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Flow visualization during solid-liquid phase change heat transfer II. Melting in a rectangular cavity
INT. CC~M. HEAT MASS TRANSFER 0735-1933/83/030183-08503.00/0 VOI. 10, pp. 183-190, 1983 ©Pergamon Press Ltd. Printed in the United States
FLOW VISUALIZATION DURING SOLID-LIQUID PHASECHANGE HEAT TRANSFER I I . MELTING IN A RECTANGULARCAVITY C. Gau, R. Viskanta and C.-J. Ho Heat Transfer Laboratory School of Mechanical Engineering Purdue University West Lafayette, Indiana 47907 (~cated
by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT The results of flow visualization in a rectangular test cell during the melting of n-octadecane are reported. The experiments provide information on buoyancy-induced f l u i d motion and its effect on the shape of the solid-liquid interface. Introduction This paper is a companion to the preceeding one by Gau and Viskanta in this issue and presents the results of flow visualization and heat transfer measurements during the melting of a solid contained in rectangular cavities which are heated from below. Aluminum powder was used as a flow tracer to visualize the buoyancy-driven f l u i d motion in the melt.
A shadowgraph system
was used to visualize the temperature gradients at the heated surface and obtain quantitative heat transfer coefficient data.
The temperature fluctuation
measurements were used to infer the flow structure and the flow regimes.
183
]84
C. Gau, R. Viskanta and C.-J. Ho
Vol. 1O, No. 3
Experiments The t e s t c e l l , instrumentation, and procedure f o r flow v i s u a l i z a t i o n measurements during s o l i d i f i c a t i o n were described in Paper I.
The melting
experiments were performed in the same t e s t cell and followed a s i m i l a r procedure. The local heat t r a n s f e r c o e f f i c i e n t s at the heated wall were measured using a shadowgraph method.
The experimental apparatus employed here was
i d e n t i c a l to the one described e a r l i e r [ 2 ] .
The technique involved i d e n t i f y i n g
the heat source surface as a reference p o s i t i o n , as well as recording the deflection of the l i g h t beam on a screen a f t e r i t passed through the t e s t c e l l . Results and Discussion Flow V i s u a l i z a t i o n In the melting experiments from below, a f t e r a c r i t i c a l based on the melt depth was exceeded, the f l u i d was f i r s t creeping motion.
Rayleigh number
found to e x h i b i t a
Later, a number of small, three-dimensional convection c e l l s
were observed c i r c u l a t i n g ( F i g s . l a and I b ) .
The c i r c u l a t i o n of the small con-
vection c e l l s in the l i q u i d caused a regular d i s t r i b u t i o n of hemisphericalcapped c e l l s in the melting f r o n t .
This d i f f e r e d somewhat from the findings of
Yen [3] for the melting of ice from below.
The f l u i d rose in the central re-
gion and the f e l l near the edge of the c e l l s .
These hemispherical-capped c e l l s
at the s o l i d - l i q u i d interface were observed s h o r t l y a f t e r natural convection was i n i t i a t e d . The t o t a l number of Benard c e l l s appeared to depend on the bottom temperature and the aspect r a t i o of the l i q u i d - f i l l e d
cavity.
I t was found that
the higher the bottom temperature and the smaller the aspect r a t i o , the larger was the number of convection c e l l s .
A maximum of approximately 17 c e l l s in the
f r o n t side of the t e s t c e l l were observed f o r Twb = 54°C (by counting the corresponding hemispherical-capped c e l l s ) immediately a f t e r the i n i t i a t i o n of natural convection.
The size and the survival of the c e l l s were d i r e c t l y pro-
portional to the depth of melt layer.
An increase in the depth of the melt
layer as the melting proceeded caused the c e l l s to grow in size and decrease in number. The c e l l s combined with neighboring ones ( F i g . l a and Ib) and were found to be d i s t o r t e d and elongated in the d i r e c t i o n of the i n t e r f a c e motion. The curvature of the i n d i v i d u a l c e l l s at the melt f r o n t was reduced as a r e s u l t of the growth and combination of the c e l l s .
