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Heat transfer characteristics of water droplets interacting with a rotating hot surface
INT. COMM. HEAT MASS TRANSFER Voh 17, pp. 419-429, 1990 ©Pergamon Press pie
0735-1933/90 $3.00 + .00 Printed in the United States
HEAT TRANSFER CHARACTERISTICS OF WATER DROPLETS INTERACTING WITH A ROTATING HOT SURFACE
K.J. Choi and J.S. Hong University of Illinois at Chicago Department of Mechanical Engineering Box 4348, Chicago Illinois 60680 (Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT The heat transfer characteristicsof monosized water droplets interacting with a rotating hot surface are experimentally investigated. The experimental parameters tested are the droplet size, the rotating speed, and the wall temperature, while liquid mass flow rate is fixed. In the tested experimental ranges, a strong dependence of the droplet impacting heat transfer upon these parameters is observed. The droplet size has an opposite effect on heat transfer between low rotating speed and high rotating speed case.
Introduction Two-phase droplet flow interacting with a moving hot surface has been encountered in various science and engineering problems. Typical examples are the liquid cooling of centrifugal compressors or rotating blades, and the spray cooling of a moving hot plate in metallurgical processing. In these industrial applications, the cooling performance by liquid spray depends to a large degree upon the two-phase droplet flow dynamics, including the droplet impacting dynamics on the moving plate. Presently, substantial studies have been reported on the impaction of liquid droplets on a s~ionary hot surface [1-5]. The droplet impact~tag dynamics of this type is quite different from the droplet impaction onto a moving surface due to the existence of a tangential velocity component of the droplet and the entrained gas layer between the droplet and the moving surface. During the impaction of liquid droplets on a moving surface the tangential velocity component provides ~ torque to the droplet. As a result, the droplet deforms in a non--symmetric manner. In addition, the gas boundary layer formed over the rotating surface will interfere the impacting droplet, and in turn, alter the droplet-wall contact behavior. Although the interaction of droplets with a moving hot surface is of great 419
420
K.J. Choi and J.S. Hong
Vol. 17, No. 4
importance to many practical applications, little information has been reported on this subject. Taga et al. [6] conducted an experimental study of an impinging water jet cooling a hot plate moving at a relatively slow speed. An analytical study of the liquid droplet dynamics and cooling rate from a rotating centrifugal compressor was reported by Pinkus [7]. However, fundamental information about the droplet dynamics and heat transfer of impacting droplets on a moving hot surface was not reported. Presently, the only work attempted to draw better understanding of these issues is the experiments conducted by Shalnev et al. [8] and Yao and Cai [9]. A rotating disk at various speeds was used, due to its simple geometrical configuration, in order to study the droplet impacting dynamics and heat transfer. They reported valuable information about the droplet dynamics. However, due to the coarse experimental system for the heat transfer measurement, the heat transfer characteristics were not well presented. The heat transfer characteristics in this specific problem are coupled to a great degree with the droplet dynamics interacting with the gas boundary layer. The important issues raised in this type of problem are whether the droplets are in direct contact with a hot moving surface or not, and how long the droplets reside on the hot surface if direct contact takes place. Understanding of the characteristics of droplet-wall contact dynamics and heat transfer is of great importance in designing a fast moving surface which is encountered with small droplets. Therefore, the purpose of this proposed research is to investigate both analytically and experimentally the flow dynamics and heat transfer behaviors of two-phase droplet flow on a moving hot surface. As a first stage of this aimed study, a simpler but well-instrumented experiment using controllable mono-sized water droplets impacting on a rotating hot surface was conducted. The experimental parameters tested in this study were droplet size in the range of 600 to 1200/~n, rotating speed in the range of 600 to 1800 rpm, and surface temperature in the range of 120 to 320°C. Apparatus and Procedure In order to conduct a systematic experiment, controllable stream(s) of pre-selected monosized droplets and a well-instrumented hot rotating surface are used. In this way, the experimental parameters are independently controlled and the heat transfer data can be collected accurately. The schematic of the experimental apparatus, consisting of two main parts (i.e, droplet generating and heat transfer target), is shown in Fig. 1. The whole rotating body has dimensions of 15.24 cm in diameter and 7.78 cm in height. The heating target of the rotating body is made of a copper solid cylinder, bored through the center. The upper portion of the cylinder has a 4.13 cm inner radius and a 0.635 cm wall thickness, while the lower portion has a 3.66 cm inner radius and a wall thickness of 1.59 cm. At the
Vol. 17, No. 4
DROPLETS INTERACTING WITH A HOT SURFACE
FUNCTION GENERATOR
]
• •
CAMERA
D
•
T.C.~
INSULATION SLIP RING
J
421
STROBE LIGHT
"(]
it
GE HEATER DATA ACQUISITION I
'
IBM/PC
I
FIG. 1 Schematic of Experimental Apparatus top of the heating target, a narrow surface was used in order to minimize air convection heat transfer from the top surface, thus maximizing the role of the droplet impacting heat transfer on the overall heat transfer behavior. The top surface of the heating target is chrome-plated with 5/an thickness to prevent corrosion and polished to a mirror finish. The rest of the top surface of the rotating body is covered with 0.125 cm thick stainless steel plates to make a flush surface as well as to prevent liquid from seeping around the copper cylinder. The space between the copper cylinder and the stainless steel casing is filled with a lightweight insulating material (fiberglass) to prevent heat loss in the radial direction. A total of four (4) electric cartridge heaters (250 w each) are embedded in the copper cylinder through the bottom surface. Two chromel-alumei (type k) thermocouples of 0.1 cm diameter are inserted into the upper portion of the copper block. The two thermocouples are located in a vertical line at 0.0625 cm and 0.435 cm, respectively from the top surface. The leads of the thermocouples and the cartridge heaters are routed through the hollow driving shaft of the rotating body and connected to a mercury slip ring. The use of the mercury slip ring allows the continuous transmission of voltage signals from the thermocouples to a data acquisition unit during an experiment. The rotating body is connected through the hollow shaft to a variable speed electric motor. A control device
422
K.J. Choi and J.S. Hong
is used to accurately vary the to 3000 rpm.
