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Flow visualization during solid-liquid phase change heat transfer I. Freezing in a rectangular cavity
INT. O3M~. HEAT MASS TRANSFER 0735-1933/83/030173-09503.00/0 Vol. 10, pp. 173-181, 1983 @Pergamon Press Ltd. Printed in the United States
FLOW VISUALIZATION DURING SOLID-LIQUID PHASE CHANGE HEAT TRANSFER I. FREEZING IN A RECTANGULARCAVITY C. Gau and R. Viskanta Heat Transfer Laboratory School of Mechanical Engineering Purdue University West Lafayette, Indiana 4 7 9 0 7 . (Ccrma/nicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT The results of flow v i s u a l i z a t i o n experiments in a rectangular test cell during the s o l i d i f i c a t i o n of n-octadecane from above are reported. The experiments provide information on buoyancy-induced f l u i d motion and i t s e f f e c t on the shape and motion of the s o l i d liquid interface. Introduction The primary objective of the present work was to provide data both on the structure of buoyancy-induced flow during melting and s o l i d i f i c a t i o n
in a
rectangular enclosure and on the e f f e c t of the flow on the shape and motion of the s o l i d - l i q u i d
interface.
in the phase-change material
Aluminimum powder was used as a flow tracer
(PCM) to delineate the f l u i d motion.
The asso-
ciated thermocouple measurements of the temperature f l u c t u a t i o n s were used to obtain a q u a l i t a t i v e indication of the flow structure and regimes and to provide information on the flow behavior f o r freezing from above. The experiments described in the paper were motivated by the need to know the natural convection c i r c u l a t i o n patterns in opaque l i q u i d s in which the flow cannot be e i t h e r visualized or measured with convectional diagnost i c techniques because of the very low v e l o c i t i e s involved. 173
174
C. Gau and R. Viskanta
Vol. i0, No. 3
Experiment% Test Cell and Instrumentation S o l i d i f i c a t i o n experiments were performed in a rectangular test cell with inside dimensions of 8.89 cm high by 6.35 cm wide by 3.81 cm deep.
The
two horizontal w a l l s , which served as the heat source/sink, were a multipass heat exchanger machined out of a copper plate.
For flow v i s u a l i z a t i o n pur-
poses, a l l the v e r t i c a l walls were made of Plexiglas.
The two v e r t i c a l side-
walls were 1.27 cm-thick plates of Plexiglas in order to support the c e l l . For better i n s u l a t i o n , the f r o n t and back walls had a 0.318 cm a i r gap between the plates. Five thermocouples were inserted through the copper plates and epoxyed separately into f i v e small-diameter holes which were d r i l l e d close to the surface of the copper plates.
A v e r t i c a l s l o t , 0.159 cm wide by 6.35 cm long,
was m i l l e d in one of the v e r t i c a l sidewalls so that the thermocouple could be inserted to measure the temperature f l u c t u a t i o n s in the l i q u i d .
To prevent
the freezing of the PCM at the outside of the v e r t i c a l s l o t , a long, smalldiameter cable e l e c t r i c heater was immersed and heated. Eighteen thermocouples, with a wire diameter of 0.127 mm and sheathed in a 1.27 mm OD stainless steel tube, were located in the center of the t e s t c e l l and were spaced equally to measure the temperatures.
This thermocouple rack
could be removed when i t was not in use. A t o t a l of f i v e sheathed thermocopules with a wire diameter of 0.0762 mm were i n s t a l l e d in the t e s t c e l l . two others in the top region.
Two were located in the bottom region and
The l a s t thermocouple was placed in the middle
region to measure the temperature f l u c t u a t i o n s .
The junctions were coated
with a thin layer of high thermal c o n d u c t i v i t y epoxy.
The DC part of the sig-
nal was suppressed by an adjustable DC suppressor so that the small AC component could be amplified and recorded. The t e s t cell was placed in a transparent box made of Lexan where the temperature could be kept constant by a temperature c o n t r o l l e r .
A heat sto-
rage medium was placed in the box to minimize the frequent on and o f f switching of the heater and to keep the temperature inside closer to a constant value.
VOI. I0, No. 3
FREEZING IN A RF_L-'TANGULARCAVITY
175
Experimental Procedures N-octadecane was selected as the phase-change material because i t is easy to handle and has reasonably well-established thermophysical properties. Before being used to f i l l
the test cell, the liquid n-octadecane was degassed.
