46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
Unsteady Heat Transfer and Phase Change Process within
Icing Water Droplets
Zheyan Jin1 and Hui Hu2()
Iowa State University, Ames, Iowa, 50011
A lifetime-based molecular tagging thermometry (MTT) technique was developed
and implemented to achieve simultaneous measurements of droplet size and
transient temperature distributions within small water droplets on cold solid
surfaces in order to quantify the unsteady heat transfer and phase changing
processes within the small icing water droplets. The dynamic changes of the
temperature distributions within small water droplets in the course of convective
cooling process were quantified clearly from the MTT measurement results. Time
evolution of the size change of the small water droplets (in terms of volume, height,
contact area and the contact angle of the water droplet) due to evaporation was
revealed quantitatively. The MTT technique was also used to visualize the transient
behavior of the phase changing process within icing water droplets. Such
measurements are highly desirable to elucidate underlying physics to improve our
understanding about micro-physical phenomena associate with aircraft icing.
I. Introduction
A
IRCRAFT icing is widely recognized as a significant hazard to aircraft operations. When an aircraft or
rotorcraft flies through a cloud of supercooled water droplets, some of the droplets follow trajectories to allow
them to impact and freeze on exposed aircraft surfaces to form ice shapes. Ice may accumulate on every exposed
frontal surface of the airplane—not just on the wings, propeller, and windshield, but also on the antennas, vents,
intakes, and cowlings. Icing accumulation can degrade the aerodynamic performance of an aircraft significantly by
increasing drag while decreasing lift [1]. In moderate to severe conditions, an aircraft can become so iced up that
continued flight is impossible. The airplane may stall at much higher speeds and lower angles of attack than normal.
It can roll or pitch uncontrollably, and recovery may be impossible [2]. Ice can also cause engine stoppage by either
icing up the carburetor or, in the case of a fuel-injected engine, blocking the engine's air source.
Advancing the technology for safe and efficient aircraft operation in atmospheric icing conditions requires a
better understanding of the micro-physical phenomena associated with the accretion and growth of ice, and the
attendant aerodynamic effects. In order to elucidate the underlying physics associate with micro-physical
phenomena for various aircraft icing studies, experimental studies capable of providing accurate measurements to
quantify important ice growth physical processes such as droplet dynamics, unsteady heat transfer process within
water droplets or ice crystals, and phase changing process within icing water droplets over smooth/rough surfaces,
are highly desirable. In the present study, we report the progress made in our recent efforts to conduct quantitative
measurements of droplet size and transient temperature distributions within small, convectively-cooled, surface
water droplets to quantify the unsteady heat transfer and phase changing process within icing water droplets over
1
2
Graduate Student, Department of Aerospace Engineering.
Assistant Professor, Department of Aerospace Engineering, AIAA Senior Member, email: huhui@iastate.edu.
1
American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
cold surfaces. A novel, lifetime-based molecular tagging thermometry (MTT) technique was developed and
implemented to achieve simultaneous measurements of droplet size and transient temperature distributions within
small water droplets to quantify unsteady mass transfer, heat transfer and phase changing process within the small,
convectively-cooled water droplets. The ultimate objective of the present study is to elucidate underlying physics to
improve our understanding about micro-physical phenomena associated with aircraft icing studies.
II. Molecular Tagging Thermometry 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 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 (LIF) techniques have been widely used for temperature measurements of liquid
droplets for combustion applications [3-5]. Laser-induced phosphorescence (LIP) techniques have also been
suggested recently to conduct temperature measurements of “in-flight” or levitated liquid droplets [6-7]. 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 (such as from solid surfaces) 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 three to four times more sensitive to
temperature variation compared with LIF [8-9], which is favorable for 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, which can be considered
as an extension of the Molecular Tagging Velocimetry and Thermometry (MTV&T) technique developed by Hu &
Koochesfahani [8]. For MTT measurement, a pulsed laser is used to “tag” phosphorescent (e.g. phosphorescent
dye) premixed in the working fluid. The long-lived LIP emission is imaged at two successive times after the same
laser excitation pulse. The LIP emission lifetime distribution is estimated from the intensity ratio of the acquired
phosphorescence image pair. The temperature distribution within a small water droplet can be derived by taking
advantage of the temperature dependence of phosphorescence lifetime.