Vol. 17, No. 4
rotating speed of the heating target in the range of 0
The monosized droplet generator shown in Fig. 1 is made in a similar fashion to the one used by Yao and Cai [9]. Therefore, the detail of this system is omitted. By providing a regular frequency of electric pulses to the droplet generator, in the range of 200 to 3000 Hz, pressure disturbances are given to the liquid jet. As a result, the liquid jet is broken into small droplets of uniform size. The droplet aize is controlled by varying the electric pulse frequency, as well as by use of different sires of orifice. By combining these two controlling parameters, two different droplet aizes (600 and 1200 p~m in diameter) at a constant flow rate are obtained. Two idcatical droplet generators are placed on a translator at opposite points so that the droplet impacting points on the heating target surface are distributed 1800 apart as shown in Fig. 1. Distilled water at a temperature of 20°C is supplied to the generators through two independent feed lines from a storage tank and controlled by two fine flow meters. A sample photo of two streams of monosized droplets is shown in Fig. 2. Experiments are conducted for a transient cooling process of the rotating hot surface with various combinations of experimental conditions.
The experimental conditions used
in this study are summarized in Table 1. The experimental procedure is as follows. Two streams of predetermined monosized droplets are generated at a constant mass flow rate of 0.35 g/s through each generator. In order to prevent the vertical interference of droplets,
FIGi 2 Sample Photograph of Two Streams of Monosized Droplets Impacting onto a Rotating Hot Surface
Vol. 17, No. 4
DROPLETS INTERACq~NG WITH A HOT SURFACE
423
the droplets are widely spaced and a relatively high rotating speed of the heating target is used. Once the desirable droplets are generated, all the droplets at0 ~011ected with a catcher to keep the stream(s) of droplets from impacting onto the rotating surface. The copper cylinder then is heated through an electric power supply. When the heater temperature reaches a predetermined value (i.e., T w ~_ about 320°C), the electric power supply is shut off. The experiment starts by removing the droplet catcher, and a high--speed data acquisition system which is inter--connected with an IBM AT/PC starts to collect transient temperatures from the two thennocouples. The heating target rotates at a predetermined rotating velocity with droplets impacting on the hot surface. When the rotating surface becomes completely wet and forms a film, the experiment is completed.
TABLE 1 Experimental Variables Used in This Study Rotating Velocity ( rpm ) With Droplet Impaction
600 1200 1BOO
Without Droplet Impaction
°00 1200 1800
Droplet Diameter
(~m)
600 & 1200
I
N/A
Mass Flow Rate ( g/sec )
Surface Temperature
(c)
0.7
100 - 320
N/A
100 - 320
I
When droplet impacting heat transfer on a rotating surface is considered, two heat transfer modes of great importance are direct hquid--solid contact heat transfer and air convection. The air flow is usually induced by the rotating surface, and the droplet impacting heat transfer depends upon the air flow motion over the rotating surface. As the dropl~bs penetrate the air boundary layers before contacting with the hot surlace, various forces, nau~oly, inertia, drag, gravity, buoyancy, and lift forces act on the droplets. As a result, the droplet impacting heat transfer is coupled with the air flow motions. In order to separate the two heat transfer modes, two independent experiments were conducted; (1) pure air coI~vection heat transfer, and (2)droplet impacting heat transfer. Results and Discussion Fig. 3 shows the typical cooling curves of the heating target, where the subscripts "air" an~: "droplet"denote the results obtained from air convection and droplet impaction, respectively. The droplet size, the mass flow rate, and the rotating speed used in the test are 1200 pm i~ diameter, 0.7 g/s, and 1200 rpm, respectively. The surface temperature of
424
K.J. Choi and J.S. Hong
Vol. 17, No. 4
350
300
A
0
........ Air Droplet
250
L. J-
200
'.,.., "'... "-,
, '""'..
,.,,
150
".,.. '"
..,. "-
100 300
I
I
800
900
.......
