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Characteristics of a wingtip vortex from an oscillating winglet

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Initial perturbations in the wingtip vortices can potentially lead to instabilities that significantly reduce their lifetime in the wake of an aircraft. An active winglet capable of oscillating about its point of attachment to the main wing-section is developed using piezoelectric macro fiber composite, to actively perturb the vortex at its onset. Resonance characteristics of the actuated winglet oscillations are evaluated at different excitation levels and aerodynamic loading. Mean near-field characteristics of the vortex, developing from a stationary and an oscillating winglet, are investigated with the help of stereoscopic particle image velocimetry. Results show that the amplitude of winglet oscillations increases linearly with input excitation, to a highest attainable value of nearly four times the airfoil thickness at the winglet tip. The vortex developing from a winglet is stretched along its axis, having an elliptical core with non-uniform vorticity distribution. Actuation leads to spatial oscillations of the vortex core together with a reduction in the mean peak vorticity levels. The amplitude of the actuated core oscillations remains constant in the investigated region of the wake.
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Exp Fluids (2017) 58:8
DOI 10.1007/s00348-016-2289-3
RESEARCH ARTICLE
Characteristics of a wingtip vortex from an oscillating winglet
T. K. Guha1 · R. Kumar1
Received: 17 August 2016 / Revised: 10 November 2016 / Accepted: 29 November 2016
© Springer-Verlag Berlin Heidelberg 2016
Cm
Chord length at the mid-span of the wing-section
Ct
Chord length at the tip of the winglet
Cb
Chord length at the base of the winglet
Cp
Coefficient of pressure
Taper ratio (=
Ct
/
Cb
)
U
Freestream velocity
Static pressure on the airfoil surface
p
Static pressure of the freestream
q
Dynamic pressure of the freestream
Re Reynolds number
ω
Vorticity in the flow direction
Γ
Circulation in a region
µ
Mean quantity
σ
Standard deviation of a quantity
1 Introduction
1.1 Wingtip vortices
Wingtip vortices develop at the tips of aircraft wings due
to a pressure imbalance in the process of generating lift.
In a highly turbulent environment these coherent trailing
vortices commonly breakdown rapidly due to the growth
of instabilities present in the flow. However, in a quiescent
environment they can exist for several hundred span lengths
downstream, before decaying due to natural diffusion. Fig-
ure 1 shows the characteristics of an aircraft wake contain-
ing a pair of such vortices. A region of downwash devel-
ops between the vortices, which leads to induced drag, that
accounts for 30–50% of the total aerodynamic drag of an
aircraft at high lift configurations, for example, during take
off and landing (Henderson and Holmes 1989). These vor-
tices are also a major source of wake turbulence, since such
a wake structure can lead to sudden lift losses and rolling
Abstract Initial perturbations in the wingtip vortices can
potentially lead to instabilities that significantly reduce
their lifetime in the wake of an aircraft. An active winglet
capable of oscillating about its point of attachment to the
main wing-section is developed using piezoelectric macro
fiber composite, to actively perturb the vortex at its onset.
Resonance characteristics of the actuated winglet oscilla-
tions are evaluated at different excitation levels and aero-
dynamic loading. Mean near-field characteristics of the
vortex, developing from a stationary and an oscillating
winglet, are investigated with the help of stereoscopic par-
ticle image velocimetry. Results show that the amplitude of
winglet oscillations increases linearly with input excitation,
to a highest attainable value of nearly four times the airfoil
thickness at the winglet tip. The vortex developing from a
winglet is stretched along its axis, having an elliptical core
with non-uniform vorticity distribution. Actuation leads to
spatial oscillations of the vortex core together with a reduc-
tion in the mean peak vorticity levels. The amplitude of the
actuated core oscillations remains constant in the investi-
gated region of the wake.
List of Symbols
α
Angle of attack
Λ
Angle of sweep
b Span of the experimental wing-section
* R. Kumar
rkumar@fsu.edu
T. K. Guha
tkg11j@my.fsu.edu
1 Department of Mechanical Engineering, FAMU-FSU College
of Engineering, Florida State University, 2003 Levy Ave,
Tallahassee, FL 32310, USA
Exp Fluids (2017) 58:8
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moments on a trailing aircraft. The problem becomes criti-
cal when the trailing aircraft is comparatively smaller in
size and cannot generate enough power to overcome such
disturbances. The probability of such encounters and acci-
dents especially increases in the vicinity of airports, where
aircraft fly at lower altitudes and often share a common
corridor for landing. To avoid accidents, strict spacing
requirements have to be obeyed by all civilian aircraft oper-
ating under instrument flight rules (IFR). These regulations,
while ensuring that the wake has sufficient time to decay
and become harmless for an approaching aircraft, restrict
the capacity of airports, thus posing a challenge to growing
volume of air traffic. These debilitating problems posed by
wingtip vortices have led to a large body of research work.
The problem of induced drag has been addressed success-
fully with a number of tip devices like winglets, which are
now commonplace in civil aviation. However, only a hand-
ful of studies have worked on developing active mecha-
nisms for exciting vortex instabilities for accelerated wake
alleviation.
1.2 Effects of winglets on wingtip vortices
Characteristics of the tip vortices are significantly modified
by the addition of tip devices. Non-planar (different dihe-
dral orientation from the wing) tip devices, such as wing-
lets help in reducing induced drag without increasing the
effective wingspan. Winglets were initially developed at
NASA (Whitcomb 1976) and consisted of two miniature
wing-sections attached to the tip of a jet transport aircraft
half-body prototype, at different dihedral orientations. They
were called the upper and lower winglets, respectively. The
study showed a 20% decrease in induced drag and a 9%
increase in the lift to drag ratio at the experimental test con-
ditions. The study suggested that winglets work as vortex
diffusers, that reduce the peak vorticity levels or strength
of the vortex at its very onset, as shown in Fig. 2. It also
suggested that the influential role is played by the upper
winglet; which is the only winglet seen in most commercial
applications. A recent study has shown that winglets are
efficient because they generate their own side forces, which
completely or partially cancel out the induced drag gen-
erated by the winglet itself (Verstraeten and Slingerland
2009). The usefulness of winglets has also been shown for
high-speed applications involving jet transport (Flechner
et al. 1976) and military aircraft (Ishimitsu et al. 1976;
Ishimitsu and Zanton 1977). Some recent studies have
shown that winglets can lead to a significant improve-
ment in the performance of unmanned air vehicles (UAVs)
(Panagiotou et al. 2014) and sailplanes (Maughmer 2003).
Recently, Boeing has used shape memory alloy (SMA) for
the development of variable geometry winglets, where the
winglet sweep and dihedral can be changed based on flight
conditions (Sankrithi and Frommer 2010). The motivation
behind the present study is to investigate whether an estab-
lished drag reducing static device, such as a winglet, can
be diversified into an active device capable of reducing the
lifetime of the hazardous wake.
1.3 Effects of vortex instabilities on wingtip vortices
Sinusoidal perturbations of a single vortex filament lead to
well-known Kelvin waves, which are neutrally stable oscil-
lations that rotate due to the self-induction of the vortex
(Kelvin 1880). The presence of a second perturbed vortex
(like in vortex pairs found in aircraft wake) induces second-
ary velocity perturbations and strain on the first vortex due
to mutual induction. A single mode (perturbation) becomes
unstable when its rotational components due to self- and
mutual induction, nullify each other and the perturbation
becomes stationary in a plane which has a positive strain
rate. The external strain then leads to exponential amplifi-
cation of the perturbation. This leads to a periodic linking
of the counter-rotating vortex pairs, which significantly
reduces its strength and lifetime. This mechanism can lead
to instabilities of long wavelengths (nearly 8 times the vor-
tex spacing) in a pair of counter-rotating vortices of equal
strength (Crow 1970) and shorter wavelengths (an order of
vortex spacing) in vortices of unequal strength (Fabre et al.