Provisions were made to avoid entrapping air bubbles during the f i l l i n g period.
A small amount of aluminum powder was added to the liquid as a tra-
cer for flow visualization.
The i n i t i a l temperature inside the cell was
kept uniform, and only a single phase was allowed to exist.
The solidifica-
tion was initiated by switching one of the two heat exchangers to another constant temperature bath that was preset at a different temperature. A mercury light source was used and arranged perpendicularly to the direction of observation in order to take advantage of the scattering from the aluminum powder.
To allow two-dimensional observation of flow patterns
( i . e . , in a plane perpendicular to the z-axis), a narrow s l i t illuminated a small test region of interest with a parallel beam of light.
The light beam
external to the region of interest was blocked. Results and Discussion Flow Visualization Natural convection was initiated immediately after solidification started.
I n i t i a l l y , a number of cooled fluid parcels (thermals) individually
fell from the cooled top plate and moved toward each of the vertical side walls.
Then a number of heated fluid parcels (thermals) individually rose
from the heated bottom plate and moved toward the central region of the cell. Finally, in a lengthy period of release, heated thermals in the central region were observed oscillating slowly from right to l e f t like a plume (Fig.la). The cooled thermals fell along the wall.
After this period of development, a
pair of well-established, two-dimensional convection r o l l s , with their axes perpendicular to the longer dimension of the test section, was observed (Fig.lb).
The rolls were symmetric and persisted during the entire process of
freezing.
This flow pattern is a l i t t l e different from the situation for
laminar natural convection in a rectangular box heated from below without a moving boundary [1,2].
The persistence of the number of the convection
r o l l s , which did not change with the aspect ratio during freezing, may be attributed to the stabilizing effect of the freezing front.
176
C. G a u and R. V i s k a n t a
Vol.
(a) Figure I.
i0, No.
"
(b)
Flow v i s u a l i z a t i o n for the freezing of n-octadecane from above, Twb = 30°C, ]w = 14.8°C: a) o s c i l l a t i o n of plume in central region, t = ~ kin. 25 sec; b) well-established natural convection c e l l s , t = 132 min.
During the experiments, the illuminated plane was moved back and forth in the d i r e c t i o n of observation.
The v e l o c i t y of the convection r o l l s near
the front and back wall regions was smaller than in the central region.
This
was due to the wall shear, which retarded the f l u i d motion. The time required f o r the convection cells to develop was found to be proportional to the temperature difference between the fusion temperature of the PCM and of the bottom plate.
The higher the temperature d i f f e r e n c e , the
longer the development time that was needed.
For the boundary temperature of
Twb = 32°C and Twt = 5.6°C, convection c e l l s were not f u l l y established a f t e r 3.28 hours of freezing (Fig.2) and a thermal j u s t released from the thermal boundary layer adjacent to the bottom plate was observed. Shape of Freezin 9 Front The freezing front was found to be f l a t the solid.
During the i n i t i a l p e r i o d o f t h e
initially
and l a t e r concave to
freezing process, heat conduction in
the s o l i d , instead of natural convection in the l i q u i d , played the dominant role in c o n t r o l l i n g the motion and shape of interface because of the large temperature gradient in the solid. We found t h a t i f t h e interface was oerturbed locally,
i t was stable, i . e .
i t followed the shape of the heat sink.
Strong
natural convection heat t r a n s f e r in the l i q u i d increased heat conduction in
Vol. i0, No. 3
FREEZING IN A RECTANGULARCAVITY
the adjacent solid. the interface.
177
The higher conduction heat transfer could have flattened
However, as the interface moved away from the heat sink,
natural convection heat transfer gradually became the controlling factor because of the increase in the thermal resistance of the solid layer.
The
interface became unstable, and natural convection eventually played the dominant role in the controlling its shape and motion.
Later in the freezing
process the interface was concave to the solid, not only in the x-axis because of the convection rolls (or the plume), but also in the z-axis because of less intense natural convection near the walls than near the center region. The interface velocity was found to decrease and eventually to vanish completely.
Figure 2.