Tlme ( sec ) FIG. 3 Comparison of Surface Temperature Variations for the Air Convection and the Droplets Impacting Cases the heating target is assumed to be the same as the temperature 0.0625 cm below the heater surface, which was measured with one of the two thermocouples imbedded in the rotating body. In fact, experimental results show that the m a x i m u m temperature difference between the two thermocouple locations, which occurs during the fast cooling process (i.e. 100 < T w < 200°C), is at most about 3 -4°C. Thus, the heat transfer rate for the experiment is calculated based on the lumped body analysis as following; AT w Q -- mc ~'t
(1)
The cooling rate A T w / A t in Eq. (I) was determined from the temperature curve shown in Fig. 3. This measurement method has also been used in previous experimental studies of droplet impacting heat transfer [1-3,5]. The heat transfer rates for both experimental cases are plotted with the surface temperature in Fig. 4. As shown in Fig. 4, the heat transfer performance with droplet impaction is much greater than pure air convection, especially in the lower surface temperature regions. Considering the droplet impacting case, the heat transfer characteristics can be divided into three regions similar to a conventional boiling curve, i.e.,film, transition, and nucleate boiling regions. It should be noted that the results of the droplet impacting case shown in Fig. 4 include both the air convection and the droplet-
Vol. 17, No. 4
DROPLETS I N T E R A C T I N G W I T H A H O T S U R F A C E
425
2500
2000
o = Droplet
o
o
o A
1500
o
o o
o 0
1000
• = Air
o
o
o
o
o 500
o
0
0 000000000000
0 ,
,
,
,
I
oeeeeeo ,
,
,eel,
100
I 200
,
e @ • ,
,
,
0 0 •
• i
,
,
300
Tw(°C ) FIG. 4 Variation of Heat Transfer Rates with Surface Temperatures wall contact heat transfer. In order to investigate the heat transfer characteristics of only droplet impaction onto a rotating hot surface, the net heat transfer rate by droplet impaction is calculated as
I AT w AT w Q = mc L(t~--~----)droplet- ( ~
] )air
(2)
The net heat transfer rates by droplet impaction are plotted with the surface temperature in Figs. 5 through 7 for the rotating speed of 600, 1200, and 1800 ~ m , respectively. The droplet sizeeffecton impacting heat transferis observed at each rotating speed. However, the droplet size has two contradictory effects on the heat transfer characteristics,depending on the rotating speed. As shown in Fig. 5 for the slow rotating case (~ = 600 rpm), droplets of 1200/~n diameter have better impacting heat transfer in the film boiling region than &oplets of 600/~m diameter. However, for the faster rotating cases (i.e.,~ = 1200 rpm and ~#= 1800 rpm), the smaller sized droplets have better impacting heat transferthan the large sized droplets,as shown in Figs. 6 and 7. The heat transfer characteristicsof impacting droplets at slower rotating speeds should be similar to the case of droplet impaction on a stationary hot surface. As reported in the previous experimental studies of droplet impaction onto a stationary plate [2---41,a
426
K.J. Choi and J.S. Hong
Vol. 17, No. 4
large sized droplet has better heat transfer effectiveness in the film boiling region due to increase of the inertial force ratio to the droplet surface tension, resulting in large contact area between the droplet and the hot surface. Therefore, if the rotating speed of a hot surface is relatively low, interaction of the droplet impacting dynamics with the gas boundary layer becomes negligible, resulting in impacting heat transfer behavior similar to 2500
D(pm) c~ • eo
2000
II A
•
1500
• = 1200
•0
v 0
o = 000
*
0o 0o
1000
.g .o og
@
eo oo
500
J
,
,
,
200
100
T.(
Droplet
300
C )
FIG. 5 on Heat Transfer for
Size Effect
w =
600 rpm
2500
D(pm)
o o 2000
o = 000
O
• = 1200 A
1500 o• •
v
0
o
1ooo
o
• o •
g. •
500 •
200
100
Tw(°C
Droplet
Size Effect
0.0.(100000000
300
)
FIG. 6 on Heat Transfer for
~ =
1200 rpm
Vol. 17, No. 4
DROPLETS INTERACTING WITH A HOT SURFACE
427
2600 0 0
2000
0 0
o~ A
D(pm)
0 •
0 0
oP
0
IJg
$
1000
• = 1200
eo
O0
1500
O eO
,.o eo eo
o
Io
8
500
600
o :
0
0
0
l
o
l
l
l
J
l
~
lOO
,
,
I
200
,
+
,
,
I
,
300
Tw(C) FIG. 7 Droplet Size Effect on Heat Transfer for ~o= 1800 rpm the case of droplet impaction onto a stationary surface. However, if the rotating velocity is high, then the droplet impacting dynamics and impacting heat transfer characteristics may change due to strong interference of the gas boundary layer. Under this circumstance, the droplet penetrating the gas boundary layer is encountered with various forces acting on the droplet, such as drag, inertia, buoyancy, and lift forces. Depending on the balance of these forces, the droplet-wall contact behaviors are determined. As shown in Figs. 6 and 7, impacting heat transfer of large size droplets (D = 1200/an) becomes inferior to that of small size droplets (D -- 600 #m). From this result, it is concluded that the direct droplet-wall contact performance of small size droplets is better than that of large size droplets. This seems to be contradictory to our general intuition that a large droplet may have better contact dynamics with a rotating surface due to the large inertial force. However, this can be explained by the fact that the increase of lift force as the droplet size increases is greater than the increase of inertial force. The visual observation of the dynamic behaviors mentioned above is also made through video photography, i.e., the droplets of 1200/an have tendency of bouncing as its initial shape off the rotating surface in the film boiling region at fast rotating speeds (~o = 1200 and 1800 rpm), while the droplets of 600 /an bounce off the rotating surface as disintegrated small droplets. At a slow rotating speed, droplets of both sizes bounce off the rotating surface as disintegrated smaller droplets. This observation indicates that the droplets of larger size can not have complete contact with the hot surface rotating at high speed due to interaction of the gas boundary layers. Detailed analysis of the impacting
428
dynamics
K.J. Choi and J.S. Hong
will
be
conducted
in
the
Vol. 17, No. 4
future
successive
research
projects.
