REVIEW OF SCIENTIFIC INSTRUMENTS 80, 054902 共2009兲
Quantification of unsteady heat transfer and phase changing process
inside small icing water droplets
Zheyan Jin and Hui Hua兲
Department of Aerospace Engineering, Iowa State University, Ames, Iowa 50011, USA
共Received 13 April 2009; accepted 28 April 2009; published online 21 May 2009兲
We report progress made in our recent effort to develop and implement a novel, lifetime-based
molecular tagging thermometry 共MTT兲 technique to quantify unsteady heat transfer and phase
changing process inside small icing water droplets pertinent to wind turbine icing phenomena. The
lifetime-based MTT technique was used to achieve temporally and spatially resolved temperature
distribution measurements within small, convectively cooled water droplets to quantify unsteady
heat transfer within the small water droplets in the course of convective cooling process. The
transient behavior of phase changing process within small icing water droplets was also revealed
clearly by using the MTT technique. Such measurements are highly desirable to elucidate
underlying physics to improve our understanding about important microphysical phenomena
pertinent to ice formation and accreting process as water droplets impinging onto wind turbine
blades. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3139005兴
I. INTRODUCTION
Wind energy is one of the cleanest renewable power
sources in the world today. US Department of Energy has
challenged the nation to produce 20% of its total power from
wind by 2030. It has been found that the majority of wind
energy potential available in US is in the northern states such
as North Dakota, Kansas, South Dakota, Montana, Nebraska,
Wyoming, Minnesota, and Iowa, where wind turbines are
subjected to the problems caused by cold climate conditions.
Wind turbine icing represents the most significant threat to
the integrity of wind turbines in cold weather. It has been
found that wind turbine icing would cause a variety of problems to the safe and efficient operations of wind turbines. Ice
accretion on turbine blades was found to reduce the aerodynamic efficiency of wind turbines considerably, which results
in wind turbine power production reduction. It has also been
found that the operation of a wind turbine with an imbalance
caused by ice accretion would experience an increase in the
loads imposed on all turbine components, which would
shorten the lifetime for wind turbine components. Uncontrolled shedding of large ice chunks from turbine blades was
also found to be of special danger to service personnel as
well as nearby residents, particularly when the wind power
plant site borders public roads, housing, power lines, and
shipping routes. In addition, icing was found to affect tower
structures by increasing stresses, due to increased loads from
ice accretion. This would lead to structural failures, especially when coupled to strong wind loads. Ice accretion was
also found to affect the reliability of anemometers, thereby,
leading to inaccurate wind speed measurements and resulting
in resource estimation errors.
Advancing the technology for safe and efficient wind
Author to whom correspondence should be addressed. Tel.: ⫹1-515-2940094; FAX: 1-515-294-3262. Electronic mail: huhui@iastate.edu.
a兲
0034-6748/2009/80共5兲/054902/5/$25.00
turbine operation in atmospheric icing conditions requires a
better understanding of the important microphysical processes pertinent to wind turbine icing phenomena. In order to
elucidate underlying physics, advanced experimental techniques capable of providing accurate measurements to quantify important ice formation and accreting process, such as
the unsteady heat transfer and phase changing processes inside small icing water droplets, are highly desirable. In the
present study, we report progress made in our recent effort to
develop and implement a novel, lifetime-based molecular
tagging thermometry 共MTT兲 technique to quantify the unsteady heat transfer and phase changing process within small
icing water droplets in order to improve our understanding
about the underlying physics pertinent to wind turbine icing
phenomena for the development of effective and robust anti-/
deicing strategies tailored for wind turbine icing mitigation.
Lifetime-based MTT technique used in the present study
can be considered as an extension of the molecular tagging
velocimetry and thermometry 共MTV and T兲 technique developed by Hu and Koochesfahani.1 In the sections that follow,
the technical basis of the lifetime-based MTT will be described briefly along with the related properties of the phosphorescent tracer used for the MTT measurements. The application of the lifetime-based MTT technique to quantify the
unsteady heat transfer and phase changing process will be
given to elucidate underlying physics to improve our understanding about important microphysical phenomena pertinent
to ice formation and accreting process as water droplets impinging on wind turbine blades.
II. LIFETIME-BASED MTT TECHNIQUE
It is well known that both fluorescence and phosphorescence are molecular photoluminescence phenomena. Compared with fluorescence, which typically has a lifetime on the
of order nanoseconds, phosphorescence can last as long as
80, 054902-1
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054902-2
Rev. Sci. Instrum. 80, 054902 共2009兲
Z. Jin and H. Hu
microseconds, even minutes. Since emission intensity is a
function of the temperature for some substances, both fluorescence and phosphorescence of tracer molecules may be
used for temperature measurements. Laser-induced fluorescence 共LIF兲 techniques have been widely used for temperature measurements of liquid droplets for combustion
applications.2,3 Laser-induced phosphorescence 共LIP兲 techniques have also been suggested recently to conduct temperature measurements of “in-flight” or levitated liquid
droplets.4,5 Compared with LIF techniques, the relatively
long lifetime of LIP could be used to prevent interference
from scattered/reflected light and any fluorescence from
other substances 共such as from solid surfaces兲 that are
present in the measurement area, by simply putting a small
time delay between the laser excitation pulse and the starting
time for phosphorescence image acquisitions. Furthermore,
LIP was found to be much more sensitive to temperature
variation compared with LIF,2–6 which is favorable for the
accurate measurements of small temperature differences
within small liquid droplets. The lifetime-based MTT technique used in the present study is a LIP-based technique.
According to quantum theory,7 the intensity of a firstorder photoluminescence process 共either fluorescence or
phosphorescence兲 decays exponentially. As described in Ref.
1, for a diluted solution and unsaturated laser excitation, the
collected phosphorescence signal 共S兲 by using a gated imaging detector with integration starting at a delay time to after
the laser pulse and a gate period of ␦t can be given by
S = AIiC␧⌽ p共1 − e−␦t/␶兲e−to/␶ ,
共1兲
where A is a parameter representing the detection collection
efficiency, Ii is the local incident laser intensity, C is the
concentration of the phosphorescent dye 共the tagged molecular tracer兲, ␧ is the absorption coefficient, and ⌽ p is the phosphorescence quantum efficiency. The emission lifetime ␶ refers to the time at which the intensity drops to 37% 共i.e., 1 / e兲
of the initial intensity.
For an excited state, the deactivation process may involve both radiative and nonradiative pathways. The lifetime
of the photoluminescence process ␶ is determined by the sum
of all the deactivation rates ␶−1 = kr + knr, where kr and knr are
the radiative and nonradiative rate constants, respectively.
According to photoluminescence kinetics,7 these rate constants are, in general, temperature-dependent. The temperature dependence of the phosphorescence lifetime is the basis
of the present lifetime-based MTT technique.
It should be noted that the absorption coefficient ␧ and
quantum yield ⌽ p are also temperature-dependent in general,
in addition to phosphorescence lifetime ␶, resulting in a
temperature-dependent phosphorescence signal 共S兲. Thus, in
principle, the collected phosphorescence signal 共S兲 may be
used to measure fluid temperature if the incident laser intensity and the concentration of the phosphorescent dye remain
constant 共or are known兲 in the region of interest. It should be
noted that the collected phosphorescence signal 共S兲 is also
the function of incident laser intensity 共Ii兲 and the concentration of the phosphorescent dye 共C兲. Therefore, the spatial
and temporal variations in the incident laser intensity and the
nonuniformity of the phosphorescent dye 共e.g., due to pho-
FIG. 1. 共Color online兲 Timing chart of lifetime-based MTT technique.
tobleaching兲 in the region of interest would have to be corrected separately in order to derive quantitative temperature
data from the acquired phosphorescence images. In practice,
however, it is very difficult, if not impossible, to ensure a
nonvarying incident laser intensity distribution, especially
for unsteady thermal phenomena with a varying index of
refraction. This may cause significant error in the temperature measurements. To overcome this problem, a lifetimebased thermometry8 was developed to eliminate the effects
of incident laser intensity and concentration of phosphorescent dye on temperature measurements.
The lifetime-based thermometry works as follows: as illustrated in Fig. 1, LIP emission is interrogated at two successive times after the same laser excitation pulse. The first
image is detected at the time t = to after laser excitation for a
gate period ␦t to accumulate the phosphorescence intensity
S1, while the second image is detected at the time t = to + ⌬t
for the same gate period to accumulate the phosphorescence
intensity S2. It is easily shown,1,8 using Eq. 共1兲, that the ratio
of these two phosphorescence signals 共R兲 is given by
R = S2/S1 = e−⌬t/␶ .
共2兲
In other words, the intensity ratio of the two successive
phosphorescence images 共R兲 is only a function of the phosphorescence lifetime ␶, and the time delay ⌬t between the
image pair, which is a controllable parameter. This ratiometric approach eliminates the effects of any temporal and spatial variations in the incident laser intensity and nonuniformity of the dye concentration 共e.g., due to bleaching兲. For a
given molecular tracer and fixed ⌬t value, Eq. 共2兲 defines a
unique relation between phosphorescence intensity ratio 共R兲
and fluid temperature T, which can be used for thermometry.
The phosphorescent molecular tracer used for the
present study is phosphorescent triplex 共1-BrNp· M␤
-CD· ROH兲. The phosphorescent triplex 共1-BrNp· M␤
-CD· ROH兲 is actually the mixture compound of three
different chemicals, which are lumophore 共indicated collectively by 1-BrNp兲, maltosyl-␤-cyclodextrin 共indicated collectively by M␤-CD兲 and alcohols 共indicated collectively
by ROH兲. Further information about the chemical and photoluminescence properties of the phosphorescent triplex
共1-BrNp· M␤-CD· ROH兲 is available in Refs. 9 and 10.
Upon the pulsed excitation of a UV laser 关quadrupled
wavelength of neodymium-doped yttrium aluminum garnet
共Nd:YAG兲 laser at 266 nm for the present study兴, the
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054902-3
Z. Jin and H. Hu
FIG. 2. 共Color online兲 Phosphorescence lifetime vs temperature.
phosphorescence lifetime of the phosphorescent triplex
共1-BrNp· M␤-CD· ROH兲 molecules in an aqueous solution
change significantly with temperature. Figure 2 shows the
measured phosphorescence lifetimes of 1-BrNp· M␤
-CD· ROH molecules as a function of temperature. It can
be seen clearly that phosphorescence lifetime of
1-BrNp· M␤-CD· ROH molecules varies significantly with
increasing temperature, decreasing from about 7.2 to 2.5 ms
as the temperature changes from 1.0 to 30.0 ° C. The relative
temperature sensitivity of the phosphorescence lifetime is
about 3.5% per ° C, which is much higher than those of fluorescent dyes.3,5,6 For comparison, the temperature sensitivity
of rhodamine B for LIF measurements is less than
2.0% per ° C.6 It is noted that, since low concentration of the
phosphorescent triplex 1-BrNp· M␤-CD· ROH 共on the order
of 10−4M兲 was used for the present study, the effects of the
molecular tracers on the physical properties of water were
believed to be negligible. During the experiments, the energy
level of the pulse laser used to tag the molecular tracers
within small water droplets was below 1.0 mJ/pulse. The
repetition rate of the pulsed excitation was 2 Hz. The energy
deposited by the excitation laser into the small water droplet
was believed to be very small.
III. EXPERIMENTAL SETUP
Figure 3 shows the schematic of the experimental setup
used to implement the lifetime-based MTT technique to
FIG. 3. 共Color online兲 Experimental setup.
Rev. Sci. Instrum. 80, 054902 共2009兲
quantify unsteady heat transfer and phase changing processes
within small icing water droplets. A syringe was used to
generate microsized water droplets 共about 400 ␮m in radius
and 250 ␮m in height兲 to impinge on a test plate to simulate
the processes of small water droplets impinging onto a wind
turbine blade. The temperature of the test plate, which was
monitored by using a thermocouple, was kept constant at a
preselected low temperature level by using a water bath circulator 共Neslab RTE-211兲. The small water droplets with initial temperature of 20.5 ° C 共room temperature兲 would be
convectively cooled after they impinged onto the cold test
plate. Phase changing process would occur inside the small
water droplets when the temperature of the test plate was
below frozen. A laser sheet 共⬃200 ␮m in thickness兲 from a
pulsed Nd:YAG at a quadrupled wavelength of 266 nm was
used to tag the premixed 1-BrNp· M␤-CD· ROH molecules
along the middle plane of the small water droplets. A 12 bit
gated intensified charge-coupled device camera 共PCO
DiCam-Pro, Cooke Corporation兲 with a fast decay phosphor
共P46兲 was used to capture the phosphorescence emission. A
10⫻ microscopic objective 共Mitsutoyo infinity-corrected,
numerical aperture= 0.28, depth of field= 3.5 ␮m兲 was
mounted in the front of the camera. The camera was operated
in the dual-frame mode, where two full frame images of
phosphorescence were acquired in a quick succession after
the same laser excitation pulse. The camera and the pulsed
Nd:YAG lasers were connected to a workstation via a digital
delay generator 共BNC 555 Digital Delay-Pulse Generator兲,
which controlled the timing of the laser illumination and the
image acquisition. Further details about the experimental
setup and procedures to implement the lifetime-based MTT
technique to quantify unsteady heat transfer and phase
changing processes within small icing water droplets are
available in Ref. 11.
IV. MEASUREMENT RESULTS
Figure 4 shows a typical pair of acquired phosphorescence images for MTT measurements and the instantaneous
temperature distribution inside the water droplet derived
from the phosphorescence image pair. The image pair was
taken at 5.0 s later after the water droplet 共initial temperature
20.5 ° C兲 impinged on the cold test plate 共Tw = 5.0 ° C兲. The
first image 关Fig. 4共a兲兴 was acquired at 0.5 ms after the laser
excitation pulse and the second image 关Fig. 4共b兲兴 at 3.5 ms
after the same laser pulse with the same exposure time of 1.5
ms for the two image acquisitions. Since the time delays
between the laser excitation pulse and the phosphorescence
image acquisitions can eliminate scattered/reflected light and
any fluorescence from other substances 共such as from solid
surface兲 in the measurement region effectively, the phosphorescence images of the water droplet are quite “clean” even
though no optical filter was used for the phosphorescence
image acquisition.
As described above, Eq. 共2兲 can be used to calculate the
phosphorescence lifetime of the tagged molecules on a pixelby-pixel basis, which resulting in a distribution of the phosphorescence lifetime over a two-dimensional domain. With
the calibration profile of phosphorescence lifetime versus
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054902-4
Z. Jin and H. Hu
Rev. Sci. Instrum. 80, 054902 共2009兲
FIG. 6. The evolution of the phase changing process within a small icing
water droplet.
FIG. 4. 共Color online兲 A typical MTT measurement. 共a兲 The first phosphorescence image, 共b兲 the second phosphorescence image, and 共c兲 the instantaneous temperature distribution derived from the image pair.
temperature, as shown in Fig. 2, a two-dimensional, instantaneous temperature distribution within the water droplet can
be derived from the phosphorescence image pair, which was
shown in Fig. 4共c兲. Based on a time sequence of the measured transient temperature distributions within the water
droplet as the one shown here, the unsteady heat transfer
process within the convectively cooled water droplets was
revealed quantitatively. Figure 5 shows the spatially averaged temperature of the water droplet as a function of the
time after it impinged on the cold test plate, which was cal-
FIG. 5. 共Color online兲 Spatially averaged temperature of the water droplet
vs time.
culated based on the time sequence of measured instantaneous temperature distributions. The characteristics of the
unsteady heat transfer within the water droplet in the course
of convectively cooling process were revealed quantitatively
from the evolution of the spatially averaged temperature of
the water droplet. Since initial temperature of the water droplet 共20.5 ° C兲 was significantly higher than that of the cold
test plate 共Tw = 5.0 ° C兲, the temperature of the water droplet
was found to decrease rapidly after it impinged on the test
plate. The measurement results given in Fig. 5 also revealed
that a thermal steady state would be reached at about 20 s
later after the water droplet impinged on the cold test plate.
The spatially averaged temperature of the water droplet
would not decrease anymore when the thermal steady state
was reached. It should be noted that, based on the uncertainty analysis of MTT measurements given in Ref. 1, the
measurement uncertainty for the temperature data given in
the present study was estimated to be within 0.5 ° C.
When the temperature of the test plate was adjusted to
below frozen temperature, water droplets on the test plate
was found to be frozen and turned to ice crystals. Figure 6
shows the time sequence of the acquired phosphorescence
images of a water droplet when it impinged onto the test
plate below frozen temperature 共Tw = −2.5 ° C兲 The transient
behavior of the phase changing process within the small icing water droplet was revealed clearly from the acquired
phosphorescence images. In the images, the “brighter” region in the upper portion of the droplet represents liquid
phase—water; while the “darker” region at the bottom indicates solid phase—ice. It can be seen clearly that the water
droplet was round, as a cap of a sphere at the beginning. As
the time goes by, the interface between the liquid phase water and solid phase ice was found to rise upward continuously, as it is expected. As a result, the droplet was found to
grow upward with more and more liquid phase water turning
into solid phase ice. Eventually, the spherical-cap-shaped
water droplet was found to turn into be a puddle-shaped ice
crystal.
The required frozen time, which is defined as the time
interval between the moment when a water droplet impinged
on the cold test plate and the moment when the water droplet
was turned into an ice crystal completely, can be determined
based on the time sequence of the acquired phosphoresce
images. Figure 7 shows the variations in the required frozen
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054902-5
Rev. Sci. Instrum. 80, 054902 共2009兲
Z. Jin and H. Hu
FIG. 7. 共Color online兲 The required frozen time vs the temperature of test
plate.
time of the water droplets with the surface temperature of the
test plate changed from ⫺1.0 to −5.0 ° C. As it is expected,
the required frozen time for the water droplets 共initial temperature at 20.5 ° C兲 turning into ice crystal was found to
strongly depend on the temperature of the test plate. The
required frozen time was found to decrease exponentially
with the decreasing surface temperature of the test plate.
Based on the measurement results, as those shown in
Figs. 4–7, important microphysical phenomena pertinent to
ice formation and accreting process as water droplets impinging on wind turbine blades were revealed quantitatively.
Such measurements are highly desirable to improve our understanding about the important microphysical processes pertinent to wind turbine icing phenomena in order to explore
effective and robust anti-/deicing strategies tailored for wind
turbine icing mitigation to ensure safer and more efficient
operation of wind turbines in cold weather.
V. CONCLUSION
A lifetime-based MTT technique was developed and
implemented to quantify unsteady heat transfer and phase
changing process inside small icing water droplets pertinent
to wind turbine icing phenomena. For MTT measurements, a
pulsed laser is used to “tag” phosphorescent molecules pre-
mixed within small water droplets. Long-lived laser-induced
phosphorescence is imaged at two successive times after the
same laser excitation pulse. The temperature measurement is
achieved by taking advantage of the temperature dependence
of phosphorescence lifetime, which is estimated from the
intensity ratio of the acquired phosphorescence image pair.
The lifetime-based MTT technique was used to achieve temporally and spatially resolved temperature distribution measurements within small, convectively cooled water droplets
to quantify unsteady heat transfer within the small water
droplets in the course of convective cooling process. Time
evolution of phase changing process within small icing water
droplets was also revealed clearly. Such measurements are
highly desirable to elucidate underlying physics to improve
our understanding about important microphysical processes
pertinent to wind turbine icing phenomena for safer and
more efficient operation of wind turbines in cold weather.
ACKNOWLEDGMENTS
The authors want to thank Dr. M. M. Koochesfahani of
Michigan State University for providing chemicals used for
the present study. The support of National Science Foundation CAREER program under Award No. CTS-0545918 is
gratefully acknowledged.
H. Hu and M. Koochesfahani, Meas. Sci. Technol. 17, 1269 共2006兲.
Q. Lu and A. Melton, AIAA J. 38, 95 共2000兲.
3
M. Wolff, A. Delconte, F. Schmidt, P. Gucher, and F. Lemoine, Meas. Sci.
Technol. 18, 697 共2007兲.
4
A. Omrane, G. Juhlin, F. Ossler, and M. Alden, Appl. Opt. 43, 3523
共2004兲.
5
A. Omrane, S. Santesson, M. Alden, and S. Nilsson, Lab Chip 4, 287
共2004兲.
6
H. Hu, C. Lum, and M. Koochesfahani, Exp. Fluids 40, 753 共2006兲.
7
P. Pringsheim, Fluorescence and Phosphorescence 共Interscience, New
York, 1949兲.
8
H. Hu and M. M. Koochesfahani, J. Visualization 6 共2兲, 143 共2003兲.
9
W. K. Hartmann, M. H. B. Gray, A. Ponce, and D. G. Nocera, Inorg.
Chim. Acta 243, 239 共1996兲.
10
M. M. Koochesfahani and D. G. Nocera, in Handbook of Experimental
Fluid Dynamics, edited by J. Foss, C. Tropea, and A. Yarin 共Springer,
Berlin, 2007兲, Chap. 5.4.
11
Z. Jin, “Experimental Investigations of Micro-Scale Thermal Flow Phenomena by Using Advanced Flow Diagnostic Techniques,” Ph.D. thesis,
Iowa State University, 2008.
1
2
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An Experimental Study of the
Laminar Flow Separation on a
Low-Reynolds-Number Airfoil
Hui Hu
Assistant Professor
e-mail: huhui@iastate.edu
Zifeng Yang
Graduate Student
Department of Aerospace Engineering,
Iowa State University,
Ames, IA 50011
1
An experimental study was conducted to characterize the transient behavior of laminar
flow separation on a NASA low-speed GA (W)-1 airfoil at the chord Reynolds number of
70,000. In addition to measuring the surface pressure distribution around the airfoil, a
high-resolution particle image velocimetry (PIV) system was used to make detailed flow
field measurements to quantify the evolution of unsteady flow structures around the airfoil
at various angles of attack (AOAs). The surface pressure and PIV measurements clearly
revealed that the laminar boundary layer would separate from the airfoil surface, as the
adverse pressure gradient over the airfoil upper surface became severe at AOAⱖ 8.0 deg.
The separated laminar boundary layer was found to rapidly transit to turbulence by
generating unsteady Kelvin–Helmholtz vortex structures. After turbulence transition, the
separated boundary layer was found to reattach to the airfoil surface as a turbulent
boundary layer when the adverse pressure gradient was adequate at AOA ⬍ 12.0 deg,
resulting in the formation of a laminar separation bubble on the airfoil. The turbulence
transition process of the separated laminar boundary layer was found to be accompanied
by a significant increase of Reynolds stress in the flow field. The reattached turbulent
boundary layer was much more energetic, thus more capable of advancing against an
adverse pressure gradient without flow separation, compared to the laminar boundary
layer upstream of the laminar separation bubble. The laminar separation bubble formed
on the airfoil upper surface was found to move upstream, approaching the airfoil leading
edge as the AOA increased. While the total length of the laminar separation bubble was
found to be almost unchanged (⬃20% of the airfoil chord length), the laminar portion of
the separation bubble was found to be slightly stretched, and the turbulent portion became slightly shorter with the increasing AOA. After the formation of the separation
bubble on the airfoil, the increase rate of the airfoil lift coefficient was found to considerably degrade, and the airfoil drag coefficient increased much faster with increasing
AOA. The separation bubble was found to burst suddenly, causing airfoil stall, when the
adverse pressure gradient became too significant at AOA ⬎ 12.0 deg.
关DOI: 10.1115/1.2907416兴
Introduction
Low-Reynolds-number airfoil aerodynamics is important for
both military and civilian applications. These applications include
propellers, sailplanes, ultralight man-carrying/man-powered aircraft, high-altitude vehicles, wind turbines, unmanned aerial vehicles 共UAVs兲, and microAir vehicles 共MAVs兲. Nondimensional
chord Reynolds number 共ReC兲 is defined as the cruise speed multiplied by the mean wing chord and divided by the kinematic
viscosity of air. For the applications listed above, the combination
of small length scale and low flight velocities results in flight
regimes with low wing-chord Reynolds number 共i.e., chord Reynolds numbers, ReC, ranging from 10,000 to 500,000兲.The aerodynamic design methods and principles developed over the past
40 years have produced efficient airfoils for conventional, largescale, high-speed aircraft whose chord Reynolds numbers are usually in the range of 106 – 109. It is well known that the aerodynamic performance of airfoils that are optimal for conventional,
large-scale and high-speed aircraft 共therefore, high chord Reynolds number兲 significantly degrades when used for lowReynolds-number applications where the chord Reynolds numbers
are several orders smaller. While conventional airfoil design principles usually either neglect viscous effects or restrict its influence
Contributed by the Fluids Engineering Division of ASME for publication in the
JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 7, 2007; final manuscript
received January 31, 2008; published online April 25, 2008. Assoc. Editor: Hamid
Johari.
