Proceedings of NHTC’01
35th National Heat Transfer Conference
June 10-12, 2001, Anaheim, California
NHTC01-11672
EFFECTS OF WEBER NUMBER AND SURFACE TEMPERATURE ON THE BOILING AND
SPREADING CHARACTERISTICS OF IMPINGING WATER DROPLETS
Satish G. Kandlikar
[email protected]
Mark E. Steinke
Ashish Singh
Mechanical Engineering Department
Rochester Institute of Technology
Rochester, NY 14623
ABSTRACT
In the present work, the effects of Weber number and
surface temperature upon the droplet impingement behavior and
boiling characteristics have been experimentally studied. High
speed photography (up to 8000 frames per second) has been
employed to visualize the interface interactions.
An experimental apparatus is designed and fabricated to
deliver constant size droplets to a heated copper surface. The
Weber number and the surface temperature are varied to
determine their effects upon the boiling characteristics. The
surface temperature range is 25°C to 350°C and the Weber
number is varied from 10 to 58. A high-speed digital camera is
utilized in capturing this dynamic. The droplet characteristic
during droplet levitation has been classified into four types;
levitation after several advance and recoil cycles, levitation
after first recoil, disintegration after first recoil, disintegration
after impact. The maximum spread diameter is also compared
with three established correlations from literature.
INTRODUCTION
Droplet impingement upon a surface is important in
numerous applications including steam impingement upon
turbine blades, fire suppression systems, fuel spray in internal
combustion engines, and spray cooling of electronic
components.
The droplet impingement on a hot surface undergoes all of
the classical boiling regimes in a matter of seconds. The
droplet Weber number just prior to impact and the heater
surface temperature have been identified as the parameters
affecting the droplet spreading behavior. The present study
focuses on the droplet characteristics as it goes past the critical
heat flux condition. The droplet breakup is also investigated.
The droplet spreading characteristics is important in many
spray applications for determining the available heat transfer
area for droplet evaporation. The maximum spreading ratio is
the maximum spreading diameter to the initial droplet diameter
is an important parameter investigated in this paper.
NOMENCLATURE
dmax maximum spread diameter, (mm)
D
droplet diameter prior to impact, (mm)
k
thermal conductivity, (W/m-K)
surface roughness, (µm)
Ra
ro
radius prior to impact, (mm)
Rmax maximum film radius, (mm)
t
time after impact, (ms)
∆t
differential time, (s)
surface temperature, (°C)
Ts
Tsat saturation temperature, (°C)
∆Tsat wall superheat (= Ts - Tsat, °C)
We
Weber number,
æ ρV 2 D ö
çç =
÷÷
σ
è
ø
Greek Letters
βmax
ρ
σ
1
maximum spread ratio, dmax/D
density, (kg/m3)
surface tension, (N/m)
Copyright © 2001 by ASME
LITERATURE REVIEW
The initial studies of the process of droplet impacting a hot
surface were done during the early part of the 20th century.
However, major progress was carried out in this field with the
development of high-speed photography. Savic and Boult
(1955), and Wachters and Westerling (1966) conducted
extensive photographic studies to study the droplet behavior
upon impact as a function of surface temperature.
Most of the recent work has been done using the highspeed photographic techniques e.g Bernardin et al. (1997),
Naber and Farrell (1993). However, some of the researchers
(such as Chandra and Avedisian, 1991) have used the singleshot flash photographic technique. The results obtained by this
technique have been quite impressive and useful in the
visualization of the dynamics of the droplet deformation.
The studies on droplet impingement can be broadly
classified into studies on – deformation dynamics, heat transfer
regimes and numerical modeling of the droplet shapes. Chandra
and Avedisian (1991) have been able to capture clear images of
n-heptane droplets, and to demonstrate the droplet deformation
in the nucleate and the transition boiling regime. This study also
indicated that the spreading rate of the droplet is independent of
the surface temperature during the early stages of the impact.
This result matches with other works like Natta et al (1998).
Some studies have been made to find the correlation
between the Reynold’s number and the droplet deformation.
Natta et al (1998) shows that there is negligible effect of
Reynolds number on the droplet deformation, especially in the
early stages of the impact.