Vol. i0, NO. 3
MELTING IN A RI]L~ANGUIARCAVITY
185
As the Rayleigh number increased, the convection cells became unstable and were more readily subjected to random disturbances. Later, some of the cells became distorted and broke down locally because of large,scale motion (Fig.lc) resulting from the ascending and descending thermals. The flow at this stage was between cellular flow and the boundary layer type. Release of the thermals from the heated plate (the solid-liquid interface) produced large-scale motion which gradually pervaded the entire melt layer. The flow at this stage had no definite pattern and was turbulent. I n i t i a l l y , the intense ascent (descent) of thermals which bombarded the solid-liquid interface (the bottom plate) was observed. Later, the heated (cooled) thermals (Fig.ld) originated on one side of the cell near the bottom plate or the solid-liquid interface and moved persistently in the horizontal direction to the other side. These heated (cooled) thermals became unstable while moving horizontally across theplate and eventually were released from the edge of the thermal boundary layer adjacent to the bottom plate (solid-liquid interface} (Fig.le). Persistent horizontal thermal motion has also been observed by others for the turbulentnatural convection between parallel plates heated from below [4].
(c)
Figure I.
(e)
Flow visualization during melting from below Twb=46°C; a} Benard convection cells t = l l min; b) growth of the Benard cells, t=17 min; c) large-scale motion of the fluid on the right-hand side breaks up the cells, t=25 min; d) persistent horizontal motion of thermals is i n i t i a t e d , t=48 min 30 sec; e) the horizontal motion of the thermals is intense so that the fluid circulates in a unitary fashion, t=62 min
186
C. Gau, R. Viskanta and C.-J. Ho
Vol.
i0, No. 3
Heat Transfer at the Bottom Figure 2 i l l u s t r a t e s
the timewise variation of the local heat transfer
c o e f f i c i e n t along the isothermal bottom surface of the cavity. The width of the base W was chosen as the c h a r a c t e r i s t i c length for both the Nusselt and the Rayleigh numbers. wall.
The distance
x
is measured from the l e f t v e r t i c a l
The variation of the local Nusselt number with time shows rather com-
plex trends because of changing vortex c i r c u l a t i o n patterns resulting from the altered shape and size of the melt zone.
During the early stages of melting
(% = 0.00201), heat transfer was predominantly by conduction because the heat transfer c o e f f i c i e n t was independent of position.
As the melting continued,
the local Nusselt number exhibited a nearly periodic variation with location along the bottom (T = 0.00278).
This was clear indication of the development
of multiple vortex c i r c u l a t i o n patterns in the melt region
As the melting
progressed (T = 0.00872), the periodic trend in the Nusselt number d i s t r i b u t i o n tended to abate, as indicated by the smaller number of peaks.
This was due to
the decrease in the number of vortex cells as the melt zone became larger with time.
0,8
aT]
r~=0.00201 no
[]
[]
m
D
[]
Q D
o61 o5i Nu
07!
RaZ4 o.6i 0.7 o.61 Q~
Figure 2.
r~r000278000872 QLOo =: a°°OAoooOa OooAO~j ~ ogo
×/W
,oo
Variation of the local heat transfer coefficients along the isothermal bottom of the cavity: ~=FoSte~, Fo:~t/W , Ste~=c~(Twb-Tf)/&h f 0.072, Sc=c~(Tf-To)/&hf=0.110. -
Temperature Distribution and Fluctuation Measurements The temperature distributions measured in the liquid (the mixed layer) were found to be uniform, owing to the effective mixing.
Later in the process, ther-
mal boundary layers near the bottom plate (or the solid-liquid interface) were observed in which steep temperature gradients existed.
Vol. I0, No. 3
MELTING IN A RECTANGUIAR CAVITY
187
The temperature fluctuation measurements are shown in Fig.3.
One of the
thermocouples was placed 2.8 mm above the bottom plate, which was close to the edge of the thermal boundary layer when the flow was turbulent.
The temperature
rose almost linearly after the melting front had just passed the sensor because of a conduction layer.
The linearly increasing temperature was expected to
level off and start oscillating slowly when the sensor was in the region where the flow was laminar.
These oscillations in temperature were due to the growth
and the combining process of the Benard convection cells.