Journal of Fluids Engineering
to a very thin region near the airfoil surface at high Reynolds
numbers, the predominance of viscous effects in low-Reynoldsnumber applications would result in boundary layers rapidly
growing and easily separating from the surfaces of airfoils.
It is well known that the boundary layers on low-Reynoldsnumber airfoils remain laminar at the onset of the pressure recovery unless artificially tripped. The behavior of the laminar boundary layers on low-Reynolds-number airfoils significantly affects
the aerodynamic performances of the airfoils. Since laminar
boundary layers are unable to withstand any significant adverse
pressure gradient, laminar flow separation is usually found on
low-Reynolds-number airfoils. Postseparation behavior of laminar
boundary layers accounts for the deterioration in the aerodynamic
performances of low-Reynolds-number airfoils. The deterioration
is exhibited by an increase in drag and decrease in lift. Extensive
reviews about aerodynamics of low-Reynolds-number airfoils and
the dependence of the laminar flow separation phenomena on the
chord Reynolds numbers can be found at Tani 关1兴, Carmichael 关2兴,
Lissaman 关3兴, Mueller 关4兴 and Gad-el-Hak 关5兴. It has been suggested that the separated laminar boundary layers would rapidly
transit to turbulence, and then reattach to the airfoil surface as a
turbulent boundary layer when the adverse pressure gradient over
the airfoil surface is adequate 关6兴. This would result in the formation of a laminar separation bubble, as schematically shown in
Fig. 1. As the adverse pressure gradient becomes more severe with
the increasing angle of attack, the separation bubble would suddenly burst, which will subsequently result in airfoil stall.
A good physical understanding is essential in order to control
Copyright © 2008 by ASME
MAY 2008, Vol. 130 / 051101-1
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Fig. 2 GA„W…-1 airfoil geometry and pressure tap locations
2
Fig. 1 Schematic of a laminar separation bubble formed on a
low-Reynolds-number airfoil
the laminar flow separations and suppress the burst of the laminar
separation bubbles for better aerodynamic performances of lowReynolds-number airfoils. This requires a detailed knowledge
about transient behavior of the separated laminar boundary layers
and the evolution of laminar separation bubbles. Although extensive experimental studies have been conducted to investigate
laminar flow separation, transition, and reattachment on lowReynolds-number airfoils, the majority of those previous studies
were carried out by using pointwise flow diagnostic techniques,
such as hot-wire anemometry 关7–10兴, hot-film anemometry
关11,12兴 and laser Doppler velocimetry 关13–15兴 to conduct flow
velocity measurements at limited points of interest. A common
shortcoming of such pointwise flow measurements is the incapability of providing spatial correlation of the unsteady flow structures to effectively reveal the transient behavior of the laminar
flow separation. The availability of temporally synchronized and
spatially resolved flow field measurements is highly desirable in
order to elucidate underlying physics to improve our understanding about the laminar boundary layer separation, transition, and
reattachment processes on low-Reynolds-number airfoils. Advanced flow diagnostic techniques, such as particle image velocimetry 共PIV兲, are capable of providing such information.
Surprisingly, only very few experimental studies were recently
conducted to provide temporally synchronized and spatially resolved flow field measurements to quantify the transient behavior
of the laminar boundary layers on low-Reynolds-number airfoils
关16–19兴. Very little in the literature can be found to correlate
detailed flow field measurements with the airfoil surface pressure
measurements to investigate laminar flow separation, transition,
and reattachment as well as the evolution of laminar separation
bubbles on low-Reynolds-number airfoils. In this study, we conducted a detailed experimental study to characterize the transient
behavior of laminar flow separation, transition, and reattachment
on a low-Reynolds-number airfoil at ReC = 70,000. In addition to
mapping the surface pressure distribution around the airfoil with
pressure sensors, a high-resolution PIV system was used to make
detailed flow field measurements to quantify the occurrence and
behavior of laminar boundary layer separation, transition, and reattachment on the low-Reynolds-number airfoil. The detailed flow
field measurements were correlated with the surface pressure measurements to elucidate the underlying physics associated with the
separation, transition, and reattachment processes of the laminar
boundary layer. To the best knowledge of the authors, this is the
first effort of its nature. The primary objective of the present study
is to gain further insight into the fundamental physics of laminar
flow separation, transition, and reattachment as well as the evolution of laminar separation bubble formed on low-Reynoldsnumber airfoils. In addition, the quantitative surface pressure and
flow field measurements will be used as the database for the validation of computational fluid dynamics 共CFD兲 simulations of such
complex flow phenomena for the optimum design of lowReynolds-number airfoils 关20兴.
051101-2 / Vol. 130, MAY 2008
Experimental Setup and the Studied Airfoil
The experiments were performed 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 ft2 共30⫻ 30 cm2兲 cross section and optically transparent
walls. The tunnel has a contraction section upstream of the test
section with honeycomb, screen structures, and cooling system
installed ahead of the contraction section to provide uniform low
turbulent incoming flow to enter the test section.
Figure 2 shows the schematic of the airfoil used in the present
study: a GA 共W兲-1 airfoil 共also labeled as NASA LS共1兲-0417兲.
The GA 共W兲-1 has a maximum thickness of 17% of the chord
length. Compared to standard NACA airfoils, the GA 共W兲-1 airfoil was especially designed for low-speed general aviation applications with a large leading-edge radius in order to flatten the peak
in pressure coefficient near the airfoil nose to discourage flow
separation 关21兴. The chord length of the airfoil model is 101 mm,
i.e., C = 101 mm, for the present study. The flow velocity at the
inlet of the test section was set as U⬁ = 10.7 m / s, which corresponds to a chord Reynolds number of Rec ⬇ 70,000.
The airfoil model is equipped with 43 pressure taps at its median span with the spanwise length of the airfoil being 1.0 ft. The
locations of the pressure taps are indicated in Fig. 2. The 43 pressure taps were connected by plastic tubing to 43 channels of a
pressure acquisition system 共Model DSA3217, Scanivalve Corp兲.
The DSA3217 digital sensor arrays incorporate temperature compensated piezoresistive pressure sensors with a pneumatic calibration valve, RAM, 16 bit A/D converter, and a microprocessor in a
compact self-contained module. The precision of the pressure acquisition system is ⫾0.2% of the full scale 共⫾10 in. H2O兲. During the experiment, each pressure transducer input was scanned at
400 Hz for 20 s. The pressure coefficient distributions, C p = 共P
1
− P⬁兲 / 共 2 ␳U2⬁兲, around the airfoil at various angles of attack were
measured by using the pressure acquisition system. The lift and
1
1
drag coefficients 共Cl = l / 共 2 ␳U2⬁C兲 and Cd = d / 共 2 ␳U2⬁C兲兲 of the 2D
airfoil were determined by numerically integrating the pressure
distribution around the airfoil.
Figure 3 shows the schematic of the experimental setup used
for the PIV measurement. The test airfoil was installed in the
middle of the test section. A PIV system was used to make flow
velocity field measurements along the chord at the middle span of
the airfoil. The flow was seeded with ⬃1 ␮m oil droplets. Illumination was provided by a double-pulsed Nd:YAG 共yttrium aluminum garnet兲 laser 共NewWave Gemini 200兲 adjusted on the second
harmonic and emitting two laser pulses of 200 mJ at a wavelength
of 532 nm with a repetition rate of 10 Hz. The laser beam was
shaped into a sheet by a set of mirrors, spherical and cylindrical
lenses. The thickness of the laser sheet in the measurement region
is about 0.5 mm. A high-resolution 12 bit 共1376⫻ 1040 pixels兲
charge-coupled device 共CCD兲 camera 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 lasers
were connected to a workstation 共host computer兲 via a Digital
Delay Generator 共Berkeley Nucleonics, Model 565兲, which controlled the timing of the laser illumination and the image acquisition. In the present study, a careful pretest, which includes testing
different seeding methods, applying different paints to the airfoil
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Fig. 3 Schematic of the experimental setup for the PIV measurements
model as well as adjusting laser excitation energy level, camera
positions, and optic lens arrangements, was conducted in order to
minimize the reflection from the airfoil surface for the near wall
PIV measurements.
Instantaneous PIV velocity vectors were obtained by a frame to
frame cross-correlation technique involving successive frames of
patterns of particle images in an interrogation window of 32
⫻ 32 pixels. An effective overlap of 50% was employed for PIV
image processing. After the instantaneous velocity vectors 共ui , vi兲
were determined, the spanwise vorticity 共␻z兲 could be derived.
The time-averaged quantities such as mean velocity 共U , V兲, turbulent velocity fluctuations 共u⬘ , v⬘兲, normalized Reynolds stress 共¯␶
= −u⬘v⬘ / U2⬁兲, and normalized turbulent kinetic energy 共TKE
= 0.5ⴱ 共u⬘2 + v⬘2兲 / U2⬁兲 were obtained from a cinema sequence of
400 frames of instantaneous velocity fields. The measurement uncertainty level for the velocity vectors is estimated to be within
2% and 5% for the turbulent velocity fluctuations 共u⬘ , v⬘兲, Reynolds stress, and turbulent kinetic energy calculations. The uncertainty level of the spanwise vorticity data is expected to be within
10.0%. It should be noted that the surface pressure mapping and
PIV measurements are designed to acquire statistical data instead
of time-resolved measurements due the limited sampling rates of
the surface pressure mapping and PIV measurements.
3
Experimental Results and Discussions
3.1 Measured Surface Pressure Distribution Around the
Airfoil. Figure 4 shows the measured surface pressure coefficient
distributions around the GA 共W兲-1 airfoil as the angle of attack
changes from 6.0 deg to 14.0 deg. While the surface pressure distribution on the lower surface of the airfoil does not notably
Fig. 4 Surface pressure distribution profiles around the airfoil
Journal of Fluids Engineering
change with the increasing angle of attack 共up to 12.0 deg兲, the
surface pressure distribution on the upper surface of the airfoil
was found to significantly vary at different angles of attack. As the
angle of attack 共AOA兲 was relatively small 共i.e., AOA⬍ 8.0 deg兲,
the surface pressure coefficient profiles along the airfoil upper
surface were found to rapidly reach their negative peaks at locations quite near to the airfoil leading edge, then the surface pressure gradually and smoothly recovered over the upper surface of
the airfoil up to the airfoil trailing edge. As the AOA increases to
8.0ⱕ AOA⬍ 12.0 deg, a distinctive characteristic of the surface
pressure coefficient profiles is the existence of a region of nearly
constant pressure 共i.e., pressure plateau region兲 at X / C
⬇ 0.05– 0.25. Sudden increase in surface pressure coefficient was
found following the pressure plateau region. Further downstream,
the surface pressure was found to gradually and smoothly recover,
which is similar as those cases with relatively low AOAs. Such a
characteristic of the surface pressure profiles is actually closely
related to laminar flow separation and the formation of laminar
separation bubbles on low-Reynolds-number airfoils.
As schematically illustrated in Fig. 5, Russell 关22兴 suggested a
theoretic model to characterize the laminar separation bubbles
formed on low-Reynolds-number airfoils. Based on the theoretic
model of Russell 关22兴, the critic points 共the separation, transition,
and reattachment points兲 of a laminar separation bubble formed
on a low-Reynolds-number airfoil can be determined from the
surface pressure measurements. The separation point refers to the
location from where the laminar boundary layer separates from
the airfoil surface. The transition point refers to the onsite point at
where the separated laminar boundary layer begins to transit to
turbulence. The reattachment point refers to the location where the
separated boundary layer reattaches to the airfoil surface after
transition. As suggested by Russell 关22兴, a laminar separation
bubble formed on a low-Reynolds-number airfoil includes two
portions: a laminar portion and a turbulent portion. The location of
the pressure plateau is coincident with that of the laminar portion
of the separation bubble. The starting point of the pressure plateau
indicates the location where the laminar boundary layer separates
from the airfoil surface 共i.e., the separation point兲. Since the transition of the separated laminar boundary layer to turbulence will
result in a rapid pressure rise brought about by fluid entrainment,
the termination of the pressure plateau can be used to locate the
transition point, at where the transition of the separated laminar
boundary layer to turbulence begins to occur. The pressure rise
due to the turbulence transition often overshoots the invisicid
pressure that exists at the reattachment location. Therefore, the
location of the point of equality between the actual and inviscid
surface pressure marks the location of reattachment 共i.e., the reattachment point兲.
Following the work of Russell 关22兴, the locations of the critic
MAY 2008, Vol. 130 / 051101-3
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Fig. 5 Pressure distribution on an airfoil with laminar separation bubble „Russell †22‡…
points 共the separation, transition, and reattachment points兲 of
laminar separation bubbles at different AOAs were estimated
based on the measured airfoil surface pressure profiles given in
Fig. 4. A summation of the locations of separation, transition, and
reattachment points on the GA共W兲-1 airfoil at different AOAs is
given in Fig. 6. The uncertainties of the estimated locations of the
critical points is about 2.0% of chord length due to the limited
numbers of the pressure taps available in the region, which are
shown in the figure as the error bars. As the AOA increases, the
laminar separation bubble was found to move upstream to approach the airfoil leading edge. The total length of the separation
bubble 共i.e., the distance between the separation and reattachment
points兲, which is about 20% of the chord length, was found to be
almost unchanged regardless of the angles of attack. Following
the terminology used by Horton 关6兴, the length of the laminar
portion of the separation bubble is defined as the distance between
the separation point and the transition point, and the turbulent
portion length corresponds to the distance between the transition
point and the reattachment point. From the experimental results
given in Fig. 6, it can be seen that, while the length of the laminar
portion of the separation bubble was found to slightly increase as
the AOA increases, the turbulent portion became slightly shorter
with the increasing AOA.
As the AOA became greater than 12.0 deg, the magnitude of
the negative pressure coefficient peak near the airfoil leading edge
was found to significantly decrease. As shown in Fig. 4, the surface pressure over most of the airfoil upper surface was found to
be nearly constant. Such a surface pressure distribution indicates
that airfoil is in stalled state 关23–25兴, which is confirmed from the
PIV measurements given in Fig 7.
3.2 PIV Measurement Results. While the surface pressure
measurements can be used to quantify the global characteristics of
the laminar separation bubble formed on the low-Reynoldsnumber airfoil, quantitative flow field measurements taken by using a high-resolution PIV system can reveal much more details
Fig. 6 The estimated locations of the separation points, transition points,
and reattachment points at various AOAs
051101-4 / Vol. 130, MAY 2008
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Fig. 7 PIV measurement results at various AOAs
about the transient behavior of laminar flow separation and the
evolution of a laminar separation bubble formed on the airfoil. In
the present study, PIV measurements were conducted at three spatial resolution levels: a coarse level to visualize the global features
of the flow structures around the airfoil at various AOAs with the
measurement window size being about 160⫻ 120 mm2, a refined
Journal of Fluids Engineering
level to reveal the transient behavior of the laminar flow separation process near the nose of the airfoil with a measurement window size of about 40⫻ 20 mm2, and a superfine level to elucidate
the details about the turbulence transition and the reattachment of
the separated boundary layer to the airfoil surface at the rear portion of the separation bubble with a measurement window size of
MAY 2008, Vol. 130 / 051101-5
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(a)
(b)
(c)
(d)
Fig. 8 PIV measurements near the airfoil leading edge with AOA= 6.0 deg; „a… instantaneous velocity vectors; „b… instantaneous vorticity distribution; „c… ensemble-averaged velocity vectors; and „d… streamlines of the mean flow
about 16⫻ 10 mm2. The time interval between the double pulsed
laser illumination for the PIV measurements was set as ⌬t
= 40.0 ␮s, 14.0 ␮s, and 4.0 ␮s, respectively. The effective resolutions of the PIV measurements 共i.e., grid sizes兲 were ⌬ / C
= 0.018, 0.0045, and 0.0018, respectively.
Figure 7 shows the PIV measurement results at the coarse resolution level. As clearly revealed by the ensemble-averaged velocity distribution and the streamlines of the mean flow around the
airfoil, incoming flow streams faithfully follow the streamlined
profile of the airfoil when the AOA is relatively small 共i.e.,
AOA⬍ 8.0 deg兲. No flow separation was found on the airfoil upper surface when the adverse pressure gradient is rather mild at
relatively small AOAs. Since the flow streams can firmly attach to
the airfoil surface, they smoothly leave the airfoil at the trailing
edge, which results in a very small wake region 共i.e., the region
with velocity deficits兲 downstream of the airfoil. The small wake
region downstream of the airfoil indicates a small aerodynamic
drag force acting on the airfoil, which is confirmed from the drag
coefficient measurement results given in Fig. 12.
As the AOA increases to 8.0– 11.0 deg, the surface pressure
measurement results given in Fig. 4 indicate that a laminar separation bubble would be generated on the upper surface of the
airfoil. However, since the height of the separation bubble is very
small 共only ⬃1.0% of the chord length based on the refined PIV
measurement results shown in Figs. 9 and Fig. 10兲, the laminar
separation bubble cannot be clearly revealed from the PIV measurement results shown in Fig. 7共B兲 due to the limited spatial
resolution of the PIV measurements 共i.e., ⌬ / C ⬇ 0.018兲. It has
been suggested that the separated laminar boundary layer would
firmly reattach to the airfoil upper surface at the downstream of
(a)
(b)
(c)
(d)
Fig. 9 PIV measurements near the airfoil leading edge with AOA= 10.0 deg; „a… instantaneous velocity vectors; „b… instantaneous vorticity distribution; „c… ensemble-averaged velocity vectors; and „d… streamlines of the mean flow
051101-6 / Vol. 130, MAY 2008
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 10 PIV measurement results at the rear portion of the separation bubble with AOA= 10.0 deg; „a… instantaneous
velocity field; „b… instantaneous vorticity distribution; „c… ensemble-averaged velocity field; „d… streamlines of the mean
flow; „e… normalized Reynolds stress distribution; and „f… normalized turbulent kinetic energy distribution
the reattachment point all the way to the airfoil trailing edge
关6,22,23兴. The mean velocity vectors and streamlines of the mean
flow shown in Fig. 7共B兲 reveal that incoming flow streams
smoothly leave the airfoil at the trailing edge at AOA= 10.0 deg,
which confirms the reattachment of the separated boundary layer
to the airfoil upper surface downstream of the laminar separation
bubble. As a result of the reattachment of the separated boundary
layer, the wake region downstream of the airfoil was found to be
reasonably small even though a separated bubble was already
formed on the airfoil upper surface. Compared to those cases at
smaller AOAs 共such as the case shown in Figs. 7共A兲 with AOA
= 6.0 deg兲, the size of the wake region for the cases with the
separation bubbles generated on the airfoil upper surface becomes
slightly larger, indicating a slightly increased aerodynamic drag
force acting on the airfoil, which is confirmed from the airfoil
drag coefficient measurement results given in Fig. 12.
The adverse pressure gradient over the upper surface of the
airfoil becomes more and more severe as the AOA increases. The
surface pressure measurement results given in Fig. 4 indicate that
the separation bubble would burst, eventually causing airfoil stall
when the AOA becomes greater than 12.0 deg. The large-scale
flow separation over almost the entire upper surface of the airfoil
due to the burst of the laminar separation bubble is visualized
clearly and quantitatively from the PIV measurement results given
in Fig. 7共C兲. The large-scale flow separation on the airfoil upper
surface resulted in the formation of a very large recirculation
bubble in the wake the airfoil. As a result, the size of the wake
region 共i.e., the region with velocity deficit兲 downstream the airfoil was found to dramatically increase, which indicates a significant increase of the aerodynamic drag force acting on the airfoil,
again quantitatively confirmed for the measured drag coefficient
data given in Fig. 12.
Although the PIV measurement results given in Fig. 7 clearly
reveal the global features of the flow structures around the airfoil,
Journal of Fluids Engineering
further details about the transient behavior of the laminar flow
separation and evolution of the separation bubble formed on the
low-Reynolds-number airfoil cannot be clearly seen due to the
limited spatial resolution of the PIV measurements. In order to
provide further insights to elucidate underlying physics associated
with the laminar flow separation process on low-Reynoldsnumber airfoils, refined PIV measurements near the nose of the
airfoil with much higher spatial resolution 共⌬ / C ⬇ 0.0045兲 were
made. The measurement results are shown in Figs. 8, 9, and 11
with the AOA being 6.0 deg, 10.0 deg, and 12.0 deg, respectively.
The laminar boundary layer around the airfoil was clearly visualized as a thin vortex layer affixing to the airfoil upper surface in
the typical instantaneous velocity field and the corresponding vorticity distribution shown in Fig. 8. The laminar boundary layer
was found to be firmly attached to the airfoil surface when the
adverse pressure gradient over the airfoil upper surface is rather
mild at relatively small AOA 共i.e., AOA⬍ 8.0 deg兲. The
ensemble-averaged velocity field and the streamlines of the mean
flow also confirmed that the incoming fluid streams would
smoothly flow to follow the streamlined profile of the airfoil when
the AOA is relatively small.
As indicated by the surface pressure measurement results described above, a laminar separation bubble would be generated on
the airfoil when the AOA became relatively high 共i.e., AOA
⬇ 8.0– 12.0 deg兲. The typical instantaneous velocity field and the
corresponding vorticity distribution given in Fig. 9 clearly show
that the laminar boundary layer 共i.e., the thin vortex layer over the
airfoil upper surface兲 would be “taking off” from the airfoil upper
surface at first, and then “landing” on the airfoil upper surface
again further downstream. The separation of the laminar boundary
layer from the airfoil upper surface and the reattachment of the
separated boundary layer can be much more clearly seen from the
ensemble-averaged velocity field and the corresponding mean
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(a)
(b)
(c)
(d)
Fig. 11 PIV measurements near the airfoil leading edge with AOA= 12.0 deg; „a… instantaneous velocity vectors; „b… instantaneous vorticity distribution; „c… ensemble-averaged velocity vectors; and „d… streamlines of the mean flow
flow streamlines. Based on the PIV measurement results shown in
Fig. 9, the location of the separation point 共i.e., from where the
laminar boundary layer begins to separate from the airfoil surface兲
was found to be in the neighborhood of X / C ⬇ 0.08, which agrees
with the starting point of the “pressure plateau” of the measured
surface pressure distribution at 10.0 deg AOA. The reattachment
point 共i.e., at where the separated boundary layer reattaches to the
airfoil surface兲 was found to be in the neighborhood of X / C
⬇ 0.28, which also agrees well with the estimated location of the
reattachment point based on the surface pressure measurements.
The laminar separation bubble, which sits in the region between
the separation point and the reattachment point, is clearly visualized from the PIV measurement results. While the length of the
separation bubble is about 20% of the chord length, the height of
the laminar separation bubble is found to be only about 1% of the
chord length.
In order to provide further insight into the fundamental physics
associated with the turbulent transition and reattachment of the
separated laminar boundary layer, PIV measurements with superfine spatial resolution 共⌬ / C ⬇ 0.0018兲 were made at the rear portion of the laminar separation bubble. The measurement results
are shown in Fig. 10 with the airfoil AOA being 10.0 deg.
The PIV measurement results given in Fig. 9 clearly show that
the laminar boundary layer would separate from the airfoil upper
surface at X / C ⬇ 0.08 due to the severe adverse pressure gradient
at 10.0 deg AOA. The instantaneous velocity field and corresponding vorticity distribution given in Fig. 10 reveal that the
separated laminar boundary layer behaved more like a free shear
layer after separation, which is highly unstable; therefore, rolling
up of unsteady vortex structures due to the Kelvin–Helmholtz
instabilities and transition to turbulent flow would be readily realized. After the separated laminar boundary layer transits to turbulent flow, the increased entrainment of the turbulent flow made
the separated boundary layer reattach to the airfoil upper surface
as a turbulent boundary layer, which consequently resulted in the
formation of a laminar separation bubble on the airfoil. The reattachment of the separated boundary layer to the airfoil upper surface and consequent formation of the laminar separation bubble
can be more clearly seen from the ensemble-averaged velocity
field and the streamlines of the mean flow shown in Figs. 10共c兲
and 10共d兲.
