Proceedings of MNHMT2009
ASME 2009 2nd Micro/Nanoscale Heat & Mass Transfer International Conference
December 18-22, 2009, Shanghai, China
MNHMT2009-18118
UNSTEADY HEAT TRANSFER AND PHASE CHANGING PROCESS WITHIN SMALL
ICING WATER DROPLETS
Hui HU 1 and Zheyan JIN 2
1
2
Department of Aerospace Engineering, Iowa State University, Ames, Iowa 50011, USA.
School of Aerospace Engineering & Applied Mechanics, Tongji University, Shanghai, 200092, China.
ABSTRACT
We report progress made in our recent effort to develop
and implement a novel, lifetime-based molecular tagging
thermometry (MTT) 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 temporallyand-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 lifetime-based MTT
technique. Such measurements are highly desirable to elucidate
underlying physics to improve our understanding about
important micro-physical phenomena pertinent to ice formation
and accreting process as water droplets impinging onto wind
turbine in cold atmospheric environment.
Keywords: Molecular Tagging Thermometry, Micro Scale
Heat Transfer, Water Droplets, Multiphase Flow, Wind Turbine
Icing
INTRODUCTION
Wind energy is one of the cleanest renewable power
sources in the world today. U.S. 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 U.S. 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
turbine operation in atmospheric icing conditions requires a
better understanding of the important micro-physical 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
1
Copyright © 2009 by ASME
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 (MTT) 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-/de-icing
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 (MTV&T) technique developed
by Hu & 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 micro-physical phenomena pertinent to ice formation
and accreting process as water droplets impinging on wind
turbine blades in cold weather.
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 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 [2, 3]. Laser-induced phosphorescence (LIP)
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 (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 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 (either fluorescence or
phosphorescence) decays exponentially. As described in
reference 1 , for a diluted 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
−to / 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.
For an excited state, the deactivation process may involve both
radiative and non-radiactive pathways. The lifetime of the
photoluminescence process, τ, is determined by the sum of all
the deactivation rates: τ −1 = k r + k nr , where kr and knr are the
radiative and non-radiative rate constants, respectively.
According to photoluminescence kinetics [7], these rate
constants are, in general, temperature-dependant. 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, ε , and
quantum yield, Φp, are also temperature dependent in general in
addition to phosphorescence lifetime,τ, 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 (e.g. due to photobleaching) 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 a varying index of refraction. This may cause
significant error in the temperature measurements. To
overcome this problem, a lifetime-based thermometry 8 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, 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 .
2
It is easily
Copyright © 2009 by ASME
R = S 2 / S1 = e
− Δt / τ
(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.
degree Celsius [6]. It is noted that, since low concentration of
the phosphorescent triplex 1-BrNp⋅Mβ-CD⋅ROH (on the order
of 10-4 M) 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.
7
Phosphorescence Lifetime (ms)
shown [1, 8], using Equation (1), that the ratio of these two
phosphorescence signals (R) is given by:
Curve fit
Experimental data
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
45
50
o
Temperature ( C)
Fig. 2: Phosphorescence lifetime vs. temperature.