Freezing from above Twb = 32°C,_Twt = 5.6°C: from the bottom plate, t = 197.b mln.
release of a thermal
Temperature Distribution and Fluctuation Measurements The temperature distribution in the solid was found to be linear and uniform in the liquid because of bouyancy-induced f l u i d motion. The temperature fluctuation measurements were made with a thermocouple placed 4 mm above the bottom plate.
Fig.3a shows that the temperature started fluctuating after
solidification was i n i t i a t e d .
The temperature fluctuations gradually died out
at the convection rolls slowly become established.
The fluctuations of the
temperature often reappeared, as shown in the left-hand side of Fig.3b, owing to the shifting of the convection rolls in the x-axis.
This is believed
to be caused by small nonuniformities of temperature in the thermal environment outside of test cell.
178
C. Gau and R. Viskanta
Vol. i0, No. 3
Lu]
Figure 3.
Temperature f l u c t u a t i o n s : a) the temperature f l u c t u a t i o n is dying out, b) the temperature f l u c t u a t i o n s a f t e r the i n i t i a t i o n of melting. The arrow on the l e f t shows the time at which the cooling f l u i d was stopped; the arrow on the r i g h t shows the time at the heating f l u i d started c i r c u l a t i n g through the top plate.
Effect of Solid-Liquid Interface Motion on the Flow The v i s u a l i z a t i o n of the r i s i n g and f a l l i n g thermals and the temperature fluctuations show that the flow was i n i t i a l l y appeared to be turbulent.
controlled by thermals and
The well-established convection r o l l s and the
absence of temperature f l u c t u a t i o n s l a t e r in the process indicate that the flow was laminar.
However, calculating the Rayleigh number for the boundary
conditions imposed during freezing shows that i t is always larger than 106 . The flow under t h i s high Rayleigh number f o r heating from below without phase change should always be turbulent [3].
Therefore, during freezing from above,
one must conclude that the t r a n s i t i o n from turbulent to laminar flow must occur and occurs at a higher c r i t i c a l
Rayleigh number.
Experiments were performed to examine the e f f e c t of interface motion on the flow patterns and on the t r a n s i t i o n to laminar flow during freezing from above.
A f t e r the convection c e l l s had been well-developed f o r approximately
one and a h a l f hours, the cooling f l u i d used to c i r c u l a t e through the top
Vol. I0, No. 3
FREEZING IN A RECTANGULAR CAVITY
179
heat exchanger was switched to the ehating f l u i d , with i t s temperature close to the fusion point of the PCM. The f l u i d r i s i n g in the center of the cavity was then found to be slowly o s c i l l a t i n g to the r i g h t and l e f t , This was observed only in the central region. have no d e f i n i t e flow pattern.
l i k e a plume.
Other regions were found to
The temperature f l u c t u a t i o n s
(Fig.4) showed
an increase in amplitude and frequency a f t e r melting was i n i t i a t e d .
Figure 4.
Temperature fluctuations a f t e r the i n i t i a t i o n of melting Twt =5.6°C and Twb = 32°C. The arrow indicates the heating f l u i d s t a r t i n g to c i r c u l a t e through the top heat exchanger.
During another freezing experiment for the boundary temperatures Twt = 7.6°C and Twb = 30°C, the cooling f l u i d c i r c u l a t i n g in the top exchanger was shut o f f a f t e r the convection r o l l s had been well established f o r hours.
Six-
teen minutes were allowed to heat the cooling f l u i d close to the fusion point of the PCM. The heated f l u i d was then circulated through the top heat exchanger.
The flow patterns were observed to change continuously a f t e r a
sufficiently
long period of time was allowed for the temperature in the solid
to come close to the fusion temperature (Fig.5). died out.
The convection r o l l s then
The flow became three-dimensional and had no d e f i n i t e pattern.
right-hand side of Fig.3b shows that a f t e r melting was i n i t i a t e d ,
The
the ampli-
tude of the temperature f l u c t a u t i o n was decreased and the frequency was increased. Observations indicated that the flow gradually changed from laminar back to turbulent flow once the melting of the solid PCM was i n i t i a t e d . vides evidence that the d i r e c t i o n of the s o l i d - l i q u i d have an e f f e c t on buoyancy-induced flow. solid-liquid
This pro-
interface motion does
During the freezing process, the
interface moved into the l i q u i d , with an e f f e c t similar to
180
C. Gau a n d R. V i s k a n t a
sucking the flow into the boundary.