Figure 10共e兲 shows the distribution of the measured normalized
051101-8 / Vol. 130, MAY 2008
Reynolds stress 共−u⬘v⬘ / U2⬁兲 near the rear portion of the laminar
separation bubble. It can be clearly seen that the transition process
of the laminar boundary layer is accompanied by the significant
increase of Reynolds stress in the flow field. It should be noted
that only the contour lines of the normalized Reynolds stress
above a critical value of 0.001 are shown in the Fig. 10共e兲. This
critical value has been chosen in the literature to locate the onset
of the turbulent transition in separated shear layers 关10,17,19兴.
Following the work of Ol et al. 关17兴, the transition onset position
was estimated as the streamwise location where the normalized
Reynolds stress first reaches a value of 0.001. The transition onset
position at 10.0 deg AOA was found to be located in the neighborhood of X / C ⬇ 0.21 based on the measured Reynolds stress
distribution shown in Fig. 10共e兲. The estimated location was found
to agree well with the estimation of the transition point given in
Fig. 5, which is based on the surface pressure measurements.
The measured turbulent kinetic energy 共TKE= 0.5ⴱ 共u⬘2
+ v⬘2兲 / U2⬁兲 distribution at the rear part of the laminar separation
bubble is given in Fig. 10共f兲. It can be clearly seen that the regions
with higher TKE was found to be confined in a thin layer in the
upstream of the transition point due to the laminar nature of the
separated laminar boundary layer. The contour lines of the regions
with higher TKE were found to rapidly diverge after the separated
laminar boundary layer began to transit to turbulence 共i.e., downstream of the transition point兲. The measured TKE distribution
also shows that the regions with higher TKE can be quite close to
the airfoil surface wall downstream of the reattachment point 共i.e.,
downstream of location X / C ⬇ 0.28兲. This confirms that the reattached turbulent boundary layer can entrain more high-speed fluid
from outside to the near wall region to make the near wall flow
much more energetic compared to the laminar boundary layer
upstream of the laminar separation bubble. Therefore, the turbulent boundary layer is much more capable of advancing against an
adverse pressure gradient without flow separation. As a result, the
reattached turbulent boundary layer can stay attached to the airfoil
surface from the reattachment point to the trailing edge of the
airfoil, which was confirmed in the PIV measurement results
given above.
As the AOA increases to 12.0 deg and higher, the adverse pressure gradient over the upper surface of the airfoil becomes much
more significant, and the separation bubble was found to eventuTransactions of the ASME
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(a)
(b)
Fig. 12 The measured airfoil lift and drag coefficients; „a… airfoil lift and
drag coefficients vs. angle of attack; and „b… lift-drag polar dot
ally burst. As clearly revealed in the instantaneous PIV measurement results given in Fig. 11, the laminar boundary layer was
found to separate from the upper surface of the airfoil very near to
the airfoil leading edge due to the significant adverse pressure
gradient. Although the separated laminar boundary layer was still
found to rapidly transit to turbulence by rolling up unsteady vortex structures due to the Kelvin–Helmholtz instabilities, the separated boundary layer could not reattach to the airfoil upper surface
anymore due to the much more significant adverse pressure gradient when the AOA became 12 deg and higher. Large-scale flow
separation was found to take place over almost entire airfoil upper
surface, and the airfoil completely stalled. The airfoil stall is
clearly visualized from the PIV measurement results.
3.3 Lift and Drag Coefficients of the Airfoil. The lift and
drag coefficients of the airfoil at various AOA were determined by
numerically integrating the measured surface pressure distribution
around the 2D airfoil model used in the present study. Figure 12
shows the profiles of the measured lift and drag coefficients as the
functions of the AOA and a lift-drag polar plot. For reference, the
predicted increase rate of the airfoil lift coefficient 共i.e., dCl / d␣
= 2␲兲 based on thin airfoil theory 关26兴 is also shown in the figure.
As revealed from the measured surface pressure distributions
and PIV measurement results discussed above, the laminar boundary layer was found to firmly attach to the airfoil surface all the
Journal of Fluids Engineering
way from the airfoil leading edge to the trailing edge when the
adverse pressure gradient over the upper surface of the airfoil is
rather mild at relatively small AOA 共i.e., AOA艋 6.0 deg兲. Therefore, the airfoil drag coefficient of the airfoil was found to be very
small. The airfoil lift coefficient of the airfoil was found to increase almost linearly with the increasing AOA. The increase rate
of the airfoil lift coefficient was found to be almost the same as
the prediction based on thin airfoil theory 共i.e., dCl / d␣ = 2␲兲 at
relatively small AOA when no laminar separation bubble was
formed on the airfoil.
The adverse pressure gradient on the airfoil upper surface becomes more and more severe as the AOA increases. Since the
laminar boundary layer on the airfoil is unable to withstand the
severe adverse pressure gradient 关2,3兴, it will separate from the
airfoil upper surface, the and laminar flow separation occurs as the
AOA relatively becomes large 共i.e., AOAⱖ 8 deg for the present
study兲. The laminar flow separation is evident as the pressure
plateau in the measured surface pressure distributions and clearly
visualized in the PIV measurement results given above. The separated laminar boundary layer was found to be able to reattach to
the upper surface of the airfoil as a turbulent boundary layer after
turbulence transition at adequate AOAs 共i.e., 8.0 deg艋 AOA
⬍ 12.0 deg兲. This results in the formation of a laminar separation
bubble on the airfoil upper surface. The airfoil lift coefficient was
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found to keep on increasing with the AOA. However, the increase
rate of the airfoil lift coefficient was found to considerably degrade due to the formation of a laminar separation bubble. The
drag coefficient of the airfoil was found to increase faster with the
increasing AOA when the laminar separation bubble was formed
on the airfoil. The adverse gradient over the airfoil upper surface
became so significant at AOAⱖ 12.0 deg that the laminar separation bubble was found to burst. The separated laminar boundary
layer was not able to reattach to the airfoil upper surface anymore.
As visualized in the PIV measurements given above, large-scale
flow separation was found to take place over almost the entire
airfoil upper surface, and the airfoil was found to completely stall.
As a result, the lift coefficient of the airfoil was found to dramatically drop and the drag coefficient was found to significantly increase with the increasing AOA.
4
Conclusion
An experimental investigation was carried out to study the transient behavior of the laminar flow separation on a NASA lowspeed GA 共W兲-1 airfoil at the chord Reynolds number of ReC
= 70,000. In addition to conducting surface pressure distribution
mapping around the airfoil, a high-resolution PIV system was
used to make detailed flow field measurements to quantify the
occurrence and behavior of laminar boundary layer separation,
transition, and reattachment at various AOAs. The detailed flow
field measurements were correlated with the surface pressure measurements to elucidate the underlying physics associated with the
separation, transition, and reattachment processes of the laminar
boundary layer on the low-Reynolds-number airfoil.
The surface pressure mapping and detailed PIV measurements
clearly revealed that the laminar boundary layer would stay firmly
attached to the airfoil surface as the adverse pressure gradient over
the airfoil upper surface was rather mild at relatively small AOA
共i.e., AOA⬍ 8.0 deg兲. As the AOA became greater than 8.0 deg,
the increased adverse pressure gradient caused the laminar boundary layer to separate from the airfoil upper surface. The separated
laminar boundary layer was found to rapidly transit to turbulent
flow by generating unsteady Kelvin–Helmholtz vortex structures.
When the adverse pressure gradient was adequate 共i.e., AOA
⬍ 12.0 deg兲, the separated laminar boundary layer was found to
be able to reattach to the upper surface of the airfoil as a turbulent
boundary layer. As a result, a laminar separation bubble was
formed on the airfoil. The length of the laminar separation bubble
was found to be about 20% of the airfoil chord length and its
height only about 1% of the chord length. While the total length of
the laminar separation bubble was found to be almost unchanged
regardless the AOA, the length of the laminar portion of the separation bubble was found to slightly increase, and the turbulent
portion became slightly shorter with the increasing AOA. The
separation bubble was found to move upstream to approach airfoil
leading edge as the AOA increased. The laminar separation bubble
was found to burst, causing airfoil stall, when the adverse pressure
gradient became very significant at AOAⱖ 12.0 deg.
The detailed PIV measurements elucidated many details about
the transient behavior of the laminar boundary layer separation,
transition, and reattachment on the low-Reynolds-number airfoil.
The transition process of the separated laminar boundary layer
was found to be accompanied by the significant increase of Reynolds stress in the flow field. The measured TKE distributions
clearly revealed that the reattached turbulent boundary layer was
much more energetic, thus more capable of advancing against an
adverse pressure gradient without flow separation, compared to
the laminar boundary layer upstream the separation bubble. As a
result, the reattached turbulent boundary layer was found to stay
firmly attached to the airfoil surface from the reattachment point
to the trailing edge of the airfoil. The critic points 共i.e., separation,
transition, and reattachment points兲 of the separation bubble identified from the PIV measurements were found to agree well with
those estimated based on the surface pressure measurements.
051101-10 / Vol. 130, MAY 2008
The lift coefficient of the airfoil was found to linearly increase
with the increasing AOA when the AOA is relatively small, while
the drag coefficient of the airfoil was found to be very small. After
the formation of the laminar separation bubble on the airfoil at
AOAⱖ 8.0 deg, the increase rate of the airfoil lift coefficient was
found to considerably degrade and the airfoil drag coefficient was
found to increase much faster with increasing AOA. As the AOA
became much higher 共i.e., AOAⱖ 12.0 deg兲, where the separation
bubble was found to burst to cause airfoil stall, the lift coefficient
of the airfoil was found to dramatically drop, and the airfoil drag
coefficient was found to significantly increase.
Acknowledgment
The authors want to thank Mr. Bill Rickard, Mr. De Huang, and
Mr. Masatoshi Tamai of Iowa State University for their help in
conducting the experiments. The support of National Science
Foundation CAREER program under Award No. CTS-0545918 is
gratefully acknowledged.
References
关1兴 Tani, I., 1964, “Low Speed Flows Involving Bubble Separations,” Prog. Aeronaut. Sci., Vol. 5, pp. 70–103.
关2兴 Carmichael, B. H., 1981, “Low Reynolds Number Airfoil Survey,” NASA
CR-165803, Vol. 1.
关3兴 Lissaman, P. B. S., 1983, “Low-Reynolds-Number Airfoils,” Annu. Rev. Fluid
Mech., 15, pp. 223–239.
关4兴 J. T. Mueller, ed., 2001, Fixed and Flapping Wing Aerodynamics for Micro Air
Vehicle Applications, Progress in Astronautics and Aeronautics, Vol. 195,
AIAA.
关5兴 Gad-el-Hak, M., 2001, “Micro-Air-Vehicles: Can They be Controlled Better,”
J. Aircr., 38共3兲, pp. 419–429.
关6兴 Horton, H. P., 1968, Laminar Separation in Two and Three-Dimensional Incompressible Flow, Ph.D. thesis, University of London.
关7兴 Hatman, A., and Wang, T., 1999, “A Prediction Model for Separated Flow
Transition,” ASME J. Turbomach., 121, pp. 594–602.
关8兴 Johnson, M. W., 1994, “A Bypass Transition Model for Boundary Layers,”
ASME J. Turbomach., 116, pp. 759–764.
关9兴 Solomon, W. J., Walker, G. J., and Gostelow, J. P., 1996, “Transition Length
Prediction for Flows With Rapidly Changing Pressure Gradients,” ASME J.
Turbomach., 118, pp. 744–751.
关10兴 Volino, R. J., and Hultgren, L. S., 2001, “Measurements in Separated and
Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions,” ASME J. Turbomach., 123, pp. 189–197.
关11兴 Haueisen, V., Henneke, D. K., and Schröder, T., 1997, “Measurements With
Surface Mounted Hot Film Sensors on Boundary Layer Transition in Wake
Disturbed Flow,” AGARD CP-598.
关12兴 Zhong, S., Kittichaikarn, C., Hodson, H. P., and Ireland, P. T., 2000, “Visualization of Turbulent Spots Under the Influence of Adverse Pressure Gradients,”
Exp. Fluids, 28, pp. 385–393.
关13兴 FItzgerald, E. J., and Mueller, T. J., 1990, “Measurements in a Separation
Bubble on an Airfoil Using Laser Velocimetry,” AIAA J., 28共4兲, pp. 584–592.
关14兴 Brendel, M., and Mueller, T. J., 1987, “Boundary Layer Measurements on an
Airfoil at Low Reynolds Numbers,” AIAA Paper No. 87-0495.
关15兴 O’Meara, M. M., and Mueller, T. J., 1987, “Laminar Separation Bubble Characteristics on an Airfoil at Low Reynolds Numbers,” AIAA J., 25共8兲, pp.
1033–1041.
关16兴 Lang, M., Rist, U., and Wagner, S., 2004, “Investigations on Controlled Transition Development in a Laminar Separation Bubble by Means of LDA and
PIV,” Exp. Fluids, 36, pp. 43–52.
关17兴 Ol, M. V., Hanff, E., McAuliffe, B., Scholz, U., and Kaehler, C., 2005, “Comparison of Laminar Separation Bubble Measurements on a Low Reynolds
Number Airfoil in Three Facilities,” 35th AIAA Fluid Dynamics Conference
and Exhibit, Toronto, Ontario, June 6–9, AIAA Paper 2005-5149.
关18兴 Raffel, M., Favier, D., Berton, E., Rondot, C., Nsimba, M., and Geissler, M.,
2006 “Micro-PIV and ELDV Wind Tunnel Investigations of the Laminar Separation Bubble Above a Helicopter Blade Tip,” Meas. Sci. Technol., 17, pp.
1652–1658.
关19兴 Burgmann, S., Brücker, S., Schröder, W., 2006, “Scanning PIV Measurements
of a Laminar Separation Bubble,” Exp. Fluids, 41, pp. 319–326.
关20兴 Gao, H., Hu, H., and Wang, Z. J., 2008, “Computational Study of Unsteady
Flows Around Dragonfly and Smooth Airfoils at Low Reynolds Numbers,”
46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 7–10,
AIAA Paper No. 2008-0385.
Transactions of the ASME
Downloaded 25 Apr 2008 to 129.186.193.37. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
关21兴 McGee, R. J., and Beasley, W. D., 1973, “Low-Speed Aerodynamics Characteristics of a 17-Percent-Thick Airfoil Section Designed for General Aviation
Applications,” NASA TN D-7428.
关22兴 Russell, J., 1979, “Length and Bursting of Separation Bubbles: A Physical
Interpretation,” Science and Technology of Low Speed Motorless Flight,
NASA Conference Publication 2085, Part 1.
关23兴 Shum, Y. K., and Marsden, D. J., 1994, “Separation Bubble Model for Low
Journal of Fluids Engineering
Reynolds Number Airfoil Applications,” J. Aircr., 31共4兲, pp. 761–766.
关24兴 Yaruseych, S., Sullivan, P. E., and Kawall, J. G., 2006, “Coherent Structure in
an Airfoil Boundary Layer and Wake at Low Reynolds Numbers,” Phys. Fluids, 18, 044101.
关25兴 Lin, J. C. M., and Pulley, L. L., 1996, “Low-Reynolds-Number Separation on
an Airfoil,” AIAA J., 34共8兲, pp. 1570–1577.
关26兴 Anderson, J. D., 2005, Fundamentals of Aerodynamics, 4th ed., McGraw-Hill
Higher Education, New York.
MAY 2008, Vol. 130 / 051101-11
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JOURNAL OF AIRCRAFT
Vol. 45, No. 6, November–December 2008
Bioinspired Corrugated Airfoil
at Low Reynolds Numbers
Hui Hu∗ and Masatoshi Tamai†
Iowa State University, Ames, Iowa 50011
DOI: 10.2514/1.37173
An experimental study was conducted to investigate the flow behavior around a bioinspired corrugated airfoil
compared with a traditional streamlined airfoil and a flat plate at the chord Reynolds number of Re 34; 000 to
explore the potential application of such bioinspired corrugated airfoils for micro air vehicle applications. The
experiments were conducted in a low-speed wind tunnel. A high-resolution particle image velocimetry system was
used to conduct detailed flowfield measurements to quantify the transient behavior of vortex and turbulent flow
structures around the studied airfoils. The particle image velocimetry measurement results demonstrated clearly
that the corrugated airfoil has better performance over the streamlined airfoil and the flat plate in preventing largescale flow separation and airfoil stall at low Reynolds numbers. It was found that the protruding corners of the
corrugated airfoil would act as turbulators to generate unsteady vortex structures to promote the transition of the
separated boundary-layer flow from laminar to turbulent. The unsteady vortex structures trapped in the valleys of
the corrugated cross section would pump high-speed fluid from outside to near-wall regions to provide sufficient
kinetic energy for the boundary layer to overcome adverse pressure gradients, thus discouraging large-scale flow
separations and airfoil stall. Aerodynamic force measurements further confirmed the possibility of using such
bioinspired corrugated airfoils in micro air vehicle designs to improve their flight agility and maneuverability.
drag) according to traditional airfoil design principles. However,
several studies on corrugated dragonfly wings in steady flow or
gliding flight [4–17] have led to a surprising conclusion: a corrugated
dragonfly wing could have comparable or even better aerodynamic
performances (i.e., higher lift and bigger lift-to-drag ratio) than
conventional streamlined airfoils in the low Reynolds number
regime in which dragonflies usually fly.
Most of the earlier experimental studies were conducted mainly
based on the measurements of total aerodynamic forces (lift and
drag) of either natural dragonfly wings or modeled corrugated wing
sections. Detailed studies were conducted more recently to try to
elucidate the fundamental physics of the dragonfly flight
aerodynamics [12–17]. A number of hypotheses have been
suggested to explain the fundamental mechanism of the rather
unexpected aerodynamic performance improvement of the
corrugated dragonfly airfoils or wings over conventional smooth
airfoils. Rees [4] suggested that airflow could be trapped in the
valleys of the corrugated structures to become stagnant or rotate
slowly in the valleys, resulting in the corrugated wing acting as a
streamlined airfoil. Newman et al. [5] suggested that the improved
aerodynamic performance would be associated with the earlier
reattachment of the flow separation on the corrugated wings. As the
angle of attack increases, airflow would separate from the leading
edge to form a separation bubble, and the separated flow would
reattach sooner due to the corrugation, compared with smooth
airfoils. Based on pressure measurements on the surfaces of a
dragonfly wing model in addition to total lift-and-drag force
measurements, Kesel [12] reported that negative pressure would be
produced at the valleys of the corrugated dragonfly wing model,
which would contribute to the increased lift. Vargas and Mittal [15]
and Luo and Sun [16] conducted numerical studies to investigate the
flow behaviors around corrugated dragonfly wings. Their simulation
results confirmed the existence of small vortex structures in the
valleys of the corrugated dragonfly airfoil. The small vortex
structures in the valleys of the corrugated cross section were also
revealed qualitatively in the flow-visualization experiments of Kwok
and Mittal [17].
Despite different explanations about the fundamental mechanism
for the improved aerodynamic performance, most of the studies
agree that corrugated dragonfly airfoils or wings work well in low
Reynolds number regimes, which naturally point to the potential
applications of employing such corrugated airfoils or wings in micro
Introduction
M
ICRO air vehicles (MAVs) with a wingspan of 15 cm or
shorter and a flight speed of around 10 m=s have attracted
substantial interest in recent years. Although a number of MAVs,
either in fixed-wing or flapping-wing designs, have already been
developed by several universities and commercial- and governmentfunded endeavors, the airfoil and wing planform designs of the
MAVs rely mainly on scaled-down versions of those used by
conventional macroscale aircraft. Chord Reynolds number Re,
which is based on airfoil chord length and flight velocity, is used to
characterize the aerodynamic performance of an airfoil. Whereas
traditional macroscale aircraft have a chord Reynolds number of
about 106 –108 , the chord Reynolds numbers of MAVs are usually in
the range of 104 –105 . The aerodynamic design principles applicable
to traditional macroscale aircraft may not be used for MAVs, due to
the significant difference in chord Reynolds numbers. As a result,
airfoil shape and wing planform designs that are optimized for
traditional macroscale aircraft are found to degrade significantly
when used for MAVs [1]. Therefore, it is very necessary and
important to establish novel airfoil shape and wing planform design
paradigms for MAVs to achieve good aerodynamic performance as
well as flight agility and versatility.
A number of insects, including locusts, dragonflies, and
damselflies, employ wings that are not smooth or simple cambered
surfaces. The cross sections of the wings have well-defined
corrugated configurations [2,3]. Such corrugated design was found
to be of great importance to the stability of the ultralight wings to
handle the spanwise bending forces and mechanical wear that the
wing experiences during flapping. The corrugated wing design does
not appear to be very suitable for flight because it would have very
poor aerodynamic performance (i.e., low lift and extremely high
Received 16 February 2008; revision received 1 May 2008; accepted for
publication 3 May 2008. Copyright © 2008 by Hui Hu and Masatoshi Tamai.
Published by the American Institute of Aeronautics and Astronautics, Inc.,
with permission. Copies of this paper may be made for personal or internal
use, on condition that the copier pay the $10.00 per-copy fee to the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include
the code 0021-8669/08 $10.00 in correspondence with the CCC.
∗
Assistant Professor, Aerospace Engineering Department; huhui@
iastate.edu. Senior Member AIAA.
†
Graduate Student, Aerospace Engineering Department.
2068
2069
HU AND TAMAI
air vehicles. With this in mind, we conducted the present study to try
to leverage the corrugation feature of dragonfly wings and to explore
the potential applications of such nontraditional bioinspired
corrugated airfoils to MAV designs for improved aerodynamic
performance.
Although several experimental studies have already been
conducted previously to investigate the aerodynamic performance
of corrugated dragonfly airfoils or wings, detailed quantitative flow
measurements have never been made to elucidate the underlying
physics of why and how corrugated airfoils or wings could have
comparable or even better aerodynamic performance for low
Reynolds number flight. It should also be noted that the majority of
previous studies on dragonfly wings or modeled dragonfly airfoils
were conducted from a biologist’s point of view to try to understand
the fundamental mechanism of dragonfly flight mechanics; thus, the
chord Reynolds number level of those studies is usually relatively
small (i.e., Re 10; 000). In the present study, we report a detailed
experimental investigation to quantify the flow behavior around a
bioinspired corrugated airfoil, compared with a conventional
streamlined airfoil and a flat plate at low Reynolds numbers. The
experimental study was conducted in a wind tunnel with particle
image velocimetry (PIV) to make detailed flowfield measurements in
addition to total aerodynamic force (drag-and-lift) measurements. It
should be noted that the present study was conducted with a fixed 2-D
corrugated-airfoil model in steady flows, whereas dragonflies fly
with flapping corrugated wings. As described by Newman et al. [5],
because the average flapping frequency of dragonfly flight is roughly
25 Hz with a forward flight speed of 10 m=s, so that in one cycle of
wing flapping, a dragonfly would move forward about 40 chord
lengths. It is therefore postulated that aerodynamics may be usefully
studied, at least initially, on a static wing in a steady flow. The present
study is conducted from the viewpoint of an aerospace engineer to
explore the potential applications of such nontraditional bioinspired
corrugated airfoils in MAV designs. Thus, we chose to conduct the
present study at the chord Reynolds number of Re 34; 000 (i.e., in
the range in which MAVs usually operate), which is much higher
than those previous experiments to study dragonfly flight
aerodynamics.
Experimental Setup and Studied Airfoils
The experimental study was conducted in a closed-circuit lowspeed 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.
Figure 1 depicts the three airfoils used in the present study: a
streamlined airfoil GA (W)-1 [also labeled as NASA LS(1)-0417]
airfoil, a flat-plate airfoil, and a bioinspired corrugated airfoil.
Fig. 1
The test airfoils.
Compared with standard NACA airfoils, the GA (W)-1 airfoil was
specially designed for low-speed aviation applications with a large
leading-edge radius to flatten the peak in the pressure-coefficient
profile near the airfoil nose to discourage flow separation [18]. The
GA (W)-1 airfoil has a maximum thickness of 17% of the chord
length. The flat plate has a rectangular cross section. The cross
section of the bioinspired corrugated airfoil corresponds to a typical
cross section of a dragonfly wing, which was digitally extracted from
the profile given in Vargas and Mittal [15]. The flat plate and the
bioinspired corrugated airfoil are made of wood plates with a
thickness of 4.0 mm. The maximum effective thickness of the
corrugated airfoil (i.e., the airfoil shape formed by fitting a spline
through the protruding corners of the corrugated cross section) is
about 15% of the chord length, which is slightly smaller than that of
the streamlined GA(W)-1 airfoil (17% of the chord length). The flatplate airfoil, bioinspired corrugated airfoil, and streamlined GA (W)1 airfoil have the same chord length: that is, C 101 mm. The flow
velocity at the inlet of the test section was set at U1 5:0 m=s for
the present study, which corresponds to a chord Reynolds number of
Re 3:4 104 . The turbulence intensity of the incoming stream
was found to be within 1.0%, measured by using a hot-wire
anemometer.