Naber and Farrell (1993) studied the impacting droplets in
different heat transfer regimes to find if and when the
atomization (break-up) of droplets occurred. They observed
that during the non-wetting regime there is no break-up of the
droplets. However in the nucleate and the transition regime,
there can be some atomization due to rapid bubbling and
nucleation at the interface.
Previous studies have used a variety of fluids for the
studies – Chandra and Avedisian (n-Heptane), Naber and Farrell
(Water, Acetone and n-Heptane). However, the majority of
studies have been done using water as a fluid. The result of
these studies indicates that the deformation dynamics and the
heat transfer phenomenon are essentially the same as far as the
different boiling regimes and characteristics are involved. In
the present work, de-ionized water has been used keeping this
point in mind and considering it’s widespread usage.
There have been a number of studies on the heat transfer
characteristics and it’s correlation with the droplet deformation.
Bernardin, et al (1997) used the droplet deformation data to
prepare the droplet heat transfer regime maps for low,
intermediate, and high Weber numbers. Pederson (1969)
established that the heat transfer increases as the approach
velocity of the drop increases.
However, the surface
temperature has little effect on the heat transfer rates in the nonwetting regime.
One of the parameters that is important in the droplet
studies is the maximum spread ratio. There are several models
available in literature. Healy et al. (1996) present a good
comparison of the correlations, and recommend KurabayashiYang (K-Y) correlation for predicting βmax. Another correlation
that is also applicable is that by Akao et al. (1980). Healy et al.
(2001) offer a correction to the K-T correlation to include the
contact angle effects. These effects will be evaluated further in
the present work.
OBJECTIVES OF THE PRESENT WORK
The objectives of the present work are to study the droplet
spread and breakup as a function of the heater surface
temperature and the Weber number, and investigate the effect of
these parameters on the maximum spreading ratio. Two high
speed video cameras are used to capture simultaneous views of
the droplet behavior upon impact. The maximum spreading
ratio βmax is measured as a function of temperature and is
compared with the available correlations in literature. The
effect of contact angle on the spreading ratio is also
investigated, and recommendations are made to improve the
accuracy of the existing correlations.
EXPERIMENTAL SET-UP
The experimental apparatus used in the present work is
designed to maintain the impact surface at a steady state surface
temperature. The apparatus consisted of the components as
shown in Figure 1. The main components of the
Figure 1. Experimental Apparatus
experimental apparatus are; the Heating Billet, Impact Surface,
Droplet Delivery System, High Speed Cameras, and Constant
Light Source.
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Copyright © 2001 by ASME
The Heating Billet is a 1 ½ inch diameter copper rod. A
600-Watt cartridge heater is placed inside the rod to provide
heating. A DC power supply is used to regulate the voltage of
the heater to provide temperature control. The billet is fully
insulated on all sides, except the upper surface. The impact
surface is placed on top of the heating billet.
The Impact Surface (test piece) is constructed to rest upon
the top of the heating billet. A piece of Graphfoil thermal
conduction material is used to minimize any contact resistance.
The test pieces are constructed of Copper. The copper is an
Electrolytic Tough Pitch alloy number C11000. It is comprised
of 99.9% copper and 0.04% oxygen (by weight). The thermal
conductivity is 388 W/m-K at 20°C. The test piece is a 1-½
inch (38.1 mm) diameter rod with a ½ inch (12.7 mm)
thickness. The test piece has two thermocouples located at a
radial location of 0.25 inches from the surface’s center. The
first thermocouple is located at a distance of 2.5 mm from the
impacting surface and the second thermocouple is 5.0 mm
below the impacting surface. The temperature readings of the
thermocouples are recorded by using a thermocouple reader
whose accuracy is ±0.1°C. Steady state condition is reached
when the temperatures remain constant. The test pieces are
polished using a one micron aluminum oxide slurry. After
polishing, the surface roughness of the test piece has an Ra
value of 0.63 µm.
The High Speed Cameras are two high-speed digital
cameras, which can capture images up to 8000 frames per
second.