In order to investigate the effect of rotating speed on droplet impacting heat transfer for droplets of a fixed size, the results presented in Figs. 5 through 7 are reconsidered. For the droplets of 600 pm diameter, there is no significant effect of rotating velocity on the impacting heat transfer characteristics in the tested range of rotating velocities. If much higher rotating velocities were applied for the 600 ~m dia. droplets, some effect of rotating velocity on the heat transfer behaviors would be observed. For the 1200 pan dia. droplets, however, the effect of rotating velocity is observed even in the tested range, as shown in Fig. 8. At the rotating velocity of 600 rpm, the net heat transfer rates in the film boiling region are higher than those at the rotating velocity of 1200 rpm or 1800 rpm. From this result, it is concluded that direct contact dynamics of droplet becomes inferior at rotating velocities of 1200 rpm or higher. Although no attempt was made in this study to get a functional relationship of droplet size, droplet impacting velocity, and rotating velocity for the criterion value at which the droplet-wall contact dynamics becomes inferior, it is obvious that there exists such a criterion value.
2600
2000
w ( rpm ) o = 600
O
• ~8
o
1500
o
.
o~ %
= 1200 =
1800
1000
go
500
o
0
' 0
O~ O000000000
' 100
200
300
Tw(C)
FIG. 8 Effect of Rotating Velocity on Heat Transfer for D = 1200/zm Conclusion Experimental investigation on the heat transfer characteristics of predetermined monosized water droplets impacting onto a rotating hot surface is performed in this study. Using an impulse-jet type of droplet generator, uniform droplets of two different diameters (D = 600 and 1200/Jm) are tested to investigate the droplet size effect on droplet impact-
Voh 17, No. 4
DROPLETS INTERACTING WITH A HOT SURFACE
429
ing heat transfer. Also, the effect of rotating speed of the hot surface is studied. For a slow rotating speed (w -- 600 rpm), the droplet-wall contact phenomena similar to the conventional case of droplet impaction onto a stationary hot surface is observed, i.e., the droplets of larger size have better impacting heat transfer in the film boiling region than that of smaller sized droplets. However, for the rotating speeds of 1200 rpm or higher the droplet size effect reverses due to the interaction of the gas boundary layer, i.e., the droplets of smaller size have better heat transfer in the overall boiling regions than that of large sized droplets. Nomenclature c D m
Q t
Specific heat Droplet size,/an mass of heating target
T Tw ~
temperature, °C surface temperature of heating target thermal diffusivity of liquid
mass flow rate of droplets, g/s
p w
density rotating speed
heat transfer rate, w time
References 1.
L.H.J. Wachters and N.A.J. Westerling, Chemical Engineering Science , 21, 1047
2:
G.E. Kendall and W.M. Rohsennow, Heat Transfer to Impacting Drops and Post Critical Heat Flux Dispersed Flow, Heat Transfer Lab. Report No. 85694-100, Massachusetts Institute of Technology, (1978).
.
(1968).
C.O. Pederson, Int. J. Heat Mass Transfer, 13, 369 (1970).
4.
S.C. Yao and K.J. Choi, Int. J. Multiphase Flow, 13, 5, 639 (1987)
5.
M. Shoji, T. Wakunaga, and K. Kodama, Heat Transfer Japanese Research, 50 (1985).
.
M. Taga, T. Ocki, and K. Akagawa, Cooling of a Hot Moving Plate by an Impinging Water Jet, ASME-JSME, Thermal Enoneering Joint Cot~[erence, Vol. 1,
183 (1983).
.
8.
.
10.
O. Pinkus, ASME, J. of Engineering for Power, 10___55,80 (1983). F.K. Schalnev, O.A. Povarov, O.I. Nazarov, and I.A. Shalobosov, Proceedines of th_..~eFifth CQnference of Fluid Machinery, Vol. 2, 1011 (1975). S.C. Yao and K.Y. Cal, The Dynamics and Leidenfrost Temperature of Drops Impacting on a HOt Surface at Small Angles, ASME 85-WA/HT--39 (1985). D.L. Oehlbeck and F.F. Erian, Int. J. Heat Mass Transfer, 22, 601 (1979).