EXPERIMENTAL SETUP
Fig. 1: Timing chart of lifetime-based MTT technique
The phosphorescent molecular tracer used for the present
study is phosphorescent triplex (1-BrNp⋅Mβ-CD⋅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-βcyclodextrin (indicated collectively by Mβ-CD) and alcohols
(indicated collectively by ROH). Further information about the
chemical and photoluminescence properties of the
phosphorescent triplex (1-BrNp⋅Mβ-CD⋅ROH) is available at
reference 9 and 10. 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. Fig. 2
shows the measured phosphorescence lifetimes of 1-BrNp⋅MβCD⋅ROH molecules as a function of temperature. It can be seen
clearly that phosphorescence lifetime of 1-BrNp⋅Mβ-CD⋅ROH
molecules varies significantly with increasing temperature,
decreasing from about 7.2 ms to 2.5 ms as the temperature
changes from 1.0oC to 30.0oC. The relative temperature
sensitivity of the phosphorescence lifetime is about 3.5% per
degree Celsius, 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
Figure 3 shows the schematic of the experimental setup
used to implement the lifetime-based MTT technique to
quantify unsteady heat transfer and phase changing process
within small icing water droplets. A syringe was used to
generate micro-sized water droplets (about 400μm in radius and
250μm in height) 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 (Neslab RTE-211). The small water droplets with
initial temperature of 20.5 oC (room temperature) 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 (~200μm in thickness) from a pulsed
Nd:YAG at a quadrupled wavelength of 266 nm was used to
tag the premixed 1-BrNp⋅Mβ-CD⋅ROH molecules along the
middle plane of the small water droplets. A 12-bit gated
intensified CCD camera (PCO DiCam-Pro, Cooke Corporation)
with a fast decay phosphor (P46) was used to capture the
phosphorescence emission. A 10X microscopic objective
(Mitsutoyo infinity-corrected, NA= 0.28, depth of field =
3.5μm) 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
3
Copyright © 2009 by ASME
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. Further details about the
experimental setup and procedures to implement the lifetimebased MTT technique to quantify unsteady heat transfer and
phase changing process within small icing water droplets are
available at reference 11.
Fig. 3: Experimental Setup
MEASUREMENT RESULTS AND DISCUSSIONS
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
5.0s later after the water droplet (initial temperature 20.5 oC)
impinged on the cold test plate (Tw =5.0 oC). The first image
(Fig. 4a) was acquired at 0.5 ms after the laser excitation pulse
and the second image (Fig. 4b) 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
Test Plate, Tw = 5.0OC
a). The 1st phosphorescence image
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” even though no optical filter
was used for the phosphorescence image acquisition.
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 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. 4c. Based on a time sequence of the
measured transient temperature distributions within the water
droplet as the one shown at here, the unsteady heat transfer
process within the convectively-cooled water droplets was
revealed quantitatively. Fig. 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 calculated 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 (20.5 oC) was
significantly higher than that of the cold test plate (TW = 5.0
o
C), 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 seconds 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 reference 1, the measurement uncertainty for the
temperature data given in the present study was estimated to be
within 0.5 oC.
Test Plate, Tw = 5.0OC
b). The 2nd phosphorescence image
c). Corresponding MTT results
Fig. 4: A typical MTT measurement
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 turn to ice crystals. Fig. 6(a) shows the
time sequence of the acquired phosphorescence images of a
water droplet when it impinged onto the test plate below frozen
temperature (TW = -2.0°C). Fig. 6(b) shows the corresponding
instantaneous temperature distributions of the remaining liquid
water within the icing droplet measured by using the lifetimebased MTT technique. The transient behavior of the phase
4
Copyright © 2009 by ASME
changing process within the small icing water droplet was
revealed clearly from the acquired phosphorescence images and
the MTT measurement results. In the phosphorescence 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 liquid water at the bottom of the droplet was found to be
frozen and turned to solid ice rapidly since the wall temperature
of the test plate was below frozen temperature, while the upper
portion of the droplet was still in liquid state. 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. At
about 35 seconds later after the droplet impinged onto the cold
test plate, the droplet was found to turn to a solid ice crystal
completely.