However, the image resolution is in inverse
relationship to the capturing frame rate. Therefore, the frame
rate and shutter speed were optimized to yield the best possible
image. The typical frame rate and shutter speeds are 2000
frames/sec and 1/40000 second respectively. The camera is
placed parallel to the impact surface at a zero degree angle to
the surface. This has been done in order to get the best view of
the surface profile of the liquid and the liquid-solid interaction
at the interface.
The Droplet Delivery System is comprised of a water
reservoir, two control valves, and a needle. The flow valves are
adjusted to allow a single droplet to fall onto the impacting
surface. The height and gauge of the needle can be varied to
change the Weber number of the impinging droplet.
The Continuous Light Source is a 600-Watt flood light that
is constantly on. The illumination of the light is made uniform
by using white paper diffusers.
EXPERIMENTAL PROCEDURE
The experimental procedure was developed to maintain a
steady state surface temperature. The transient effect of the
impingement behavior was not studied in the present work. The
reported surface temperatures are the steady state values just
prior to impingement.
The heated surface was allowed to remain at steady state
conditions for several minutes before the data is collected. The
surface temperatures ranged from 25°C to 350°C with 25°C
increments. The surface was closely observed for any visible
signs of oxidation or coating with impurities. When the test
piece became tarnished, it was replaced with a freshly polished
piece and the new test piece was allowed to reach steady state
condition before data collection resumed.
The height of the needle relative to the heated surface was
adjusted to five heights: 12.7mm, 19.1 mm, 25.4 mm, 38.1 mm,
and 76.2 mm. The needle gage was held constant for the
experiment.
RESULTS
The present work focuses on the effect of Weber number
upon the behavior of an impinging droplet on a heated surface.
The visual part of the study investigated the droplet behavior
with respect to the droplet levitation and disintegration
phenomena. The dynamics are studied for five Weber numbers
of 10, 14, 19, 29, and 58. The droplet diameter is calculated by
measuring the weight of 20 droplets and calculating the
diameter; it was found to be 2.8 ± 0.1 mm. The image capture
software was also used to measure the droplet diameters. The
two methods showed good agreement.
Figure 2. Droplet Behavior: The droplet impingement
behaviors as depicted in four major characteristics;
(a) levitation after several advance and recoil cycles,
(b) levitation after first recoil, (c) disintegration after
first recoil, (d) disintegration on impact.
The droplet levitation phenomenon is studied by varying
the Weber number and the surface temperature. The surface
temperatures range from 25°C to 375°C. The levitation of the
droplet has been defined as the instant when the main mass of
the droplet completely departs from the surface. At different
temperatures, this results in different droplet shapes.
Figure 2 depicts different types of droplet interactions
proposed in this study for classifying the basic impinging
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Copyright © 2001 by ASME
droplet behaviors. The first condition shown in Fig. 2(a) is
droplet levitation after a few advance and recoil cycles. In
Figure 2(b), the droplet levitation immediately following the
first recoil is shown. The droplet disintegration after the first
recoil is shown in Figure 2(c). Figure 2(d) shows the droplet
disintegration upon impact.
Furthermore, these shapes are
dependent upon the Weber number and surface temperature. It
is known that for a given Weber number there is a minimum
temperature after which an impacting droplet rebounds from the
hot surface after recoiling. It has been found that the time
required for the drop to completely leave the surface is
dependent upon both the Weber number and the surface
temperature.
The Weber number is 58 for droplet images shown in
Figures 3 through 8. The droplet displays conventional impact
behavior through all of the subcooled surface temperatures. It
strikes the surface, recoils, and oscillates before reaching the
final equilibrium shape. When the ∆Tsat is less than 50°C, the
droplet begins to exhibit limited bubble generation within the
droplet. For a surface temperature of 150°C, there is large
amount of bubble nucleation occurring within the droplet. At
this temperature, the droplet still does not lift off in the first
receding motion. The droplet remains in contact with the
surface for a few spread and recoil cycles. During this time, the
heat is transferred into the droplet and vapor is formed. The
droplet’s mass begins to reduce due to the evaporation. At
some point after several spread and recoil cycles, the droplet
begins to levitate. The shape of the drop during this time is
shown in Figure 3.