Fig. 1 Nature of the wake produced by wingtip vortices and its del-
eterious effects on trailing aircraft
Fig. 2 Schematic of the structure of the vortices developing at wing-
tips, with and without a winglet
Exp Fluids (2017) 58:8
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2002). Crow instabilities are commonly seen in the con-
trails of jet aircraft, like the one shown in Fig. 3, captured
by the author at Tallahassee in 2016. In a four vortex sys-
tem, like those observed in the near-field of an aircraft dur-
ing flap down configuration, there is the existence of both
short- and long-wavelength instabilities (Crouch 1997).
Generally, the growth of the fast growing shorter wave-
length instability in the inboard vortex pair excites the long
wavelength Crow instability in the outboard vortex pair,
leading to accelerated decay of the overall wake (Rennich
and Lele 1999). A pair of Kelvin modes, satisfying cer-
tain conditions, can also lock on to a plane having positive
strain and lead to short or elliptical instabilities (Kerswell
2002). In a counter-rotating vortex pair, it enhances the
mixing in the residual vortex rings created by Crow insta-
bility, leading to the transfer of energy from large coherent
structures to smaller structures (Leweke and Williamson
1998; Roy et al. 2011).
The excitation of the unstable modes and the associ-
ated kinetic energy are probabilistic in nature, because
they depend on the state of atmospheric turbulence (Spalart
and Wray 1996). Hence, several studies have looked into
developing active perturbation mechanisms. For exam-
ple, Bilanin and Widnall (1973) showed through tow tank
experiments that periodic oscillations of wing flaps can
lead to perturbation of the vorticity centroid, leading to
Crow instabilities. Crouch et al. (2001) conducted numeri-
cal analysis and tow tank experiments to show that out-of-
phase oscillations of wing control surfaces can lead to short
and long wavelength instabilities in a system of multiple
wake vortices. In a different approach, Matalanis and Eaton
(2007) experimentally showed that perturbations of the
order of 1% of the vortex separation produced by gurney
flaps could lead to long and short-wavelength instabilities.
In a recent experimental study, Gupta (2011) showed that
certain characteristic perturbations produced by an actively
controlled trailing edge flap, led to the simultaneous growth
of Crow and elliptical instabilities. Pertaining to the use of
winglets for exciting instabilities, Kauertz and Neuwerth
(2006) developed winglets with radars that can be actively
oscillated to introduce perturbations. Tow tank visualiza-
tion showed that certain radar configurations led to strong
instabilities but active oscillation of the radar had no added
benefits. These studies clearly suggest the potential benefit
of perturbing the tip vortex by oscillating wing tips. More-
over, most of the analysis conducted till date has focused
on ideal vortices rather than wing tip vortices commonly
found in the wake of an aircraft (Roy et al. 2011). The pre-
sent study focuses on the vortices developing from winglets
that have several distinguishable characteristics, discussed
in Sect 3.3.
1.4 Piezoelectric macro fiber composite (MFC) and its
applications
The winglet actuator is developed using piezoelectric
Macro Fiber Composite (MFC), which was developed
at NASA and is currently manufactured and marketed by
Smart Materials Corp. (http://www.smart-material.com/).
These planar piezoelectric devices not only provide high
force, broad bandwidth actuation and electrically induced
small strains, but are also light-weight, flexible and easily
embeddable. MFC-based actuators and sensors have been
used successfully in problems such as separation control
(Kumar et al. 2011; Bilgen et al. 2011) and free shear flow
(Wiltse and Glezer 1993).
1.5 Objectives of the present study
The role of non-planar tip devices like winglets in the
reduction in induced drag has been well established, but
their role as active devices for wake alleviation has not been
investigated. There is also a lack of experimental data on
the near-field characteristics of wingtip vortices developing
from non-rectangular wing configurations with tip devices.
The objectives of this study are to characterize the mean
near-field characteristics of a vortex developing from a
winglet and the nature of perturbations introduced by oscil-
lating the winglet at different amplitudes. Once the nature
of perturbation is ascertained, it can be used for studying
Fig. 3 Contrails showing the
development of Crow instabili-
ties in the wake of an aircraft
Exp Fluids (2017) 58:8
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the stability of one or more pairs of perturbed vortices.
In this study, a piezoelectric MFC-based winglet actuator
has been developed, which can be assembled and made to
oscillate about the main wing-section. The structural oscil-
lations of the winglet actuator are characterized at differ-
ent excitation levels with and without aerodynamic loading.
The mean flow field developing from the stationary and the
oscillating winglet is captured with stereoscopic particle
image velocimetry (SPIV).
2 Experimental methodology and setup
Figure 4 shows the region of interrogation, which extended
from 4 to 20 chord lengths (
Ct
) downstream of the wing-
let trailing edge. The leading edge of the airfoil tip corre-
sponds to
z/Ct=0
. All the experiments were performed
at a freestream velocity of 20 m/s and an angle of attack
of 4°. The Reynolds number based on the wing mid-
chord (
Rec=U
×Cm
) and the mean circulation
(
ReΓ=Γ /ν
) are
1.4 ×105
and
3×104
, respectively.
2.1 Test facility
Experiments were conducted in the open-return low speed
wind tunnel facility at Florida Center for Advanced Aero-
Propulsion (FCAAP) at Florida State University. It is a sin-
gle pass, Eiffel-type wind tunnel, driven by a 200 hp fan,
which minimizes noise during testing. The test-section is
1.524 m (60 in.) long and has a cross section of 0.762 m
×
0.762 m (30 in.
×
30 in.). The walls of the test-section are
made of acrylic for optical access from all the four sides.
Freestream velocity inside the test-section can be changed
by altering the fan rpm with a variable frequency drive and
is measured with a pitot-static probe located at the entrance
of the test-section. Attainable velocity range is 2–80 m/s
with a variation of less than ±1%. Present experiments
were carried out at a freestream velocity of 20 m/s and
the freestream turbulence intensity at this condition was
0.5%.
2.2 Test model
The test model, as shown in Fig. 5, was a scaled, half-
body model of a generic transport aircraft. The model
consisted of a fuselage (ogive body), a swept and
tapered wing-section and the winglet actuator assembled
together. This assembly was attached to a hollow metal-
lic rod, which was rigidly held by a turn-table placed
below the wind tunnel test-section. The model was flush
mounted in the test-section and set to different angles of
attack using the turn-table. The various design param-
eters are tabulated in Table 1 and are similar to those
used in the initial study on winglets by Whitcomb (1976).
The fuselage ensured proper development of boundary
layer at the base of the wing-section. NACA 0015 sym-
metric airfoil geometry was used for both the wing and
the winglet. The dihedral orientation of the wing was 0°
and that of the winglet was 75°. Hence, a small curva-
ture was provided at the root of the winglet, to ensure
a smooth transition. The wing-section had static pres-
sure ports at three spanwise locations. The model was
(3D) printed using stereolithography resin (SL Somos
NeXt) by Engineering & Manufacturing Services, Inc.
(https://www.ems-usa.com/). The cured resin had a ten-
sile strength of 2.370–2.490 GPa and a flexural modulus
of 2.415–2.525 Gpa. The expected aerodynamic loads on
the model during wind tunnel tests were on the order of
1 KPa. At these relatively small loads, the deformation of
the structure was expected to be negligible in comparison
to the embedded MFC winglet structure.