When the convection
in the liquid was between the cellular and the boundary layer type (Fig.3a), the frequency of thetemperature~fluctuations
increased because the flow was
disturbed by local large-scale motion. I n i t i a l l y , the intense activity produced by the ascending, heated thermals in the mixed layer caused the high frequency and large amplitude of the temperature fluctuations.
After a persistent
horizontal thermal motion was initiated, only the frequent and signficant upward temperature spikes (Fig.3a on the right-hand side and Fig.3b) near the edge of the thermal boundary layer were observed. The amplitude of the temperature spikes was determined by what part of the thermal passed across the sensor during its ascent.
I t should be noted that there was only a negligible
number of downward temperature spikes after the persistent horizontal thermal motion had been initiated. For the thermocouple located 24 mm above the bottom plate, the flow was already turbulent once the melting front had passed over the sensor. The conduction layer was so thin that the temperature started fluctuating (Fig.3c) immediately after the melting front had passed the sensor. The amplitude and the average temperature increased until the edge of the thermal boundary layer was reached, owing to the advancing melting front.
For the boundary tempera-
ture of Twb = 47.8°C (Fig.3c}, approximately eight minutes were required to reach the edge of the thermal boundary layer.
The descending cooled thermals
produced frequent and significant downward temperature spikes. significant upward spikes.
There were no
After the thermocouple l e f t the thermal boundary
layer because of the advancing melting front, the frequency and the amplitude of the downward temperature spikes were reduced (Fig.3c and 3d). time, upward spikes of smaller amplitude appeared frequently.
At the same
188
C. Gau, R. Viskanta and C.-J. Ho
Vol. i0, No. 3
(a)
(b) Figure 3.
(c)
Flow v i s u a l i z a t i o n during melting from below Twb = 32.6°C: a) bombardment or the release of the thermals on the s o l i d - l i q u i d i n t e r face makes the interface i r r e g u l a r ; b) two c i r c u l a t i o n r o l l s , t = 325 min; c) immediately a f t e r the disappearance of the c i r c u l a tion r o l l s , the flow shows the ascending and descending thermals, t = 501. 5 min.
Structure of Turbulence and Its Effect on the Shape of the Melting Front For natural convection at high Rayleigh number in the absence of phase change, all of the k i n e t i c energy of the r i s i n g ( f a l l i n g ) sipated by viscous e f f e c t s in the turbulent core [ 5 ] . natural convection with phase change.
thermals may be dis-
This is also true for
The thermal energy of the heated (cooled)
thermal was found to be n e g l i g i b l e near the cooled upper (heated bottom) thermal boundary layer once horizontal thermal motion was i n i t i a t e d . solid-liquid
Thus, the
interface boundary became more uniform both in the x- and z - d i r e c -
tions (Figs.ld and le) as a r e s u l t of the persistent horizontal flow produced by the thermals as they swept over the interface.
For a higher boundary tem-
perature, the persistent horizontal motion became so intense that a largescale, two-dimenaional, unitary counterclockwise c i r c u l a t i o n of flow ( F i g . l e ) frequently appeared u n t i l unity.
the aspect r a t i o of the melt layer became close to
Vol. I0, No. 3
MELTING IN A RECTANGUIARCAVITY
For early times and low (release) of the heated (cooled) (Fig.4a)
may cause
irregular
in shape.
the
the
boundary thermals
interface to
As a result
of
189
temperatures, the bombardment or plumes at the interface become three-dimensional and
the continuous rising and f a l l i n g of
thermals at the same location, large-scale circulating motions may de-
velop locally and pervade th~ entire melt layer. A pair of circulation r o l l s (in which the flow rose near the side walls and f e l ! near the central region) with t h e i r axes perpendicular to the longer dimension of ~he test section developed (fig.4b) when the aspect ratio of the melt layer' was close to one-half. made themelting front a semihollow shape.
This
The circulation r o l l s disappeared
when the aspect r a t i o of the melt layter became close to 1 (Fig.4c).
A per-
sistent horizontal motion of the rising and f a l l i n g thermals reappeared.
The
frequent bombardment of the interface at the same location by the heated thermals was s i g n i f i c a n t l y reduced.
Hence, a smooth, but not necessarily f l a t ,
s o l i d - l i q u i d interface was produced during melting late in the process. Conclusions Regularly arranged Benard convection cells were observed early in the process.