t = 0.5 s
20
O
Temperature ( C)
12
8
4
0
0
5
15
20
25
30
35
40
Time (s)
t = 20.0 s
Test Plate, Tw = -2.0OC
t = 35.0 s
Liquid
water
Solid
ice
Test Plate, Tw = -2.0OC
10
Fig. 5: Spatially-averaged temperature vs. time
t = 5.0 s
~250μm
Curve fit
Experimental data
16
Test Plate, Tw = -2.0OC
Test Plate, Tw = -2.0OC
(a). Phosphorescence images
t = 0.5 s
200
0
400
t = 5.0 s
200
0
O
-200
0
X (μm)
200
-400
400
200
0
-200
0
X (μm)
200
0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0
t = 35.0 s
200
0
O
Test Plate (TW=-2.0 C)
400
Temperature
O
( C)
0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0
t = 20.0 s
O
Test Plate (TW=-2.0 C)
-400
Temperature
O
( C)
0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0
Y (μm)
400
Y (μm)
Y (μm)
Temperature
O
( C)
0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0
Y (μm)
Temperature
O
( C)
400
O
Test Plate (TW=-2.0 C)
400
-400
-200
0
X (μm)
200
Test Plate (TW=-2.0 C)
400
-400
-200
(b). MTT measurement results
Fig. 6: Time evolution of the phase changing process within a small icing water droplet
Based on the time sequences of the instantaneous MTT
measurements results as those shown in Fig. 6, the averaged
temperature of the remaining liquid water within the icing
droplet in the course of icing process can be determined. Fig. 7
should the measured profile of the spatially-averaged
temperature of the remaining liquid water within the icing
droplet in the course of the icing process. As described above,
the initial temperature of the liquid water droplet before it
impinged onto the cold test plate (TW = -2.0°C) was 20.5 oC. It
should be noted that, since the frame rate for the
phosphorescence image acquisition used in the present study is
relative low, (i.e., f = 2Hz), the rapid temperature deceasing of
the water droplet at the moment as it impinged onto the frozen
test plate was not be able to be captured due to the limited
0
X (μm)
200
400
temporal resolution of the present MTT measurements. As
shown in Fig. 5, it is expected that the temperature of the water
droplet would decrease with the time after it impinged onto the
cold test plate if the temperature of the cold test plate is above
frozen (i.e., there is not phase change involved). Surprisingly,
the measurement data for the icing droplet given in Fig. 7
reveal a completely different trend. The averaged temperature
of the remaining liquid water within the icing droplet was
found to increase monotonically with time in the course of
icing process. The increasing temperature of the remaining
liquid water in the icing droplet is believed to be closely related
to the releasing of the latent heat of solidification in the course
of the icing process.
5
Copyright © 2009 by ASME
20
16
12
measurement data
Curve fit
8
4
0
0
5
10
15
20
25
30
35
Time (s)
Fig. 7: The averaged temperature of the liquid water in the
icing droplet vs. time
As visualized clearly from the MTT measurement results
given in Fig. 7, the liquid water at the bottom of the icing
droplet would turn to solid ice rapidly after the droplet
impinged onto the frozen test plate. It is well known that there
will be a significant amount of latent heat of solidification
being released as liquid water turning into solid ice. According
to reference 12, the specific latent heat of solidification for
water is 334 KJ/Kg. While the majority of the released latent
heat of solidification would be conducted through the cold test
plate and dissipated by the thermal bath circulator, a portion of
the latent heat of solidification would be conducted through the
interface between the solid ice and the liquid water within the
icing droplet, which would heat the remaining liquid water. In
the course of icing process, more and more liquid water would
turn to ice with the latent heat of solidification released
continuously as the time goes by, while the total amount of the
remaining liquid water within the icing droplet became less and
less. As a result, the averaged temperature of the remaining
liquid water within the icing droplet would increase
monotonically with time until the droplet was found to turn to
ice crystal completely at about 35 seconds later after it
impinged onto the frozen cold test plate.
The variations of the droplet shape profiles given in Fig. 8
also reveal clearly that the volume of the droplet would be
expended continuously in the course of the icing process. As
described above, since the laser illuminating plane is along the
middle plane of the droplet for the MTT measurements, the
volume of the droplet can be determined based on the measured
droplet shape profiles with a reasonable assumption of the
droplet being axisymmetric. Fig. 9 shows the time histogram of
the volume expansion, V/VO, of the droplet in the course of the
icing process, where VO is the initial volume of the water
droplet. It can be seen clearly that the volume of the droplet
was found to increase significantly at the beginning of the icing
process since the majority of the droplet was still liquid water.