Fig. 4 A schematic of the MFC actuated winglet and the region of
wake measurements
Fig. 5 A photograph of the test model mounted in the wind tunnel
test-section
Exp Fluids (2017) 58:8
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2.2.1 Winglet actuator design
The winglet actuator was constructed using a piezo-metal-
lic composite, which consisted of a piezoelectric MFC
film bonded to a trapezoidal aluminum plate, using Loc-
tite® epoxy adhesive. The top section of the wing consisted
of two parts, A and B, assembled via a dovetail joint, as
shown in Fig. 6a. The winglet had a small cavity at the bot-
tom. One end of the plate was mounted inside the cavity
and the other end was mounted onto part A, Fig. 6b. Upon
MFC actuation the plate along with the winglet oscillated
like a cantilever about the point of attachment in part A.
Appropriate clearances were provided to avoid any colli-
sion between the plate (or the winglet) with the surfaces of
the wing. A thin elastic band was used to cover the clear-
ance provided at the junction between the wing and the
winglet, to avoid any leakage of air from pressure to suc-
tion side (yellow band in Fig. 7a).
2.3 Setup for the structural characterization of MFC
actuated winglet
The winglet oscillated when the MFC was excited with a
sinusoidal voltage signal. The resonance characteristics of
these oscillations were characterized at different excitation
and pressure loading conditions. The pressure loading con-
ditions included point pressure load (applied by a jet on the
winglet tip) and distributed load (aerodynamic loads during
Table 1 Design parameters for
the wing and the winglet Parameters Airfoil
Cb
(mm)
Ct
(mm) b (mm)
Λ
(°)
Wing NACA 0015 156.21 54.7 369.1 37.5 0.35
Winglet NACA 0015 54.7 16.4 54.7 38 0.3
Fig. 6 a Parts constituting the
top section of the wing; and b
assembly of the MFC embedded
winglet actuator
Fig. 7 Experimental setup for
winglet structural characteri-
zation using, a a capacitance
probe and b a high-speed
camera
Exp Fluids (2017) 58:8
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wind tunnel tests). A brief discussion on the experimen-
tal setup for these measurements is presented here, but a
detailed description is available in Guha et al. (2015). The
sinusoidal excitation signal was generated by a waveform
generator (Tektronix® CFG280), which was amplified by
a factor of
103
, using a high-voltage amplifier (TREK®,
Model 10/40 A). The lower and upper limits of the excita-
tion for the used MFC model (M2814-P1) were 0.5 and
1.5 kV, respectively. The amplitude of these oscillations
was minimum at the winglet root and maximum at the tip.
The tip movement was measured independently using a
capacitance probe and a high-speed imaging system. The
capacitance probe (Lion precision C5-D) had a range of
2 mm and a sensitivity of 10 V/mm and was primarily used
for obtaining the resonance frequencies at no load and point
load conditions. The experimental setup for measurements
with the capacitance probe is shown in Fig. 7a. Figure 7b
shows the high-speed imaging setup which consisted of a
high-speed camera (IDT, Red Lake Y5) and a white LED
cluster, which were triggered synchronously using a delay
generator (Stanford Research Systems; Model: DG 535).
The high-speed camera was used for measuring the ampli-
tude of oscillation with varying magnitude of excitation
at all loading conditions. During wind tunnel testing, this
setup was mounted above the test-section, Fig. 8.
2.4 Surface static pressure measurements
Surface static pressure distributions were measured at three
spanwise locations (
y/b=0.25, 0.5, 0.75
), designated as
pressure ports-series 1, 2 and 3, respectively in Fig. 5. The
aim was to characterize the effect of winglet oscillations on
the mean load distribution over the wing surface. Each of
these locations had twenty surface pressure ports of diam-
eter 0.8 mm. Pressure lines (ID = 1.6 mm in hypodermic
tubing, Tygon S3TM E-3603) from these ports were drawn
through the model and the turn-table and were connected to
the pressure transducer via a scanivalve mechanical switch-
ing unit. The transducer (OMEGA® PX277-05D5V) has
a range of ±0.09 psi and a full scale error of ±1%. Data
were acquired at 10 Hz for 100 s at each port, in order to
obtain statistically valid steady pressure values.
2.5 Stereoscopic particle image velocimetry
The experimental setup for stereo particle image velocity
(SPIV) measurements at different downstream locations is
shown in Fig. 8. The flow was seeded using glycol particles
having dimensions on the order of 2–5 μm, produced by
vaporizing ROSCO clear fog fluid using a ROSCO DELTA
3000 fog machine. The seed particles were illuminated
using a Quantum® Nd: YAG double pulsed laser, that pro-
duces a beam of 200 mJ/pulse. The laser beam was focused
using a plano-convex lens (focal length = 1 m) and fanned
into a sheet using a cylindrical lens (focal length = 20 mm),
which was reflected into the test-section using a high power
mirror. The approximate thickness of the sheet in the SPIV
window of interrogation was 3 mm. The delay between the
two pulses was kept at 30 μs, to obtain a mean pixel shift
of about 6 pixels for the seed particles. Flow field images
were acquired using two 5.5 megapixel sCMOS cameras,
each fitted with a Nikon lens (focal length = 105 mm) and
a scheimpflug adapter. The 105-mm lenses were chosen for
acquiring a field of view encompassing the entire winglet.
The scheimpflug adapters were used to correct the oblique
view of the laser sheet by the cameras. The size of the
sCMOS array was 2560
×
2160 pixels and the dimensions
of the SPIV interrogation window along x and y axes were
12.67 and 7.87 times
Ct
, respectively. The flow field vector
resolution was 0.75 mm along both axes. The laser, lenses
and cameras were attached to a single frame and mounted
on axial and transversal traverses above the test-section.
This allowed a single calibration of the cameras to be used
while traversing from one downstream plane to the next.
Table 2 tabulates the downstream measurement planes,
non-dimensioanlized using
Cm
and
Ct
. A schematic of the
same is shown in Fig. 9, in the form of mean vorticity fields
stacked according to their acquisition location.
The dotted red line in the figure gives the area encom-
passed by the SPIV interrogation window. The dotted black
arrow gives the direction of rotation associated with the
vortex. The acquired images were processed with LaVi-
sion DaVis 8.3.1 software using GPU-based PIV algorithm.
Vector calculations were done using a multi-pass, decreas-
ing size algorithm. The initial passes had a correlation win-
dow size of
96 ×96
pixels with 50% window overlap. The
Fig. 8 Experimental setup for stereo particle image velocimetry
(SPIV) measurements
Exp Fluids (2017) 58:8
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final passes had a window of
48 ×48
pixels with a 75%
overlap. The processed SPIV snapshots were post-pro-
cessed using MATLAB® PIVmat 4.00 toolbox, in order to
extract and plot the flow field statistics.
Uncertainties in PIV measurements can be attributed to a
number of different factors such as calibration error, regis-
tration error, spatial resolution and pixel locking, to name a
few (Adrian and Westerweel 2011; Willert 1996). A variety
of different methods have been developed to quantify these
uncertainties (Sciacchitano et al. 2015). The correlation
statistics method suggested by Wieneke (2015) is a poste-
riori method in which the computed vector field is used to
symmetrically dewarp the two frames of a standard double-
frame PIV onto each other. The effect of standard deviation
in intensity of an interrogation window on the shape of the
correlation peak is used to quantify the uncertainty of the
displacement vector. In this study, the instantaneous SPIV
uncertainty field was obtained directly from DaVis, which
uses the aforementioned method for its quantification. The
average of the uncertainty fields of a thousand instantane-
ous velocity vector fields, for the stationary and the oscil-
lating vortex at the first measurement plane (
z/Ct=4.1
), is
shown in Fig. 10. The contour levels represent uncertainty
as a percentage of the mean freestream velocity (
U
). The
highest uncertainty levels of approximately 2.5% occurs at
the junction of the wing and the winglet and approximately
1.5% in the rest of the wake. Similar uncertainty levels were
observed in all the test cases.