Vo].
This s t a b i l i z e d the flow.
10, No.
B
During
melting the s o l i d - l i q u i d interface is moving out of the l i q u i d region, with the s i m i l a r e f f e c t of blowing the f l u i d away from the boundary.
This des-
t a b i l i z e d the flow.
(a) Fiqure 5. "
(b)
Flow v i s u a l i z a t i o n f o r freezing from above, Twb = 30°C, T , t = 7"5°C The cooling f l u i d was shut o f f at t = 170 min. The c i r c u l a t i o n of the heating f l u i d was resumed at t = 186 min: a) 12 min a f t e r the cooling f l u i d stopped c i r c u l a t i n g ~ b) 36 min a f t e r the cooling f l u i d stopped c i r c u l a t i n g . Conclusions
Flow v i s u a l i z a t i o n experiments and associated temperature f l u c t u a t i o n measurements have provided both information on the structure of buoyancyinduced flow and evidence of i t s e f f e c t on the shape and the motion of the interface.
The interrupted freezing experiments have given f u r t h e r evidence
of the e f f e c t of interface motion on natural convection c i r c u l a t i o n . The s t a b i l i z i n g e f f e c t of the freezing f r o n t caused the formation of two p e r s i s t e n t horizontal convection r o l l s .
The c i r c u l a t i o n caused the s o l i d -
l i q u i d i n t e r f a c e to become concave to the s o l i d at l a t e r stages of freezing. Natural convection in the l i q u i d not only gradually retarded but also, in the end, completely terminated the motion of the s o l i d - l i q u i d i n t e r f a c e . Acknowledgements . This work was supported by the National Science Foundation Heat Transfer Program under grant MEA-8014061.
Vol. i0, No. 3
FREEZING IN A RECTAN~KAR CAVITY
References [l]
K. Stork and U. MUller, "Convection in boxes: experiments," J. Fluid Mech. 54, 599-611 (1972).
[2]
S.H. Davis, "Convection in a box: linear theory," J. Fluid Mech. 30, 465-478 (1967).
[3]
R. Krishnamurti, "Some further studies on the transition to turbulent convection," J. Fluid Mech. 60, 285-303 (1973).
181
FLOW VISUALIZATION DURING SOLID-LIQUID PHASE CHANGE HEAT TRANSFER I. FREEZING IN A RECTANGULARCAVITY C. Gau and R. Viskanta Heat Transfer Laboratory School of Mechanical Engineering Purdue University West Lafayette, Indiana 4 7 9 0 7 . (Ccrma/nicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT The results of flow v i s u a l i z a t i o n experiments in a rectangular test cell during the s o l i d i f i c a t i o n of n-octadecane from above are reported. The experiments provide information on buoyancy-induced f l u i d motion and i t s e f f e c t on the shape and motion of the s o l i d liquid interface. Introduction The primary objective of the present work was to provide data both on the structure of buoyancy-induced flow during melting and s o l i d i f i c a t i o n
in a
rectangular enclosure and on the e f f e c t of the flow on the shape and motion of the s o l i d - l i q u i d
interface.
in the phase-change material
Aluminimum powder was used as a flow tracer
(PCM) to delineate the f l u i d motion.
The asso-
ciated thermocouple measurements of the temperature f l u c t u a t i o n s were used to obtain a q u a l i t a t i v e indication of the flow structure and regimes and to provide information on the flow behavior f o r freezing from above. The experiments described in the paper were motivated by the need to know the natural convection c i r c u l a t i o n patterns in opaque l i q u i d s in which the flow cannot be e i t h e r visualized or measured with convectional diagnost i c techniques because of the very low v e l o c i t i e s involved. 173
174
C. Gau and R. Viskanta
Vol. i0, No. 3
Experiment% Test Cell and Instrumentation S o l i d i f i c a t i o n experiments were performed in a rectangular test cell with inside dimensions of 8.89 cm high by 6.35 cm wide by 3.81 cm deep.
The
two horizontal w a l l s , which served as the heat source/sink, were a multipass heat exchanger machined out of a copper plate.
For flow v i s u a l i z a t i o n pur-
poses, a l l the v e r t i c a l walls were made of Plexiglas.