The volume expansion rate was found to decrease rapidly with
time since less and less liquid water was found to remain in the
droplet. At the time about 35 seconds (i.e., t ≈ 35.0s) after the
droplet impinged onto the frozen test plate, the volume
expansion profile was found to become a flat line, which
indicates that the volume of the droplet will not change with
time anymore since the water droplet has been turned into solid
ice crystal completely, which was visualized also quantitatively
from the MTT measurement results given in Fig. 6.
350
300
250
200
t = 35.0s
t = 30.0s
t = 20.0s
t = 10.0s
t = 5.0s
t = 0.0s
150
100
50
0
-400
-300
-200
-100
0
100
200
300
400
X (μm)
Fig. 8: The shape profile of the icing droplet vs. time
Specific weight (γ)
Based on the phosphorescent images and MTT
measurement results given in Fig. 6, the contour profiles of the
icing droplet in the course of icing process can also be
extracted, which are given in Fig. 8. The dynamic change of the
droplet shape with time in the course of icing process was
revealed quantitatively. It can be seen clearly that the water
droplet was round, as a cap of a sphere, at the beginning (i.e.,
the contour profile of t = 0.5s). As visualized clearly in the
MTT measurements described above, the liquid water at the
bottom of the droplet would be frozen and turned to solid ice
rapidly, while the upper portion of the droplet was still in liquid
state. As the time goes by, the droplet would grow upward
with more and more liquid water turning into solid ice within
the droplet. The rounded, spherical-cap-shaped profile was
1.10
1.10
1.05
1.05
Specific weight (γ)
Volume expension (V/VO)
γ = 0.9167 for pure ice
1.00
0.95
0.90
1.00
0.95
0
5
10
15
20
25
30
Volume expension (V/VO)
24
Y (μm)
O
Averaged liquid temperature in the droplet ( C)
found to become sharpened substantially to become an oliveseed-shaped profile. Eventually, the spherical-cap-shaped water
droplet was found to turn to be a puddle-shaped ice crystal.
28
0.90
35
Time (s)
Fig. 9: The volume (V/VO) and the specific weight (γ) of
the icing droplet vs. time
6
Copyright © 2009 by ASME
The time variation of the averaged specific weight (thereby
density) of the droplet, γ , in the course of the icing process can
also be determined based on the measured volume expansion
profile. The results were also given in Fig. 9. For comparison,
the standard value of the specific weight of pure ice (i.e., γice
=0.9168) was also given in the figure as the dashed straight
line. It can be seen clearly that the specific weight (or density)
of the droplet was found to become smaller and smaller as more
and more liquid water within the droplet turned into solid ice.
As it is expected, the profile of the measured specific weight of
the icing droplet was found to approach the standard value of
the specific weight of ice (i.e., γ ice = 0.9168) as the time goes
by. When the water droplet has been turned into solid ice
crystal completely at t = 35.0s, the measured value of the
specific weight of the ice crystal was found to be γ = 0.9165,
which agree with the standard value of specific weight of pure
ice γ ice = 0.9168 very well.
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
found to turn to an ice crystal completely, can also be
determined based on the time sequence of the MTT
measurements. 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. As it is
expected, the required frozen time for the water droplets (initial
temperature at 20.5°C) 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.
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 test plate temperature
Based on the measurement results as those shown in Fig. 4
to Fig. 10, important micro-physical 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 micro-physical processes
pertinent to wind turbine icing phenomena in order to explore
effective and robust anti-/de-icing strategies tailored for wind
turbine icing mitigation to ensure safer and more efficient
operation of wind turbines in cold weather.
CONCLUSIONS
A lifetime-based molecular tagging thermometry (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 premixed 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 first 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 time
evolution of phase changing process within small icing water
droplets was also quantified based on the MTT measurements.