In these experiments, the actuation frequency for the
winglet was fixed at 35 Hz. The reason for choosing this
frequency is discussed in the structural characterization
(Sect. 3.1). However, because the maximum laser rep-
etition rate was 15 Hz, for ensemble averaging, the image
acquisition rate was set at 9 Hz. Figure 11 shows that a
9 Hz acquisition rate captures various phases (locations) of
a 35 Hz signal (oscillating winglet), whereas, acquisition at
a multiple of the actuation frequency (5 Hz) leads to phase-
locking (singular location). Hence, when mean flow fields
with actuation are compared with the baseline, it shows the
effects of complete winglet oscillation cycle.
3 Results and analysis
3.1 Structural characterization of the actuated winglet
Figure 12 shows the winglet actuator with and without
MFC excitation, acquired during wind tunnel testing. A
detailed study was performed to find the resonance charac-
teristics of the winglet oscillations with and without actua-
tion. Once the resonance modes were identified, the effects
of parameters such as excitation strength, the mean position
of oscillation and pressure loading on the modes, and the
amplitude of oscillation at these modes were investigated.
It included point pressure loading on bench-top and dis-
tributed pressure loading during the wind tunnel tests. The
focus of this paper is primarily on the flow field results;
therefore, only a brief discussion of the necessary structural
characterization results is presented here. The details have
been reported in Guha et al. (2015).
To find the resonance modes of oscillation with actua-
tion, the MFC was excited with a chirp signal having an
amplitude of 0.5 kV. The resulting oscillations at the wing-
let tip were measured with the capacitance probe at a sam-
pling rate of 3 kHz. The actuated winglet oscillations show
bimodal resonance characteristics, Fig. 13a. The two modes
of resonance are 13 and 35 Hz and are designated as Mode 1
and Mode 2, respectively. The aim was to get the maximum
amplitude of oscillation for perturbing the wingtip vortex;
therefore, most of the tests were carried out at the dominant
Mode 2. The allowable excitation strength for the piezoelec-
tric MFC was between 0.5 and 1.5 kV. Within this range,
there is a linear increase in the amplitude of oscillation with
excitation magnitude, as shown in Fig. 13b. These ampli-
tude measurements were made on the winglet under aerody-
namic loading inside the wind tunnel, using the high-speed
camera. The first data point in this figure corresponds to the
negligible amplitude vibrations exhibited by the baseline
un-actuated winglet. At the highest input excitation of 2 kV
at Mode 2, the maximum mean amplitude of oscillation at
Table 2 SPIV measurement
locations SPIV Plane 1 2 3 4 5 6
z/Cm
0.6 1.1 1.6 2.1 2.6 3.1
z/Ct
4.1 7.2 10.3 13.4 16.5 19.6
Fig. 9 Schematic indicating the location of SPIV measurement planes
Exp Fluids (2017) 58:8
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the winglet tip is nearly 3.6 times the airfoil thickness at the
winglet tip (2.54 mm) or 0.6
Ct
.
Winglet tip position as a function of time, with and with-
out the highest excitation (2 kV at Mode 2) are compared
in Fig. 14a. The power spectra extracted from this instan-
taneous position data are shown in Fig. 14b. The winglet
oscillates smoothly upon actuation and shows a strong peak
corresponding to the excitation frequency. The movement
without actuation is almost zero and does not exhibit any
dominant frequency content. Therefore, the unexcited wing-
let behaves almost like a static winglet attached rigidly to the
wingtip. The actuated winglet oscillates smoothly following
the characteristics of the sinusoidal excitation signal.
Fig. 10 Average of uncertainty
fields of instantaneous velocity
vector fields at
z/Ct
=
4.1
. a
Static winglet and b oscillat-
ing winglet. Contour levels
represent percentage error in
velocity vector with respect to
the freestream velocity
U
Fig. 11 Effect of acquisition rate on ensemble averaging
Fig. 12 a Static un-actuated
winglet; and b oscillating wing-
let upon actuation
Fig. 13 a Frequency spectra of
the MFC activated winglet; and
b mean amplitude of oscillation
corresponding to different mag-
nitudes of excitation at Mode 2
Exp Fluids (2017) 58:8
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3.2 Surface pressure measurements
Surface pressure measurements were conducted to estimate
the effect of winglet oscillations on the mean load distri-
bution over the wing surface. These measurements were
conducted at three spanwise locations of
y/b
=
0.25, 0.5
and 0.75, respectively. Figure 15 compares the
Cp
distribu-
tion with and without actuation at
y/b
=
0.75
. The winglet
oscillations (0.6
Ct
) produce no observable effect on the
mean
Cp
distribution (at this and other locations), within
measurement uncertainty. Hence, it is stated that actua-
tion does not affect the mean loading of at least 75% of the
wing-section. It may be possible that pressure fluctuations
exist, particularly near the wingtip (
y/b
0.9
), which may
lead to unsteady loading, but such effects are not investi-
gated in this study.
3.3 Stereoscopic particle image velocimetry (SPIV)
measurements
In this section, we will look into the characteristics of the
vortex developing from a stationary winglet and its modi-
fications due to the introduction of actuated winglet oscil-
lations. The results correspond to SPIV measurements in a
region of interrogation spanning from 4 to 20
Ct
(0.6–3.1
Cm
) downstream of the winglet tip. All length and veloc-
ity parameters are non-dimensionalized using
Ct
and
U
,
respectively. The mean cross-stream velocity fields (
Ux
and
Uy
) developing from the stationary winglet at the first
downstream plane are shown in Fig. 16a, b, respectively.
The velocity fields are inlaid with velocity vectors. A
black dotted line is added to represent the trailing edge of
the winglet and the adjoining wing-section, covered in the
interrogation window. The flow travels along the curvature
of the winglet from the pressure to the suction side to com-
plete the vortex formation. The trailing edge forms a clear
demarcation between the positive and the negative regions
of the two velocity fields. The highest absolute (positive
or negative) velocity values are attained at locations cor-
responding to the tip (
x/Ct=−1
,
y/Ct=2
) and the root
(
x/Ct=2
,
y/Ct=1
) of the winglet, respectively, where
the flow experiences maximum curvature. The spatial gra-
dients of these velocity fields (
Uxy
and
Uyx
) and the result-
ant vorticity field (
ωz=Uyx Uxy
) are shown in Fig. 16c–
e, respectively.
The
Uxy
velocity component is present all along the
winglet trailing edge with highest values near the winglet
tip region.
Uxy
being negative leads to positive vorticity in
this region. The
Uyx
component is positive and prominent
only at the turning regions near the tip and the root, with
highest values at the tip. The core of the resultant vortex
has vorticity all along the winglet’s trailing edge. In other
words, the core of the vortex is stretched along the axis of
the winglet. The distribution is non-uniform with the high-
est values observed at the tip and the largest concentration
observed at the root.