A flow in these cells produced a melting front which was distributed
with numerous hemispherical-capped cells.
The cells grew in size and combined
with neighboring ones as the melting progressed.
Temperature fluctuation
measurements suggested that at that time, the kinetic energy of the heated (cooled) thermals generated near the thermal boundary layer was completely dissipated in the turbulent core (mixed layer) region by viscous dissipation. The persistent horizontal motion of the thermals produced a nearly plane i n t e r face.
Forlowboundarytemperatures, bombardment by the thermals made the i n t e r -
face irregular. References [I]
C. Gau and R. Viskanta, "Flow visualization during s o l i d - l i q u i d phase change heat transfer.
I.
solidification
in a rectangular cavity," Let.
Heat Mass Transfer (this issue). [2]
A.G. Bathelt and R. Viskanta, "Heat transfer and interface motion during melting and s o l i d i f i c a t i o n
from a finned heat source/sink," J. Heat
Transfer 103, 720-726 (1981). [3]
Y.C. Yen, "Free convection heat transfer characteristics in a melt water layer," J. Heat Transfer 102, 550-556, (1980).
190
[4]
C. Gau, R. Viskanta and C.-J. Ho
Voi~ i0, NO. 3
T.Y. Chu and R.J. Goldstein, "Turbulent convection in a horizontal layer of water," J. Fluid Mech. 60_0, 141-159, {1973).
[5]
H. Tanaka and H. Miyata, "Turbulent natural convection in a horizontal water layer heated from below," Int. J. Heat Mass Transfer 23, 1273-1281
(1980).
(b)
(d)
(c) Figure 4.
Temperature f l u c t u a t i o n measurements during melting from below: a) thermocouple located 2.8 mm above the bottom p l a t e , t r a n s i t i o n from c e l l u l a r to turbulent flow, b) the trace shows the s i g n i f i c a n t upward and n e g l i g i b l e downward spikes in temperatures, c) thermocouple located 24 mm above the bottom plate -- the two downward arrows representing the adjustments of the temperature f l u c t u a t i o n s in the range of the recorder, the two upward arrows indicating the time interval when the thermocouple is in the thermal boundary layer; d) the downward temperature spikes have been s i g n i f i c a n t l y reduced, and the amplitude for both the upward and the downward temperature spikes are about the same.
FLOW VISUALIZATION DURING SOLID-LIQUID PHASECHANGE HEAT TRANSFER I I . MELTING IN A RECTANGULARCAVITY C. Gau, R. Viskanta and C.-J. Ho Heat Transfer Laboratory School of Mechanical Engineering Purdue University West Lafayette, Indiana 47907 (~cated
by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT The results of flow visualization in a rectangular test cell during the melting of n-octadecane are reported. The experiments provide information on buoyancy-induced f l u i d motion and its effect on the shape of the solid-liquid interface. Introduction This paper is a companion to the preceeding one by Gau and Viskanta in this issue and presents the results of flow visualization and heat transfer measurements during the melting of a solid contained in rectangular cavities which are heated from below. Aluminum powder was used as a flow tracer to visualize the buoyancy-driven f l u i d motion in the melt.
A shadowgraph system
was used to visualize the temperature gradients at the heated surface and obtain quantitative heat transfer coefficient data.
The temperature fluctuation
measurements were used to infer the flow structure and the flow regimes.
183
]84
C. Gau, R. Viskanta and C.-J. Ho
Vol. 1O, No. 3
Experiments The t e s t c e l l , instrumentation, and procedure f o r flow v i s u a l i z a t i o n measurements during s o l i d i f i c a t i o n were described in Paper I.
The melting
experiments were performed in the same t e s t cell and followed a s i m i l a r procedure. The local heat t r a n s f e r c o e f f i c i e n t s at the heated wall were measured using a shadowgraph method.
The experimental apparatus employed here was
i d e n t i c a l to the one described e a r l i e r [ 2 ] .
The technique involved i d e n t i f y i n g
the heat source surface as a reference p o s i t i o n , as well as recording the deflection of the l i g h t beam on a screen a f t e r i t passed through the t e s t c e l l . Results and Discussion Flow V i s u a l i z a t i o n In the melting experiments from below, a f t e r a c r i t i c a l based on the melt depth was exceeded, the f l u i d was f i r s t creeping motion.