0735-1933/90 $3.00 + .00 Printed in the United States
HEAT TRANSFER CHARACTERISTICS OF WATER DROPLETS INTERACTING WITH A ROTATING HOT SURFACE
K.J. Choi and J.S. Hong University of Illinois at Chicago Department of Mechanical Engineering Box 4348, Chicago Illinois 60680 (Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT The heat transfer characteristicsof monosized water droplets interacting with a rotating hot surface are experimentally investigated. The experimental parameters tested are the droplet size, the rotating speed, and the wall temperature, while liquid mass flow rate is fixed. In the tested experimental ranges, a strong dependence of the droplet impacting heat transfer upon these parameters is observed. The droplet size has an opposite effect on heat transfer between low rotating speed and high rotating speed case.
Introduction Two-phase droplet flow interacting with a moving hot surface has been encountered in various science and engineering problems. Typical examples are the liquid cooling of centrifugal compressors or rotating blades, and the spray cooling of a moving hot plate in metallurgical processing. In these industrial applications, the cooling performance by liquid spray depends to a large degree upon the two-phase droplet flow dynamics, including the droplet impacting dynamics on the moving plate. Presently, substantial studies have been reported on the impaction of liquid droplets on a s~ionary hot surface [1-5]. The droplet impact~tag dynamics of this type is quite different from the droplet impaction onto a moving surface due to the existence of a tangential velocity component of the droplet and the entrained gas layer between the droplet and the moving surface. During the impaction of liquid droplets on a moving surface the tangential velocity component provides ~ torque to the droplet. As a result, the droplet deforms in a non--symmetric manner. In addition, the gas boundary layer formed over the rotating surface will interfere the impacting droplet, and in turn, alter the droplet-wall contact behavior. Although the interaction of droplets with a moving hot surface is of great 419
420
K.J. Choi and J.S. Hong
Vol. 17, No. 4
importance to many practical applications, little information has been reported on this subject. Taga et al. [6] conducted an experimental study of an impinging water jet cooling a hot plate moving at a relatively slow speed. An analytical study of the liquid droplet dynamics and cooling rate from a rotating centrifugal compressor was reported by Pinkus [7]. However, fundamental information about the droplet dynamics and heat transfer of impacting droplets on a moving hot surface was not reported. Presently, the only work attempted to draw better understanding of these issues is the experiments conducted by Shalnev et al. [8] and Yao and Cai [9]. A rotating disk at various speeds was used, due to its simple geometrical configuration, in order to study the droplet impacting dynamics and heat transfer. They reported valuable information about the droplet dynamics. However, due to the coarse experimental system for the heat transfer measurement, the heat transfer characteristics were not well presented. The heat transfer characteristics in this specific problem are coupled to a great degree with the droplet dynamics interacting with the gas boundary layer. The important issues raised in this type of problem are whether the droplets are in direct contact with a hot moving surface or not, and how long the droplets reside on the hot surface if direct contact takes place. Understanding of the characteristics of droplet-wall contact dynamics and heat transfer is of great importance in designing a fast moving surface which is encountered with small droplets. Therefore, the purpose of this proposed research is to investigate both analytically and experimentally the flow dynamics and heat transfer behaviors of two-phase droplet flow on a moving hot surface. As a first stage of this aimed study, a simpler but well-instrumented experiment using controllable mono-sized water droplets impacting on a rotating hot surface was conducted. The experimental parameters tested in this study were droplet size in the range of 600 to 1200/~n, rotating speed in the range of 600 to 1800 rpm, and surface temperature in the range of 120 to 320°C. Apparatus and Procedure In order to conduct a systematic experiment, controllable stream(s) of pre-selected monosized droplets and a well-instrumented hot rotating surface are used. In this way, the experimental parameters are independently controlled and the heat transfer data can be collected accurately. The schematic of the experimental apparatus, consisting of two main parts (i.e, droplet generating and heat transfer target), is shown in Fig. 1. The whole rotating body has dimensions of 15.24 cm in diameter and 7.78 cm in height. The heating target of the rotating body is made of a copper solid cylinder, bored through the center. The upper portion of the cylinder has a 4.13 cm inner radius and a 0.635 cm wall thickness, while the lower portion has a 3.66 cm inner radius and a wall thickness of 1.59 cm. At the
Vol. 17, No. 4
DROPLETS INTERACTING WITH A HOT SURFACE
FUNCTION GENERATOR
]
• •
CAMERA
D
•
T.C.~
INSULATION SLIP RING
J
421
STROBE LIGHT
"(]
it
GE HEATER DATA ACQUISITION I
'
IBM/PC
I
FIG. 1 Schematic of Experimental Apparatus top of the heating target, a narrow surface was used in order to minimize air convection heat transfer from the top surface, thus maximizing the role of the droplet impacting heat transfer on the overall heat transfer behavior. The top surface of the heating target is chrome-plated with 5/an thickness to prevent corrosion and polished to a mirror finish. The rest of the top surface of the rotating body is covered with 0.125 cm thick stainless steel plates to make a flush surface as well as to prevent liquid from seeping around the copper cylinder. The space between the copper cylinder and the stainless steel casing is filled with a lightweight insulating material (fiberglass) to prevent heat loss in the radial direction. A total of four (4) electric cartridge heaters (250 w each) are embedded in the copper cylinder through the bottom surface. Two chromel-alumei (type k) thermocouples of 0.1 cm diameter are inserted into the upper portion of the copper block. The two thermocouples are located in a vertical line at 0.0625 cm and 0.435 cm, respectively from the top surface. The leads of the thermocouples and the cartridge heaters are routed through the hollow driving shaft of the rotating body and connected to a mercury slip ring. The use of the mercury slip ring allows the continuous transmission of voltage signals from the thermocouples to a data acquisition unit during an experiment. The rotating body is connected through the hollow shaft to a variable speed electric motor. A control device
422
K.J. Choi and J.S. Hong
is used to accurately vary the to 3000 rpm.