To further quantify the vorticity distribution in the core,
the maximum vorticity value is extracted at every
x/Ct
loca-
tion from the mean vorticity field (Fig. 16e). The result-
ant contour, which gives the highest mean vorticity values
along the vortex core is shown in Fig. 17a. Three prominent
vorticity peaks are observed, which develop from locations
corresponding to the tip, middle and the root of the winglet,
Fig. 14 Comparison of a
amplitude; and b power spectra
of the winglet oscillations, with
and without MFC actuation of
2 kV at 35 Hz
Fig. 15 Comparison of
Cp
distribution at
y/b
=
0.75
, with and with-
out winglet actuation
Exp Fluids (2017) 58:8
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8 Page 10 of 18
respectively. This three-peak core structure is observed at
nearly all downstream measurement planes and has been
used extensively for defining the trajectory of the core and
evaluating the effects of actuation. Hence, for conveni-
ence, these peaks will be referred to as “Tip”, “Middle” and
Root” peaks, respectively. The Tip peak is the strongest,
followed by the Root and the Middle. The center of fluidic
rotation is located at the Root peak, which is the broadest
and contains the largest percentage of the total vorticity pre-
sent in the core. The Root peak being broader than the rest
of the core gives the associated streamlines a teardrop struc-
ture as seen in Fig. 17b (the black arrows represent velocity
vectors). The eccentricity of the streamlines suggest that the
near-field vortex can be characterized as an elliptical vortex
Fig. 16 Mean cross-stream
velocity fields (a
Ux
, b
Uy
) and the velocity gradients
(c
Uxy
, d
Uyx
) constituting the
mean vorticity field (e
ωz
) at
the downstream location of
z/Ct
=
4.1, z/Cm
=
0.6
Fig. 17 a Peak vorticity dis-
tribution along the vortex core;
and b associated streamlines, at
z/Ct
=
4.1, z/Cm
=
0.6
Exp Fluids (2017) 58:8
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Page 11 of 18 8
with multiple unequal vorticity peaks. Thus, the stability
analysis of a pair of winglet generated wingtip vortices in
the near-field wake may be better addressed by that of non-
uniform elliptical vortices in the strained field. Stability
analysis of vortices with elliptical cross section and uniform
vorticity distribution, also known as Moore-Saffman vorti-
ces, have received a lot of importance in the literature. In
the presence of an external field, they are highly susceptible
to short-wavelength instabilities (Pierrehumbert 1986; Rob-
inson and Saffman 1984; Le Dizes et al. 1996). Thus, axial
diffusion or stretching of vortices by winglets (and other
similar tip devices) potentially makes them more prone to
instabilities. These results suggest the merits of perform-
ing the stability analysis and developing active perturbation
mechanisms for such tip vortices.
Winglet oscillations upon actuation lead to correspond-
ing oscillations in the initial orientation of the elliptical
vortex developing from it. Similar to the movement of the
winglet itself, the amplitude of core oscillations is maxi-
mum at the tip and minimum at the root. The mean effects
of gradually increasing the amplitude of winglet oscilla-
tions at a constant frequency of 35 Hz (resonance Mode 2)
were studied. Four amplitudes of oscillations correspond-
ing to a MFC excitation range of 0.5–2.0 kV were investi-
gated. The results presented herein focus on the variations
at the Tip peak, which experiences maximum oscillation,
followed by that of the entire core.
The instantaneous position along y-axis and the corre-
sponding vorticity magnitude of the Tip peak is extracted
from a series of a hundred consecutive SPIV snapshots and
shown in Figs. 18 and 19, respectively. These plots com-
pare the stationary winglet (no actuation) with the lowest
and the highest amplitude of oscillations, corresponding to
excitation levels of 0.5 and 2.0 kV, respectively.
Freestream turbulence leads to unsteadiness in the loca-
tion of tip vortices. This phenomenon is commonly known
as vortex wandering (Devenport et al. 1997). The variation
in the Tip position observed in the baseline case (
0.08
Ct
) is attributed to this natural wandering and small flow
induced oscillations of the un-actuated winglet, Fig. 18.
When the winglet is excited at 0.5 kV, the mean amplitude
of oscillation at the tip of the winglet is 0.4 times the air-
foil thickness (Fig. 13b) or 0.06
Ct
. It is observed that at
this amplitude of oscillation, the variation in the Tip posi-
tion with actuation is almost comparable to the baseline,
Fig. 18a. As the excitation is increased to 2.0 kV, the mean
amplitude of winglet oscillations increases significantly to
0.6
Ct
. Correspondingly, the variation in the Tip peak posi-
tion is observed to increase significantly from the baseline.
The sinusoidal nature observed in the data points corre-
spond to a 9 Hz SPIV acquisition for a winglet oscillating
at 35 Hz, as discussed previously in the experimental setup
(Sect. 2.5). The vorticity magnitude of the Tip also shows a
variation with its position, whether it is due to the inherent
Fig. 18 Comparison of
instantaneous position of the tip
vorticity peak along the y-axis.
a Baseline with 0.5 kV excita-
tion, and b baseline with 2.0 kV
excitation
Fig. 19 Comparison of instan-
taneous vorticity magnitude of
the Tip peak. a Baseline with
0.5 kV excitation, and b base-
line with 2.0 kV excitation
Exp Fluids (2017) 58:8
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8 Page 12 of 18
unsteadiness of the flow or actuation. Similar to the vari-
ation in position, the variation in Tip vorticity is seen to
be comparable to baseline for actuation at 0.5 kV and sig-
nificantly higher for 2.0 kV. Upon comparing Figs. 18b
and 19b, it is observed that though the position of the actu-
ated Tip shows both positive and negative variation with
respect to the baseline, the vorticity values mainly show a
negative variation. As the dihedral of the winglet changes
about the mean position during oscillation, it is expected
that the vorticity will change accordingly. These results
suggest that the change in vorticity is due to the combined
effect of variation in winglet dihedral and the movement
of flow around the oscillating winglet. These underlying
mechanisms will be investigated in a future study with the
help of SPIV that is phase locked, with respect to different
phases of the winglet oscillation.
Finally, the mean (
µ
) and the limiting values (
µ±σ
)
of the Tip position and vorticity data, extracted from the
complete dataset (thousand image pairs) for all the cases
(baseline and actuation) are summarized in Fig. 20a, b,
respectively. It shows that the mean position of the Tip (and
the entire core) is unaffected by actuation. The variation in
position (
µ±σ
) is distinguishably higher than the baseline
only beyond an excitation level of 1 kV (corresponding
mean amplitude of winglet oscillation
=
0.2
Ct
). Actuation
leads to a reduction in the mean vorticity levels. The higher
limiting values remain unchanged while the lower limit-
ing values decrease, leading to the reduction in the mean.
Similar to the position, the effect of actuation on vorticity is
clearly distinguishable beyond 1 kV excitation.
Following the analysis of the Tip peak, the study moves
to the analysis of the rest of the core. The movement of the
core follows similar characteristics as the Tip, hence the
focus will be primarily on the variation in vorticity levels.
The actuation leads to the movement of the vortex core,
therefore, computation of mean vorticity fields through
direct averaging leads to errors in the form of lower peak
vorticity values and higher circulation. In such a scenario,
the vortex with actuation will seem to diffuse in compari-
son to the baseline vortex. These errors are simply the
amplified version of the error caused by the vortex wander-
ing (Devenport et al. 1997). To overcome this additional
uncertainty, a different approach is used for analyzing these
results. The peak vorticity value is extracted at every
x/Ct
location from every instantaneous vorticity field. Since the
highest vorticity value occurs inside the core, this gives a
contour of peak vorticity values across the vortex core. The
mean and standard deviation of contours extracted from a
thousand images are used for comparing the various cases,
eliminating bias due to spatial movement. Vorticity con-
tour obtained by averaging the contours extracted from
the individual fields separately (“Indirect”), is compared
to that extracted directly from the mean field (“Direct”) in
Fig. 21. It is clearly observed that the overall vorticity val-
ues obtained by this indirect approach are higher than the
direct method, as those have not been artificially smeared
during averaging.