Figure 4. Droplet Levitation: The droplet is levitated
above the surface after its impact. Ts = 225°°C; We =
58 ; t = 17.5 ms.
Figure 5. Droplet Disintegration: The droplet is
broken up after the initial recoil. Ts = 250°°C; We = 58;
t = 10 ms.
Above a surface temperature of 300°C, the droplet breaks
up into several smaller droplets upon impact. All of the smaller
droplets quickly begin to levitate above the surface in mutually
expanding motion as shown in Figure 6.
Figure 3. Delayed Droplet Levitation: The droplet is
levitated above the surface after a few advance and
recoil cycles. Ts = 150°°C ; We = 58; t = 28.5 ms.
For surface temperatures of 175°C, 200°C and 225°C, the
droplet levitates on its first recoil motion. The shape of the
drop is shown in Figure 4. The droplets begins to disintegrate
upon impact for surface temperatures greater than 250°C. For
surface temperatures from 250°C to 350°C, the drop levitates
on the first recoil only and then breaks into several smaller
fragments. Figure 5 depicts this behavior.
Figure 6. Droplet Disintegration Upon Impact: The
droplet is broken up upon impact. Ts = 350°°C; We =
58; t = 10 ms.
The drop exhibits the same behavior for a Weber number of
29 for surface temperature from 25°C to 200°C. For surface
temperatures greater than 200°C, the partial separation of the
droplet is more pronounced as compared to the higher Weber
number case. Therefore, the levitated drop has the shape as
shown in Figure 5 from 225 to 300°C.
Figure 7 depicts a plot of levitation time, defined as the
elapsed time before levitation after impact, versus surface
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Copyright © 2001 by ASME
temperatures for Weber numbers 58 and 29. The levitation time
reduces dramatically as the surface temperature exceeds about
150°C-170°C. After reaching a minimum value at 350°C, it
seems to increase a little bit.
Levitation Time ( ms )
150
125
100
We = 58
75
We = 29
50
25
0
100
150
200
250
300
350
400
Surface Temperature ( °C )
Figure 7. Time Elapsed before Levitation versus
Surface Temperature, We = 29 and 58.
This behavior may be due to differences in the boiling
phenomena as the droplet traverses through the transition
boiling regime. The minimum time is reached at a temperature
close to the upper limit of the transition regime. This occurs
because, during the transition regime there is still some liquid to
surface contact. Consequently, the heat transfer rate is
increased. Due to increased temperature and increased heating
rate, there is rapid nucleation and bubbling inside the droplet.
This creates a higher pressure of vaporizing liquid below the
droplet finally resulting in early levitation of the droplet from
the surface. As the temperature is increased beyond the
transition regime, the heat transfer gradually reduces because
the liquid to surface contact is minimal or absent. The droplet
rests upon a cushion of vapor, and the heat transfer rate is
reduced. Therefore, there is less nucleation within the droplet
resulting in an increased levitation time for the droplet.
It was found that the levitation time for the two Weber
numbers follows a similar pattern. However, the levitation time
is somewhat lower for the lower Weber number case than the
higher Weber number case.
Previous studies have indicated a direct relationship
between the droplet breaking and the Weber number. These
results have been confirmed during the present work. The
droplet dynamics at different surface temperatures and Weber
numbers can be studied from the photographs of the droplet
impinging on the hot surface.
Figure 8 - Part 1. Droplet Impact for We = 58 From
Impact to 10 ms: The droplet impingement history for
a Weber number of 58. The surface temperatures are;
100°°C, 150°°C, 200°°C, 225°°C, and 250°°C. We = 58; ∆t =
1 ms.
Figures 8 and 9 depict the history of the droplet
impingement for a Weber number of 58 and 29 respectively.
The surface temperatures are; 100°C, 150°C, 200°C, 225°C,
and 250°C. The time ranges from impact to 20 ms after impact
in a 1 ms time step.
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Copyright © 2001 by ASME
Figure 8 - Part 2. Droplet Impact for We = 58 From 11
ms to 20 ms: The droplet impingement history for a
Weber number of 58. The surface temperatures are;
100°°C, 150°°C, 200°°C, 225°°C, and 250°°C. We = 58; ∆t =
1 ms.