The technical basis of the MTT measurements is given briefly at here. According to quantum theory, the
intensity of phosphorescence emission decays exponentially. As described in Hu & Koochesfahani[8], for a dilute
solution and unsaturated laser excitation, the collected phosphorescence signal (S) by using a gated imaging detector
with integration starting at a delay time to after the laser pulse and a gate period of δt can be given by
(
S = AI i Cε Φ p 1 − e
−δ t / τ
)e
−t o / τ
(1)
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 (the tagged molecular tracer), ε is the absorption coefficient, and Φp is the
phosphorescence quantum efficiency. The emission lifetime τ refers to the time at which the intensity drops to 37%
(i.e. 1/e) of the initial intensity.
In general, the absorption coefficient ε , quantum yield Φp, and the emission lifetime τ are temperature
dependent, resulting in a temperature-dependent phosphorescence signal (S). Thus, in principle, the collected
phosphorescence signal (S) may be used to measure fluid temperature if the incident laser intensity and the
concentration of the phosphorescent dye remain constant (or are known) in the region of interest. It should be noted
that the collected phosphorescence signal (S) is also the function of incident laser intensity (Ii) and the concentration
of the phosphorescent dye (C). Therefore, the spatial and temporal variations of the incident laser intensity and the
non-uniformity of the phosphorescent dye 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 non-varying incident laser intensity distribution, especially for unsteady
thermal phenomena with varying index of refraction. This may cause significant error in the temperature
measurements. To overcome this problem, a lifetime-based thermometry [10] was developed to eliminate the effects
of incident laser intensity and concentration of phosphorescent dye on temperature measurements.
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
Fig. 1: Timing chart for lifetime-based thermometry technique
The lifetime-based thermometry works as follows: As illustrated in Fig. 1, laser-induced phosphorescence
emission is interrogated at two successive times after the same laser excitation pulse. The first image is detected at
the time t = t o after laser excitation for a gate period δ t to accumulate the phosphorescence intensity S1 , while the
second image is detected at the time t = t o + Δt for the same gate period to accumulate the phosphorescence
intensity S 2 . It is easily shown, using Equation (1), that the ratio of these two phosphorescence signals (R) is given
by
R=
S2
− Δt / τ
=e
S1
(2) .
In other words, the intensity ratio of the two successive phosphorescence images (R) is only a funtion of the
phosphorescence lifetime τ, and the time delay Δt 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
non-uniformity of the dye concentration (e.g. due to bleaching). For a given molecular tracer and fixed Δt value,
Equation (2) defines a unique relation between phosphorescence intensity ratio (R) and fluid temperature T, which
can be used for thermometry.
The phosphorescent molecular tracer used in the present study is phosphorescent triplex (1-BrNp⋅MβCD⋅ROH). The phosphorescent triplex (1-BrNp⋅Mβ-CD⋅ROH) is actually the mixture compound of three different
chemicals, which are lumophore (indicated collectively by 1-BrNp), maltosyl-β-cyclodextrin (indicated collectively
by Mβ-CD) and alcohols (indicated collectively by ROH). Further information about the chemical and
photoluminescence properties of the phosphorescent triplex is available at [11-14]. In the present study, we used a
concentration of 2×10−4 M for Mβ-CD, a saturated (approximately 1×10−5 M) solution of 1-BrNp and a
concentration of 0.06 M for the alcohol (ROH), as suggested by Gendrich et al. [13].