Figures 22 and 23 show a comparison of the mean (
µ
)
and limiting (
µ±σ
) vorticity levels extracted from the
baseline vortex and the various excitation cases, respec-
tively. Actuation leads to a significant reduction of the Tip
peak (as seen previously) and a small reduction in the Mid-
dle peak. The rest of the core appears to be unaffected.
To summarize this section, winglet oscillations lead
to spatial sinusoidal perturbation of the elliptical vortex
Fig. 20 Variation in a position,
and b magnitude of the Tip
vorticity peak at various input
excitation levels
Fig. 21 Comparison of the mean vorticity levels with (indirect) and
without (direct) accounting for errors caused by the winglet move-
ment
Exp Fluids (2017) 58:8
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Page 13 of 18 8
Fig. 22 Comparison of the
mean peak vorticity contours
across the core of the vortex for
a stationary and an oscillating
winglet at different levels of
excitation; a 0.5 kV, b 1.0 kV, c
1.5 kV, and d 2.0 kV
Fig. 23 Comparison of limit-
ing values of peak vorticity
contours across the core of the
vortex of a stationary and an
oscillating winglet at different
levels of excitation; a 0.5 kV, b
1.0 kV, c 1.5 kV, and d 2.0 kV
Exp Fluids (2017) 58:8
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8 Page 14 of 18
along its minor axis. The amplitude of this axial perturba-
tion is maximum at the tip and minimum at the root, at
all excitation levels. The approximate wavelength of this
perturbation wave is obtained by dividing the freestream
velocity with the winglet oscillation frequency, which
equates to 35
Ct
. A significant perturbation of the core is
produced at higher excitation levels. The maximum attain-
able amplitude at the Tip peak (along the minor axis), is
approximately 8% of the length of the core (along the
major axis; Tip peak-Root peak). Actuation leads to a sig-
nificant reduction in the peak vorticity values and a minor
reduction in the net circulation. At the highest excitation
level, the reduction in peak vorticity level and total cir-
culation are nearly 10 and 2%, respectively. The follow-
ing sections discuss the properties of the baseline and the
oscillating vortex as it moves further downstream. Only
the effects of the highest excitation level are discussed for
the remaining planes.
3.3.1 Vortex core structure at various downstream
measurement locations
A system of two co-rotating vortices having unequal cir-
culation rotates about the center of their vorticity distribu-
tion due to mutual induction, as shown in Fig. 24a. Such
a system of rotating vortices moving downstream devel-
ops a double helix trajectory (Meunier and Leweke 2001).
The trajectory of the stretched vortex core observed in this
study is extracted by tracking the mean position of the three
primary vorticity peaks (Tip, Middle and Root) at different
downstream planes, as shown in Fig. 24b. The dotted lines
show the trajectory of the individual peaks and the gray
connecting lines show the axis of the vortex at any given
plane. The stretched vortex core also seems to rotate about
its vorticity center, leading to a helical trajectory of the
individual peaks and the core as a whole. It is to be noted
that the center of rotation of the fluid in the plane rotating
with the vortex is located at the Root of the core, while the
core itself rotates about its center of vorticity.
The length (L) of this rotating core is defined as the
intermediate distance between the Tip and the Root peak in
the
xy
plane. Its orientation (
θ
) is defined as the angle
that the line joining the two peaks makes with the y-axis,
Fig. 25a. The mean length and its horizontal and vertical
components (
Lx
and
Ly
) at different downstream planes
are plotted in Fig. 25b. The data points at
z/Ct=1
, cor-
respond to the physical length of the winglet trailing edge.
As the vortex moves downstream, the vorticity peaks inside
the core start to diffuse and move closer to each other.
This is very similar to a vortex merging process (Fig. 27),
which explains the gradual decrease in the overall length
of the core. The horizontal component (
Lx
) closely follow
the trend of the total length. The vertical component (
Ly
)
gradually decreases to zero at
z/Ct=10.3
, where the core
becomes horizontal (
θ
= 90 °C) and then increases with
further increment in
θ
. Figure 25c, shows the mean orienta-
tion of the core at different downstream planes. The data
point at
z/Ct=1
is 75°, which is the dihedral orientation
of the winglet itself. The angle made by the core increases
almost linearly with downstream distance traversed. The
linear angular velocity of the core calculated from this data
is approximately 40 rad/s.
Winglet oscillates like a cantilever and results in the
oscillation of the vortex core. The amplitude of these core
oscillations are maximum at the tip; hence, the effect of
actuation on the geometry of the core can be quantified by
tracking the movement of the Tip peak. Figure 26 shows
the mean (
µ
) and standard deviation (
σ
) of the Tip posi-
tion along y-axis, with and without actuation, at different
downstream planes. The mean position with actuation is
the same as baseline, implying parameters like mean length
and mean orientation of the core remain unaffected. If
the vortex helix is imagined as a surface, actuation leads
to perturbation waves on this surface. The variation in the
Fig. 24 a In-plane rotation
of two co-rotating vortices of
unequal circulation about the
vorticity centroid, and b the
location of the three core vorti-
city peaks at different down-
stream planes
Exp Fluids (2017) 58:8
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Page 15 of 18 8
amplitude of this perturbation wave with downstream dis-
tance is shown in Fig. 26b.
As discussed in the previous section, although the wave-
length of the perturbation wave is 35
Ct
, the interrogation
window extends only till 19.6
Ct
or 56% of the wavelength.
Because the standard deviation in Tip position with actua-
tion remains almost constant, it can be stated that the ampli-
tude of perturbation remains constant at least until 56% of
its wavelength. A gradual increase in the standard devia-
tion for the baseline vortex is observed. This is attributed
to unsteadiness in position caused by freestream turbulence
(vortex wandering), which has been shown to grow with
downstream distance traversed (Devenport et al. 1997). An
interesting observation is that the increasing effect of natu-
ral wandering does not affect the actuated vortex. This may
indicate that when a large amplitude (controlled) forced
perturbation is introduced at the vortex onset, it is free of
small-scale perturbations (uncontrolled) introduced by
freestream turbulence.
3.3.2 Vorticity at different downstream locations
In this final section, the gradual dissipation process of the
vortex is discussed. The non-dimensionalized mean vor-
ticity distribution inside the core of the baseline vortex at
six downstream planes is shown as surface plots in Fig. 27.
Two primary observations are made. First, the Tip and the
Root peaks become progressively smaller and broader,
whereas the weaker Middle peak almost disappears by
the time it reaches the last plane. This is primarily due to
Fig. 25 a Schematic shows the
mean length and orientation of
the core and their variation with
downstream distance is shown
in b, c, respectively
Fig. 26 a Mean, and b standard
deviation in the position of the
Tip vorticity peak, with and
without actuation
Exp Fluids (2017) 58:8
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8 Page 16 of 18
the gradual diffusion of the core and partially due to the
increased effects of wandering. It is also observed that the
vorticity in the middle region, which is initially oriented
along a straight line joining the Tip and the Root peaks,
gets gradually re-oriented along a diagonal between the
two peaks (shown by gray dotted line in Fig. 27e). This is
probably caused by the straining effect of the two neigh-
boring peaks due to the nature of their rotation (shown by
gray arrows) and the vortex (peaks) merging process. The
streamlines associated with the vortex, at three planes are
shown in Fig. 28. At the first downstream plane, the stream-
lines are highly eccentric due to the presence of a strong
Tip peak and the vorticity in the middle. As this middle
vorticity hump disappears and the peaks start to move
closer, the eccentricity of the streamlines also starts to
reduce. Coherent circular streamlines are observed around
the broader Root peak at
z/Ct=19.6
. Hence, as a result
of gradual diffusion and merging of the vorticity peaks,
the near-field elliptical vortex developing from the winglet
appears to gradually morph into a circular vortex.