Vol. 17, No. 4
rotating speed of the heating target in the range of 0
The monosized droplet generator shown in Fig. 1 is made in a similar fashion to the one used by Yao and Cai [9]. Therefore, the detail of this system is omitted. By providing a regular frequency of electric pulses to the droplet generator, in the range of 200 to 3000 Hz, pressure disturbances are given to the liquid jet. As a result, the liquid jet is broken into small droplets of uniform size. The droplet aize is controlled by varying the electric pulse frequency, as well as by use of different sires of orifice. By combining these two controlling parameters, two different droplet aizes (600 and 1200 p~m in diameter) at a constant flow rate are obtained. Two idcatical droplet generators are placed on a translator at opposite points so that the droplet impacting points on the heating target surface are distributed 1800 apart as shown in Fig. 1. Distilled water at a temperature of 20°C is supplied to the generators through two independent feed lines from a storage tank and controlled by two fine flow meters. A sample photo of two streams of monosized droplets is shown in Fig. 2. Experiments are conducted for a transient cooling process of the rotating hot surface with various combinations of experimental conditions.
The experimental conditions used
in this study are summarized in Table 1. The experimental procedure is as follows. Two streams of predetermined monosized droplets are generated at a constant mass flow rate of 0.35 g/s through each generator. In order to prevent the vertical interference of droplets,
FIGi 2 Sample Photograph of Two Streams of Monosized Droplets Impacting onto a Rotating Hot Surface
Vol. 17, No. 4
DROPLETS INTERACq~NG WITH A HOT SURFACE
423
the droplets are widely spaced and a relatively high rotating speed of the heating target is used. Once the desirable droplets are generated, all the droplets at0 ~011ected with a catcher to keep the stream(s) of droplets from impacting onto the rotating surface. The copper cylinder then is heated through an electric power supply. When the heater temperature reaches a predetermined value (i.e., T w ~_ about 320°C), the electric power supply is shut off. The experiment starts by removing the droplet catcher, and a high--speed data acquisition system which is inter--connected with an IBM AT/PC starts to collect transient temperatures from the two thennocouples. The heating target rotates at a predetermined rotating velocity with droplets impacting on the hot surface. When the rotating surface becomes completely wet and forms a film, the experiment is completed.
TABLE 1 Experimental Variables Used in This Study Rotating Velocity ( rpm ) With Droplet Impaction
600 1200 1BOO
Without Droplet Impaction
°00 1200 1800
Droplet Diameter
(~m)
600 & 1200
I
N/A
Mass Flow Rate ( g/sec )
Surface Temperature
(c)
0.7
100 - 320
N/A
100 - 320
I
When droplet impacting heat transfer on a rotating surface is considered, two heat transfer modes of great importance are direct hquid--solid contact heat transfer and air convection. The air flow is usually induced by the rotating surface, and the droplet impacting heat transfer depends upon the air flow motion over the rotating surface. As the dropl~bs penetrate the air boundary layers before contacting with the hot surlace, various forces, nau~oly, inertia, drag, gravity, buoyancy, and lift forces act on the droplets. As a result, the droplet impacting heat transfer is coupled with the air flow motions. In order to separate the two heat transfer modes, two independent experiments were conducted; (1) pure air coI~vection heat transfer, and (2)droplet impacting heat transfer. Results and Discussion Fig. 3 shows the typical cooling curves of the heating target, where the subscripts "air" an~: "droplet"denote the results obtained from air convection and droplet impaction, respectively. The droplet size, the mass flow rate, and the rotating speed used in the test are 1200 pm i~ diameter, 0.7 g/s, and 1200 rpm, respectively. The surface temperature of
424
K.J. Choi and J.S. Hong
Vol. 17, No. 4
350
300
A
0
........ Air Droplet
250
L. J-
200
'.,.., "'... "-,
, '""'..
,.,,
150
".,.. '"
..,. "-
100 300
I
I
800
900
.......