Upon the pulsed excitation of a UV laser (quadrupled wavelength of Nd:YAG laser at 266nm for the present
study), the phosphorescence lifetime of the phosphorescent triplex (1-BrNp⋅Mβ-CD⋅ROH) molecules in an aqueous
solution change significantly with temperature. Figure 2 shows the measured phosphorescence lifetimes of 1BrNp⋅Mβ-CD⋅ROH molecules as a function of temperature, which were obtained though a calibration experiment
similar as those described in Hu & Koochesfahani [8, 10]. It can be seen clearly that phosphorescence lifetime of 1BrNp⋅Mβ-CD⋅ROH molecules varies significantly with increasing temperature, decreasing from about 7.0ms to
2.5ms as the temperature changes from 2.0oC to 30.0oC.
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
8
7
Lifetime (ms)
6
5
4
3
Curve fit
Experimental data
2
1
0
0
5
10
15
20
25
30
35
O
temperature ( C)
Fig. 2: Phosphorescence lifetime of 1-BrNp⋅Mβ-CD⋅ROH vs. temperature
III. Experimental Setup
Figure 3 shows the schematic of the experimental setup used in the present study. A syringe was used to
generate small water droplets for the experiments. The temperature of the test plate was adjustable by using a thermo
circulator (Neslab, RTE-211). Phosphorescent triplex 1-BrNp⋅Mβ-CD⋅ROH was premixed within the water droplet.
A laser sheet from a pulsed Nd:YAG at quadrupled wavelength of 266nm was used to tag the premixed 1-BrNp⋅MβCD⋅ROH molecules along the middle plane of the small water droplet, as shown in Fig. 3.
A 12-bit gated intensified CCD camera (PCO DiCam-Pro) with a fast decay phosphor (P46) was used to capture
the phosphorescence emission. One lens (AF MICRO NIKKRR 105mm, Nikon) and two 2× teleconverters (Nikon
TC-201) were mounted in the front of the camera. The depth of focus of the lens was about1.0 mm. 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 (BNC 555 Digital Delay-Pulse Generator), which controlled the timing of
the laser illumination and the image acquisition.
Fig. 3: The experimental setup
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
IV. Experimental Results and Discussions
A. Droplet size and transient temperature measurements within convectively cooled water droplets
During the experiments, the surface temperature of the test plate was maintained at a pre-selected low
temperature level. The surface temperature of the test plate was monitored by using a thermocouple. Small water
droplets with initial temperature of 20.5oC (room temperature) would be convectively cooled after it was placed on
the cold test plate.
Figure 4 shows a typical pair of acquired phosphorescence images of a small water droplet on the test plate with
the surface temperature of the test plate being 2.0 oC. The first image was acquired at 0.5 ms after the laser pulse
and the second image at 3.5 ms after the same laser pulse with the same exposure time of 1.5 ms for the two image
acquisitions. As described above, 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 (such as from
solid surface) in the measurement region effectively, the phosphorescence images of the water droplet are quite
“clean”.
As described above, Equation (2) can be used to calculate the phosphorescence lifetime of the tagged molecules
on a pixel-by-pixel basis, which resulting in a distribution of the phosphorescence lifetime over a two-dimensional
domain. With the calibration profile of phosphorescence lifetime vs. temperature shown in Fig. 2, a twodimensional, instantaneous temperature distribution within the water droplet can be derived from the
phosphorescence image pair, which was shown in Fig. 5.
b
a
Test plate, T=2.0 oC
Test plate, T=2.0 oC
b). The second phosphorescence image
acquired at 3.5ms after the same laser pulse
a). The first phosphorescence image
acquired at 0.5ms after laser pulse
Fig. 4: A typical pair of acquired phosphorescence images
1000
Temperature
(oC)
2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0
800
8.0
16.0
8.0
200
16.0
8.0
18.0
8.