The impingement characteristics are represented using the
five different surface temperatures. For a surface temperature
of 100°C, the droplet behaves as previously described. The
droplet undergoes no nucleation and performs many advancing
and recoiling oscillations. The 150°C surface temperature
causes nucleation and some liquid spattering during oscillations.
The 200°C surface temperature causes the droplet to eventually
levitate above the surface after the droplet mass is reduced. The
droplet is now approaching the Leidenfrost temperature for
water. For a surface temperature of 225°C, the droplet is past
the Leidenfrost point of ∆Tsat = 120°C. The droplet is in film
boiling as it levitates after its first recoil. The 250°C surface
temperature shows the droplet disintegrating upon impact.
Figure 9 - Part 1. Droplet Impact for We = 29 From
Impact to 10 ms: The droplet impingement history for
a Weber number of 29. The surface temperatures are;
100°°C, 150°°C, 200°°C, 225°°C, and 250°°C. We = 29; ∆t =
1 ms.
Figure 9 depicts the impingement history of the droplet for
a Weber number of 29. For a surface temperature of 100°C, the
droplet behaves as previously described. The droplet undergoes
no nucleation and performs many spreading and recoiling
oscillations. This behavior is the same as for the higher Weber
number case. The 150°C surface temperature causes nucleation
and some liquid spattering during oscillations. The 200°C
surface temperature causes the droplet to eventually levitate
above the surface after the droplet mass is reduced. The droplet
is now approaching the Leidenfrost temperature for water. The
first three surface temperatures match closely for the behavior
found in the higher Weber number. For a surface temperature
of 225°C, the droplet behaves the same way as for the higher
Weber number.
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Copyright © 2001 by ASME
Figure 10. Vapor Cut Back: The droplet displays a
progression of a liquid to vapor interface cutting from
beneath the droplet. We = 58; ∆t = 0.5 ms.
interface continues to move inward and change the contact
angle. In the 3.0 ms frame, the interface continues to cut in
beneath the bulk of the droplet.
The maximum spreading ratio is another factor that is of
interest in the heat transfer studies. A correlation given by
Akao et al. (1980) was used to compare the predicted maximum
spreading ratio to the experimental maximum spreading ratio as
shown in Figure 11. Akao et al.’s correlation, given by eq. (1),
included studies on water droplets in the diameter range of 2.1
mm to 2.9 mm, initial velocity range from 0.66 to 3.21 m/s, and
a surface temperature of 400°C.
Figure 9 - Part 2. Droplet Impact for We = 29 From 11
ms to 20 ms: The droplet impingement history for a
Weber number of 29. The surface temperatures are:
100°°C, 150°°C, 200°°C, 225°°C, and 250°°C. We = 29; ∆t =
1 ms.
However, the levitation seems to be more pronounced.
The droplet is in film boiling as it levitates after its first recoil.
The 250°C surface temperature shows the droplet levitating
after impact. This behavior differs from the higher Weber
number case. The lower Weber number allows the droplet to
remain clustered together and undergo levitation instead of
disintegration.
As the evaporation occurs at the liquid-solid interface, the
liquid solid contact line is pushed back rapidly due to high rate
of evaporation. This vapor cut back phenomenon is depicted in
Figure 10. The first frame represents the beginning of the event
that occurs approximately 10 ms after impact of the droplet. At
the 1.5 ms frame, the contact angle begins to change. In the 2.0
ms frame, the contact interface on the left side of the droplet has
moved toward the droplet’s center, beneath the droplet. The
R max
= 0.613 * We 0.39
ro
(1)
In the present work, the droplet diameter was 2.8 mm, the
initial velocities ranged from 0.499 m/s to 1.223 m/s, and the
surface temperature was somewhat lower than used by Akao et
al.
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Copyright © 2001 by ASME
3.50
Akao ( 1980 )
We = 58
2.50
We = 29
2.00
We = 19
We = 14
1.50
We = 10
1.00
0.50
We = 10
We = 14
We = 29
We = 58
We = 19
0.00
0
50
100
150
200
250
β max = dmax / D
β max = dmax / D
3.00
300
Ts ( °C )
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
Kurabayashi and Yang ( 1975 )
We = 58
We = 29
We = 19
We =
We = 10
We = 10
We = 29
0
Figure 11. Comparison of the experimental data for
the maximum spreading ratio versus surface
temperature and Akao et al. (1980) correlation for We
= 10, 14, 19, 29, 58 ; 50°°C < Ts < 250°°C ; 2.779 mm < D
< 2.881 mm.