Tlme ( sec ) FIG. 3 Comparison of Surface Temperature Variations for the Air Convection and the Droplets Impacting Cases the heating target is assumed to be the same as the temperature 0.0625 cm below the heater surface, which was measured with one of the two thermocouples imbedded in the rotating body. In fact, experimental results show that the m a x i m u m temperature difference between the two thermocouple locations, which occurs during the fast cooling process (i.e. 100 < T w < 200°C), is at most about 3 -4°C. Thus, the heat transfer rate for the experiment is calculated based on the lumped body analysis as following; AT w Q -- mc ~'t
(1)
The cooling rate A T w / A t in Eq. (I) was determined from the temperature curve shown in Fig. 3. This measurement method has also been used in previous experimental studies of droplet impacting heat transfer [1-3,5]. The heat transfer rates for both experimental cases are plotted with the surface temperature in Fig. 4. As shown in Fig. 4, the heat transfer performance with droplet impaction is much greater than pure air convection, especially in the lower surface temperature regions. Considering the droplet impacting case, the heat transfer characteristics can be divided into three regions similar to a conventional boiling curve, i.e.,film, transition, and nucleate boiling regions. It should be noted that the results of the droplet impacting case shown in Fig. 4 include both the air convection and the droplet-
Vol. 17, No. 4
DROPLETS I N T E R A C T I N G W I T H A H O T S U R F A C E
425
2500
2000
o = Droplet
o
o
o A
1500
o
o o
o 0
1000
• = Air
o
o
o
o
o 500
o
0
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,
,
300
Tw(°C ) FIG. 4 Variation of Heat Transfer Rates with Surface Temperatures wall contact heat transfer. In order to investigate the heat transfer characteristics of only droplet impaction onto a rotating hot surface, the net heat transfer rate by droplet impaction is calculated as
I AT w AT w Q = mc L(t~--~----)droplet- ( ~
] )air
(2)
The net heat transfer rates by droplet impaction are plotted with the surface temperature in Figs. 5 through 7 for the rotating speed of 600, 1200, and 1800 ~ m , respectively. The droplet sizeeffecton impacting heat transferis observed at each rotating speed. However, the droplet size has two contradictory effects on the heat transfer characteristics,depending on the rotating speed. As shown in Fig. 5 for the slow rotating case (~ = 600 rpm), droplets of 1200/~n diameter have better impacting heat transfer in the film boiling region than &oplets of 600/~m diameter. However, for the faster rotating cases (i.e.,~ = 1200 rpm and ~#= 1800 rpm), the smaller sized droplets have better impacting heat transferthan the large sized droplets,as shown in Figs. 6 and 7. The heat transfer characteristicsof impacting droplets at slower rotating speeds should be similar to the case of droplet impaction on a stationary hot surface. As reported in the previous experimental studies of droplet impaction onto a stationary plate [2---41,a
426
K.J. Choi and J.S. Hong
Vol. 17, No. 4
large sized droplet has better heat transfer effectiveness in the film boiling region due to increase of the inertial force ratio to the droplet surface tension, resulting in large contact area between the droplet and the hot surface. Therefore, if the rotating speed of a hot surface is relatively low, interaction of the droplet impacting dynamics with the gas boundary layer becomes negligible, resulting in impacting heat transfer behavior similar to 2500
D(pm) c~ • eo
2000
II A
•
1500
• = 1200
•0
v 0
o = 000
*
0o 0o
1000
.g .o og
@
eo oo
500
J
,
,
,
200
100
T.(
Droplet
300
C )
FIG. 5 on Heat Transfer for
Size Effect
w =
600 rpm
2500
D(pm)
o o 2000
o = 000
O
• = 1200 A
1500 o• •
v
0
o
1ooo
o
• o •
g. •
500 •
200
100
Tw(°C
Droplet
Size Effect
0.0.(100000000
300
)
FIG. 6 on Heat Transfer for
~ =
1200 rpm
Vol. 17, No. 4
DROPLETS INTERACTING WITH A HOT SURFACE
427
2600 0 0
2000
0 0
o~ A
D(pm)
0 •
0 0
oP
0
IJg
$
1000
• = 1200
eo
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1500
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o
Io
8
500
600
o :
0
0
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l
o
l
l
l
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l
~
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,
,
I
200
,
+
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,
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,
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Tw(C) FIG. 7 Droplet Size Effect on Heat Transfer for ~o= 1800 rpm the case of droplet impaction onto a stationary surface. However, if the rotating velocity is high, then the droplet impacting dynamics and impacting heat transfer characteristics may change due to strong interference of the gas boundary layer. Under this circumstance, the droplet penetrating the gas boundary layer is encountered with various forces acting on the droplet, such as drag, inertia, buoyancy, and lift forces. Depending on the balance of these forces, the droplet-wall contact behaviors are determined. As shown in Figs. 6 and 7, impacting heat transfer of large size droplets (D = 1200/an) becomes inferior to that of small size droplets (D -- 600 #m). From this result, it is concluded that the direct droplet-wall contact performance of small size droplets is better than that of large size droplets. This seems to be contradictory to our general intuition that a large droplet may have better contact dynamics with a rotating surface due to the large inertial force. However, this can be explained by the fact that the increase of lift force as the droplet size increases is greater than the increase of inertial force. The visual observation of the dynamic behaviors mentioned above is also made through video photography, i.e., the droplets of 1200/an have tendency of bouncing as its initial shape off the rotating surface in the film boiling region at fast rotating speeds (~o = 1200 and 1800 rpm), while the droplets of 600 /an bounce off the rotating surface as disintegrated small droplets. At a slow rotating speed, droplets of both sizes bounce off the rotating surface as disintegrated smaller droplets. This observation indicates that the droplets of larger size can not have complete contact with the hot surface rotating at high speed due to interaction of the gas boundary layers. Detailed analysis of the impacting
428
dynamics
K.J. Choi and J.S. Hong
will
be
conducted
in
the
Vol. 17, No. 4
future
successive
research
projects.