0
8.0
0
.0
400
20.0
14.0 12.0
.0
10
18
Y (μm)
600
Test plate (T= 2.0 oC)
-800
-600
-400
-200
0
200
400
600
80
X (μm)
Fig. 5: Instantaneous temperature distribution derived from the acquired phosphorescent image pair
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
Figure 6 shows the spatially-averaged temperature of the water droplet as a function of the time, which was
calculated based on the time sequence of the measured instantaneous temperature distributions. The characteristics
of the unsteady heat transfer process within the convectively cooled water droplet were revealed quantitatively from
the evolution of the spatially-averaged temperature of the water droplet. Since initial temperature of the water
droplet (20.5 oC) was significantly higher than that of the cold test plate (2.0 oC), the spatially-averaged temperature
of the water droplet was found to decrease rapidly and monotonically after it was placed on the cold test plate. The
temperature measurement results given in Fig. 6 also revealed that a thermal steady state would be reached at about
160 seconds later after the water droplet was placed on the cold test plate. The spatially-averaged temperature of the
water droplet would not decrease anymore when the thermal steady state was reached. The spatially-averaged
temperature of the water droplet was found to be about 6.0 oC after the thermal steady state was reached.
10
o
Temperature ( C)
8
6
4
Curve fitting
Experimental data
2
0
80
100
120
140
160
180
200
Time (s)
Fig. 6: Averaged temperature of the convectively-cooled small droplet vs. time
In additional to the transient temperature distribution measurements within the small water droplet, the size (in
terms of volume, height, contact area and contact angle) of the water droplet on the test plate can be also determined
simultaneously from the acquired phosphorescence images with a pre-determined scale ratio between the image
plane and objective plane. Therefore, the characteristics of unsteady mass process of the water droplet on the test
plate due to evaporation can also be quantified from the MTT measurements.
V
H
Water
droplet
R
Solid
surface
Fig. 7: Schematic of a surface water droplet
Figure 7 shows schematically the definitions of water droplet height, H, contact radius, R, contact angle, θ, and
volume, V, used in the present study. As shown in Fig. 4, the edge of the water droplet can be easily detected based
on the significant intensity changes in the acquired phosphorescence images. Thus, the contact radius, R, and droplet
height, H, can be measured directly form the acquired phosphorescence images with a pre-determined scale ratio
between the image plane and objective plane. The contact angle, θ, and volume, V, were determined by using the
following equations based on the fact that a surface droplet is normally a sphere cap.
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
θ = 2 tan −1 (
V=
H
)
R
(3)
πR 3 (1 − cos θ ) 2 (2 + cos θ )
3 sin 3 θ
(4)
1.2
70
1.0
65
0.8
60
0.6
55
Droplet volume, V
Droplet heigth, h
Contact angle, θ
0.4
50
0.2
0
60
Contact angle (degrees)
V/Vo , h/ho
It is well known that there are two modes for the evaporation of a liquid droplet on a solid surface [15-17]; one
consists of a constant contact angle with diminishing contact area and the other one of a constant contact area with
diminishing contact angle. The phosphorescence image pair given in the Fig. 4 revealed clearly that the contact
angle of the water droplet on the test plate was less than 90o. The radius of the contact area of the water droplet on
the test plate was found be almost constant during the experiments, which indicates that the evaporation process of
the water droplet followed the constant contact-area mode. Figure 8 shows the measured water droplet size (in the
terms of droplet volume, height and contact angle) on the test plate as a function of time after it was placed on the
test plate. It can be seen clearly that the droplet height, volume and contact angle decreased linearly with the time
due the evaporation. The results were found to agree with the findings of Birdi et al. [17], who suggested that, for a
liquid drop on a low-surface-tension solid surface, the evaporation rate would be linear and follows the constant
contact-area mode if the initial contact angle of the droplet is less than 90o.
45
80
100
120
140
160
40
180
Time (second)
Fig. 8: Evolution of the size of water droplets due to evaporation.
B. Visualization of the transient behavior of phase changing process within icing water droplets
When the surface temperature of the test plate was adjusted to be lower than the frozen temperature (i.e., Tsurface
< 0.0 oC), water droplets on the test plate would be frozen and turn to ice crystals. In the present study, MTT
technique was also used to investigate the dynamic phase changing process within small icing water droplets.
Figure 9 shows the time sequence of the acquired phosphorescence images when a water droplets (initial
temperature at 20.5°C) was placed on a cold test plate (-2.5°C). The transient behavior of the phase changing
process within the icing water droplet was visualized clearly from the acquired images.