The effect of actuation on the vorticity levels at vari-
ous downstream locations is shown in Fig. 29. These plots
compare the mean peak vorticity levels of the baseline
and the actuated vortex obtained by the indirect method
Fig. 27 Mean vorticity distribution of the baseline vortex at various downstream measurement planes; a
z/Ct
= 4.1, b
z/Ct
=
7.2
, c
z/Ct
=
10.3
, d
z/Ct
=
13.4
, e
z/Ct
=
16.5
, and f
z/Ct
=
19.6
Fig. 28 Streamlines associated with the vortex at selected downstream planes. a
z/Ct
=
4.1
, b
z/Ct
=
13.4
, and c
z/Ct
=
19.6
Exp Fluids (2017) 58:8
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discussed previously (Fig. 21). Actuation essentially leads
to a reduction in peak vorticity levels. A 10% reduction
in the magnitude of the Tip peak is observed at all down-
stream planes. Minor reductions in the Root and the Middle
peaks are also observed from
z/Ct
= 10.3 onwards. Based
on these results, the vortex diffusion process appears to be
faster with winglet actuation, which in turn, will reduce the
wake hazard.
4 Conclusions
The aim of this experimental study was to develop a wing-
let that can be actively oscillated to introduce perturbations
in a wingtip vortex. Such an active device can be used to
excite instabilities in the wake of an aircraft, leading to
accelerated decay. The piezoelectric MFC-based winglet
actuator was attached to the tip of a transport wing model
and tested at low subsonic speeds. Investigations consisted
of characterization of the actuated winglet, particularly its
resonance modes, followed by detailed flow field measure-
ments using stereo particle image velocimetry (SPIV).
Structural characterization revealed bimodal resonance
behavior of the winglet oscillations upon actuation. The
two resonance modes were 13 and 35 Hz, with the lat-
ter being the dominant mode. The un-actuated winglet
exhibited negligibly small structural vibrations at its natural
frequency. Upon actuation, the winglet oscillated smoothly
with a linear increase in the amplitude of oscillation with
the magnitude of input excitation. The amplitude of oscil-
lation measured at the winglet tip at the highest excitation
level is nearly 4 times the airfoil thickness or 0.6 times the
chord length at the tip.
The vortex developing from the winglet was found to
be elliptical in the near-field with a core that elongated
along the axis of the winglet. The core has non-uniform
vorticity distribution with three prominent vorticity peaks
located at the tip, middle and root of the core, respectively.
The highest vorticity values occur at the tip and the high-
est concentrations occur at the root, making it the center of
fluidic rotation. The core itself rotates about its center of
vorticity due to mutual induction, resulting in a helical tra-
jectory as it travels downstream. Winglet actuation leads to
oscillations of the vortex core and a reduction in the peak
vorticity levels. The baseline vortex is found to have a cer-
tain level of unsteadiness due to its natural wandering. The
unsteadiness introduced by actuation is of comparable level
to the wandering at low excitation levels and significantly
larger at high excitation levels. The maximum ampli-
tude of transverse oscillations at the tip is approximately
8% of the length of the core, at a downstream location of
four tip-chord lengths from the winglet trailing edge. This
Fig. 29 Mean peak vorticity contours of baseline with actuation at different downstream planes; a
z/Ct
= 4.1, b
z/Ct
= 7.2, c
z/Ct
= 10.3, d
z/Ct
= 13.4, e
z/Ct
= 16.5, and f
z/Ct
= 19.6
Exp Fluids (2017) 58:8
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amplitude of perturbation is found to remain constant over
the region investigated, up to 20 tip-chord lengths. It is
found that actuation leads to a 10% reduction in the mean
peak vorticity levels at all downstream locations and a 2%
reduction in the mean total circulation. Therefore, winglet
oscillations lead to sustainable perturbation of the vortex
core that result in a diffused vortex of a reduced strength.
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... Such applications involve reduction of aerodynamic noise, increase of operational envelope and, more relevant to the application in hand, change of vortex wandering characteristics. For example, past work in vortices produced by a wingtip [32,24] indicates that actuating the wingtip vortex in its instability modes can cause it to diffuse more quickly, which in part can be associated to increased wandering of the vortex core. This is evidently beneficial when the goal of the actuation is to reduce the effect of the downwash produced by a vortex pair downstream of an airplane. ...
Thesis
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Experimental studies on the flow over an aligned cylinder with a slanted afterbody were conducted in this work for several Reynolds numbers and slant angles. Two different flow topologies, formerly only conjectured in the literature, were observed and thoroughly documented as a function of both slant angle and Reynolds number. The flow topology studies conducted herein with three-dimensional flow reconstruction through Stacked Stereoscopic Particle Image Velocimetry (S-SPIV) allowed for a comprehensive examination of the flow structures that comprise the flow fields in both regimes. The 3D flow fields obtained in the experiments are published as open-access data sets and can serve as a benchmark for validation of computational studies. Most of the focus in this work is geared towards the characterization of the ``Vortex Regime'', which displays the formation of a horseshoe vortex in the near wake and whose understanding immediately applies to military cargo aircraft fuselage shapes. The dynamical behavior of these vortices is analyzed with Time-Resolved Particle Image Velocimetry and the flow appears to have fundamental frequencies with a potential relationship to the dynamics of the shear layer produced at the sides of the cylinder and the vortex pair. Finally, an innovative, optimization-based approach is proposed to find the most effective pattern of actuators for active flow control of this wake through microjet disturbances, with very encouraging results that outperform a well-informed researcher and can provide not only engineering answers, but further physical insight on other complex flows.
... Under optimal conditions, turbulent fluctuations emerge in the core of the vortex, and they promote diffusion of the wingtip vortex. Guha and Kumar (2017) used a vibrating winglet to affect the initial development stage of the wing-tip vortex. Their work indicated that the winglet vibration induces a periodic meandering, and the distributions of the time-averaged statistics are elongated and diffused. ...
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External forcing on a wing-tip vortex can affect its instability, and therefore an optimal perturbation can improve the aerodynamic performance of the wing. The present study examined the unsteadiness of the wing-tip vortex under periodic wing-tip vibration, and revealed its effect on the aerodynamic performance of the wing. A 3D-printed vibrating wing-tip model was prepared, which was driven by a sheet-type piezo actuator. Phase-averaged stereo particle image velocimetry (PIV) measurements clarified that the averaged position of the vortex depends on the phase of the wing-tip vibration, and the vortex shifted further from the wing as the actuation frequency increased. The phase-averaged velocity distributions indicate that the velocity deficit inside the vortex is significantly enhanced near the end of the downstroke of the wing-tip motion. The wing-tip vortex is weakened in the mid-upstroke, and its impact depends on the actuation frequency. This is because the motion of the wing is in the same direction as the flow rolling up from the pressure side, which prevents the formation of the vortex. In the mid-upstroke phase, the turbulence quantities, e.g., the turbulent kinetic energy and the Reynolds shear stress, are significantly suppressed; these effects depend monotonically on the actuation frequency. These arguments are supported by time-resolved recordings of the flow and the wing motion. The force measurements reveal that the vibration of the wing-tip brings a positive effect on the lift-to-drag ratio.