In order to investigate the effect of rotating speed on droplet impacting heat transfer for droplets of a fixed size, the results presented in Figs. 5 through 7 are reconsidered. For the droplets of 600 pm diameter, there is no significant effect of rotating velocity on the impacting heat transfer characteristics in the tested range of rotating velocities. If much higher rotating velocities were applied for the 600 ~m dia. droplets, some effect of rotating velocity on the heat transfer behaviors would be observed. For the 1200 pan dia. droplets, however, the effect of rotating velocity is observed even in the tested range, as shown in Fig. 8. At the rotating velocity of 600 rpm, the net heat transfer rates in the film boiling region are higher than those at the rotating velocity of 1200 rpm or 1800 rpm. From this result, it is concluded that direct contact dynamics of droplet becomes inferior at rotating velocities of 1200 rpm or higher. Although no attempt was made in this study to get a functional relationship of droplet size, droplet impacting velocity, and rotating velocity for the criterion value at which the droplet-wall contact dynamics becomes inferior, it is obvious that there exists such a criterion value.
2600
2000
w ( rpm ) o = 600
O
• ~8
o
1500
o
.
o~ %
= 1200 =
1800
1000
go
500
o
0
' 0
O~ O000000000
' 100
200
300
Tw(C)
FIG. 8 Effect of Rotating Velocity on Heat Transfer for D = 1200/zm Conclusion Experimental investigation on the heat transfer characteristics of predetermined monosized water droplets impacting onto a rotating hot surface is performed in this study. Using an impulse-jet type of droplet generator, uniform droplets of two different diameters (D = 600 and 1200/Jm) are tested to investigate the droplet size effect on droplet impact-
Voh 17, No. 4
DROPLETS INTERACTING WITH A HOT SURFACE
429
ing heat transfer. Also, the effect of rotating speed of the hot surface is studied. For a slow rotating speed (w -- 600 rpm), the droplet-wall contact phenomena similar to the conventional case of droplet impaction onto a stationary hot surface is observed, i.e., the droplets of larger size have better impacting heat transfer in the film boiling region than that of smaller sized droplets. However, for the rotating speeds of 1200 rpm or higher the droplet size effect reverses due to the interaction of the gas boundary layer, i.e., the droplets of smaller size have better heat transfer in the overall boiling regions than that of large sized droplets. Nomenclature c D m
Q t
Specific heat Droplet size,/an mass of heating target
T Tw ~
temperature, °C surface temperature of heating target thermal diffusivity of liquid
mass flow rate of droplets, g/s
p w
density rotating speed
heat transfer rate, w time
References 1.
L.H.J. Wachters and N.A.J. Westerling, Chemical Engineering Science , 21, 1047
2:
G.E. Kendall and W.M. Rohsennow, Heat Transfer to Impacting Drops and Post Critical Heat Flux Dispersed Flow, Heat Transfer Lab. Report No. 85694-100, Massachusetts Institute of Technology, (1978).
.
(1968).
C.O. Pederson, Int. J. Heat Mass Transfer, 13, 369 (1970).
4.
S.C. Yao and K.J. Choi, Int. J. Multiphase Flow, 13, 5, 639 (1987)
5.
M. Shoji, T. Wakunaga, and K. Kodama, Heat Transfer Japanese Research, 50 (1985).
.
M. Taga, T. Ocki, and K. Akagawa, Cooling of a Hot Moving Plate by an Impinging Water Jet, ASME-JSME, Thermal Enoneering Joint Cot~[erence, Vol. 1,
183 (1983).
.
8.
.
10.
O. Pinkus, ASME, J. of Engineering for Power, 10___55,80 (1983). F.K. Schalnev, O.A. Povarov, O.I. Nazarov, and I.A. Shalobosov, Proceedines of th_..~eFifth CQnference of Fluid Machinery, Vol. 2, 1011 (1975). S.C. Yao and K.Y. Cal, The Dynamics and Leidenfrost Temperature of Drops Impacting on a HOt Surface at Small Angles, ASME 85-WA/HT--39 (1985). D.L. Oehlbeck and F.F. Erian, Int. J. Heat Mass Transfer, 22, 601 (1979).