Figure 2 shows the experimental setup used in the present study for
PIV measurements. The test airfoils were installed in the middle of
the test section. A PIV system was used to make flow-velocity field
measurements along the chord at the middle span of the airfoils. The
flow was seeded with 1–5-m 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 and spherical and
cylindrical lenses. The thickness of the laser sheet in the
measurement region is about 0.5 mm. A high-resolution 12-bit
(1376 1040 pixels) CCD camera (SensiCam-QE, Cooke Corp.)
was used for PIV image acquisition, with the axis of the camera
perpendicular to the laser sheet. The CCD cameras and the doublepulsed Nd:YAG lasers were connected to a workstation (host
computer) via a digital delay generator (Berkeley Nucleonics, model
Fig. 2 Experimental set up for PIV measurements.
2070
HU AND TAMAI
565), which controlled the timing of the laser illumination and image
acquisition.
Instantaneous PIV velocity vectors were obtained by a frame-toframe cross-correlation technique involving successive frames of
patterns of particle images in an interrogation window of
32 32 pixels. An effective overlap of 50% of the interrogation
windows was employed in PIV image processing. The PIV
measurements were conducted at two spatial resolutions: a coarse
level to study the global features of the flowfields around the airfoils,
with a measurement window size of about 200 160 mm, and a
finer level to investigate the detailed flow structures near the leading
edges of the airfoils, with a measurement window size of about
50 40 mm. The effective resolutions of the PIV measurements
(i.e., grid sizes) were D=C 0:048 and 0.012, respectively. After the
instantaneous velocity vectors ui and vi were determined,
instantaneous spanwise vorticity !z could be derived. The timeaveraged quantities such as mean velocity U; V, ensembleaveraged spanwise vorticity, turbulent velocity fluctuations u 0 ; v 0 ,
2
and normalized turbulent kinetic energy [TKE u 02 v 02 =2U1
]
distributions were obtained from a cinema sequence of 280 frames of
instantaneous velocity fields. The measurement uncertainty level for
the velocity vectors is estimated to be within 2.0% and that of the
turbulent velocity fluctuations u 0 ; v 0 and TKE are about 5.0%. The
aerodynamic forces (lift and drag) acting on the test airfoils were also
measured by using a force-moment sensor cell (JR3, model 30E12AI40). The force-moment sensor cell is composed of foil strain-gauge
bridges, which are capable of measuring the forces on three
orthogonal axes and the moment (torque) about each axis. The
precision of the force-moment sensor cell for force measurements is
0:25% of the full scale (40 N).
Experimental Results and Discussions
Figure 3 shows the measured ensemble-averaged velocity field
and corresponding streamlines around the test airfoils at a 5.0-deg
angle of attack. As shown in the results given in Fig. 3a, incoming
fluid streams were found to flow smoothly along the streamlined nose
of the GA(W)-1 airfoil, as expected. However, flow separation was
found to take place near the trailing edge of the airfoil even at a 5.0deg angle of attack because of the low Reynolds number. As a result
of the flow separation, a large circulation region was found in the
wake of the GA(W)-1 airfoil.
For the flat plate, as revealed clearly from the measurement results
given in Fig. 3b, incoming fluid streams were found to separate from
the surface of the flat plate right from the leading edge and then
reattach to the upper surface of the flat plate in the near leading-edge
portion of the flat plate; that is, a circulation bubble was found to form
on the upper surface near the leading edge of the flat plate. Because of
the reattachment of the separated fluid streams, no apparent flow
separation or large circulation region could be found in the wake of
the flat plate.
For the bioinspired corrugated airfoil, the existence of a circulation
bubble near the leading edge of the airfoil can be seen clearly from the
measurement results given in Fig. 3c at a 5.0-deg angle of attack.
Smaller circulation bubbles (an enlarged view is given later) were
found to sit in the valleys of the corrugated cross section. High-speed
fluid streams outside the corrugation valleys were found to flow
smoothly along a virtual envelope profile constructed by fitting a
spline through the protruding corners of the corrugated cross section
(i.e., a smooth shape formed by filling the small circulation bubbles
solidly into the corrugation valleys). No apparent large-scale flow
separation or circulation region could be found in the wake of the
corrugated airfoil at a 5.0-deg angle of attack.
Figure 4 shows the PIV measurement results when the angle of
attack of the airfoils increases to 10.0 deg. For the GA (W)-1 airfoil,
the separation point at which high-speed flow streams begin to
separate from the upper surface of the GA (W)-1 airfoil was found to
move further upstream to approach the airfoil leading edge. Flow
separation was found to take place on almost the entire upper surface
of the airfoil; that is, the GA (W)-1 airfoil was found to stall, resulting
in a very large circulation region in the wake of the airfoil. The large
deficit of the velocity profile in the wake of the GA (W)-1 airfoil
would indicate a rapid increase of the aerodynamic drag force acting
on the airfoil due to the airfoil stall, which was confirmed from the
drag force measurement data given in Fig. 10.
For the flat plate, the circulation bubble on the upper surface near
the leading edge was found to burst when the angle of attack
increased to 10.0 deg. The high-speed flow streams separated from
the upper surface at the leading edge of the flat plate could no longer
reattach to the upper surface of the flat plate. Large-scale flow
separation was found to occur on entire upper surface of the flat plate
(i.e., airfoil stall), due to a more severe adverse pressure gradient at a
10.0-deg angle of attack. However, for the corrugated airfoil, highspeed fluid streams were still found to faithfully follow the envelope
profile of the corrugated cross section, and no large-scale flow
separation could be found over the corrugated airfoil at a 10.0-deg
angle of attack.
The adverse pressure gradient over the upper surface of the airfoils
would become more and more severe as the angle of attack increased.
Compared with those at a 10.0-deg angle of attack, the circulation
regions in the wakes of the GA (W)-1 airfoil and the flat plate were
found to be enlarged significantly when the angle of attack increased
to 15.0 deg (Fig. 5a and 5b), which would indicate increased
aerodynamic drag forces acting on the airfoils. Because of the severe
adverse pressure gradient at a 15.0-deg angle of attack, high-speed
flow streams around the corrugated airfoil were not able to follow the
envelope profile of the corrugated cross section any longer. Largescale flow separation was found to occur over almost the entire upper
surface of the corrugated airfoil; that is, airfoil stall was also found for
the bioinspired corrugated airfoil at a 15.0-deg angle of attack.
The PIV measurement results demonstrated clearly that the
bioinspired corrugated airfoil could delay large-scale flow separation
and airfoil stall to a much higher angle of attack (up to about 12.0 deg)
compared with the streamlined GA-1(W) airfoil (airfoil stall at a 9.0deg AOA) and the flat plate (airfoil stall at an 8.0-deg AOA). To
elucidate the fundamental reason why corrugated airfoils have better
performance in preventing large-scale flow separation and delaying
airfoil stall compared with streamlined airfoils and flat plates at low
Reynolds numbers, refined PIV measurements near the leading
edges of the airfoils were made to investigate detailed flow structures
around the leading edges of the airfoils. The refined PIV
measurement results are given in Figs. 6–9.
As described in the review articles of Lissaman [19] and Gad-elHak [20] for streamlined airfoils at low Reynolds numbers, the
boundary layers would remain laminar at the onset of the pressure
recovery unless artificially tripped. Laminar boundary layers are
unable to withstand any significant adverse pressure gradient.
Therefore, the aerodynamic performances of traditional streamlined
airfoils at low Reynolds numbers are entirely dictated by the
relatively poor separation resistance of the laminar boundary layers.
The laminar boundary layer over the streamlined GA (W)-1 airfoil
was visualized clearly as a thin vortex layer over the nose of the
airfoil in the instantaneous vorticity distribution given in Fig. 6. As
indicated in the PIV measurement results, the laminar boundary layer
would separate from the upper surface of the streamlined airfoil
because the laminar boundary layer has a very poor capacity to
overcome the adverse pressure gradient. Laminar flow separation
would take place on the upper surface of the GA (W)-1. The
separated laminar boundary layer would behave more like a free
shear layer, which is highly unstable; therefore, rolling up of Kelvin–
Helmohtz vortex structures and transition to turbulence would be
readily realized. Because of the laminar nature of the flow around the
nose of the streamlined airfoil, the regions with higher TKE were
found to be confined within the thin separated shear layer.
Figure 7 reveals the flow behavior around the leading edge of the
flat plate at a 10-deg angle of attack. Because of the low Reynolds
number, incoming flow streams were found to separate from the
leading edge of the flat plate to form a separated laminar shear layer.
The laminar shear layer was found to transition to turbulence by
generating unsteady Kelvin–Helmohtz vortex structures. Compared
with those found near the nose of the streamlined GA (W)-1 airfoil,
the Kelvin–Helmohtz vortex structures near the flat-plate leading
HU AND TAMAI
2071
Fig. 3 PIV measurement results at 5.0-deg AOA; ensemble-averaged velocity field (left) and corresponding streamlines (right).
edge were found to be much stronger, which results in a much higher
turbulent kinetic energy level compared with that of the streamlined
GA(W)-1 airfoil. As shown in Fig. 3, due to the sharp leading edge of
the flat plate, incoming fluid streams would separate from the upper
surface of the flat plate right from the shape leading edge. The
separated fluid streams could reattach to the upper surface of the plate
to form a circulation bubble on the upper surface of the flat plate
when the advance pressure gradient on the upper surface of the flat
plate is rather mild at relatively small angles of attack. However,
when the angle of attack is relatively large (AOA > 8:0) and the
adverse pressure gradient over the upper surface of the flat plate
becomes more significant, the separated fluid streams would no
longer be able to reattach to the upper surface of the flat plate. The
circulation bubble near the leading edge would then burst to cause
airfoil stall, as shown in Fig. 4.
Flow around the leading edge of the corrugated airfoil is much
more involved than those of the flat plate and the GA (W)-1 airfoil.
As visualized in the PIV measurement results given in Fig. 8, due to
the sharp leading edge, incoming fluid streams were found to
separate from the corrugated airfoil right from the sharp leading edge
to form a laminar shear layer at first. Then the separated laminar
boundary layer was found to transition to turbulent rapidly as it
approached the first protruding corner of the corrugated airfoil.
Unsteady vortices were found to shed periodically from the
protruding corners of the corrugated cross section; that is, the
protruding corners of the corrugated airfoil seem to act as turbulators
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HU AND TAMAI
Fig. 4
PIV measurement results at a 10.0-deg AOA; ensemble-averaged velocity field (left) and corresponding streamlines (right).
to generate unsteady vortex structures that promote the transition of
the separated boundary layer from laminar to turbulent. For the
streamlined GA (W)-1 airfoil and flat plate at the same angle of attack
of 10 deg, the turbulent transition and the generation of the unsteady
vortex structures were found to take place in the regions relatively far
away from the surfaces of the airfoils, as revealed in the measurement
results given in Figs. 6 and 7. For the corrugated airfoil, the turbulent
transition and the generation of the unsteady vortex structures were
found to take place in the region quite close to the protruding corners
of the corrugated airfoil. The unsteady vortex structures were found
to be trapped in the valleys of the corrugated cross section, which
would dynamically interact with the high-speed flow streams outside
the valleys. Because of the interaction between the unsteady vortex
structures and outside high-speed fluid streams, high-speed fluid was
found to be pumped from outside to near-wall regions (the pumping
effect of the unsteady vortex structures to move high-speed fluid
from outside to near-wall regions can be seen clearly from the
animations of the time sequence of instantaneous PIV measurements). The pumping of high-speed fluid to near-wall regions
provided sufficient kinetic energy for the boundary layer to
overcome the adverse pressure gradient to suppress large-scale flow
separation and airfoil stall. The mean velocity vectors and
corresponding streamlines revealed clearly that small circulation
bubbles would be formed in the valleys of the corrugated airfoil.
High-speed fluid streams outside the valleys would flow smoothly
along the envelope profile of the corrugated cross section (i.e., the
HU AND TAMAI
Fig. 5
2073
PIV measurement results at a 15.0-deg AOA; ensemble-averaged velocity field (left) and corresponding streamlines (right).
profile was formed as the valleys were solidly filled with the small
circulation bubbles). The rotation direction of the circulation bubbles
in the valleys was found to be clockwise (flow moving from left to
right) to accommodate the high-speed fluid streams outside the
valleys. For the corrugated airfoil, the rapid transition of the
boundary layer from laminar to turbulent due to the effect of the
protruding corners as turbulators could also be seen clearly from the
measured TKE distribution, in which the contour lines of the regions
with higher turbulent kinetic energy were found to diverge rapidly
after reaching the first protruding corner of the corrugate airfoil. The
entrainment of high-speed fluid to near-wall regions by the unsteady
vortex structures resulted in a much higher TKE level in the near-wall
regions.
It should be noted that Vargas and Mittal [15] conducted a
numerical study to investigate flow structures around a corrugated
airfoil similar to that used in the present study, but at a lower
Reynolds number level of Re 10; 000. Despite the difference in
Reynolds number of the two studies, the measurement results of the
present study were found to agree well with the numerical simulation
of Vargas and Mittal in revealing the global pattern of the flowfield
around the corrugated airfoil and the small vortex structures in the
valleys of the corrugated cross section.
Compared with those of the streamlined GA (W)-1 airfoil and
flat plate, the energetic turbulent boundary layer over the upper
surface of the corrugated airfoil would be much more capable of
advancing against an adverse pressure gradient, suppressing flow
2074
HU AND TAMAI
separation [19,20]. Therefore, flow streams would be able to attach
to the envelope profile of the corrugated airfoil faithfully even at
much larger angles of attack (up to 12.0 deg), whereas the
large-scale flow separation and airfoil stall had already been found
to take place for the flat plate and the streamlined GA (W)-1
airfoil.
As shown in Fig. 9, although the separated laminar boundary layer
was found still to transition to turbulence rapidly by generating
Fig. 6 Around the nose of the GA (W)-1 airfoil at AOA 10:0 deg.
Fig. 7 Around the nose of the flat plate at AOA 10:0 deg.
HU AND TAMAI
2075
unsteady Kelvin–Helmohtz vortex structures in the flowfield when
the angle of attack increases to 15.0 deg, the shedding path of the
unsteady vortex structures was found to be relatively far from the
surface of the corrugated airfoil. The unsteady vortex structures
could no longer be trapped in the valleys of the corrugation. The
ensemble-averaged velocity field and the corresponding streamlines
also show clearly that the high-speed flow streams permanently
separate from the upper surface of the airfoil. Although small
Fig. 8 Around the nose of the corrugated airfoil at AOA 10:0 deg.
Fig. 9
Around the nose of the corrugated airfoil at AOA 15:0 deg.
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HU AND TAMAI
circulation bubbles were still found to sit in the valleys of the
corrugated cross section, they became much weaker (i.e., much
lower rotating velocity, as revealed from the velocity distributions),
and their rotating direction was also found to be reversed to
accommodate the reversed flow outside the valleys. The adverse
pressure gradient over the upper surfaces of the airfoils would
become much more significant as the angle of attack increased to
15.0 deg, which requires a much more energetic boundary layer to
overcome the adverse pressure gradient over the upper surface of the
airfoil. However, the measured TKE distribution reveals that the
regions with higher turbulent kinetic energy were along the shedding
path of the Kelvin–Helmohtz vortex structures, which is quite far
from the surface of the corrugated airfoil. Therefore, large-scale flow
separation and airfoil stall were found to take place on the corrugated
airfoil, due to the lack of enough kinetic energy in the boundary layer
to overcome the significant adverse pressure gradient, as shown in
Fig. 5c.
Figure 10 shows the measured aerodynamic forces (lift and drag)
acting on the test airfoils at different angles of attack. The estimated
measurement uncertainties are also shown in the figure as error bars.
The corrugated airfoil was found to have almost comparable lift
coefficient with those of the GA (W)-1 airfoil and the flat plate when
the angle of attack is relatively small (AOA < 8:0). As expected, the
lift coefficient would increase almost linearly with the increasing
angle of attack. As revealed in the preceding PIV measurement
results, airfoil stall was found to take place at an 8.0-deg angle of
attack for the flat plate. After airfoil stall, the lift coefficient profile of
the flat plate was found to become almost flat, and the drag coefficient
was found to increase rapidly as the angle of attack increased. Such
trends of the drag-and-lift coefficient profiles for a flat plate were also
reported by Kesel [12] and Sunada et al. [13]. For the GA (W)-1
airfoil, airfoil stall was found to occur at about a 9.0-deg angle of
attack. As expected, the lift coefficient of the GA (W)-1 airfoil
dropped significantly after airfoil stall, and the drag coefficient
increased rapidly as the angle of attack increased. Because the
corrugated airfoil could delay large-scale flow separation and airfoil
stall up to a 12.0-deg angle of attack, the measured maximum lift
coefficient for the corrugated airfoil was found to be 0.94, which is
approximately 26% higher than that of the flat plate (about 0.70 at
AOA 8:0 deg) and 10% higher than that of the GA(W)-1 airfoil
(about 0.84 at AOA 9:0 deg). After airfoil stall, the lift coefficient
of the corrugated airfoil was found to drop significantly, which is
similar to that of the streamlined GA (W)-1 airfoil. Kesel [12]
reported similar results when he measured the aerodynamic forces
(lift and drag) acting on a corrugated airfoil similar to that in the
present study at a lower Reynolds number of Re 10; 000.
As shown in Fig. 10, the measured drag coefficient data were more
qualitative rather than quantitative, due to the relatively poor
measure accuracy at low angles of attack. The measured drag
coefficient of the corrugated airfoil was found to be slightly larger
than the other two airfoils when the angle of attack was relatively
small (AOA < 8:0 deg). As the angle of attack became large enough
(AOA > 10:0 deg), the drag coefficient of the corrugated airfoil was
found to become very comparable with those of the streamlined GA
(W)-1 airfoil and flat plate. This can be explained as follows: it is well
known that the total drag force acting on an airfoil can be divided into
friction drag and pressure drag. The friction drag is due to the shear
stress acting on the surface of the airfoil. The pressure drag is due to
the pressure difference around the surface of the airfoil. The pressure
drag is also often referred to as the form drag, because of its strong
dependence on the effective shape of the airfoil, which is usually
indicated by the averaged streamline pattern around the airfoil. The
pressure drag is generally much larger than the friction drag. When
the angle of attack is relatively small (AOA < 8:0 deg), the slightly
higher drag acting on the corrugated airfoil is believed to be closely
related to the fact that the corrugated airfoil has a much larger contact
area with moving flow streams (i.e., increased friction drag), due to
its complex shape of the corrugated cross section. As the angle of
attack becomes large enough, airfoil stall takes place for the test
airfoils (i.e., flat plate at AOA 8:0 deg, GA(W)-1 airfoil at
AOA 9:0 deg, and corrugated airfoil at AOA 12:0 deg). After
airfoil stall, large-scale flow separation covers the entire upper
surfaces of the airfoils. The pressure drag increases dramatically, and
the friction drag becomes negligible. Therefore, the drag force acting
on the airfoil is mainly determined by pressure drag, which could be
indicated by the streamline pattern around the airfoil. As revealed
clearly in the PIV measurement results given in Fig. 5, the streamline
patterns for the flow around the corrugated airfoil are very much the
same as those around the GA(W)-1 airfoil and flat plate after airfoil
stall; that is, a very large separation bubble would be generated to
cover the entire upper surface of the airfoil. Therefore, the drag
coefficient of the corrugated airfoil would become comparable with
those of the GA (W)-1 airfoil and flat plate at relatively large angles
of attack.
It should be noted that although the relatively big drag coefficients
of the corrugated airfoil at low angles of attack may be an issue to
limit their applications, especially for the MAVs flying at low angles
of attack, the unique feature of the corrugated airfoil in preventing
large-scale flow separations and airfoil stall can be leveraged in
MAV designs to improve their flight agility and maneuverability at
high angles of attack. It should also be noted that the geometric
parameters of the corrugated-airfoil model used in the present study
were chosen rather arbitrarily. Further systematic studies are needed
to explore/optimize such bioinspired airfoil shape and wing planform
design paradigms (i.e., the effects of the design parameters such as
the geometry of the corrugated profile, the camber of the airfoil, the
thickness of the airfoil, the stiffness of the material or flexibility of the
airfoil, the corner sharpness of the corrugations, etc.) to achieve
improved aerodynamic performance for MAV applications.
Conclusions
Fig. 10 Measured lift-and-drag coefficient profiles.
An experimental study was conducted to investigate the flow
features around a bioinspired corrugated airfoil compared with a
streamlined GA (W)-1 airfoil and a flat plate at a low chord Reynolds
number of 34,000 to explore the potential applications of
nontraditional bioinspired corrugated airfoils for MAV designs.
The experimental study was conducted in a wind tunnel with particle
image velocimetry to make detailed flowfield measurements in
addition to total aerodynamic force measurements. The quantitative
flowfield measurement results demonstrated clearly that the
HU AND TAMAI
corrugated airfoil could have a better performance over the
streamlined airfoil and flat plate in preventing large-scale flow
separation and airfoil stall at low Reynolds numbers. Because of the
low Reynolds number, flow separation was found near the trailing
edge of the GA (W)-1 airfoil when the angle of attack was a mere
5.0 deg, and airfoil stall was found to take place at about a 9.0-deg
angle of attack for the streamlined GA (W)-1 airfoil. Large-scale flow
separation was found over the entire upper surface of the flat plate as
the angle of attack reached 8.0 deg. However, no apparent large-scale
flow separation or airfoil stall could be found for the bioinspired
corrugated airfoil up to a 12.0-deg angle of attack. The aerodynamic
force (lift-and-drag) measurement results further confirmed the
possibility of using such nontraditional bioinspired corrugated
airfoils in MAV designs for improved agility and maneuverability.
The detailed PIV measurements elucidated the underlying physics
about how and why corrugated airfoils could suppress large-scale
flow separation and airfoil stall at low Reynolds numbers. It was
found that the protruding corners of the corrugated airfoils would act
as turbulators to generate unsteady vortex structures to promote the
transition of the boundary layer from laminar to turbulent. The
unsteady vortices trapped in the valleys of the corrugated cross
section could pump high-speed fluid from outside to near-wall
regions to provide sufficient kinetic energy within the boundarylayer flow to overcome adverse pressure gradients, thus discouraging
flow separation and airfoil stall.
It should be noted that the although the bioinspired corrugatedairfoil model used in the present study has the same corrugated
profile as the midsection of a dragonfly forewing, the relative
thickness of the airfoil, the material stiffness, the complexity of the
wing planform, the motion of the airfoil, and the working chord
Reynolds number used for the present study are quite different from
those of a real dragonfly. Although some of the findings derived from
the present study may be useful to understand dragonfly flight
aerodynamics, the flow structures revealed from the present study
could be quite different from those of previous studies with free or
tethered dragonflies at much lower Reynolds numbers. It is worthy of
noting again that the purpose of the present study is to try to explore a
nontraditional airfoil design for MAV applications through
bioinspiration (i.e., by leveraging the corrugated feature of dragonfly
wings), rather than to try to understand the fundamental physics of
dragonfly flight aerodynamics.
Acknowledgments
The support of National Science Foundation CAREER program
under award number CTS-0545918 is gratefully acknowledged.
References
[1] Mueller, T. J. (ed.), Fixed and Flapping Wing Aerodynamics for Micro
Air Vehicle Applications Progress in Astronautics and Aeronautics,
AIAA, Reston, VA, 2001.
[2] Rees, C. J. C., “Form and Function in Corrugated Insect Wings,”
Nature, Vol. 256, July 1975, pp. 200–203.
doi:10.1038/256200a0
2077
[3] Kesel, A. B., Philippi, U., and Nachtigall, W., “Biomechanical Aspects
of Insect Wings–An Analysis Using the Finite Element Method,”
Computers in Biology and Medicine, Vol. 28, No. 4, 1998, pp. 423–
437.
doi:10.1016/S0010-4825(98)00018-3
[4] Rees, C. J. C., “Aerodynamic Properties of an Insect Wing Section and a
Smooth Aerofoil Compared,” Nature, Vol. 258, No. 13, 1975, pp. 141–
142.
doi:10.1038/258141a0
[5] Newman, B. G., Savage, S. B., and Schouella, D., “Model Test on a
Wing Section of an Aeschna Dragonfly,” Scale Effects in Animal
Locomotion, edited by T. J. Pedley, Academic Press, London, 1977,
pp. 445–477.