The two v e r t i c a l side-
walls were 1.27 cm-thick plates of Plexiglas in order to support the c e l l . For better i n s u l a t i o n , the f r o n t and back walls had a 0.318 cm a i r gap between the plates. Five thermocouples were inserted through the copper plates and epoxyed separately into f i v e small-diameter holes which were d r i l l e d close to the surface of the copper plates.
A v e r t i c a l s l o t , 0.159 cm wide by 6.35 cm long,
was m i l l e d in one of the v e r t i c a l sidewalls so that the thermocouple could be inserted to measure the temperature f l u c t u a t i o n s in the l i q u i d .
To prevent
the freezing of the PCM at the outside of the v e r t i c a l s l o t , a long, smalldiameter cable e l e c t r i c heater was immersed and heated. Eighteen thermocouples, with a wire diameter of 0.127 mm and sheathed in a 1.27 mm OD stainless steel tube, were located in the center of the t e s t c e l l and were spaced equally to measure the temperatures.
This thermocouple rack
could be removed when i t was not in use. A t o t a l of f i v e sheathed thermocopules with a wire diameter of 0.0762 mm were i n s t a l l e d in the t e s t c e l l . two others in the top region.
Two were located in the bottom region and
The l a s t thermocouple was placed in the middle
region to measure the temperature f l u c t u a t i o n s .
The junctions were coated
with a thin layer of high thermal c o n d u c t i v i t y epoxy.
The DC part of the sig-
nal was suppressed by an adjustable DC suppressor so that the small AC component could be amplified and recorded. The t e s t cell was placed in a transparent box made of Lexan where the temperature could be kept constant by a temperature c o n t r o l l e r .
A heat sto-
rage medium was placed in the box to minimize the frequent on and o f f switching of the heater and to keep the temperature inside closer to a constant value.
VOI. I0, No. 3
FREEZING IN A RF_L-'TANGULARCAVITY
175
Experimental Procedures N-octadecane was selected as the phase-change material because i t is easy to handle and has reasonably well-established thermophysical properties. Before being used to f i l l
the test cell, the liquid n-octadecane was degassed.
Provisions were made to avoid entrapping air bubbles during the f i l l i n g period.
A small amount of aluminum powder was added to the liquid as a tra-
cer for flow visualization.
The i n i t i a l temperature inside the cell was
kept uniform, and only a single phase was allowed to exist.
The solidifica-
tion was initiated by switching one of the two heat exchangers to another constant temperature bath that was preset at a different temperature. A mercury light source was used and arranged perpendicularly to the direction of observation in order to take advantage of the scattering from the aluminum powder.
To allow two-dimensional observation of flow patterns
( i . e . , in a plane perpendicular to the z-axis), a narrow s l i t illuminated a small test region of interest with a parallel beam of light.
The light beam
external to the region of interest was blocked. Results and Discussion Flow Visualization Natural convection was initiated immediately after solidification started.
I n i t i a l l y , a number of cooled fluid parcels (thermals) individually
fell from the cooled top plate and moved toward each of the vertical side walls.
Then a number of heated fluid parcels (thermals) individually rose
from the heated bottom plate and moved toward the central region of the cell. Finally, in a lengthy period of release, heated thermals in the central region were observed oscillating slowly from right to l e f t like a plume (Fig.la). The cooled thermals fell along the wall.
After this period of development, a
pair of well-established, two-dimensional convection r o l l s , with their axes perpendicular to the longer dimension of the test section, was observed (Fig.lb).
The rolls were symmetric and persisted during the entire process of
freezing.
This flow pattern is a l i t t l e different from the situation for
laminar natural convection in a rectangular box heated from below without a moving boundary [1,2].
The persistence of the number of the convection
r o l l s , which did not change with the aspect ratio during freezing, may be attributed to the stabilizing effect of the freezing front.
176
C. G a u and R. V i s k a n t a
Vol.
(a) Figure I.
i0, No.
"
(b)
Flow v i s u a l i z a t i o n for the freezing of n-octadecane from above, Twb = 30°C, ]w = 14.8°C: a) o s c i l l a t i o n of plume in central region, t = ~ kin. 25 sec; b) well-established natural convection c e l l s , t = 132 min.