The Akao et al. correlation predicts the maximum spreading
ratio in terms of the radius of the droplet prior to impact and the
Weber number. The correlation was applied to the all
experimental data obtained in the present work. The surface
temperatures ranged from 50°C to 250°C with Weber numbers
of 10, 14, 19, 29, and 58.
It can be seen from Fig. 11 that the predictions from Akao
et al. correlation are in good agreement for the lower Weber
number case.
For the higher Weber number case, the
correlation overpredicts the maximum spread ratio for lower
surface temperatures. However, Akao et al. recommend this
correlation in the high temperature range.
The overall
agreement is therefore seen to be quite reasonable for We ≤ 29.
Another maximum spreading ratio correlation is given by
Kurabayashi and Yang given by Yang (1975). Kurabayashi and
Yang (K-Y) correlation expresses the maximum spreading ratio
in terms of Weber number, Reynolds number, and fluid
viscosity. The correlation is given below.
0.14
é 3We æ
β 2 − 1 ö÷ æ µdrop ö ùú
We 3
÷
= βmax2 ê1 +
* ç βmax2 ln(βmax ) − max
* çç
− 6 (2)
÷ µwall ÷ ú
ê
2 2
Re çè
2
ø û
ø è
ë
The K-Y correlation includes the effects of Weber number like
Akao (1980). In addition, the K-Y correlation includes the
effect of Reynolds number (initial droplet diameter as length
scale) and the liquid viscosity ratio at droplet and surface
temperatures.
50
We = 14
We = 58
100
150
We = 19
200
250
300
Ts ( °C )
Figure 12. Comparison of the experimental data for
the maximum spreading ratio versus surface
temperature and Kurabayashi and Yang, K-Y
Correlation, given by Yang (1975), for We = 10, 14,
19, 29, 58 ; 50°°C < Ts < 250°°C ; 2.779 mm < D < 2.881
mm.
The K-Y correlation was compared to the experimental
data. As seen in Figure 12, the K-Y correlation drastically
overpredicts the maximum spreading ratio. However, this
correlation incorporates the effect of Reynolds number and fluid
viscosity.
Another improvement in the maximum spreading ratio
correlations comes from Healy et al. (2001). They incorporated
the liquid contact angle as a correction factor in the original KY correlation.
æ 45 ö
β KY ,corr = β KY ç ÷
èθ ø
0.241
(3)
Equation (3) is the Healy correction for the K-Y
correlation. Healy determined the best exponent to properly fit
several data sets available in literature. The Weber number for
the data sets included in their investigation is less than 150.
The contact angles used in the correlation is apparently the
static equilibrium contact angle. The two contact angles used in
their comparison were 45° and 70°.
In the present work, the equilibrium contact angle was
measured to be 40° and a static advancing contact angle was
found to be 70°. In addition, the dynamic advancing contact
angle was measured to be 110°.
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Copyright © 2001 by ASME
We = 29
We = 14
We = 19
We = 10
We = 10
We = 29
We = 14
We = 58
β max = dmax / D
We = 58
3.50
3.00
We = 58
We = 29
We = 19
We = 14
We = 10
2.50
2.00
1.50
1.00
We = 10
We = 29
0.50
We = 19
50
100
150
We = 14
We = 58
We = 19
0.00
0
0
200
250
300
100
Ts ( °C )
200
300
Ts ( °C )
Figure 13. Comparison of the experimental data for
the maximum spreading ratio versus surface
temperature and Healy et al. (2001) correction for We
= 10, 14, 19, 29, 58 ; 50°C < Ts < 250°C ; 2.779 mm < D
< 2.881 mm.; θ = 40°.