[6] Azuma, A., Azuma, S., Watanabe, I., and Furuta, T., “Flight Mechanics
of a Dragonfly,” Journal of Experimental Biology, Vol. 116, No. 1,
1985, pp. 79–107.
[7] Somps, C., and Luttges, M., “Dragonfly Flight: Novel Uses of
Unsteady Separation Flows,” Science, Vol. 228, No. 4705, June 1985,
pp. 1326–1329.
doi:10.1126/science.228.4705.1326
[8] Azuma, A., and Watanabe, T., “Flight Performance of a Dragonfly,”
Journal of Experimental Biology, Vol. 137, No. 1, 1988, pp. 221–252.
[9] Rüppell, G., “Kinematic Analysis of Symmetrical Flight Maneuvers of
Odonata,” Journal of Experimental Biology, Vol. 144, No. 1, 1989,
pp. 13–42.
[10] Okamoto, M., Yasuda, K., and Azuma, A., “Aerodynamic Characteristics of the Wings and Body of a Dragonfly,” Journal of Experimental
Biology, Vol. 199, No. 2, 1996, pp. 281–294.
[11] Wakeling, J. M., and Ellington, C. P., “Dragonfly Flight 1: Gliding
Flight and Steady-State Aerodynamic Forces,” Journal of Experimental Biology, Vol. 200, No. 3, 1997, pp. 543–556.
[12] Kesel, A. B., “Aerodynamic Characteristics of Dragonfly Wing
Sections Compared with Technical Aerofoil,” Journal of Experimental
Biology, Vol. 203, No. 20, 2000, pp. 3125–3135.
[13] Sunada, S., Yasuda, T., Yasuda, K., and Kawachi, K., “Comparison of
Wing Characteristics at an Ultralow Reynolds Number,” Journal of
Aircraft, Vol. 39, No. 2, 2002, pp. 331–338.
[14] Thomas, A. L. R., Taylor, G. K., Srygley, R. B., Nudds, R. L., and
Bomphrey, R. J., “Dragonfly Flight: Free-Flight and Tethered Flow
Visualizations Reveal a Diverse Array of Unsteady Lift-Generating
Mechanisms, Controlled Primarily via Angle of Attack,” Journal of
Experimental Biology, Vol. 207, No. 24, 2004, pp. 4299–4323.
doi:10.1242/jeb.01262
[15] Vargas, A., and Mittal, R., “Aerodynamic Performance of Biological
Airfoils,” 2nd AIAA Flow Control Conference, Portland, OR, AIAA
Paper 2004-2319, 2004.
[16] Luo, G., and Sun, M., “The Effects of Corrugation and Wing Planform
on the Aerodynamic Force Production of Sweeping Model Insect
Wings,” Acta Mechanica Sinica, Vol. 21, No. 6, 2005, pp. 531–541.
doi:10.1007/s10409-005-0072-4
[17] Kwok, M., and Mittal, R., “Experimental Investigation of the
Aerodynamics of a Modeled Dragonfly Wing Section,” AIAA Region IMA Student Conference, AIAA, Reston, VA, 8–9 Apr. 2005, pp. 1–7.
[18] McGee, R. J., and Beasley, W. D., “Low-Speed Aerodynamics
Characteristics of a 17-Percent-Thick Airfoil Section Designed for
General Aviation Applications,” NASA TN D-7428, 1973.
[19] Lissaman, P. B. S., “Low-Reynolds-Number Airfoils,” Annual Review
of Fluid Mechanics, Vol. 15, 1983, pp. 223–239.
doi:10.1146/annurev.fl.15.010183.001255
[20] Gad-el-Hak, M., “Micro-Air-Vehicles: Can They Be Controlled
Better,” Journal of Aircraft, Vol. 38, No. 3, 2001, pp. 419–429.
INSTITUTE OF PHYSICS PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 17 (2006) 1269–1281
doi:10.1088/0957-0233/17/6/S06
Molecular tagging velocimetry and
thermometry and its application to the
wake of a heated circular cylinder
Hui Hu1 and Manoochehr M Koochesfahani2
1
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA
Department of Mechanical Engineering, Michigan State University, East Lansing,
MI 48824, USA
2
E-mail: huhui@iastate.edu and koochesf@egr.msu.edu
Received 8 August 2005, in final form 26 October 2005
Published 26 April 2006
Online at stacks.iop.org/MST/17/1269
Abstract
We report improvements to the molecular tagging velocimetry and
thermometry (MTV&T) technique for the simultaneous measurement of
velocity and temperature fields in fluid flows. A phosphorescent molecule,
which can be turned into a long lifetime tracer upon excitation by photons of
appropriate wavelength, is used as a tracer for both velocity and temperature
measurements. A pulsed laser is used to ‘tag’ the regions of interest, and
those tagged regions are imaged at two successive times within the lifetime
of the tracer molecules. The measured Lagrangian displacement of the
tagged molecules provides the estimate of the fluid velocity vector. The
simultaneous temperature measurement is achieved by taking advantage of
the temperature dependence of phosphorescence lifetime, which is
estimated from the intensity ratio of the tagged molecules in the two images.
In relation to the original molecular tagging thermometry work of
Thompson and Maynes (2001 J. Fluid Eng. 123 293–302), the
improvements reported here are the use of lifetime imaging as a ratiometric
method to enhance the robustness and accuracy of temperature
measurements and the extension of the technique to simultaneous
whole-field planar mapping of velocity and temperature fields. Compared
with other simultaneous velocity and temperature measurement techniques
such as combined PIV-LIF (Sakakibara et al 1997 Int. J. Heat Mass
Transfer 40 3163–76, Grissino et al 1999 Proc. 3rd Int. Workshop on
Particale Image Velocimetry (Santa Barbara, CA, USA, 16–18 September
1999)) and the DPIV/T technique (Park et al 2001 Exp. Fluids 30 327–38),
this method accomplishes the same objectives but with a completely
molecular-based approach. Because of its molecular nature, issues such as
tracking of the flow by the seed particles and the thermal response of the
thermal tracer particles are eliminated. In addition, the use of a single
molecular tracer and a dual-frame CCD camera provides for a much reduced
burden on the instrumentation and experimental set-up. The implementation
and application of the new technique are demonstrated by conducting
simultaneous velocity and temperature measurements in the wake region of
a heated circular cylinder at a Richardson number of 0.36, a value large
enough for the buoyancy effects to potentially influence the flow.
0957-0233/06/061269+13$30.00
© 2006 IOP Publishing Ltd Printed in the UK
1269
H Hu and M M Koochesfahani
Keywords: fluid flow velocity and temperature, molecular tagging
velocimetry, molecular tagging thermometry, optical diagnostics, heated
cylinder wake
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Velocity and temperature are two important variables in studies
of thermofluid problems. Simultaneous information on these
two variables is often required to further our understanding
of the fundamental mechanisms of complex thermofluid
phenomena. In turbulent flows, the temperature field is
determined by the molecular diffusion of heat and transport
by the turbulent flow field. When one considers the Reynoldsaveraged energy conservation equation, the effect of turbulent
transport appears in terms of the correlation between the
temperature and velocity fluctuations, i.e. turbulent heat flux
uj T . Experimental characterization of these correlation terms
is needed for the development and validation of physical
models.
In order to measure the correlation between velocity
and temperature fluctuations in turbulent flows, early studies
were conducted using intrusive probes.
Antonia et al
(1975) and Chevray and Tutu (1978) employed a cold-wire
sensor mounted on an X-wire probe to obtain simultaneous
measurements of temperature and velocity in a heated jet flow.
Kotsovinos (1977) used the combination of one-component
laser Doppler velocimetry (LDV) and fast response thermistors
to measure the velocity and temperature simultaneously in
turbulent buoyant jets.
More recently, the advent of optical diagnostics such
as LDV, laser-induced fluorescence (LIF) and Raman
scattering techniques has presented new opportunities for
the non-intrusive simultaneous measurements of velocity and
temperature in fluid flows. By combining LDV and vibrational
Raman scattering, Dibble et al (1984) measured the velocity
and temperature in turbulent flames. Taking advantage of the
temperature dependence of fluorescence emission, a combined
LIF and LDV technique was used by Lemoine et al (1999) to
conduct temperature and velocity measurements at the points
of interest in a turbulent heated jet. These investigations,
however, involved single-point measurements.
Whole-field diagnostic techniques such as particle image
velocimetry (PIV) and LIF have led to recent efforts in
the simultaneous quantification of velocity and temperature
distributions over a plane. A combination of PIV and
LIF has been used by Sakakibara et al (1997), Hishida
and Sakakibara (2000) and Grissino et al (1999) to obtain
simultaneous measurements of velocity and temperature fields
in a study of heat transfer characteristics in turbulent flows.
By using thermochromic liquid crystal (TLC) encapsulated
microspheres as tracer particles, a digital particle image
velocimetry/thermometry (DPIV/T) technique has also been
developed (Dabiri and Gharib 1991, Park et al 2001) to achieve
such simultaneous measurements.
Since the optical velocimetry techniques mentioned above
are particle based, the potential implications associated with
the use of seed particles need to be evaluated for each
1270
experiment. Some of these implications are related to flow
tracking issues, such as particle size, density mismatch, etc.
Even if particles track the flow perfectly, strong out-ofplane motions that may bring the particle tracers into and
out of the laser sheet can affect the accuracy of the inplane velocity measurements in PIV. If particles are used
also for temperature measurement (e.g., TLC encapsulated
microspheres), additional considerations are also required
about the thermal response of the particle tracers. When PIV
is combined with LIF, complications such as the influence of
laser light absorption/scattering by the seed particles on the
LIF signal need to be carefully considered. For the combined
PIV/LIF technique, at least two cameras with various optical
filters are required to record the particle scattering and LIF
signals separately. A very careful image registration or
coordinate mapping procedure is also required in order to
get the quantitative spatial relation between the simultaneous
velocity and temperature measurements.
In this paper, a completely molecular-based method
is presented for the simultaneous whole-field mapping of
velocity and temperature fields. The method is based on a
molecular tagging approach that combines molecular tagging
velocimetry (MTV) with molecular tagging thermometry
(MTT). Because of its molecular nature, this method
eliminates issues such as the tracking of the flow by the seed
particles. A molecular-based approach has been previously
reported for the simultaneous measurement of velocity and
scalar concentration fields by combining MTV with LIF using
two tracers, one for MTV and one for LIF (Koochesfahani
et al 2000). The present work employs a single tracer for
both MTV and MTT. The particular tracer used here is a
water-soluble long-lived phosphorescent triplex that has found
extensive use as a tracer for MTV (Koochesfahani et al
1996, Gendrich et al 1997). The use of this triplex for
thermometry was first reported by Thompson and Maynes
(2001) who coined the term molecular tagging thermometry
(MTT). In that work, an intensity-based approach was utilized;
the variation of phosphorescence intensity with temperature
was used as the basis for thermometry. By taking advantage of
the temperature dependence of the phosphorescence lifetime,
Hu and Koochesfahani (2003) advanced MTT by developing a
lifetime-based thermometry technique, a ratiometric approach
to eliminate the effects of the temporal and spatial variations
in the incident laser intensity and the non-uniformity of the
dye concentration (e.g., due to bleaching).
Due to the nature of their implementation based on
tagging molecules along single lines, however, both Thompson
and Maynes (2001) and Hu and Koochesfahani (2003) were
limited to combined thermometry and only one-component
velocimetry in unidirectional flows. In this work, the lifetimebased ratiometric approach of Hu and Koochesfahani (2003)
is extended for simultaneous whole-field planar mapping of
velocity and temperature fields in a general flow field. A
laser is used to ‘tag’ the molecules in the regions of interest;
Molecular tagging velocimetry and thermometry and its application
(a)
(b)
(c)
Figure 1. Typical MTV image pairs and the resultant two-component velocity field (Gendrich et al 1997). The flow shown is from a vortex
ring impacting on a flat wall at normal incidence. The axis of symmetry is indicated by the dashed lines: (a) The grid imaged 1 µs after the
laser pulse. (b) The same grid imaged 8 ms later. (c) The velocity field derived from (a) and (b).
the displacement of the tagged regions provides the velocity
information and the phosphorescence intensity decay within
those regions is used to determine the temperature. In the
following sections, a brief general overview of MTV is given
along with more details of lifetime-based MTT and the related
properties of the phosphorescent tracer used. A demonstration
of the application of this molecular-based approach is provided
by carrying out simultaneous measurements of the velocity and
temperature fields in the wake of a heated cylinder.
2. Molecular tagging velocimetry (MTV)
MTV is a whole-field optical technique which relies on
molecules that can be turned into long lifetime tracers upon
excitation by photons of appropriate wavelength. Typically,
a pulsed laser is used to ‘tag’ the regions of interest, and
those tagged regions are interrogated at two successive times
within the lifetime of the tracer. The measured Lagrangian
displacement of the tagged molecules provides the estimate
of the velocity vector. The technique can be thought of
as essentially a molecular counterpart of PIV and can offer
advantages in situations where the use of seed particles is
either not desirable, difficult, or may lead to complications.
Figure 1 illustrates one implementation of the technique where
the particular tracer used is a water-soluble phosphorescent
supramolecule. A planar grid of intersecting laser beams,
formed from a pulsed excimer laser (20 ns pulse, 308 nm
wavelength), turns on the luminescence of the supramolecules
that are premixed in a water flow of a vortex ring approaching
a solid wall at normal incidence (Gendrich et al 1997). The
displacement of the tagged regions is determined, in this case,
using a direct spatial correlation method. The conventional
planar imaging shown in figure 1 provides information on
two components of the velocity vector, the projection onto the
viewed plane. Stereo imaging can produce the complete three
components of the velocity vector (Bohl et al 2001). Various
advances in this measurement technique in terms of available
molecular tracers, methods of tagging, detection/imaging and
data processing can be found in several review articles (Falco
and Nocera 1993, Koochesfahani et al 1996, Koochesfahani
1999, Lempert and Harris 2000), in addition to a special
issue of Measurement Science and Technology on this topic
(Koochesfahani 2000).
The work described here takes advantage of a
phosphorescent supramolecule as a common molecular tracer
for both velocimetry and thermometry. It has been shown that
water-soluble supramolecular complexes may be designed to
exhibit long-lived phosphorescence, which is not quenched
by O2, upon mixing a lumophore, an appropriate alcohol,
and cyclodextrin (Ponce et al 1993, Mortellaro and Nocera
1996, Hartmann et al 1996). The original design used
in MTV (Koochesfahani et al 1996, Gendrich et al 1997)
is 1-BrNp·Gβ-CD·ROH, a triplex formed by mixing the
lumophore (1-BrNp), certain alcohols (indicated collectively
by ROH), and an aqueous solution of glucosyl-β-cyclodextrin
(Gβ-CD). The resulting long-lived green phosphorescence has
a typical lifetime of up to several milliseconds. The current
work utilizes the laser-induced phosphorescence of a slightly
different triplex, 1-BrNp·Mβ-CD·ROH. In this triplex, the
original glucose sugar subunits that are hanging off the rim
of the cyclodextrin for increased solubility (i.e., glucosyl-βcyclodextrin, Gβ-CD) have been replaced by maltose (i.e.,
maltosyl-β-cyclodextrin, Mβ-CD). The measured properties
of both glucose- and maltose-based triplexes are quite similar
and the two can be used interchangeably. The dependence of
the phosphorescence lifetime on temperature, the property that
is used for thermometry, will be discussed in section 3.
Tagging the molecular tracers along single or multiple
parallel lines is perhaps the simplest method of tagging and has
been utilized in a large fraction of studies to date. It is clear that
line tagging allows the measurement of only one component
of velocity that is normal to the tagged line. In addition,
the estimate of this velocity component has an inherent error
associated with it, which is connected with the ambiguity in the
unique determination of the displacements of various portions
of a (continuous) tagged line. This ambiguity can also cause
significant errors in the temperature inferred from MTT in
three-dimensional flows with non-uniform temperature field.
In order to unambiguously measure two components of the
velocity in a plane, the luminescence intensity field from a
tagged region must have spatial gradients in two, preferably
orthogonal, directions. For single-point velocimetry, this
is easily achieved using a pair of crossing laser beams; a
grid of intersecting laser lines allows multi-point velocity
measurements as shown in figure 1. As already mentioned,
stereo imaging would allow the recovery of the third, out-ofplane, velocity component as well.
In the original work of Gendrich et al (1997), for each
laser pulse the MTV image pairs were acquired by a pair of
aligned image detectors viewing the same region in the flow.
1271
H Hu and M M Koochesfahani
In the current work, the two detectors are replaced by a single
intensified CCD camera (PCO DiCam-Pro) operating in the
dual-frame mode, which allows the acquisition of two images
of the tagged regions with a programmable time delay between
them. The displacement of the tagged regions is determined
by a direct digital spatial correlation technique. The details of
this approach and its performance are described in Gendrich
and Koochesfahani (1996). A small window, referred to as
the source window, is selected from a tagged region in the
earlier image, and it is spatially correlated with a larger roam
window in the second image. A well-defined correlation peak
occurs at the location corresponding to the displacement of the
tagged region by the flow; the displacement peak is located
to sub-pixel accuracy using a multi-dimensional polynomial
fit. According to Gendrich and Koochesfahani (1996), the
accuracy in measuring the displacement of the tagged regions
depends on the signal/noise ratio of the images acquired;
it can be typically determined with a 95% confidence limit
of ±0.1 sub-pixel accuracy (i.e., 95% of the displacement
measurements are accurate to better than 0.1 pixel). This
corresponds to an rms accuracy of ±0.05 pixel, assuming a
Gaussian distribution for error. For high values of image
signal/noise ratio, the 95% confidence level can be as low as
0.015 pixel (0.0075 pixel rms). An example of the application
of this procedure is provided in figure 1; the velocity vectors
shown in this figure are ‘raw’ and have not been filtered or
smoothed.
For velocity measurement, MTV utilizes the information
about the spatial distribution of the photoluminescence
of the tagged molecules within a region to determine
the displacement and, therefore, the spatially averaged
velocity of a tagged region. As described in the following
section, monitoring the phosphorescence intensity decay rate
(i.e., emission lifetime) within the tagged regions provides
information on the spatially averaged temperature within those
regions simultaneous with velocity information.
3. Molecular tagging thermometry (MTT)
Fluorescence and phosphorescence are molecular
photoluminescence phenomena and their general properties
can be found in texts on photochemistry (e.g., Turro 1978,
Ferraudi 1988). Fluorescence refers to the radiative process
when a molecule transitions from a singlet excited state
to its singlet ground state. Since singlet–singlet transitions
are quantum mechanically allowed, they occur with a
high probability, making fluorscence short lived with
short emission lifetimes on the order of nanoseconds.
Phosphorescence, on the other hand, is a radiative process
when a molecule transitions from a triplet excited state to its
singlet ground state. Because such transitions are quantum
mechanically forbidden, phosphorescence is long lived
with emission lifetimes that may approach microseconds or
even minutes. For some molecules, the photoluminescence
(either fluorescence or phosphorescence) emission intensity
is temperature dependent, allowing the measurement of the
emission intensity of tracer molecules to be used to quantify
the temperature field in a fluid flow.
The laser-induced fluorescence (LIF) technique has been
widely used for fluid flow temperature measurement in recent
1272
years. Since the fluorescence emission has a very short lifetime
of order nanoseconds, molecular tagging velocimetry based
on direct fluorescence is practical only for extremely fast flow
velocities. Furthermore, because of the short lifetime, LIF
methods typically rely on the information obtained from the
‘intensity axis’ of the emission process, i.e. the fluorescence
intensity is used to infer the temperature. The artefacts caused
by the variations in the incident laser intensity distribution
are eliminated using ratiometric LIF techniques such as the
two-dye approach (Coppeta and Rogers 1998, Sakakibara and
Adrian 1999) and the single-dye two-emission-band method
(Lavielle et al 2001). For these ratiometric LIF techniques,
two cameras with various optical filters are required, along
with a very careful image registration or coordinate mapping
procedure in order to get the quantitative spatial relation
between the two images. In addition, other complications also
need to be carefully considered, such as the spectral conflicts
and photobleaching behaviour of the two dyes in the twodye approach (Coppeta and Rogers 1998). In the single-dye
two-emission-band method, the LIF signal reduction caused
by the integration of emission over a narrow spectral band
necessitates special attention to issues such as signal-to-noise
ratio and the choices of the image recording system and optical
filters (Lavielle et al 2001).
Laser-induced phosphorescence has not been used as
commonly as LIF for flow diagnostics in liquids because longlived excited states suffer from O2 quenching and, as a result,
suitable molecular complexes, such as the phosphorescent
triplex used here, have not been available for aqueous flows
until recently. Use of phosphorescent tracers can offer certain
advantages for imaging in fluid flows since the relatively long
lifetime of phosphorescence allows one to take advantage of
the ‘time axis’ in the emission process. One such advantage
is the ability to perform molecular tagging velocimetry,
as already described in section 2. Another is ratiometric
thermometry simultaneous with velocimetry, based on the
temperature dependence of phosphorescence lifetime, which
is described in the following sections. Finally, two additional
features inherent in phosphorescence imaging are worth noting
(see Hu et al 2005). Recording the phosphorescence emission
with a slight time delay after the excitation laser pulse can
effectively eliminate the artefacts (i.e., scattering, reflection)
caused by the intense excitation source. Eliminating such
artefacts can be more challenging in LIF studies. Furthermore,
the Stokes shift (i.e., shift in wavelength towards red) between
the absorption and emission spectra is typically much larger
for phosphorescence compared to fluorescence, providing yet
another means to optically filter out potential contamination
of the emission signal by the excitation source.
3.1. Technique basis
According to quantum theory (Pringsheim 1949), the intensity
decay of a first-order photoluminescence process (either
fluorescence or phosphorescence) from a single excited state
can be expressed in the form
Iem = I0 e−t/τ ,
(1)
where the lifetime τ refers to the time when the intensity drops
to 37% (i.e., 1/e) of the initial intensity I0 . For an excited state,
Molecular tagging velocimetry and thermometry and its application
t0
In this expression, the initial intensity I0 contains all
the information about the incident laser intensity, the
dye concentration, its absorption coefficient and the
phosphorescence quantum yield (Hu and Koochesfahani 2003,
Hu et al 2005). Thus, the phosphorescence signal may, in
principle, be used to measure the temperature if the incident
laser intensity and the concentration of the phosphorescent dye
remain constant (or are known) in the measurement region.
This is the approach taken in the original work of Thompson
and Maynes (2001), where they quantified the temperature
using the phosphorescence intensity of 1-BrNp·Gβ-CD·ROH
acquired with a short fixed time delay (8 µs) after the laser
pulse. Furthermore, the fact that the phosphorescence signal is
a function of delay time t0, which is a controllable parameter,
can be utilized to significantly increase the sensitivity of
temperature measurements (Hu et al 2005).
Now consider imaging the phosphorescence signal at two
successive times, as in MTV measurements described earlier;
see the schematic in figure 2. The first image is detected at
the time t = t0 after laser excitation for a gate period δt to
accumulate the phosphorescence intensity S1 , while the second
Laser excitation pulse
Phosphorescence intensity
the deactivation processes may involve both radiative and nonradiative pathways and the lifetime of the photoluminescence
process, τ , is determined by the sum of all the deactivation
rates, i.e. τ −1 = kr + knr , where kr and knr are the radiative
and non-radiative rate constants, respectively. According to
photoluminescence kinetics, the non-radiative rate constant
is, in general, temperature dependent (Ferraudi 1988), and
the resulting temperature dependence of the phosphorescence
lifetime is the basis of the present technique for temperature
measurement. The non-radiative rate constant knr encompasses
all decay pathways that do not lead to photon emission
and can include processes such as collisional deactivation,
internal conversion, intersystem crossing and back intersystem
crossing. Among these, collisional deactivation is generally
temperature dependent and the back intersystem crossing
becomes temperature dependent with the introduction of a
rate constant with a non-zero activation energy.