It was revealed clearly that the water droplet was round, as a
cap of a sphere, at the beginning as it impinged onto the test
plate. The liquid water at the bottom of the droplet would be
frozen and turned to solid ice rapidly, while the upper portion
of the droplet was still in liquid state. As the time goes by, the
interface between the liquid phase water and solid phase ice
was found to rise upward continuously, indicating more and
more liquid water within the droplet turned into solid ice. The
rounded, spherical-cap-shaped profile of the water droplet was
found to become sharpened continuously to become a prolatespheroid-shaped profile. Eventually, the spherical-cap-shaped
water droplet was found to turn to a prolate-spheroid-shaped ice
crystal. Due to the releasing of the latent heat of solidification
as the liquid water turned to solid ice, the temperature of the
remaining liquid water within the icing droplet was found to
increase rather than decrease continuously in the course of icing
process until the droplet was turned to solid ice crystal
completely. While the volume of the droplet was found to
increase with time monotonically, the specific weight, thereby
the density, of the droplet was found to decrease with time in
the course of icing process, approaching the standard value of
pure ice when the droplet turned into ice crystal completely.
The required frozen time of the droplet was found to strongly
depend on the temperature of the test plat, which would
decrease exponentially with the decreasing surface temperature
of the test plate. Such measurements are highly desirable to
elucidate underlying physics to improve our understanding
about important micro-physical processes pertinent to wind
turbine icing phenomena for safer and more efficient operation
of wind turbines in cold weather.
7
Copyright © 2009 by ASME
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 number of CTS-0545918 is
gratefully acknowledged.
REFERENCES
[1]. H. Hu and M. Koochesfahani, Molecular tagging
velocimetry and thermometry and its application to the
wake of a heated circular cylinder, Meas. Sci. Technol.,
17 (2006) 1269-1281.
[2]. Q. Lu and A. Melton, Measurement of transient
temperature field within a falling droplet, AIAA Journal,
38, (2000) 95-101.
[3]. M. Wolff, A. Delconte, F. Schmidt, P. Gucher and F.
Lemoine, High-pressure diesel spray temperature
measurements using two-color laser induced fluorescence,
Meas. Sci. Technol., 18 (2007) 697-706.
[4]. A. Omrane, G. Juhlin, F. Ossler, and M. Alden,
Temperature measurements of single droplets by use of
laser-induced phosphorescence, Applied Optics, 43
(2004) 3523-3529.
[5]. A. Omrane, S. Santesson, M. Alden and S. Nilsson, Laser
techniques in acoustically levitated micro droplets, Labon-a-Chip, 4 (2004) 287-291.
[6]. H. Hu, C. Lum and M. Koochesfahani, Molecular tagging
thermometry with adjustable temperature sensitivity,
Exp. Fluids, 40 (2006) 753-763.
[7]. Pringsheim, P., Fluorescence and Phosphorescence New
York: Interscience, 1949.
[8]. H. Hu and M. M. Koochesfahani, A novel technique for
quantitative temperature mapping in liquid by measuring
the lifetime of laser induced phosphorescence, Journal of
Visualization,.6 (2003)143–153.
[9]. W. K. Hartmann, M. H. B. Gray, A. Ponce and D. G.
Nocera, Substrate induced phosphorescence from
cyclodextrin-lumophore host-guest complex, Inorg. Chim.
Acta., Vol. 243 (1996) 239-248.
[10]. M. M. Koochesfahani and D. G. Nocera, Molecular
Tagging Velocimetry, Handbook of Experimental Fluid
Dynamics, Chapter 5.4, editors: J. Foss, C. Tropea and A.
Yarin, Springer-Verlag, 2007.
[11]. Z. Jin, Experimental Investigations of Micro-scale
Thermal Flow Phenomena by Using Advanced Flow
Diagnostic Techniques, Ph.D. Thesis, Iowa State
University, Dec. 2008.
[12]. J. D. Cutnell and K. W. Johnson. Physics, 3rd Edition.
New York: Wiley, 1995: 315.
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Copyright © 2009 by ASME