... Recently, there has been considerable interest in active flow control because it can be adapted to changing flow conditions as it is the case for typical flight envelopes. Active flow control seems to provide an effective control authority over trailing vortices which generally involves blowing and/or suction in the vicinity of the wing tip [5][6][7][8][9] and the use of articulated surfaces such as oscillating flaps, spoilers and winglets [10][11][12][13]. The former includes expelling a mass of fluid from various locations in the vicinity of the wing tip, which is usually provided by an engine bleed that may result in a reduction of the engine efficiency. ...
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The development of a wing tip vortex under the effect of synthetic jet (SJ) actuation was examined for a rectangular, square-tipped wing having a NACA 0012 airfoil using hotwire anemometry at a chord Reynolds number Rec=8×10⁴. Three control configurations were considered for a comparative study, namely case C1 with momentum coefficient Cμ=0.004 and an actuation frequency F⁺=0.96, case C2 with Cμ=0.04 and F⁺=0.96 and case C3 with Cμ=0.04 and F⁺=0.29. Under case C3, the vortex was stretched into an ellipsoid shape with a nearly 60% decrease in the peak circumferential velocity and the core axial vorticity. The vortex core radius largely broadened suggesting that the lower frequency control configuration allowed the synthetic jet to travel larger distances into the vortex bringing turbulent structures within its core. This resulted in an increased mixing and subsequently a more diffuse vortex. Measurements of the vortex development in the near and mid-wake regions (up to x/c=5) showed that the circumferential velocity was largely reduced under the effect of the SJ actuation. The enhanced turbulent mixing at the inner region of the vortex resulted in an accelerated outward diffusion of its core even under non-optimal control configurations.
... Since their introduction in 1975 by National Aeronautics and Space Agency (NASA) engineer Richard Whitcomb [1,2], winglets have undergone major geometrical changes, driven by the quest for a sustainable efficiency throughout the entire flight envelope of modern airliners. Due to the largely different flow field nature at the wing tip area at different flight conditions, and the challenge of achieving a winglet shape optimal throughout the whole flight envelope, recent winglet geometry optimization studies in the last decade were mostly focused on cruise as a 'design case' for this wingtip device, resulting in trade-off solutions less optimal for take-off and climb at high angles of attack [3][4][5][6][7][8][9][10]. Few innovative solutions have been suggested including morphing winglets which adapt their cant and/or twist depending on the flow regime [11][12][13], or using an integrated moving device such as a winglet-integrated rudder [14,15] or a gust alleviating conventional aileron [16], as well as active vortex wake control with an oscillating mechanism [14,17,18]. Bio-inspired devices were studied of non-planar wings through a configuration-invariant analytic formulation of the unknown circulation distribution. ...
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In this article, the growth of aerodynamic efficiency and the growth of the wing structural stress is studied for DLR-F4 typical transport aircraft wing-body, after installing classical Whitcomb winglets of different configurations and a delta wingtip fence. A new-concept curved-span winglet was mathematically developed and approved through Computational Fluid Dynamics (CFD) and static structural experiments, revealing the interaction of sub- and transonic air flow dynamics with the wingtip device geometry. The design space of the winglet geometry was explored briefly, and an evaluation of the lift-to-drag ratio increment depending on various winglet input parameters was performed. In particular, the winglet cant angle effect on lift and drag was thoroughly analyzed at various flow regimes and angles of attack, revealing an ambiguity and a conflicting character of results between highly canted winglets and nearly vertical ones. As a result of cant angle impact analysis, a curved winglet concept is suggested and mathematically parametrized, that could provide an innovative solution, alternative to a morphing winglet, but much simpler with a fixed structure. In conclusion, a multidisciplinary winglet efficiency estimation criterion is suggested for comparing the aerodynamic efficiency of different wingtip devices with respect to their structural weight penalty in real flight conditions.
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View Video Presentation: https://doi.org/10.2514/6.2022-3390.vid Towing tank experiments are conducted to investigate the effect of the wing span-wise load profile on the structure and strength of trailing vortices. In the framework of the lifting line theory, the local circulation Γy (with y the span-wise coordinate) depends on the local chord, effective incidence and lift coefficient. For a commercial aircraft, the wing geometry varies depending on the phase of flight (eg. deployment of high-lift devices for take-off/landing) which modifies Γy. Theoretical models found in the literature allow to relate the configurations of trailing vortices about this span-load. However, few experimental validation exists for complex cases. The question of how a given span load influences the vortex wake structure and its dynamics is of high interest. Furthermore this question also relates to that of the wake control strategies. In this work, we investigate the wake dynamics resulting from two different span-loads to answer these questions. The baseline case is a NACA 4412 rectangular wing with no twist. A second model creates a load variation about this reference by twisting a specific inboard section. On top of the main external tip vortices, this introduces additional vortices downstream. SPIV measurements in sections of the wake generated by the towed wings are made to asses the vortex characteristics such as radius, circulation, swirl number and trajectory in each configuration. The development of the vortex wake is investigated from the roll-up stage up to 170 spans downstream at a chord based Reynolds number of Re= 10^5. In both wing configurations, the towing velocity U0 and angle of attack a are modified to produce the same total lift as the baseline case and compare the distribution of downstream vorticity. In the case of the high-lift wing, the ratio of circulation between the flap and wingtip vortices is studied. Results show that at high a axial flow deficit grows. The swirl number decreases as a consequence but stagnates towards the value of 1.5 which is a threshold for instability onset. Under similar total loading conditions, vortices trailing behind the high-lift wing have a higher circulation, core size, and axial velocity than those of the untwisted wing.
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The present study primarily focuses on the design, development, and structural characterization of an oscillating winglet actuated using a piezoelectric macrofiber composite (MFC). The primary objective is to study the effect of controlled wingtip oscillations on the evolution of wingtip vortices, with a goal of weakening these potentially harmful tip vortices by introducing controlled instabilities through both spatial and temporal perturbations producible through winglet oscillations. MFC-actuated winglets have been characterized under different input excitation and pressure-loading conditions. The winglet oscillations show bimodal behavior for both structural and actuation modes of resonance. The oscillatory amplitude at these actuation modes increases linearly with the magnitude of excitation. During wind-tunnel tests, fluid-structure interactions led to structural vibrations of the wing. The effect of these vibrations on the overall winglet oscillations decreased when the strength of actuation increased. At high input excitation, the actuated winglet was capable of generating controlled oscillations. As a proof of concept, the current study has demonstrated that microfiber composite-actuated winglets produce sufficient displacements to alter the development of the wingtip vortex.
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Although theoretical tools for the design of winglets for high-performance sailplanes were initially of limited value, simple methods were used to design winglets that gradually became accepted as benefiting overall sailplane performance. As understanding was gained, improved methods for winglet design were developed. The current approach incorporates a detailed component drag buildup that interpolates airfoil drag and moment data across operational lift coefficient, Reynolds number, and flap-deflection ranges. Induced drag is initially predicted using a relatively fast multiple lifting-line method. In the final stages of the design process, a full panel method, including relaxed-wake modeling, is employed. The drag predictions are used to compute speed polars for both level and turning flight. The predicted performance is in good agreement with flight-test results. The straight- and turning-flight speed polars are then used to obtain average cross-country speeds because they depend on thermal strength, size, and shape, which are used to design the winglets that provide the greatest gain in overall performance. Flight-test measurements and competition results have demonstrated that the. design methods produce winglets that provide an important performance advantage over much of the operating range. for both span-limited and span-unlimited high-performance sailplanes.
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