β max = dmax / D
β max = dmax / D
4.50 Healy K-Y Correction : θ = 110°
4.00
Healy K-Y Correction : θ = 40°
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
Healy K-Y Correction : θ = 70°
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
We = 58
We = 29
We = 19
We = 14
We = 10
We = 10
We = 29
0
50
We = 14
We = 58
100
150
We = 19
200
250
Figure 15. Comparison of the experimental data for
the maximum spreading ratio versus surface
temperature and Healy et al. (2001) correction for We
= 10, 14, 19, 29, 58 ; 50°C < Ts < 250°C ; 2.779 mm < D
< 2.881 mm.; θ = 110°.
Figures 13, 14, and 15 show the comparison of the Healy
K-Y correction with the contact angles of 40°, 70°, and 110°,
respectively. As expected, the use of a 40°contact angle does
not change the K-Y correlation significantly. The use of a 70°
contact angle provides a slight improvement. However, the
corrected correlation still over predicts the data by a large
amount. Using the advancing contact angle of 110° does
continue to provide an improvement in the correlation.
Despite the overprediction, the Healy corrected K-Y
correlations seems to be on the right track. The surface wetting
and fluid properties contribute to the maximum spreading ratio.
However, the corrected correlation still drastically overpredicts
the experimental data. The effect of contact angle expressed by
Healy K-Y correlation does not correctly predict the data
presented in this work.
300
Ts ( °C )
Figure 14. Comparison of the experimental data for
the maximum spreading ratio versus surface
temperature and Healy et al. (2001) correction for We
= 10, 14, 19, 29, 58 ; 50°C < Ts < 250°C ; 2.779 mm < D
< 2.881 mm.; θ = 70°.
CONCLUSIONS
• Four characteristic impingement patterns are identified
in the present work as shown in Figure 2: (a) levitation
after several advance and recoil cycles, (b) levitation
after first recoil, (c) disintegration after first recoil, (d)
disintegration after impact.
• The present work shows a direct dependence of droplet
impingement behavior upon Weber number. As the
Weber number increases, the droplet impingement
characteristics observed at higher temperatures is
pushed toward lower surface temperatures. Figures 8
and 9 display the dependence upon Weber number.
Ultimately, the droplet disintegration occurs at lower
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Copyright © 2001 by ASME
surface temperatures with a higher Weber number. All
of the other behaviors are shifted accordingly.
• The time elapsed before droplet levitation is found to
be independent of the Weber number. The results for
the two Weber numbers, 29 and 58, are very close to
each other as shown in Fig. 7. However, the surface
temperature is seen to the most important factor for the
droplet levitation time.
• The surface temperature affects the maximum
spreading ratio. The Akao et al. correlation is able to
predict the maximum droplet spread ratio quite
accurately, within 10 percent, for the lower Weber
numbers and at lower surface temperatures. However,
the correlation seems to over predict for the higher
Weber numbers at lower temperatures, but seems to be
reasonable at higher temperatures (above 180°C).
• The correlations by Kurabayashi and Yang and Healy
et al. (2001) are unable to predict the maximum
spreading ratio.
The contact angle parameter
introduced by Healy et al. (2001) provides a slightly
better agreement with the use of the aadvancing
contact angle in the model. However, the correlation
still overpredicts by a large margin (>40%).
Future work is recommended to develop an improved
correlation for the maximum spreading ratio, especially at
higher Weber numbers. The improvement should include the
effect of the changing contact angle during the spreading
process.
Journal of Fluids Engineering September 1995, Vol. 117 pp
394-401.
Healy, W.M., Hartley, J.G., and Abdel-Khalik, S.I., 1996,
“Comparison between Theoretical Models and Experimental
Data for the Spreading of Liquid Droplets Impacting on a Solid
Surface,” International Journal of Heat and Mass Transfer,
Vol. 39, pp. 3079-3082.
Healy, W.M., Hartley, J.G., and Abdel-Khalik, S.I., 1996,
“Surface Wetting Effects on the Spreading of Liquid Droplets
Impacting a Solid Surface at Low Weber Numbers,” 2001,
International Journal of Heat and Mass Transfer, Vol. 44, pp.
235-240.
Naber J.D. and Farrell P.V., 1993 “Hydrodynamics of
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Pedersen C.O., 1969, “An experimental study of the
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