Rayleigh number
found to e x h i b i t a
Later, a number of small, three-dimensional convection c e l l s
were observed c i r c u l a t i n g ( F i g s . l a and I b ) .
The c i r c u l a t i o n of the small con-
vection c e l l s in the l i q u i d caused a regular d i s t r i b u t i o n of hemisphericalcapped c e l l s in the melting f r o n t .
This d i f f e r e d somewhat from the findings of
Yen [3] for the melting of ice from below.
The f l u i d rose in the central re-
gion and the f e l l near the edge of the c e l l s .
These hemispherical-capped c e l l s
at the s o l i d - l i q u i d interface were observed s h o r t l y a f t e r natural convection was i n i t i a t e d . The t o t a l number of Benard c e l l s appeared to depend on the bottom temperature and the aspect r a t i o of the l i q u i d - f i l l e d
cavity.
I t was found that
the higher the bottom temperature and the smaller the aspect r a t i o , the larger was the number of convection c e l l s .
A maximum of approximately 17 c e l l s in the
f r o n t side of the t e s t c e l l were observed f o r Twb = 54°C (by counting the corresponding hemispherical-capped c e l l s ) immediately a f t e r the i n i t i a t i o n of natural convection.
The size and the survival of the c e l l s were d i r e c t l y pro-
portional to the depth of melt layer.
An increase in the depth of the melt
layer as the melting proceeded caused the c e l l s to grow in size and decrease in number. The c e l l s combined with neighboring ones ( F i g . l a and Ib) and were found to be d i s t o r t e d and elongated in the d i r e c t i o n of the i n t e r f a c e motion. The curvature of the i n d i v i d u a l c e l l s at the melt f r o n t was reduced as a r e s u l t of the growth and combination of the c e l l s .
Vol. i0, NO. 3
MELTING IN A RI]L~ANGUIARCAVITY
185
As the Rayleigh number increased, the convection cells became unstable and were more readily subjected to random disturbances. Later, some of the cells became distorted and broke down locally because of large,scale motion (Fig.lc) resulting from the ascending and descending thermals. The flow at this stage was between cellular flow and the boundary layer type. Release of the thermals from the heated plate (the solid-liquid interface) produced large-scale motion which gradually pervaded the entire melt layer. The flow at this stage had no definite pattern and was turbulent. I n i t i a l l y , the intense ascent (descent) of thermals which bombarded the solid-liquid interface (the bottom plate) was observed. Later, the heated (cooled) thermals (Fig.ld) originated on one side of the cell near the bottom plate or the solid-liquid interface and moved persistently in the horizontal direction to the other side. These heated (cooled) thermals became unstable while moving horizontally across theplate and eventually were released from the edge of the thermal boundary layer adjacent to the bottom plate (solid-liquid interface} (Fig.le). Persistent horizontal thermal motion has also been observed by others for the turbulentnatural convection between parallel plates heated from below [4].
(c)
Figure I.
(e)
Flow visualization during melting from below Twb=46°C; a} Benard convection cells t = l l min; b) growth of the Benard cells, t=17 min; c) large-scale motion of the fluid on the right-hand side breaks up the cells, t=25 min; d) persistent horizontal motion of thermals is i n i t i a t e d , t=48 min 30 sec; e) the horizontal motion of the thermals is intense so that the fluid circulates in a unitary fashion, t=62 min
186
C. Gau, R. Viskanta and C.-J. Ho
Vol.
i0, No. 3
Heat Transfer at the Bottom Figure 2 i l l u s t r a t e s
the timewise variation of the local heat transfer
c o e f f i c i e n t along the isothermal bottom surface of the cavity. The width of the base W was chosen as the c h a r a c t e r i s t i c length for both the Nusselt and the Rayleigh numbers. wall.
The distance
x
is measured from the l e f t v e r t i c a l
The variation of the local Nusselt number with time shows rather com-
plex trends because of changing vortex c i r c u l a t i o n patterns resulting from the altered shape and size of the melt zone.
During the early stages of melting
(% = 0.00201), heat transfer was predominantly by conduction because the heat transfer c o e f f i c i e n t was independent of position.