In the phosphorescence images, the “brighter” region in the upper portion of the droplet represents the liquid
phase water; while the “darker” region at the bottom of the droplet indicates solid phase ice. It can be seen clearly
that the water droplet was round, as a cap of a sphere at beginning. As the time goes by, the interface between the
liquid phase water and solid phase ice was found to keep on rising upward, 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
sphere-cap-shaped water droplet was found to turn into be a puddle-shaped ice crystal.
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
Test plate, T=-2.5OC
Test plate, T=-2.5OC
a. t =1.0s
Test plate, T=-2.5OC
b. t =5.0s
c. t =10.0s
Test plate, T=-2.5OC
Test plate, T=-2.5OC
d. t =15.0s
Test plate, T=-2.5OC
e. t =20.0s
f. t =30.0s
Fig.9: The evolution of the phase changing process within an icing water droplet
The required frozen time, which is defined as the time interval between the moment when a water droplet is
placed on the cold test plate and the moment when the water droplet is turned into an ice crystal completely, can be
determined based on the time sequence of the acquired phosphoresce images. As it is expected, the required frozen
time for water droplets (initial temperature at 20.5°C) turning into ice crystal was found to strongly depend on the
surface temperature of the test plate. Fig. 10 shows the variations of the required frozen time of the water droplets
with the surface temperature of the test plate changed from -1.0 °C to -5.0 °C. It can be seen clearly that the
required frozen time was found to decrease exponentially with the decreasing surface temperature of the test plate.
70
60
Experimental data
Exponential curve fit
Time (s)
50
40
30
20
10
-6
-5
-4
-3
-2
-1
0
0
Surface Temperature of Test Plate ( C)
Fig. 10: The required frozen time vs. the surface temperature of the test plate
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
Concluding Remarks
In the present study, a lifetime-based molecular tagging thermometry (MTT) technique was developed and
implemented for achieving simultaneous measurements of droplet size and transient temperature distribution within
small water droplets over cold solid surfaces to quantify the unsteady heat transfer and phase changing process
within the small water droplets in order to elucidate underlying physics to improve our understanding about microphysical phenomena associated with aircraft icing.
For MTT measurements, a pulsed laser is used to “tag” phosphorescent 1-BrNp⋅Mβ-CD⋅ROH molecules
premixed within small water droplets. Long-lived laser-induced phosphorescence is imaged at two successive times
after the same laser excitation pulse. While the size of the water droplet (in terms of volume, height, contact area and
contact angle of the water droplet) were determined instantaneously from the acquired phosphorescence images, the
transient temperature measurement was achieved by taking advantage of the temperature dependence of
phosphorescence lifetime, which was estimated from the intensity ratio of the acquired phosphorescence image pair.
The lifetime-based MTT technique was used to conduct simultaneous measurements of droplet size and
temporally-and-spatially resolved temperature distribution within small, convectively-cooled water droplets placed
on cold test plate to quantify unsteady mass and heat transfer process within the small water droplets. Dynamic
change of the temperature distributions within small water droplets in the course of the convective cooling process
were quantified clearly from the MTT measurement results. Time evolution of the size change of the small water
droplets (in terms of volume, height, contact area and the contact angle of the water droplet) due to evaporation was
revealed quantitatively. The MTT technique was also used to visualize the transient behavior of the phase changing
process within icing water droplets. Such measurements are highly desirable to elucidate underlying physics to
improve our understanding about micro-physical phenomena associate with aircraft icing studies.
Acknowledgments
The authors also want to thank Mr. Bill Rickard of Iowa State University for his help in conducting the experiments.
The support of National Science Foundation CAREER program under award number of CTS-0545918 is gratefully
acknowledged.
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American Institute of Aeronautics and Astronautics
46th AIAA Aerospace Sciences Meeting and Exhibit
AIAA-2009-1269
Jan. 5 – 8, 2008, Orlando, Florida
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