at 50% wingspan, 75% wingspan and 100% wingspan (i.e., wingtip) of the rootfixed 3-D flapping wings were compared quantitatively in order to elucidate underlying physics for better
understanding of the unsteady aerodynamics of the flapping flight for the development of novel insect-sized,
flapping-wing-based NAVs.
The phase-locked PIV measurements revealed clearly that the formation and separation processes of the
positive (clockwise) and negative (counter-clockewise) leading edge vortex (LEV) structures on the lower and upper
surface of the 3-D flapping wing at different wingspan locations were quite similar. A negative (clockwise) LEV
would be formed on the upper surface of the flapping wing as each down stroke of the flapping motion starts.
Meanwhile, a negative (clockwise) wake vortex formed during previous down stoke cycle would shed from the
trailing edge of the flapping wing as a wake vortex. During each down stroke, while growing up in size and
becoming stronger, the negative (clockwise) LEV on the upper surface would stay attached to the leading edge
firmly all the way until the down stroke ends. As the following upstroke starts, the negative (clockwise) LEV on the
upper surface would separate from the leading edge and moved downstream to approach the trailing edge of the
wing. During the upstroke of the flapping motion, the separated negative (clockwise) LEV on the upper surface
would be stretched and eventually shed from trailing edge of the flapping wing as the upstroke ends. Similar
scenario were experienced by the positive (counter-clockwise) LEV structures, which were found to form on the
lower surface at the beginning of the upstrokes and shed from the trailing edge at the end of the down strokes.
The evolutions of the wake vortex structures in the cross planes at 50%, 75% and 100% wingspan were found to
be quite varied significantly. After shed from the wing trailing edge, the wake vortices were found to be highly
concentrated vortex structures in the cross plane at 50% wing span. As they travelling downstream, the concentrated
wake vortices were found to align them nicely in two parallel rows with the clockwise (i.e., negative) vortices above
and anticlockwise (i.e., positive) vortices below, which is a typical von Karman vortex street wake configuration for
the incoming flow from left to right. As expected, momentum deficits in the time-averaged streamwise velocity
profiles (i.e., drag-producing wake) were confirmed for the wake flow in the cross plane at 50% wingspan. The
wake vortex structures were found to be stretched to have long braids in the cross planes at 75% wingspan. As they
travelling downstream, the stretched wake vortex structures were found to break down with the braids of the vortex
structures separated from the core potion to form additional two rows of smaller and weaker vortex structures. As a
result, four rows of wake vortex structures were found in the wake region in the cross plane at 75% wingspan, the
wake flow was found to bifurcate into two jet-like wakes. For each jet-like wake, the clockwise (i.e., negative)
vortices were found to be above the anti-clockwise (i.e., positive) vortices, which represents a reversed von Karman
vortex street configure for the incoming flow from left to right. It indicates that the wake flow in the cross plane at
75% wingspan was thrust producing, which was confirmed from the time-averaged PIV measurement results. Due to
the additional effects of the wingtip vortex structures, the evolution of the wake vortex structures in the cross plane
passing the wingtip were found to become much more involved. Although the flapping amplitude at the wingtip was
much larger than that at 75% wingspan, the momentum surfeits in wake at wingtip was found to be much less
compared with that at 75% wingspan. It suggests that the effects of the wingtip vortex would be detrimental for a
root-fixed 3-D flapping wing in the term of thrust generation.
Acknowledgments
The authors also want to thank Mr. Bill Rickard of Iowa State University for his help in conducting the wind
tunnel experiments. The support of National Science Foundation CAREER program under award number of CTS0545918 is gratefully acknowledged.
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American Institute of Aeronautics and Astronautics
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