As the melting continued,
the local Nusselt number exhibited a nearly periodic variation with location along the bottom (T = 0.00278).
This was clear indication of the development
of multiple vortex c i r c u l a t i o n patterns in the melt region
As the melting
progressed (T = 0.00872), the periodic trend in the Nusselt number d i s t r i b u t i o n tended to abate, as indicated by the smaller number of peaks.
This was due to
the decrease in the number of vortex cells as the melt zone became larger with time.
0,8
aT]
r~=0.00201 no
[]
[]
m
D
[]
Q D
o61 o5i Nu
07!
RaZ4 o.6i 0.7 o.61 Q~
Figure 2.
r~r000278000872 QLOo =: a°°OAoooOa OooAO~j ~ ogo
×/W
,oo
Variation of the local heat transfer coefficients along the isothermal bottom of the cavity: ~=FoSte~, Fo:~t/W , Ste~=c~(Twb-Tf)/&h f 0.072, Sc=c~(Tf-To)/&hf=0.110. -
Temperature Distribution and Fluctuation Measurements The temperature distributions measured in the liquid (the mixed layer) were found to be uniform, owing to the effective mixing.
Later in the process, ther-
mal boundary layers near the bottom plate (or the solid-liquid interface) were observed in which steep temperature gradients existed.
Vol. I0, No. 3
MELTING IN A RECTANGUIAR CAVITY
187
The temperature fluctuation measurements are shown in Fig.3.
One of the
thermocouples was placed 2.8 mm above the bottom plate, which was close to the edge of the thermal boundary layer when the flow was turbulent.
The temperature
rose almost linearly after the melting front had just passed the sensor because of a conduction layer.
The linearly increasing temperature was expected to
level off and start oscillating slowly when the sensor was in the region where the flow was laminar.
These oscillations in temperature were due to the growth
and the combining process of the Benard convection cells.
When the convection
in the liquid was between the cellular and the boundary layer type (Fig.3a), the frequency of thetemperature~fluctuations
increased because the flow was
disturbed by local large-scale motion. I n i t i a l l y , the intense activity produced by the ascending, heated thermals in the mixed layer caused the high frequency and large amplitude of the temperature fluctuations.
After a persistent
horizontal thermal motion was initiated, only the frequent and signficant upward temperature spikes (Fig.3a on the right-hand side and Fig.3b) near the edge of the thermal boundary layer were observed. The amplitude of the temperature spikes was determined by what part of the thermal passed across the sensor during its ascent.
I t should be noted that there was only a negligible
number of downward temperature spikes after the persistent horizontal thermal motion had been initiated. For the thermocouple located 24 mm above the bottom plate, the flow was already turbulent once the melting front had passed over the sensor. The conduction layer was so thin that the temperature started fluctuating (Fig.3c) immediately after the melting front had passed the sensor. The amplitude and the average temperature increased until the edge of the thermal boundary layer was reached, owing to the advancing melting front.
For the boundary tempera-
ture of Twb = 47.8°C (Fig.3c}, approximately eight minutes were required to reach the edge of the thermal boundary layer.
The descending cooled thermals
produced frequent and significant downward temperature spikes. significant upward spikes.
There were no
After the thermocouple l e f t the thermal boundary
layer because of the advancing melting front, the frequency and the amplitude of the downward temperature spikes were reduced (Fig.3c and 3d). time, upward spikes of smaller amplitude appeared frequently.
At the same
188
C. Gau, R. Viskanta and C.-J. Ho
Vol. i0, No. 3
(a)
(b) Figure 3.
(c)
Flow v i s u a l i z a t i o n during melting from below Twb = 32.6°C: a) bombardment or the release of the thermals on the s o l i d - l i q u i d i n t e r face makes the interface i r r e g u l a r ; b) two c i r c u l a t i o n r o l l s , t = 325 min; c) immediately a f t e r the disappearance of the c i r c u l a tion r o l l s , the flow shows the ascending and descending thermals, t = 501. 5 min.