During the experiments, the illuminated plane was moved back and forth in the d i r e c t i o n of observation.
The v e l o c i t y of the convection r o l l s near
the front and back wall regions was smaller than in the central region.
This
was due to the wall shear, which retarded the f l u i d motion. The time required f o r the convection cells to develop was found to be proportional to the temperature difference between the fusion temperature of the PCM and of the bottom plate.
The higher the temperature d i f f e r e n c e , the
longer the development time that was needed.
For the boundary temperature of
Twb = 32°C and Twt = 5.6°C, convection c e l l s were not f u l l y established a f t e r 3.28 hours of freezing (Fig.2) and a thermal j u s t released from the thermal boundary layer adjacent to the bottom plate was observed. Shape of Freezin 9 Front The freezing front was found to be f l a t the solid.
During the i n i t i a l p e r i o d o f t h e
initially
and l a t e r concave to
freezing process, heat conduction in
the s o l i d , instead of natural convection in the l i q u i d , played the dominant role in c o n t r o l l i n g the motion and shape of interface because of the large temperature gradient in the solid. We found t h a t i f t h e interface was oerturbed locally,
i t was stable, i . e .
i t followed the shape of the heat sink.
Strong
natural convection heat t r a n s f e r in the l i q u i d increased heat conduction in
Vol. i0, No. 3
FREEZING IN A RECTANGULARCAVITY
the adjacent solid. the interface.
177
The higher conduction heat transfer could have flattened
However, as the interface moved away from the heat sink,
natural convection heat transfer gradually became the controlling factor because of the increase in the thermal resistance of the solid layer.
The
interface became unstable, and natural convection eventually played the dominant role in the controlling its shape and motion.
Later in the freezing
process the interface was concave to the solid, not only in the x-axis because of the convection rolls (or the plume), but also in the z-axis because of less intense natural convection near the walls than near the center region. The interface velocity was found to decrease and eventually to vanish completely.
Figure 2.
Freezing from above Twb = 32°C,_Twt = 5.6°C: from the bottom plate, t = 197.b mln.
release of a thermal
Temperature Distribution and Fluctuation Measurements The temperature distribution in the solid was found to be linear and uniform in the liquid because of bouyancy-induced f l u i d motion. The temperature fluctuation measurements were made with a thermocouple placed 4 mm above the bottom plate.
Fig.3a shows that the temperature started fluctuating after
solidification was i n i t i a t e d .
The temperature fluctuations gradually died out
at the convection rolls slowly become established.
The fluctuations of the
temperature often reappeared, as shown in the left-hand side of Fig.3b, owing to the shifting of the convection rolls in the x-axis.
This is believed
to be caused by small nonuniformities of temperature in the thermal environment outside of test cell.
178
C. Gau and R. Viskanta
Vol. i0, No. 3
Lu]
Figure 3.
Temperature f l u c t u a t i o n s : a) the temperature f l u c t u a t i o n is dying out, b) the temperature f l u c t u a t i o n s a f t e r the i n i t i a t i o n of melting. The arrow on the l e f t shows the time at which the cooling f l u i d was stopped; the arrow on the r i g h t shows the time at the heating f l u i d started c i r c u l a t i n g through the top plate.
Effect of Solid-Liquid Interface Motion on the Flow The v i s u a l i z a t i o n of the r i s i n g and f a l l i n g thermals and the temperature fluctuations show that the flow was i n i t i a l l y appeared to be turbulent.
controlled by thermals and
The well-established convection r o l l s and the
absence of temperature f l u c t u a t i o n s l a t e r in the process indicate that the flow was laminar.
However, calculating the Rayleigh number for the boundary
conditions imposed during freezing shows that i t is always larger than 106 . The flow under t h i s high Rayleigh number f o r heating from below without phase change should always be turbulent [3].
Therefore, during freezing from above,
one must conclude that the t r a n s i t i o n from turbulent to laminar flow must occur and occurs at a higher c r i t i c a l
Rayleigh number.
Experiments were performed to examine the e f f e c t of interface motion on the flow patterns and on the t r a n s i t i o n to laminar flow during freezing from above.