The idea of temperature measurement by measuring the
phosphorescence lifetime was also suggested by Brewster et al
(2001) in a single-point feasibility study using oscilloscopebased instrumentation and a water-soluble phosphorescent
compound. The compound utilized, however, had a relatively
short lifetime of 100 µs (at room temperature), nearly 50
times smaller than that reported herein, which makes it suitable
for simultaneous velocity and temperature measurements only
for very high-speed water flows. The work described in
the present paper represents, to our knowledge, the first
whole-field temperature field measurements over a plane
conducted in an aqueous flow based on the direct imaging of
phosphorescence lifetime with a conventional image detecting
CCD camera.
Consider capturing the phosphorescence emission by a
gated CCD detector where the integration starts at a delay
time t0 after the laser excitation pulse with an integration
(or gate) period of δt. The phosphorescence signal S collected
by the detector is then given by
t0 +δt
S=
I0 e−t/τ dt = I0 τ (1 − e−δt/τ ) e−t0 /τ .
(2)
lifetime τ =
S1
δt
∆t
ln ( S1 / S 2 )
S2
∆t
δt
Time, t
Figure 2. Timing chart for phosphorescence image pair acquisition
and calculation of lifetime.
image is detected at the time t = t0 + t for the same gate
period to accumulate the phosphorescence intensity S2 . It is
easily shown, using equation (2), that the ratio of these two
phosphorescence signals is given by
S2
= e−t/τ .
(3)
S1
In other words, the intensity ratio of the two successive
phosphorescence images is only a function of the
phosphorescence lifetime τ and the time delay t between
the images, which is a controllable parameter. This ratiometric
approach eliminates the variations in the initial intensity and,
along with it, any temporal and spatial variations in the incident
laser intensity and non-uniformity of the dye concentration
(e.g., due to bleaching). The phosphorescence lifetime can be
calculated according to
t
,
(4)
τ=
ln(S1 /S2 )
resulting in the distribution of the phosphorescence lifetime
over a two-dimensional domain, and the temperature
distribution in the flow as long as the temperature dependence
of phosphorescence lifetime is known. The next section
describes the calibration of the phosphorescence lifetime
variation with temperature for the phosphorescent triplex used
here.
3.2. Calibration procedure for temperature dependence of
phosphorescence lifetime
The current work is based on the laser-induced
phosphorescence of the water-soluble triplex 1-BrNp·MβCD·ROH. The alcohol (ROH) used here was cyclohexanol.
The chemical composition of the triplex affects the emission
intensity and lifetime. The molar concentrations of the
three constituents of the triplex were according to those
recommended by Gendrich et al (1997), i.e. 2 × 10−4 M for
Mβ-CD, approximately 1 × 10−5 M for 1-BrNp (a saturated
solution) and 0.06 M for the alcohol. The same composition
was used for the calibration and the actual experiments
described in section 4.
Figure 3 shows the schematic set-up of the calibration
procedure employed to quantify the temperature dependence
of phosphorescence lifetime. A Lambda-Physik XeCl excimer
laser (wavelength λ = 308 nm, energy 50 mJ/pulse, pulse
width 20 ns) with appropriate optics was used to generate a
laser sheet (thickness about 1 mm) to illuminate a cube-shaped
1273
H Hu and M M Koochesfahani
RTD probe
laser sheet
mirror
12-bit gated intensified CCD camera
optics
(DiCam-Pro)
stirring rod
excimer UV laser (308 nm)
heating plate
1-BrNp•Mβ-CD•ROH
aqueous solution
host
computer
digital delay generator
(SRS DG535)
Figure 3. Schematic set-up for temperature calibration procedure.
6 months later
3 months later
1 month later
3 days later
5
Lifetime (ms)
1.0
Normalized intensity
6
exponential fit
o
T = 50 C
o
T = 40 C
o
T = 30 C
o
T = 25 C
1.2
0.8
0.6
4
3
2
1
0.4
20
0.2
25
30
35
40
45
50
O
Temperature ( C)
(a)
1.5
2.0
2.5
3.0
Time delay to after laser pulse (ms)
Figure 4. Phosphorescence intensity decay curves at several
temperatures.
test cell (about 3 l in volume) containing an aqueous solution
of 1-BrNp·Mβ-CD·ROH complex. The apparatus was placed
on a heating plate and a stirring rod was used to achieve
thermal equilibrium in the test cell. An RTD probe (Hart
Scientific Model 1502A, temperature accuracy ±0.01 ◦ C) was
placed in one corner of the apparatus to measure the actual
temperature in the test cell. During the experiment, the
temperature uniformity inside the test cell was checked and
was found to be within 0.1 ◦ C.
A 12-bit, 1280 × 1024 pixel, gated intensified CCD
camera (PCO DiCam-Pro) with a fast decay phosphor (P46)
was used to capture the phosphorescence emission. The
laser and the camera were synchronized using a digital delay
generator (SRS DG535), which controlled the delay time
t0 between the laser pulse and the start of image capture.
The phosphorescence images captured by the CCD camera
were subsequently transferred to a host computer for analysis.
In the present study, the exposure (gate) period was set to a
fixed value of δt = 1 ms.
To acquire the calibration data, the aqueous solution
of 1-BrNp·Mβ-CD·ROH was first heated to a predetermined temperature level T. After thermal equilibrium
was established, the phosphorescence images were acquired
as a function of time delay t0. The process was repeated
1274
1.4
6 months later
3 months later
1 month later
3 days later
polynomial fit
O
1.0
Normalized lifetime (τ /τT=25 C)
0
0.5
1.2
1.0
0.8
0.6
0.4
0.2
0
20
25
30
35
40
45
50
O
Temperature ( C)
(b)
Figure 5. Variation of phosphorescence lifetime versus temperature.
(a) The aging effect of the solution. (b) Normalized lifetime versus
temperature.
for different solution temperatures. Figure 4 depicts the
measured phosphorescence intensity decay curves at several
temperatures. It can be seen that the phosphorescence
intensity decay curves are very well approximated by singleexponential curves, as expected theoretically. The variation
of the measured lifetime versus temperature τ (T ) is shown
in figure 5(a) at different times after the preparation of the
original solution. We note that the absolute values of measured
lifetime initially change slightly after the solution preparation
before they finally stabilize. This ‘aging’ effect is believed to
be connected to the solubility of the three constituents of the
phosphorescent triplex and their reaching the final equilibrium
state. It is found, however, that the normalized lifetime,
10
Calculated lifetime, τ
Second image, S2
First image, S1
1600
overflow
constant head tank
flow management unit
8
1200
6
800
4
lifetime (ms)
Phosphorescence intensity (grey level)
Molecular tagging velocimetry and thermometry and its application
heated cylinder
12-bit intensified
CCD camera
dc power
supply
Y
400
2
0
0
90
0
10
20
30
40
50
60
70
80
thermometer
i.e. lifetime normalized by its value at a reference temperature,
collapses the various lifetime curves of figure 5(a) onto a single
‘universal’ curve that is characteristic of the phosphorescent
triplex used here. The normalized lifetime, using 25 ◦ C as
the reference temperature, is shown in figure 5(b). It is this
curve that is used for the lifetime-based thermometry in this
work.
It can be seen in figure 5(b) that the phosphorescence
lifetime of 1-BrNp·Mβ-CD·ROH varies significantly with
temperature. The relative temperature sensitivity of the
phosphorescence lifetime ranges between 5.0% per ◦ C at 20 ◦ C
to 20.0% per ◦ C at 50 ◦ C. To put these values in perspective, we
note that the temperature sensitivity of the commonly used LIF
dye rhodamine B is about 2.0% per ◦ C. The calibration profiles
of Thompson and Maynes (2001) indicate a temperature
sensitivity of 3% per ◦ C for their intensity-based approach
with the same phosphorescent tracer used here.
In order to demonstrate the effectiveness of the present
ratiometric technique for temperature measurement, sample
intensity profiles are shown in figure 6 from the first and
second phosphorescence images in the calibration test cell
with the fluid temperature being maintained at a constant
temperature of T = 20 ◦ C. These intensity profiles were
extracted from an arbitrarily selected horizontal row in the
two images. It can be seen that the phosphorescence intensities
of the first and second images change significantly along the
beam propagation direction due to the combined effect of nonparallel beam propagation, attenuation effects and possible dye
bleaching. However, the calculated phosphorescence lifetime
remains constant, as expected, at a level corresponding to the
test cell temperature.
4. Application to the wake of a heated cylinder
In order to demonstrate the feasibility of the technique
described above, MTV&T is applied to conduct simultaneous
temperature and velocity measurements in the wake of a heated
cylinder. This feasibility study is similar in nature to the work
of Park et al (2001) in connection with the development of
the DPIV/T technique, except that here we consider a flow
direction opposite to the gravity vector and a much higher
Richardson number of 0.36 (compared to their quoted value
To laser
X
Distance along a horizontal row in the image (mm)
Figure 6. Intensity profiles extracted from an arbitrarily selected
horizontal row in the two phosphorescence images and the derived
lifetime (test cell temperature T = 20 ◦ C).
DiCam-Pro
pulsed UV
laser grid
digital delay
generator
50mm
quartz
windows
reservoir
valve
host
computer
pump
Figure 7. Experimental set-up.
of 0.01), a value large enough for the buoyancy effects to
potentially influence the flow. More detailed discussion of
issues affecting the measurement accuracy and resolution will
be given in section 5.
4.1. Experimental set-up and flow conditions
A schematic of the experimental set-up is shown in figure 7.
The test cylinder was installed horizontally in a gravity-driven
vertical water channel. The dimensions of the test section
were 50 mm (width) × 30 mm (height) × 200 mm (length).
Two sides of the test section contained quartz windows to
allow the transmission of the excimer laser UV light. The
1-BrNp·Mβ-CD·ROH phosphorescent triplex was premixed
with water in a reservoir tank. A constant head tank was used
to maintain a steady inflow condition during the experiment.
The constant head tank was filled from the reserve tank by
using an electric pump. A convergent section with honeycomb
and mesh structures was used upstream of the test section to
produce a uniform condition for the flow approaching the test
cylinder. The velocity of the flow in the water channel was
adjustable by operating the valve at the downstream end of the
water channel.
A copper tube with outer diameter of D = 4.76 mm and
inner diameter of 4.00 mm was used as the test cylinder. The
cylinder was heated using a 3.1 mm diameter rod cartridge
heater (Watlow Firerod) that was placed inside the copper tube.
High thermal conductivity paste (OMEGATHERM 201) was
pressed in to fill the gap between the rod cartridge heater and
the inner wall of the copper tube. The rod cartridge heater
was powered by a dc power supply (Kepco, BOP-200-2M).
Two J-type thermocouples were embedded in the gap at the
mid-span of the cylinder at two angular locations to provide
the estimate of the cylinder temperature. The thermocouples
were connected to a two-channel thermometer (Omega HH23),
which had a resolution of ±0.1 ◦ C.
1275
H Hu and M M Koochesfahani
mirror
plan view of the
beam blocker
beam blocker
heated cylinder
the test cylinder was Uinlet = 0.032 m s−1 and the temperature
of the incoming flow was Tinlet = 23.2 ◦ C. The temperature
of the test cylinder was maintained at Tc = 56.5 ◦ C. Using
the properties of water at the temperature of incoming flow,
the flow conditions correspond to a Reynolds number ReD =
3
Uinlet D
inlet )D
= 160, Grashof number GrD = gβ(Tc −T
= 9100
ν
ν2
D
and Richardson number RiD = Gr
2 = 0.36.
Re
D
beam
splitter
quartz
window
water
channel
cylindrical
lens set 2
beam
blocker
cylindrical
lens set 1
mirror
rectangular beam
from excimer UV laser
Figure 8. Schematic of optical set-up.
In order to measure two components of the velocity in the
wake of the test cylinder, a grid of intersecting laser lines were
used for molecular tagging. Figure 8 shows the schematic
of the optical set-up, which is based on the earlier work of
Gendrich et al (1997). The 20 ns, 150 mJ/pulse rectangular
beam from an excimer UV laser (308 nm wavelength) was
manipulated by a set of cylindrical optics to increase its aspect
ratio. The resulting laser sheet was split by a 50:50 beam
splitter; each of the two resulting sheets passed through a
beam blocker to generate the grid pattern. The beam blocker
was simply an aluminium plate with a series of thin slots.
The camera and timing electronics arrangement for image
acquisition were exactly the same as previously described
for the calibration procedure, except that the camera was
operated in the dual-frame mode, where two full-frame images
of phosphorescence were acquired in quick succession from
the same laser excitation pulse. For the present study, the first
and second phosphorescence images were captured at time
delays of 1 ms and 5 ms, respectively, after the laser pulse,
resulting in a fixed time delay t = 4 ms between the two
images. The integration (gate) period was 1 ms for both.
For the present study, the approach flow velocity in the
water channel measured at about ten diameters upstream of
(a)
4.2. Measurement results
Figure 9 shows a typical pair of phosphorescence images
acquired after the excitation laser pulse for the experimental
conditions described above. The dark bands on the top right
of the images are shadows caused by the cylinder blocking
the laser beams. The ‘dark regions’ in the phosphorescence
images downstream of the cylinder correspond to the warm
fluid shedding periodically from the hot boundary layer around
the heated cylinder. From the comparison of the two images,
it can be seen that the dark regions become more pronounced
as the time delay between the laser pulse and phosphorescence
acquisition increases. This is due to the fact that the warmer
fluid has a shorter phosphorescence lifetime, resulting in a
larger decay in emission intensity than that in the cooler
ambient fluid.
From the image pair shown in figure 9, the instantaneous
velocity distribution can be derived by measuring the
displacements of the tagged regions using a spatial correlation
approach described briefly in section 2, with details given
in Gendrich and Koochesfahani (1996).
A source (or
interrogation) window size of 32 × 32 pixels (corresponding
to a region 1.12 mm × 1.12 mm in physical space) was used in
the present study, along with 50% overlap between consecutive
windows. Figure 10(a) shows the instantaneous velocity
distribution determined from the image pair of figure 9. Each
velocity vector represents an average over the source window,
which dictates the spatial resolution of the measurement in
this case (the maximum measured displacement of the source
window by the flow was about 4 pixels, much smaller than
the size of the source window). Note that velocity data are
not available within the shadow regions caused by the cylinder
blocking the laser light. An important aspect that needs to be
emphasized is that the fixed 32 × 32 pixel (0.25D × 0.25D)
(b)
Figure 9. A typical phosphorescence image pair used for MTV&T measurements. (a) First image acquired 1 ms after laser pulse.
(b) Second image acquired 5 ms after laser pulse.
1276
Molecular tagging velocimetry and thermometry and its application
0
0
U inlet
1
Temperature
1
2
0.090
0.080
0.070
0.060
0.050
0.040
0.030
0.020
X/D
X/D
2
3
3
4
4
5
5
6
6
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
Y/D
Y/D
(a)
(b)
2
3
4
Figure 10. The instantaneous velocity and temperature fields derived from the image pair in figure 9. Temperature normalization is
(T − Tinlet)/(Tc − Tinlet); the contour map starts at 0.02 with a contour spacing of 0.01. (a) Instantaneous velocity field. (b) Instantaneous
temperature field.
source window used here is too large to resolve the details of
the initial shear layers that separate from the cylinder. The
measurements become reliable once the scales of the flow
become comparable to the cylinder diameter after the shear
layers roll up (beyond a downstream location x/D > 2.5).
The instantaneous velocity field, figure 10(a), shows a
long re-circulation region downstream of the heated cylinder,
extending to an x/D of about 3.2 in this realization, and
unsteady shedding of vortex structures. These general
features are similar to the case of an unheated, isothermal,
cylinder. By contrast, however, the time series of the measured
instantaneous velocity field indicates that the unsteady vortex
structures shed periodically at a frequency of f ≈ 1.03 Hz,
corresponding to a Strouhal number St ≡ f D/U ≈ 0.15 for
the present experimental condition. This value is noticeably
smaller than the Strouhal number of about 0.18 found in
the literature (also confirmed in our experiments, results not
shown) for an unheated cylinder at the Reynolds number of
160 in this experiment. This is believed to be a buoyancyinduced effect; a systematic study of the influence of increasing
Richardson number on vortex shedding is currently under
way.
The image pair in figure 9 allows the determination of the
temperature distribution simultaneous with the velocity field
already described. Consistent with the correlation method
used for the measurement of the displacement of tagged
regions, the same interrogation regions of 32 × 32 pixels
in size were chosen in the first phosphorescence image
to provide the average phosphorescence intensity S1 within
those regions. The molecules tagged within each region
convect to a new region in the second phosphorescence image
according to their Lagrangian displacement by the flow over
the time delay between the two images. This displacement
field is, of course, the basis of measuring the velocity field
with MTV and is already available from figure 10(a). The
mass diffusion of tagged molecules out of interrogation
windows is negligibly small (the mass diffusion length in
this experiment is about 1/500 of the interrogation window
size). Therefore, for each interrogation window in the first
phosphorescence image, the position of the corresponding
‘displaced’ window in the second phosphorescence image
was determined based on the already measured velocity field,
and this provided the corresponding average phosphorescence
intensity S2 within each region. Note that the procedure
here is a first-order method that uses a linear displacement
model consistent with small Lagrangian displacements (i.e.,
small time delay between images) and small distortion of the
tagged regions due to velocity gradients. Once the average
phosphorescence intensities, S1 and S2, were determined
for the corresponding regions in the two phosphorescence
images, the phosphorescence lifetime was calculated based on
equation (4), resulting in the measurement of temperature
according to the lifetime-versus-temperature calibration
curve in figure 5. This measurement represents an
average temperature over the interrogation window. The
phosphorescence intensity averaging treatment described
above is helpful to improve the temperature measurement
accuracy, but at the expense of reducing the spatial resolution
of the measurement (see further discussion in section 5).
The simultaneous temperature field derived from the
phosphorescence image pair, which is shown in figure 10(b),
illustrates the overall temperature distribution in the wake
of the heated cylinder. The alternate shedding of ‘warm
blobs’ associated with the Karman vortices is clearly seen.
Similar to velocity results, the fixed 32 × 32 pixel (0.25D ×
0.25D) source window that was used is too large to resolve the
details of the initial thermal shear layers that separate from the
cylinder. The dark regions in figure 9 highlighting the warm
boundary layers that separate from the cylinder surface suggest
a value of about 0.1D for the initial thickness of these thermal
shear layers. The temperatures indicated in figure 10(b) in
those regions are, therefore, highly averaged spatially and
1277
H Hu and M M Koochesfahani
0
0
Temperature
U inlet
1
1
2
0.060
0.055
0.050
0.045
0.040
0.035
0.030
0.025
0.020
X/D
X/D
2
3
3
4
4
5
5
6
6
-3
-2
-1
0
1
2
3
4
Y/D
-3
-2
-1
0
1
2
3
4
Y/D
(a)
(b)
Figure 11. Mean velocity and temperature distributions. Temperature normalization is (T − Tinlet)/(Tc − Tinlet); the contour map starts at
0.02 with a contour spacing of 0.005. (a) Mean velocity field. (b) Mean temperature field.
1278
1.25
1.00
U/Uinlet
0.75
0.50
0.25
X/D=5
X/D=4
X/D=3
X/D=2
X/D=1
0
-0.25
-0.50
-3
-2
-1
0
1
2
3
Y/D
(a)
0.07
X/D=5
X/D=4
X/D=3
X/D=2
X/D=1
0.06
0.05
(T-Tinlet)/(Tc-Tinlet)
underestimated in magnitude. The measurements become
reliable once the scales of the flow become comparable to
the cylinder diameter after the shear layers roll up, after about
x/D > 2.5. We note that the peak temperature in the centre
of the warm blob (x/D ≈ 4.5) reaches a normalized value
of (T − Tinlet )/(Tc − Tinlet ) ≈ 0.095, corresponding to a
temperature differential of only (T − Tinlet ) ≈ 3.1 ◦ C.
The mean velocity and temperature fields were calculated
from 350 instantaneous measurements, and their overall
distributions are shown in figure 11. Sample transverse
profiles of the mean streamwise velocity and temperature at
five downstream locations x/D = 1, 2, 3, 4 and 5 are also
extracted from figure 11 and are given in figure 12 for a more
quantitative interpretation of results. From the mean velocity
results, it can be seen that the mean length of the re-circulation
region in the wake behind the heated cylinder is about 2.9
cylinder diameters for the present experimental condition.
The downstream evolution of the mean streamwise velocity
is as expected, with a decreasing velocity deficit in the wake
and an increasing width of the wake. The mean temperature
distribution and the corresponding transverse profiles reveal
a double-peaked temperature distribution with the two high
temperature regions occurring at the two sides of the wake
corresponding to the shedding paths of the ‘warm blobs’
revealed in the instantaneous temperature fields.
Since the velocity and temperature fields were measured
simultaneously, the correlation between the velocity and
temperature fluctuations can be calculated to generate the
distribution of the mean turbulent heat flux uj T , as shown
in figure 13. In interpreting this figure, it is again important
to recognize the resolution difficulties in the initial regions of
the wake that was mentioned earlier. We note that heat flux
vectors become pronounced at about x/D ≈ 2.5, the location
where the shear layers roll up into large Karman vortices. The
largest heat flux vectors are observed on the two sides of the
wake corresponding to the passage of the Karman vortices.
0.04
0.03
0.02
0.01
0
-0.01
-3
-2
-1
0
1
2
3
Y/D
(b)
Figure 12. Mean velocity and temperature profiles at various
downstream locations. (a) Mean velocity profiles. (b) Mean
temperature profiles.
5. Resolution limitations and measurement accuracy
The present MTV&T technique, like most measurement
techniques, does not give information at a ‘point’. Rather, it
provides the spatially averaged velocity and temperature of a
molecularly tagged region. Similar to PIV, the effective spatial
resolution of the measurement is given by the sum of the source
Molecular tagging velocimetry and thermometry and its application
0
0.01
1
X/D
2
3
4
5
6
-3
-2
-1
0
1
2
3
4
Y/D
Figure 13. Spatial map of the mean turbulent heat flux;
normalization: uj T /Uinlet (Tc − Tinlet ).
window size and the measured Lagrangian displacement.
In the work presented here, the spatial resolution was
dominated by the source window size of 32 × 32 pixels
(1.12 mm × 1.12 mm in physical space or 0.25D × 0.25D).
Clearly, obtaining resolved data for small scales would
require tagging regions, and selecting interrogation windows,
consistent with the scales to be resolved. While the best
spatial resolution that can be achieved with MTV&T is set
by the diffraction limitations of optics used to generate the
tagging pattern and the resolution characteristics of image
detection; the selection of the source (interrogation) window
often involves a choice between the spatial resolution of
the measurement versus the accuracy of the instantaneous
measurement. This aspect will be further discussed later in
this section in the context of thermometry. The temporal
resolution of the present measurement methodology is set by
the time delay t between the phosphorescence image pair,
which in these experiments was 4 ms. The choice of this time
delay influences the accuracy of the velocity data (larger t
leads to larger Lagrangian displacement of tagged molecules)
and the temperature estimation through equation (4); see later
discussion.
The accuracy of velocity measurements using MTV
depends on many parameters such as the signal-to-noise
ratio in the MTV image pair, the intersection angle and
width of the laser beams used for tagging, and the size of
the source window used for the correlation process. These
effects have been systematically studied and documented in
Gendrich and Koochesfahani (1996). Based on the results
of Gendrich and Koochesfahani (1996), and the present
experimental conditions, the uncertainty in the measurement
of the displacement of tagged regions is given by a 95%
confidence limit of about ±0.2 pixel, or an rms accuracy
of ±0.1 pixel, assuming a Gaussian distribution for error.
Considering a maximum displacement of 4 pixels in the
current measurements, the instantaneous velocity accuracy is
about 2.5%.
The accuracy of temperature measurements is affected
by two primary factors, the image noise in the two
phosphorescence images leading to noise in the estimated
lifetime and potential inaccuracies in the identification of the
region in the second phosphorescence image corresponding to
the original tagged region in the first image. These issues are
separately addressed below.