Structure of Turbulence and Its Effect on the Shape of the Melting Front For natural convection at high Rayleigh number in the absence of phase change, all of the k i n e t i c energy of the r i s i n g ( f a l l i n g ) sipated by viscous e f f e c t s in the turbulent core [ 5 ] . natural convection with phase change.
thermals may be dis-
This is also true for
The thermal energy of the heated (cooled)
thermal was found to be n e g l i g i b l e near the cooled upper (heated bottom) thermal boundary layer once horizontal thermal motion was i n i t i a t e d . solid-liquid
Thus, the
interface boundary became more uniform both in the x- and z - d i r e c -
tions (Figs.ld and le) as a r e s u l t of the persistent horizontal flow produced by the thermals as they swept over the interface.
For a higher boundary tem-
perature, the persistent horizontal motion became so intense that a largescale, two-dimenaional, unitary counterclockwise c i r c u l a t i o n of flow ( F i g . l e ) frequently appeared u n t i l unity.
the aspect r a t i o of the melt layer became close to
Vol. I0, No. 3
MELTING IN A RECTANGUIARCAVITY
For early times and low (release) of the heated (cooled) (Fig.4a)
may cause
irregular
in shape.
the
the
boundary thermals
interface to
As a result
of
189
temperatures, the bombardment or plumes at the interface become three-dimensional and
the continuous rising and f a l l i n g of
thermals at the same location, large-scale circulating motions may de-
velop locally and pervade th~ entire melt layer. A pair of circulation r o l l s (in which the flow rose near the side walls and f e l ! near the central region) with t h e i r axes perpendicular to the longer dimension of ~he test section developed (fig.4b) when the aspect ratio of the melt layer' was close to one-half. made themelting front a semihollow shape.
This
The circulation r o l l s disappeared
when the aspect r a t i o of the melt layter became close to 1 (Fig.4c).
A per-
sistent horizontal motion of the rising and f a l l i n g thermals reappeared.
The
frequent bombardment of the interface at the same location by the heated thermals was s i g n i f i c a n t l y reduced.
Hence, a smooth, but not necessarily f l a t ,
s o l i d - l i q u i d interface was produced during melting late in the process. Conclusions Regularly arranged Benard convection cells were observed early in the process.
A flow in these cells produced a melting front which was distributed
with numerous hemispherical-capped cells.
The cells grew in size and combined
with neighboring ones as the melting progressed.
Temperature fluctuation
measurements suggested that at that time, the kinetic energy of the heated (cooled) thermals generated near the thermal boundary layer was completely dissipated in the turbulent core (mixed layer) region by viscous dissipation. The persistent horizontal motion of the thermals produced a nearly plane i n t e r face.
Forlowboundarytemperatures, bombardment by the thermals made the i n t e r -
face irregular. References [I]
C. Gau and R. Viskanta, "Flow visualization during s o l i d - l i q u i d phase change heat transfer.
I.
solidification
in a rectangular cavity," Let.
Heat Mass Transfer (this issue). [2]
A.G. Bathelt and R. Viskanta, "Heat transfer and interface motion during melting and s o l i d i f i c a t i o n
from a finned heat source/sink," J. Heat
Transfer 103, 720-726 (1981). [3]
Y.C. Yen, "Free convection heat transfer characteristics in a melt water layer," J. Heat Transfer 102, 550-556, (1980).
190
[4]
C. Gau, R. Viskanta and C.-J. Ho
Voi~ i0, NO. 3
T.Y. Chu and R.J. Goldstein, "Turbulent convection in a horizontal layer of water," J. Fluid Mech. 60_0, 141-159, {1973).
[5]
H. Tanaka and H. Miyata, "Turbulent natural convection in a horizontal water layer heated from below," Int. J. Heat Mass Transfer 23, 1273-1281
(1980).
(b)
(d)
(c) Figure 4.
Temperature f l u c t u a t i o n measurements during melting from below: a) thermocouple located 2.8 mm above the bottom p l a t e , t r a n s i t i o n from c e l l u l a r to turbulent flow, b) the trace shows the s i g n i f i c a n t upward and n e g l i g i b l e downward spikes in temperatures, c) thermocouple located 24 mm above the bottom plate -- the two downward arrows representing the adjustments of the temperature f l u c t u a t i o n s in the range of the recorder, the two upward arrows indicating the time interval when the thermocouple is in the thermal boundary layer; d) the downward temperature spikes have been s i g n i f i c a n t l y reduced, and the amplitude for both the upward and the downward temperature spikes are about the same.