A f t e r the convection c e l l s had been well-developed f o r approximately
one and a h a l f hours, the cooling f l u i d used to c i r c u l a t e through the top
Vol. I0, No. 3
FREEZING IN A RECTANGULAR CAVITY
179
heat exchanger was switched to the ehating f l u i d , with i t s temperature close to the fusion point of the PCM. The f l u i d r i s i n g in the center of the cavity was then found to be slowly o s c i l l a t i n g to the r i g h t and l e f t , This was observed only in the central region. have no d e f i n i t e flow pattern.
l i k e a plume.
Other regions were found to
The temperature f l u c t u a t i o n s
(Fig.4) showed
an increase in amplitude and frequency a f t e r melting was i n i t i a t e d .
Figure 4.
Temperature fluctuations a f t e r the i n i t i a t i o n of melting Twt =5.6°C and Twb = 32°C. The arrow indicates the heating f l u i d s t a r t i n g to c i r c u l a t e through the top heat exchanger.
During another freezing experiment for the boundary temperatures Twt = 7.6°C and Twb = 30°C, the cooling f l u i d c i r c u l a t i n g in the top exchanger was shut o f f a f t e r the convection r o l l s had been well established f o r hours.
Six-
teen minutes were allowed to heat the cooling f l u i d close to the fusion point of the PCM. The heated f l u i d was then circulated through the top heat exchanger.
The flow patterns were observed to change continuously a f t e r a
sufficiently
long period of time was allowed for the temperature in the solid
to come close to the fusion temperature (Fig.5). died out.
The convection r o l l s then
The flow became three-dimensional and had no d e f i n i t e pattern.
right-hand side of Fig.3b shows that a f t e r melting was i n i t i a t e d ,
The
the ampli-
tude of the temperature f l u c t a u t i o n was decreased and the frequency was increased. Observations indicated that the flow gradually changed from laminar back to turbulent flow once the melting of the solid PCM was i n i t i a t e d . vides evidence that the d i r e c t i o n of the s o l i d - l i q u i d have an e f f e c t on buoyancy-induced flow. solid-liquid
This pro-
interface motion does
During the freezing process, the
interface moved into the l i q u i d , with an e f f e c t similar to
180
C. Gau a n d R. V i s k a n t a
sucking the flow into the boundary.
Vo].
This s t a b i l i z e d the flow.
10, No.
B
During
melting the s o l i d - l i q u i d interface is moving out of the l i q u i d region, with the s i m i l a r e f f e c t of blowing the f l u i d away from the boundary.
This des-
t a b i l i z e d the flow.
(a) Fiqure 5. "
(b)
Flow v i s u a l i z a t i o n f o r freezing from above, Twb = 30°C, T , t = 7"5°C The cooling f l u i d was shut o f f at t = 170 min. The c i r c u l a t i o n of the heating f l u i d was resumed at t = 186 min: a) 12 min a f t e r the cooling f l u i d stopped c i r c u l a t i n g ~ b) 36 min a f t e r the cooling f l u i d stopped c i r c u l a t i n g . Conclusions
Flow v i s u a l i z a t i o n experiments and associated temperature f l u c t u a t i o n measurements have provided both information on the structure of buoyancyinduced flow and evidence of i t s e f f e c t on the shape and the motion of the interface.
The interrupted freezing experiments have given f u r t h e r evidence
of the e f f e c t of interface motion on natural convection c i r c u l a t i o n . The s t a b i l i z i n g e f f e c t of the freezing f r o n t caused the formation of two p e r s i s t e n t horizontal convection r o l l s .
The c i r c u l a t i o n caused the s o l i d -
l i q u i d i n t e r f a c e to become concave to the s o l i d at l a t e r stages of freezing. Natural convection in the l i q u i d not only gradually retarded but also, in the end, completely terminated the motion of the s o l i d - l i q u i d i n t e r f a c e . Acknowledgements . This work was supported by the National Science Foundation Heat Transfer Program under grant MEA-8014061.
Vol. i0, No. 3
FREEZING IN A RECTAN~KAR CAVITY
References [l]
K. Stork and U. MUller, "Convection in boxes: experiments," J. Fluid Mech. 54, 599-611 (1972).
[2]
S.H. Davis, "Convection in a box: linear theory," J. Fluid Mech. 30, 465-478 (1967).
[3]
R. Krishnamurti, "Some further studies on the transition to turbulent convection," J. Fluid Mech. 60, 285-303 (1973).
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