The accuracy in the determination of lifetime from
equation (4), and the resulting accuracy in temperature
measurement, is directly influenced by noise in the two
phosphorescence signals S1 and S2. Even though a 12-bit
camera is used in the present study, the actual image noise
at each pixel, characterized by the standard deviation of the
signal, is much higher and is in the 3% range. This noise level
is connected to the CCD depth of well and the intensifier stage
of the CCD. The accuracy in calculating the phosphorescence
lifetime can be estimated by
2 2
στ
1
σS 2
σS1
=
+
,
τ
ln(S1 /S2 )
S1
S2
suggested by Ballew and Demas (1999), where σS1 , σS2 and στ
are the standard deviations of S1, S2 and τ , respectively. The
aforementioned 3% phosphorescence signal accuracy at each
pixel will, therefore, result in a lifetime measurement accuracy
of about 4% and an instantaneous temperature error of 0.8 ◦ C
(using the lifetime temperature sensitivity of 5.0% per ◦ C
at 20 ◦ C for reference). Since this error is unbiased, it
can be substantially reduced by averaging over neighbouring
pixels. Assuming statistical
√ independence, the error can be
reduced by the factor 1/ N, where N is the number of
pixels in the interrogation window. For the results given
in the present study based on 32 × 32 pixel interrogation
windows, the instantaneous measurement error due to the noise
in the phosphorescence images is estimated to be less than
0.10 ◦ C.
The MTT method described here is a Lagrangian
approach. The molecular region tagged in the first image
convects to a new region in the second image according to its
Lagrangian displacement over the time delay between the two
images. To determine the phosphorescence lifetime correctly,
this new region in the second phosphorescence image needs to
be identified. The effect of mass diffusion being negligible, the
new region is determined solely on the basis of advection by
the flow. In this work, for each interrogation window in the first
phosphorescence image, the identification of its corresponding
region in the second phosphorescence image was based on the
Lagrangian displacement by the amount already determined
by the correlation method in MTV. This is a first-order method
that uses a linear displacement model consistent with small
Lagrangian displacements (i.e., small time delay between
images) and small distortion of the tagged regions due to
velocity gradients. Higher order processing methods can,
in principle, be developed to take image distortions into
account. Meanwhile, two methods were used to obtain a
quantitative estimate of temperature measurement error caused
by distortions due to velocity gradients and the inaccuracy
of the velocity measurement itself. The temperature field
was computed using regions in the second phosphorescence
image that were deliberately displaced an additional ±1 pixel
(i.e., 25% of maximum displacement) relative to the actual
location computed by MTV. This ‘induced’ mismatch resulted
in a temperature error of about 0.1 ◦ C for the conditions of
1279
H Hu and M M Koochesfahani
the present experiments. In addition, when the procedure
described here was applied to the case of an unheated cylinder,
for which the temperature field is uniform and constant,
the measured instantaneous temperature in the freestream
region was found to have an uncertainty of about 0.16 ◦ C.
In the wake region, where the effect of distortion would be
more noticeable, the maximum uncertainty in temperature
measurement increased to about 0.23 ◦ C. This is the total
uncertainty and accounts for all the effects discussed above.
6. Conclusions
A completely molecular-based method is presented for the
simultaneous whole-field mapping of velocity and temperature
fields in aqueous flows. The method uses a molecular tagging
approach that combines molecular tagging velocimetry (MTV)
with molecular tagging thermometry (MTT), and because of
its molecular nature it eliminates issues such as the tracking of
the flow by seed particles. The water-soluble phosphorescent
triplex, 1-BrNp·Mβ-CD·ROH, is used as a tracer for both
velocity and temperature measurements. A pulsed laser is
used to ‘tag’ the molecules in the regions of interest; the
displacement of the tagged regions provides the velocity
information and the phosphorescence intensity decay within
those regions is used to determine the temperature through
the temperature dependence of phosphorescence lifetime.
The resolution limitations and measurement uncertainties are
discussed and they provide information on how to optimize
these characteristics for particular flow conditions.
The implementation of the MTV&T method is
demonstrated by its application to a study of the wake behind
a heated cylinder at Re = 160. In addition to the simultaneous
measurements of the instantaneous velocity and temperature
fields, other mean flow quantities are measured, such as
the mean velocity, temperature and velocity–temperature
correlation fields. These measurements demonstrate MTV&T
can be a viable tool for accurate whole-field mapping of
velocity and temperature in fluid flows.
Acknowledgments
This work was supported by the CRC Program of the National
Science Foundation, grant number CHE-0209898, and made
use of shared facilities of the MRSEC Program of the National
Science Foundation, award number DMR-9809688.
References
Antonia R A, Prubhu A and Stephenson S E 1975 Conditionally
sampled measurements in a heated turbulent jet J. Fluid Mech.
72 455–80
Ballew R M and Demas J N 1999 An error analysis of the rapid
lifetime determination method for the evaluation of single
exponential decay Anal. Chem. 61 30–3
Brewster R E, Kidd M J and Schuh M D 2001 Optical thermometer
based on the stability of a phosphorescent 6-bromo-2naphthal/α-cyclodextrin2 ternary complex Chem. Commun.
1134–5
Bohl D, Koochesfahani M and Olson B 2001 Development of
stereoscopic molecular tagging velocimetry Exp.
Fluids 30 302–8
Chevray R and Tutu N K 1978 Intermittency and preferential
transport of heat in a round jet J. Fluid Mech. 88 133–60
1280
Coppeta J and Rogers C 1998 Dual emission laser induced
fluorescence for direct planar scalar behavior measurements
Exp. Fluids 25 1–15
Dabiri D and Gharib M 1991 Digital particle image thermometry:
the method and implementation Exp. Fluids 11 77–86
Dibble R W, Kollmann W and Schefer R W 1984 Conserved scalar
fluxes measurement in a turbulent non-premixed flame by
combined laser Doppler velocimetry and laser Raman
scattering Combust. Flame 55 307–21
Falco R E and Nocera D G 1993 Quantitative multipoint
measurements and visualization of dense solid–liquid flows
using laser induced photochemical anemometry (LIPA)
Particulate Two-Phase Flow ed M C Rocco (Portsmouth, NH:
Butterworth-Heinemann) pp 59–126
Ferraudi G J 1988 Elements of Inorganic Photochemistry (New
York: Wiley-Interscience)
Gendrich C P and Koochesfahani M M 1996 A spatial correlation
technique for estimating velocity fields using molecular
tagging velocimetry (MTV) Exp. Fluids 22 67–77
Gendrich C P, Koochesfahani M M and Nocera D G 1997
Molecular tagging velocimetry and other novel application of a
new phosphorescent supramolecule Exp. Fluids 23 361–72
Grissino A S, Hart D P and Lai W T 1999 Combined dual emission
LIF and PIV to resolve temperature and velocity Proc. 3rd Int.
Workshop on Particle Image Velocimetry (Santa Barbara, CA,
USA, 16–18 September 1999)
Hartmann W K, Gray M H B, Ponce A and Nocera D G 1996
Substrate induced phosphorescence from cyclodextrin ·
lumophore host–guest complex Inorg. Chim. Acta 243 239–48
Hishida K and Sakakibara J 2000 Combined planar laser-induced
fluorescence—particle image velocimetry technique for
velocity and temperature fields Exp. Fluids 29 s129–40
Hu H and Koochesfahani M M 2003 A novel technique for
quantitative temperature mapping in liquid by measuring the
lifetime of laser induced phosphorescence J. Vis. 6 143–53
Hu H, Lum C and Koochesfahani M M 2006 Molecular tagging
thermometry with adjustable temperature sensitivity Exp.
Fluids DOI:10.1007/s00348-006-0112-2
Koochesfahani M M 1999 Molecular tagging velocimetry (MTV):
progress and applications AIAA Paper No. AIAA-99-3786
Koochesfahani M M (ed) 2000 Special feature: molecular tagging
velocimetry Meas. Sci. Technol. 11 1235–300
Koochesfahani M M, Cohn R K, Gendrich C P and Nocera D G
1996 Molecular tagging diagnostics for the study of kinematics
and mixing in liquid phase flows Proc. 8th Int. Symp. on
Applications of Laser Techniques to Fluids Mechanics (Lisbon,
Portugal, 8–11 July 1996) vol I pp 1.2.1–1.2.12; also in: 1997
Developments in Laser Techniques and Fluid Mechanics
ed R J Adrian et al (Berlin: Springer) chapter 2, section 1,
p 125
Koochesfahani M M, Cohn R K and Mackinnon C G 2000
Simultaneous whole-field measurements of velocity and
concentration fields using combined MTV and LIF Meas. Sci.
Technol. 11 1289–300
Kotsovinos N E 1977 Plane turbulent buoyant jets J. Fluid Mech. 81
45–92
Lavielle P, Lemoine F, Lavergne G and Lebouche M 2001
Evaporating and combusting droplet temperature
measurements using two-color laser-induced fluorescence
Exp. Fluids 31 45–55
Lemoine L, Antonie Y, Wolff M and Lebouche M 1999
Simultaneous temperature and 2D velocity measurements in a
turbulent heated jet using combined laser-induced fluorescence
and LDA Exp. Fluids 26 315–23
Lempert W R and Harris S R 2000 Molecular tagging velocimetry
Flow Visualization—Techniques and Examples ed A J Smits
and T T Lim (London: Imperial College Press) pp 73–92
Mortellaro M A and Nocera D G 1996 A turn-on for optical sensing
Chem. Technol. 26 17–23
Park H G, Dabiri D and Gharib M 2001 Digital particle image
velocimetry/thermometry and application to the wake of a
heated circular cylinder Exp. Fluids 30 327–38
Molecular tagging velocimetry and thermometry and its application
Ponce A, Wong P A, Way J J and Nocera D G 1993 Intense
phosphorescence trigged by alcohol upon formation of a
cyclodextrin ternary complex J. Phys. Chem. 97 11137–42
Pringsheim P 1949 Fluorescence and Phosphorescence (New York:
Interscience)
Sakakibara J and Adrian R J 1999 Whole field measurement of
temperature in water using two-color laser induced
fluorescence Exp. Fluids 26 7–15
Sakakibara J, Hishida K and Maeda M 1997 Vortex structure and
heat transfer in the stagnation region of an impinging plane jet
Int. J. Heat Mass Transfer 40 3163–76
Thompson S L and Maynes D 2001 Spatially resolved temperature
measurement in a liquid using laser induced phosphorescence
J. Fluid Eng. 123 293–302
Turro N J 1978 Modern Molecular Photochemistry (Menlo Park,
CA: Benjamin-Cummings)
1281
PHYSICS OF FLUIDS
VOLUME 14, NUMBER 7
JULY 2002
Simultaneous measurements of all three components of velocity and
vorticity vectors in a lobed jet flow by means of dual-plane stereoscopic
particle image velocimetry
Hui Hu,a) Tetsuo Saga, Toshio Kobayashi, and Nubuyuki Taniguchi
Institute of Industrial Science, University of Tokyo, Komaba 4-6-1, Meguro-Ku, Tokyo 153-8505, Japan
共Received 8 January 2002; accepted 8 April 2002; published 23 May 2002兲
Results from an advanced particle image velocimetry 共PIV兲 technique, named as dual-plane
stereoscopic PIV technique, for making simultaneous measurements of all three components of
velocity and vorticity vectors are presented for a lobed jet flow. The dual-plane stereoscopic PIV
technique uses polarization conservation characteristic of Mie scattering to achieve simultaneous
stereoscopic PIV measurements at two spatially separated planes. Unlike ‘‘classical’’ PIV systems or
conventional stereoscopic PIV systems, which can only get one component of vorticity vectors, the
present dual-plane stereoscopic PIV system can provide all three components of velocity and
vorticity distributions in fluid flows instantaneously and simultaneously. The evolution and
interaction characteristics of the large-scale streamwise vortices and azimuthal Kelvin–Helmholtz
vortices in the lobed jet flow are revealed very clearly and quantitatively from the simultaneous
measurement results of the dual-plane stereoscopic PIV system. A discussion about the satisfaction
of the measurement results of the present dual-plane stereoscopic PIV system to mass conservation
equation is also conducted in the present paper to evaluate the error levels of the measurement
results. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1481741兴
INTRODUCTION
Velocity and vorticity are two most important defining
properties of turbulence, whether in development or in equilibrium. The simultaneous information revealed from velocity vector and vorticity vector distributions in fluid flows
could help us very much to improve our understanding of
complex flow phenomena. It is well known that the vorticity
vector is defined as the curl of the velocity vector and can be
expressed in the tensor notation in the Cartesian coordinate
system as
⍀ i ⫽E i, j,k
⳵Uk
,
⳵x j
共1兲
where E i, j,k is the alternating tensor and U k is the velocity
vector. Obviously, it is desirable to obtain all three components of the vorticity field simultaneously in order to gain a
complete understanding of the instantaneous vorticity fields.
As a nonintrusive whole field measuring technique, particle image velocimetry 共PIV兲1 is a most common used tool
for conducting velocity field measurements of fluid flows.
The simultaneous whole-field vorticity distributions can be
obtained as the derivatives of the velocity vector fields obtained from PIV measurements. However, since ‘‘classical’’
PIV technique is a two-component, two-dimensional 共2C–
2D兲 measuring technique, which is only capable of obtaining
two components of velocity vectors in an illuminated plane
a兲
Author to whom correspondence should be addressed. Present address:
Turbulent Mixing and Unsteady Aerodynamics Laboratory, A22, Research
Complex Engineering, Michigan State University, East Lansing, Michigan
48824. Electronic mail: huhui@egr.msu.edu
1070-6631/2002/14(7)/2128/11/$19.00
2128
instantaneously. Therefore, only one component of vorticity
vectors can be obtained simultaneously as the measurement
results of ‘‘classic’’ PIV systems.
Stereoscopic particle image velocimetry technique2 always employs two cameras to record simultaneous but distinct off-axial views of the same region of interest 共an illuminated plane within a fluid flow seeded with tracer
particles兲. By doing view reconstruction, the corresponding
image segments in the two views are matched to get all three
components of flow velocity vectors. Compared with ‘‘classical’’ PIV technique, stereoscopic PIV technique can provide additional information about the out-of-plane velocity
component simultaneously besides the two in-plane velocity
components. However, from the view of vorticity vector
measurement, it is still only one component of the vorticity
vectors that can be obtained instantaneously from the measurement results of a conventional ‘‘single-plane’’ stereoscopic PIV system.
An advanced PIV technique, named as dual-plane stereoscopic PIV technique, will be described in the present
paper for the simultaneous measurements of all three components of velocity and vorticity vector distributions in fluid
flows. Unlike ‘‘classical’’ PIV systems or conventional
‘‘single-plane’’ stereoscopic PIV systems, the dual-plane stereoscopic PIV system described in the present study can provide all three components of velocity and vorticity vector
distributions in fluid flows instantaneously and simultaneously.
The main technical aspects and system setup of the dualplane stereoscopic PIV system will be described at first in the
following context. Then, the measurement results of the
© 2002 American Institute of Physics
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Phys. Fluids, Vol. 14, No. 7, July 2002
Dual-plane stereoscopic particle image velocimetry
2129
FIG. 1. The schematic setup of the dual-plane stereoscopic PIV system.
dual-plane stereoscopic PIV system in a lobed jet flow will
be present to demonstrate the achievements of the simultaneous measurement of all three components of velocity and
vorticity vectors. The evolution and interaction characteristics of the large-scale streamwise vortices and azimuthal
Kelvin–Helmholtz vortices in the lobed jet flow will be discussed based on the simultaneous measurement results. A
discussion about the satisfaction of the measurement results
of the dual-plane stereoscopic PIV system to the mass conservation equation will also be given in the present paper to
evaluate the error levels of the measurement results. The
research described here represents, to our knowledge, the
first quantitative, instantaneous and simultaneous measurement results of all three components of the velocity and vorticity vector distributions in a lobed jet flow. It is also believed to be the first to discuss the satisfaction of PIV
measurement results to the mass conservation equation instantaneously and quantitatively.
DUAL-PLANE STEREOSCOPIC PIV TECHNIQUE AND
SYSTEM SETUP
It is well known that particle scattering can be either Mie
scattering or Rayleigh scattering depending on the relative
diameter of the particles compared with the wavelength 共␭兲
of the incident light. According to McCartney,3 Mie scattering is generally defined as scattering from particles which is
greater than 1/10 of the incident light wavelength 共␭兲, while
Rayleigh scattering is defined as scattering from particles
with diameters less than 1/10␭. Most of the PIV systems
work in the Mie scattering regime.
In the Mie scattering regime, the scattering will have a
dominant forward direction, and nonuniform ‘‘lobed’’ scattering towards the sides. The scattering distributions will depend upon the particle size, the wavelength and polarization
of incident light. It should be noted that the polarization di-
rection of Mie scattering is conservative under certain conditions. If the incident light is linearly polarized, the light
scattered from small particles 共⬃1 ␮m in diameter兲 maintains the polarization of the incident light. Further discussions about the polarization conservation of Mie scattering
can be found from Ref. 4. As the same as Keahler and
Kompenhans,5 the dual-plane stereoscopic PIV system described in the present paper utilizes the polarization conservation characteristic of Mie scattering to do separation of the
scattered light from two illuminating laser sheets with orthogonal polarization direction in order to achieve simultaneous stereoscopic PIV measurements at two spatially separated planes.
Figure 1 shows the schematic setup of the dual-plane
stereoscopic PIV system used in the present study. Two sets
of widely used double-pulsed Nd:YAG lasers 共New Wave, 50
mJ/pulse, ␭⫽532 nm兲 with additional optics 共half wave
plate, mirrors, polarizer, and cylindrical lens兲 were used to
setup the illumination system of the dual-plane stereoscopic
PIV system. The P-polarized laser beams from the doublepulsed Nd:YAG laser set A is turned into S-polarized light by
passing a half wave 共␭/2兲 plate before they are combined
with the P-polarized laser beams from the double-pulsed
Nd:YAG laser set B. The P-polarized laser beams from the
laser set B transmit through the Polarizer cube, while the
S-polarized light from the double-pulsed Nd:YAG laser set A
are reflected by the Polarizer cube. By adjusting the angle
and/or the location of mirror #1, the laser beams from the
laser set A and laser set B can be overlapped or not. Passing
through a set of cylindrical lenses and reflected by mirror #2,
the laser beams are expanded into two paralleling laser
sheets with orthogonal polarization to illuminate the studied
flow field at two spatially separated planes or overlapped at
Downloaded 24 May 2002 to 35.8.10.28. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/phf/phfcr.jsp
2130
Phys. Fluids, Vol. 14, No. 7, July 2002
one plane. In the present study, the thickness of the illuminating laser sheets is about 2.0 mm, and the gap between the
centers of the two illuminating laser sheets is adjusted as
2.0 mm.
Two pairs of high-resolution CCD cameras with polarizing beam splitter cubes and mirrors were used to capture the
stereoscopic PIV images simultaneously at the two measurement planes illuminated by the two laser sheets with orthogonal linear polarization. The two pairs of the highresolution CCD cameras 共1 K by 1 K, TSI PIVCAM 10–30兲
were settled on an optical table with a pair of polarizing
beam splitter cubes and two high reflectivity mirrors installed in front of the cameras to separate the scattered light
from the two illuminating laser sheets with orthogonal linear
polarization. The illuminating laser light with orthogonal linear polarization is scattered by the tracer particles seeded in
the objective fluid flow. Due to the polarization conservation
characteristic of Mie scattering, the scattered light from the
P-polarized laser sheet will keep the P-polarization direction
and pass straight through the polarizing beam-splitter cubes
and is detected by camera 2 and camera 3. The scattered light
from the S-polarized laser sheet will keep the S-polarization
direction and emerge from the polarizing beam splitter cubes
at the right angles to the incident direction. Reflected by the
two high reflectivity mirrors 共mirror #3 and #4兲, the scattered
S-polarized light is detected by camera 1 and camera 4.
The two pairs of high-resolution CCD cameras were arranged in an angular displacement configuration in order to
get a large measurement window. With the installation of
tilt-axis mounts, the lenses and camera bodies were adjusted
to satisfy Scheimpflug condition6 to obtain focused particle
images everywhere in the image recording planes. In the
present study, the distance between the illuminating laser
sheets and image recording planes of the CCD cameras is
about 650 mm, and the angle between the view axles of the
cameras is about 50°. For such arrangement, the size of the
stereoscopic PIV measurement windows is about 80 mm by
80 mm.
The CCD cameras and double-pulsed Nd:YAG laser sets
were connected to a workstation 共host computer兲 via a synchronizer 共TSI LaserPulse synchronizer兲, which controlled
the timing of the laser sheet illumination and the CCD camera data acquisition. In the present study, the time interval
between the two pulsed illuminations of each double-pulsed
Nd:YAG laser set was set as 30 ␮s.
A general three-dimensional 共3D兲 in situ calibration
procedure7 was conducted in the present study to obtain the
mapping functions between the image planes and object
planes. A target plate 共100 mm by 100 mm兲 with 100 ␮m
diameter dots spaced at the interval of 2.5 mm was used for
the 3D in situ calibration. The front surface of the target plate
was aligned with the centers of the laser sheets, and then
calibration images were captured at several locations across
the depth of the laser sheets. The space interval between
these locations was 0.5 mm for the present study. The 3D
mapping function used in the present study was taken to be a
multidimensional polynomial, which is fourth order for the
directions 共X and Y directions兲 paralleling the laser sheet
planes and second order for the direction 共Z direction兲 nor-
Hu et al.
mal to the laser sheet planes. The coefficients of the multidimensional polynomial were determined from the calibration images by using a least-square method. The twodimensional particle image displacements in each image
plane was calculated separately by using a hierarchical recursive PIV 共HR–PIV兲 software developed ‘‘in-house.’’ The
HR–PIV software is based on hierarchical recursive processes of conventional spatial correlation operation with offsetting of the displacements estimated by the former iteration
step, and hierarchical reduction of the interrogation window
size and search distance in the next iteration step.8 Compared
with conventional cross-correlation based PIV image processing methods, the hierarchical recursive PIV method has
advantages in the spurious vector suppression and spatial
resolution improvement of PIV result.
Finally, by using the mapping functions obtained by the
3D in situ calibration and the two-dimensional displacements
in each image planes, all three components of the velocity
vectors in the two illuminating laser sheet planes were reconstructed. Further details about the system setup, 3D in situ
calibration and image processing of the present dual-plane
stereoscopic PIV system can be found from Refs. 9 and 10.
LOBED JET FLOW AND EXPERIMENTAL APPARATUS
A lobed nozzle, which consists of a splitter plate with
convoluted trailing edge, is considered a very promising fluid
mechanic device for efficient mixing of two co-flow streams
with different velocity, temperature and/or species. The
large-scale streamwise vortices generated by lobed nozzles
and azimuthal vortices due to the Kelvin–Helmholtz instability have been suggested to play important roles in the
mixing processes of lobed mixing flows.11,12 Since most of
previous studies on lobed mixing flows were conducted by
using conventional measurement techniques like Pitot
probes, hot film anemometer and laser doppler velocimetry,
instantaneous, quantitative whole-field velocity and vorticity
distributions in lobed mixing flows have never been obtained
until the recent work of the authors.13,14 In the earlier work
of the authors, planar laser induced fluorescence 共PLIF兲 and
‘‘classical’’ PIV techniques13 and conventional ‘‘singleplane’’ stereoscopic PIV technique14 were used to study
lobed jet mixing flows. Based on the directly perceived PLIF
flow visualization images and quantitative velocity, vorticity
and turbulence intensity distributions of the PIV measurement results, the evolution and interaction characteristics of
various vortical and turbulent structures in lobed jet mixing
flows were discussed.
The measurement results obtained in the earlier works of
the authors are from a ‘‘classical’’ PIV system and a conventional ‘‘single-plane’’ stereoscopic PIV system. Only the
streamwise vortical structures or the azimuthal Kelvin–
Helmholtz vortical structures in the lobed jet flows can be
revealed instantaneously from the measurement results.
Since the present dual-plane stereoscopic PIV system can
provide all three components of velocity and vorticity vector
distributions simultaneously, the large-scale streamwise vortices and azimuthal Kelvin–Helmholtz vortical structures in
lobed mixing flows can be revealed simultaneously from the
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Phys. Fluids, Vol. 14, No. 7, July 2002
Dual-plane stereoscopic particle image velocimetry
2131
FIG. 2. The lobed nozzle and experimental rig used in the present study.
共a兲 Lobed nozzle. 共b兲 Experimental
rig.
measurement results. The simultaneous information will be
very helpful to understand the evolution and interaction characteristics of the streamwise vortices and azimuthal Kelvin–
Helmholtz vortical structures in the lobed mixing flows.
Figure 2共a兲 shows the geometry parameters of the lobed
nozzle used in the present study. The lobed nozzle has six
lobes. The width of each lobe is 6 mm and the height of each
lobe is 15 mm (H⫽15 mm). The inward and outward penetration angles of the lobed structures are ␪ in⫽22° and ␪ out
⫽14°, respectively. The diameter of the lobed nozzle is 40
mm (D⫽40 mm).
Figure 2共b兲 shows the jet flow experimental rig used in
the present study. A centrifugal compressor was used to supply the air jet. A cylindrical plenum chamber with honeycomb structures was used for settling the airflow. Through a
convergent connection 共convergent ratio is about 50:1兲, the
airflow is exhausted from the test nozzle. The velocity range
of the air jet out of the convergent connection 共at the inlet of
the test nozzle兲 could be varied from 5 to 35 m/s. In the
present study, a mean speed of the air jet at the inlet of the
lobed nozzle of U 0 ⫽20.0 m/s was used. The corresponding
Reynolds number is 5.517⫻105 based on the nozzle diameter. The air jet flow was seeded with 1–5 ␮m DEHS 共Di-2EthlHexyl-Sebact兲 droplets generated by a seeding
generator.15 The DEHS droplets out of the seeding generator
were divided into two streams; one is used to seed the core
jet flow and the other for ambient air seeding.
SIMULTANEOUS MEASUREMENT RESULTS OF ALL
THREE COMPONENTS OF VELOCITY AND
VORTICITY VECTORS
A pair of typical instantaneous measurement results of
the dual-plane stereoscopic PIV system in two parallel cross
planes 共Z⫽10 mm and Z⫽12 mm兲 near to the trailing edge
of the lobed nozzle is shown in Fig. 3. Since the characteristics of the mixing process in lobed mixing flows revealed
from velocity distributions have been discussed intensively
in the earlier work of the authors,13,14 the results and discussions given in the present paper will mainly focus on the
simultaneous measurement results of all three components of
vorticity distributions to reveal the evolution and interaction
characteristics of various vortical and turbulent structures in
the lobed jet flow.
According to the definition of vorticity vector given in
Eq. 共1兲, the three components of normalized vorticity vectors
in the lobed jet flow can be expressed by following equations:
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2132
Hu et al.
Phys. Fluids, Vol. 14, No. 7, July 2002
FIG. 3. A pair of typical instantaneous measurement results of the dual-plane stereoscopic PIV system. 共a兲 Instantaneous velocity field in the Z⫽10 mm cross
plane. 共b兲 Simultaneous velocity field in the Z⫽12 mm cross plane.
冉
冉
冉
冊
冊
冊
␼ x⫽
D ⳵w ⳵v
,
⫺
U0 ⳵y ⳵z
共2兲
␼ y⫽
D ⳵u ⳵w
⫺
,
U0 ⳵z ⳵x
共3兲
␼ z⫽
D ⳵v ⳵u
,
⫺
U0 ⳵x ⳵y
共4兲
where D is the diameter of the lobed nozzle, and U 0 is the
velocity of the jet flow at the nozzle inlet. While, u, v , and w
are the instantaneous velocity in X, Y, and Z directions 共Fig.
2兲.
It should be noted that the terms like ⳵ u/ ⳵ z and ⳵ v / ⳵ z in
the above equations cannot be determined from the measurement results of a ‘‘classical’’ PIV system or a conventional
‘‘single-plane’’ stereoscopic PIV system. Therefore, only the
out-of-plane component (␼ z ) of the vorticity vector can be
obtained instantaneously from the measurement results.
Since the present dual-plane stereoscopic PIV system can
provide the velocity fields 共all three components兲 at two illuminated planes simultaneously, all the terms in the above
vorticity definition equations can be determined. Besides the
out-of-plane component ␼ z , the other two in-plane components of the vorticity vectors 共␼ x and ␼ y 兲 can be obtained in
either of the two illuminated planes with first-order approximation, and in the central plane between the two parallel
illuminated planes with second-order approximation accuracy. Based on the simultaneous velocity distributions in Z
⫽10 mm and Z⫽12 mm cross planes given in Fig. 3, all the
three components of the instantaneous vorticity distributions
in the Z⫽10 m cross plane were calculated. The results are
shown in Figs. 4共a兲, 4共b兲, and 4共c兲.
As described previously, there are two kinds of vortical
structures are very important for the mixing process in lobed
mixing flows. One is the large-scale streamwise vortices generated by the special geometry of lobed nozzle. The other is
the azimuthal vortices rolled up at the interface of shear lay-
ers due to the Kelvin–Helmholtz instability. For the largescale streamwise vortices generated by the special trailing
edge of the lobed nozzle, their existence were revealed very
clearly from the instantaneous streamwise vorticity distribution shown in Fig. 4共c兲. In order to reveal the azimuthal
vortices in the lobed jet flow due to the Kelvin–Helmholtz
instability, the x component and y component of the vorticity
vectors were combined into in-plane 共azimuthal兲 vorticity by
using the following equation:
␼ in-plane⫽ 冑␼ 2x ⫹␼ 2y .
共5兲
The distribution of the in-plane 共azimuthal兲 vorticity in
the Z⫽10 mm cross plane of the lobed jet flow is given in
Fig. 4共d兲. As it is expected, the azimuthal Kelvin–Helmholtz
vortices was found to be a vortex ring, which has the same
geometry as the lobed trailing edge at the exit of the lobed
nozzle.
The ensemble-averaged streamwise vorticity and azimuthal 共in-plane兲 vorticity distributions in the lobed jet flow
at Z⫽10 mm cross plane were calculated based on 400 instantaneous measurement results, which are given in Figs.
4共e兲 and 4共f兲. Compared with the instantaneous streamwise
and azimuthal vorticity distributions, the iso-vorticity contours of the ensemble-averaged streamwise and azimuthal
vortices were found much smoother. However, they have almost the same distribution patterns and magnitudes as their
instantaneous counterparts, which may indicate that the generations of the streamwise vortices and azimuthal vortex ring
at the exit of the lobed nozzle are quite steady.
Figure 5 shows the simultaneous measurement results of
the dual-plane stereoscopic PIV system in the Z⫽40 mm
共Z/D⫽1.0, Z/H⫽2.67兲 cross plane of the lobed jet flow.
Compared with that at the exit of the lobed nozzle, the lobed
jet flow has become much more turbulent. However, the
‘‘signature’’ of the lobed nozzle in a form of ‘‘six-lobe structure’’ can still be identified in the instantaneous and
ensemble-averaged velocity fields 关Figs. 5共a兲 and 5共b兲兴. The
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Phys. Fluids, Vol. 14, No. 7, July 2002
Dual-plane stereoscopic particle image velocimetry
2133
FIG. 4. All three components of the vorticity vector distributions in the Z⫽10 mm (Z/D⫽0.25) cross plane of the lobed jet flow. 共a兲 Instantaneous vorticity
共X component兲, 共b兲 simultaneous vorticity 共Y component兲, 共c兲 simultaneous streamwise vorticity 共Z component兲 distribution, 共d兲 simultaneous azimuthal
共in-plane兲 vorticity distribution, 共e兲 ensemble-averaged streamwise vorticity distribution, 共f兲 ensemble-averaged azimuthal 共in-plane兲 vorticity distribution.
six pairs of counter-rotating streamwsie vortices generated
by the lobed nozzle were found to deform very serious in the
instantaneous streamwise vorticity distribution 关Fig. 5共c兲兴.
Some of the large-scale streamwise vortices were found to
break into smaller vortices. From the ensemble-averaged
streamwise vorticity distribution shown in Fig. 5共d兲, the six
pairs of ensemble-averaged streamwise vortices were found
to expand radially. The strength of these ensemble-averaged
streamwise vortices were found to decrease very much with
the maximum value of the ensemble-averaged streamwise
vorticity only about the half of that at the exit of the lobed
nozzle.
From the instantaneous azimuthal vorticity distribution
given in Fig. 5共e兲, it can be seen that the azimuthal vortical
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2134
Phys. Fluids, Vol. 14, No. 7, July 2002
Hu et al.
FIG. 5. The measurement results of the dual-plane stereoscopic PIV system in the Z⫽40 mm (Z/D⫽1.0) cross plane of the lobed jet flow. 共a兲 Instantaneous
velocity distribution, 共b兲 ensemble-averaged velocity distribution, 共c兲 simultaneous streamwise vorticity distribution, 共d兲 ensemble-averaged streamwise
vorticity distribution, 共e兲 simultaneous azimuthal 共in-plane兲 vorticity distribution, 共f兲 ensemble-averaged azimuthal 共in-plane兲 vorticity distribution.
ring, which has the same geometry as the nozzle trailing
edge at the exit of the lobed nozzle, has broken into many
disconnected vortical tubes in this cross plane. The broken
azimuthal vortical fragments at the lobe troughs were found
to connect again to form a new circular-ring-liked structure
in the center of the lobed jet flow.
Based on qualitative flow visualization results, McCormick and Bennett11 suggested that the streamwise vortices
would deform the azimuthal Kelvin–Helmholtz vortical
tubes into pinch-off structures due to the interaction between
the streamwise vortices and azimuthal Kelvin–Helmholtz
vortical tubes. Such pinched-off effect is revealed very
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Phys. Fluids, Vol. 14, No. 7, July 2002
Dual-plane stereoscopic particle image velocimetry
2135
FIG. 6. The measurement results of the dual-plane stereoscopic PIV system in the Z⫽80 mm (Z/D⫽2.0) cross plane of the lobed jet flow. 共a兲 Instantaneous
velocity distribution, 共b兲 ensemble-averaged velocity distribution, 共c兲 simultaneous streamwise vorticity distribution, 共d兲 ensemble-averaged streamwise
vorticity distribution, 共e兲 simultaneous azimuthal 共in-plane兲 vorticity distribution, 共f兲 ensemble-averaged azimuthal 共in-plane兲 vorticity distribution.
clearly and quantitatively from the ensemble-averaged azimuthal vorticity distribution given in Fig. 5共f兲.
As the downstream distance increases to Z⫽80 mm
共Z/D⫽2.0, Z/H⫽5.33兲, the lobed jet flow was found to become more and more turbulent. The ‘‘signature’’ of the lobed
nozzle in the form of ‘‘six-lobed structure’’ is almost indistinguishable in the instantaneous velocity field given in Fig.
6共a兲. The iso-velocity contours of the high-speed core jet
flow were found to become small concentric circles in the
ensemble-averaged velocity distribution 关Fig. 6共b兲兴. The
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2136
Hu et al.
Phys. Fluids, Vol. 14, No. 7, July 2002
FIG. 7. A typical instantaneous and ensemble-averaged ‘‘mass quantity’’ Q distributions in the Z⫽40 mm cross plane of the lobed jet flow. 共a兲 Instantaneous
‘‘mass quantity’’ Q distribution, 共b兲 ensemble-averaged ‘‘mass quantity’’ Q distribution.
smaller instantaneous streamwise vortices originated from
the breakdown of the large-scale streamwise vortices generated by the lobed nozzle almost fully filled the measurement
window 关Fig. 6共c兲兴. Since these instantaneous small-scale
streamwise vortices are so unsteady that they appear very
randomly in the flow field, only very vague vortical structures can be identified in the ensemble-averaged streamwise
vorticity distribution 关Fig. 6共d兲兴. The ensemble-averaged
streamwise vorticity distribution also revealed that the
ensemble-averaged streamwise vortices have been dissipated
so seriously that their strength is only about one-eighth of
those at the exit of the lobed nozzle. Due to the intensive
mixing between the core jet flow and ambient flow, the broken azimuthal vortex tubes dissipated even more extensively.
Only a few fragments of the broken azimuthal vortex tubes
can be found from the instantaneous azimuthal vorticity distribution 关Fig. 6共e兲兴. A circular-ring-liked structure can be
seen clearly in the center of the lobed jet flow from the
ensemble-averaged azimuthal vorticity distribution given in
Fig. 6共f兲.
The authors have suggested that the mixing enhancement caused by the special geometry of a lobed nozzle concentrates mainly within the first two diameters downstream
of the lobed nozzle 共first six lobe heights兲.13,14 The mixing
between the core jet flow and ambient flow further downstream in a lobed jet flow will occur by the same gradienttype mechanism as that for a circular jet flow. The measurement results of the present dual-plane stereoscopic PIV
system show that the azimuthal Kelvin–Helmholtz vortical
rings and large-scale streamwise vortices broke down and
dissipated very rapidly in the first two diameters of the lobed
nozzle 共first six lobe heights兲. Circular-ring-liked structures
were found further downstream in the lobed jet flow. These
results are found to prove the conjectures suggested in the
earlier work of the authors.13,14
EVALUATION OF THE MEASUREMENT RESULTS BY
USING MASS CONSERVATION EQUATION
It is well known that the equation
⳵u ⳵v ⳵w
⫹ ⫹
⫽0
⳵x ⳵y ⳵z
共6兲
should be satisfied theoretically and automatically for an incompressible fluid flow, which is usually referred to as mass
conservation equation.
Since a ‘‘classical’’ PIV system or a conventional stereoscopic PIV system only can provide measurement results of
velocity vectors in one single plane, and the term of ⳵ w/ ⳵ z
in the above mass conservation equation cannot be determined instantaneously. The satisfaction of the measurement
results to the mass conservation equation cannot be checked.
The present dual-plane stereoscopic PIV system can measure
all three components of velocity vectors in two parallel
planes instantaneously and simultaneously, and all the terms
in the mass conservation equation 共6兲 can be calculated instantaneously based on the measurement results of the
present dual-plane stereoscopic PIV system.
A parameter named as ‘‘mass quantity’’ Q is introduced
in the present study to quantify the satisfaction of the present
dual-plane stereoscopic PIV measurement results to the mass
conservation equation. The ‘‘mass’’ quantity Q is defined as
Q⫽
冉
冊
D ⳵u ⳵v ⳵w
⫹ ⫹
.
U0 ⳵x ⳵y ⳵z
共7兲
It should be noted that the ‘‘mass quantity’’ Q should be
zero theoretically in order to satisfy the mass conservation
equation 共6兲. However, since any measurement result may be
contaminated by measurement errors, and the ‘‘mass quantity’’ Q will not always be zero due to the measurement
errors.
Figure 7共a兲 shows a typical instantaneous distribution of
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Phys. Fluids, Vol. 14, No. 7, July 2002
Dual-plane stereoscopic particle image velocimetry
the ‘‘mass quantity’’ Q based on the measurement results of
the present dual-plane stereoscopic PIV system in the Z
⫽40 mm cross plane of the lobed jet flow. Based on 400
frames of the instantaneous results, the ensemble-averaged
value of the ‘‘mass quantity’’ Q was calculated, which is
given in Fig. 7共b兲. From the instantaneous and ensembleaveraged distributions of ‘‘mass quantity’’ Q, it can be seen
that the value of ‘‘mass quantity’’ Q is not always zero over
the measurement window due to measurement errors.
From both the instantaneous distribution and ensembleaveraged distribution of the ‘‘mass quantity’’ Q, it is found
that the regions with bigger ‘‘mass quantity’’ Q always appear in the higher vorticity regions, where the shear motion
is very serious. This may be explained by that since the
accuracy level of the PIV results from the correlation-based
PIV image procession method used in the present study is
very sensitive to the shear motions in fluid flows. Therefore,
bigger errors always appear in the regions with stronger
shear motions.
Lawson and Wu16 suggested that the velocity error of the
out-of-plane component (w error) will be much bigger than
those in the two in-plane components 共u error and v error兲 when
the half-view angle between the stereoscopic image recording cameras is less than 45°. In the present study, it is found
that the largest source of the ‘‘mass quantity’’ Q always
comes from the term of ⳵ w/ ⳵ z. This result is considered to
agree with the prediction of Lawson and Wu16 qualitatively
since the half-angle between the stereoscopic image recording cameras of the present dual-plane stereoscopic PIV system is about 25°.
In order to quantify the measurement error levels of the
dual-plane stereoscopic PIV measurement results more
clearly, the measurement results of the present dual-plane
stereoscopic PIV system are discomposed into accurate values and measurement errors, i.e., u measurement⫽u⫹u error ;
v measure⫽ v ⫹ v error ; w measure⫽w⫹w error . Then, Eq. 共7兲 may
be rewritten as
Q⫽
冉
冋冉
冉
D ⳵ u measure ⳵ v measure ⳵ w measure
⫹
⫹
U0
⳵x
⳵y
⳵z
冊冉
冊
⳵u ⳵v ⳵w
⳵ u error ⳵ v error ⳵ w error
⫹ ⫹
⫹
⫹
⫹
⳵x ⳵y ⳵z
⳵x
⳵y
⳵z
⫽
D
U0
⫽
D ⳵ u error ⳵ v error ⳵ w error
⫹
⫹
.
U0
⳵x
⳵y
⳵z
冊
冉
冊册
共8兲
冊
distance. Then, the measurement error level (⌬U error /U 0 ) of
the present dual-plane stereoscopic PIV measurement may
be evaluated by
⌬U error ⌬zQ
⫽
.
U0
D
共10兲
For the typical instantaneous distribution of the ‘‘mass
quantity’’ Q shown in Fig. 7共a兲, the maximum value of the
‘‘mass’’ quantity Q is about 1.5, i.e., 兩 Q max兩⫽1.5. The spatialaveraged absolute value of ‘‘mass quantity’’ Q over the
whole measurement window is about 0.22, i.e.,
i⫽NI j⫽NJ
兩 Q 兩 spatial-averaged⫽
兺 j⫽1
兺
i⫽1
兩 Q i, j 兩 ⫽0.22.
According to Eq. 共10兲, the error levels of the instantaneous measurement results of the present dual-plane stereoscopic PIV system may be
冏
冏
⌬U error
U0
⫽7.5%
and
max
冏
冏
⌬U error
U0
⫽1.1%.
spatial-averaged
For the ensemble-averaged value of the ‘‘mass quantity’’
shown in Fig. 7共b兲, the maximum value of the ensembleaveraged ‘‘mass quantity’’ Q is about 0.6, i.e.,
兩 Q ensemble-averaged兩 max⫽0.60. The spatial-averaged absolute
value of the ensemble-averaged ‘‘mass quantity’’ Q over the
whole measurement window is about 0.12, i.e.,
i⫽NI j⫽NJ
兩 Q ensemble-averaged兩 spatial-averaged⫽
兺 j⫽1
兺
i⫽1
兩 Q ensmble-averagedi, j 兩
⫽0.12.
Therefore, the error levels of the ensemble-averaged measurement results obtained by the present dual-plane stereoscopic PIV system may be 兩 (⌬U error) ensemble-averaged /U 0 兩 max
⫽3.0%, 兩 (⌬U error) ensemble-averaged /U 0 兩 spatial-averaged⫽0.60%.
CONCLUSIONS
The terms of ⳵ u error / ⳵ x, ⳵ v error / ⳵ y, and ⳵ w error / ⳵ z in
the above equation are recast into the finite difference form
⌬u error /⌬x, ⌬ v error /⌬y, and ⌬w error /⌬z. A total velocity error ⌬U error is defined by ⌬U error⫽⌬u error⫹⌬ v error
⫹⌬w error , and ⌬x⫽⌬y⫽⌬z⫽2 mm for the present study.
Then, Eq. 共8兲 is rewritten as
Q⫽
2137
D ⌬u error ⌬ v error ⌬w error
D ⌬U error
⫹
⫹
.
⫽
•
U0
⌬x
⌬y
⌬z
U0
⌬z
共9兲
It is assumed that the error in the derivative calculation
mainly comes from the error in the velocity rather than the
An advanced stereoscopic PIV system, which named as
dual-plane stereoscopic PIV system, was described in the
present paper to achieve simultaneous measurement of all
three components of the velocity and vorticity vector fields
in a fluid flow. The dual-plane stereoscopic PIV system uses
the polarization conservation characteristic of Mie scattering
to achieve simultaneous stereoscopic PIV measurements at
two spatially separated planes. The objective fluid flow was
illuminated with two orthogonally linearly polarized laser
sheets at two spatially separated planes. The light scattered
by the tracer particles in the two illuminating laser sheets
with orthogonal linear polarization were separated by using
polarizing beam splitter cubes, then recorded separately by
using high resolution CCD cameras. A 3D in situ calibration
procedure was used to determine the relationships between
the two-dimensional image planes and three-dimensional object fields for both position mapping and velocity threecomponent reconstruction. Unlike ‘‘classical’’ PIV systems
or single-plane stereoscopic PIV systems, which can only get
one-component of vorticity vectors, the dual-plane stereo-
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2138
scopic PIV system can provide all three components of the
velocity and vorticity vector distributions instantaneously
and simultaneously.
The dual-plane stereoscopic PIV system was used to
conduct measurement in an air jet flow exhausted from a
lobed nozzle. The large-scale streamwise vortices generated
by the lobed nozzle and azimuthal vortical structures due to
the Kelvin–Helmholtz instability in the lobed jet flow were
revealed simultaneously and quantitatively from the measurement results of the dual-plane stereoscopic PIV system.
The evolution and interaction characteristics of the largescale streamwise vortices and azimuthal Kelvin–Helmholtz
vortices in the lobed jet flow were discussed based on the
simultaneous measurement results. A discussion about the
satisfaction of the measurement results of the present dualplane stereoscopic PIV system to the mass conservation
equation was also conducted to evaluate the error levels of
the measurement results.
1
Hu et al.
Phys. Fluids, Vol. 14, No. 7, July 2002
R. J. Adrian, ‘‘Particle-image technique for experimental fluid mechanics,’’ Annu. Rev. Fluid Mech. 23, 261 共1991兲.
2
A. K. Prasad, ‘‘Stereoscopic particle image velocimetry,’’ Exp. Fluids 29,
103 共2000兲.
3
E. McCartney, Optics of the Atmosphere: Scattering by Molecules and
Particles 共Wiley, New York, 1976兲.
4
C. C. Landreth and R. J. Adrian, ‘‘Electrooptical image shifting for particle
image velocimetry,’’ Appl. Opt. 27, 4216 共1988兲.
5
C. J. Kaehler and J. Kompenhans, ‘‘Multiple plane stereo PIV: Technical
realization and fluid-mechanical significance,’’ Proceedings of the Third
International Workshop on PIV, Santa Barbara, 16 –18 September 1999.
6
A. K. Prasad and K. Jensen, ‘‘Scheimpflug stereocamera for particle image
velocimetry in liquid flows,’’ Appl. Opt. 34, 7092 共1995兲.
7
S. M. Soloff, R. J. Adrian, and Z. C. Liu, ‘‘Distortion compensation for
generalized stereoscopic particle image velocimetry,’’ Meas. Sci. Technol.
8, 1441 共1997兲.
8
H. Hu, T. Saga, T. Kobayashi, N. Taniguchi, and S. Segawa, ‘‘The spatial
resolution improvement of PIV result by using hierarchical recursive operation,’’ Proceedings of 9th International Symposium on Flow Visualization, Edinburgh, Scotland, UK, 22–25 August 2000.
9
H. Hu, T. Saga, T. Kobayashi, N. Taniguchi, and M. Yasuki, ‘‘Dual-plane
stereoscopic particle image velocimetry: System setup and its application
on a lobed jet mixing flow,’’ Exp. Fluids 31, 277 共2001兲.
10
H. Hu, Ph.D. thesis, University of Tokyo, Tokyo, Japan, 2001.
11
D. C. McCormick and J. C. Bennett, ‘‘Vortical and turbulent structure of a
lobed mixer free shear layer,’’ AIAA J. 32, 1852 共1994兲.
12
V. M. Belovich and M. Samimy, ‘‘Mixing process in a coaxial geometry
with a central lobed mixing nozzle,’’ AIAA J. 35, 838 共1997兲.
13
H. Hu, T. Saga, T. Kobayashi, and N. Taniguchi, ‘‘Research on the vortical
and turbulent structures in the lobed jet flow by using LIF and PIV,’’ Meas.
Sci. Technol. 11, 698 共2000兲.
14
H. Hu, T. Saga, T. Kobayashi, and N. Taniguchi, ‘‘A study on a lobed jet
mixing flow by using stereoscopic particle image velocimetry technique,’’
Phys. Fluids 13, 3425 共2001兲.
15
A. Melling, ‘‘Tracer particles and seeding for particle image velocimetry,’’
Meas. Sci. Technol. 8, 1406 共1997兲.
16
N. J. Lawson and J. Wu, ‘‘Three-dimensional particle image velocimetry:
Error analysis of stereoscopic techniques,’’ Meas. Sci. Technol. 8, 894
共1997兲.
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