0735-1933/90 $3.00 + .00 Printed in the United States
INT. COMM. HEAT MASS TRANSFER Vol. 17, pp. 637-645, 1990 ©Pergamon Press pie
GRAVITY-ASSISTED MELTING IN A HORIZONTAL CYLINDER HEATED BY EXTERNAL FORCED CONVECTION
J . J . Maldonado Unversldad Francisco de Paula Santander, Colombia
S. Sengupta, S.K. Roy Department of Mechanical Engineering University of Miami, Coral Gables, FL 33124
(Communicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT The results of an experimental study of melting of a free solid in a cylinder heated by external forced convection have been presented. The ranges for the average wall Stefan number and Archimedes number have been varied between 0.026 to 0.053 and 8.76xi06 to 3.34xi08 respectively. Multiple runs have been made for most of these cases using different values of Reynolds number and free stream temperature to obtain the desired average wall Stefan number. Though the melt rate is almost identical to that for the isothermally heated capsule in about half the tests, it is strongly affected by the dynamics of the melting process in other cases, where two different melt patterns are observed.
Introduction There are a large number of engineering problems where one encounters a change
in phase from solid to liquid and vice-versa.
include materials processing operations storage
systems,
cooling, etc.
temperature
Typical applications
such as casting,
thermal energy
control units for electronics and spacecraft
Latent heat storage systems using phase change materials have
been the object of a number of studies over the last decade because of their high energy density, their isothermal behaviour during charging and discharging,
and
their
ability
to t r a n s f e r
the stored energy with a limited
temperature difference as the driving force. A number of experimental and theoretical studies of the melting process in enclosures have been done over the years.
Extensive reviews on the phase
change process related to problems in thermal energy storage have been published by Viskanta
[i] and Sengupta and Roy
conditions with an isothermal
[2].
For typical operating
enclosure wall, previous studies have shown
that the solid phase of the phase change material usually drops down as it melts due to its higher density (or rises up if the solid phase density is lower than the liquid phase density).
As a result, 637
conduction between the
638
J.J. Maldonado, S. Sengupta and S.K. Roy
Vol. 17, No. 5
enclosure wall and the solid core which remains close to the wall is the dominant mode of heat transfer.
Problem Definition
In practical thermal energy storage systems, perature
is extremely unlikely.
an isothermal wall tem-
Heat addition under most circumstances will
be achieved by forcing air over the phase change capsules.
Thus the melting
process when the heat transfer from the wall is by external forced convection is of practical importance.
The melting process in general will vary depend-
ing on the direction of the flow with respect to the gravity vector.
If the
flow is symmetric about the vertical axis, the theoretical model developed for the isothermal wall temperature case can be easily modified to obtain the appropriate correlations. vertical direction, process.
On the other hand,
if the flow is not in the
asymmetry may cause drastically change the melting
In this technical note, results of a study of the melting process
in a horizontal cylinder are presented.
As opposed to the isothermal wall
condition used in earlier works, melting in this investigation is induced by forced convection heat transfer from air flowing in the horizontal direction past the tube (Fig. i).
L
+T1
u ..........
T4 ~>il\
.
T2
FIG I The geometry
Vol. 17, No. 5
GRAVITY-ASSISTED M E L T I N G IN A C Y L I N D E R
639
Experimental Auuaratus
The test cell consisted
of a 40mm long copper
tube with different
diameters containing n-octadecane as the phase change material. closed at both ends by 3.175mm thick plexiglas
to minimize
The tube was
end effects
and
permit visualization and photographic recording of the melting process. test cell was installed in the test section of a wind
tunnel where
The
the air
velocity
was controlled by an autotransformer connected to the blower motor
circuit.
The air was heated by a wire resistance mesh,
which was controlled by another autotransformer.
the voltage
across
Extension tubes of the same
diameter as the test cell were used in order to ensure two-dimenslonal past
flow
the test cell and to locate the test cell at the center of the tunnel
test section.
Complete details of the experimental apparatus
are given in Maldonado
and procedure
[3].
Results and Discussions
Experiments were conducted for eight different combinations of average wall Stefan number and Archimedes number. Stefan number
and Archimedes
3.34xi0 s respectively. binations
using
The ranges
number were 0.026
Multiple runs were made
different
values
for the average wall
to 0.053
and 8.76x106 to
for five of the eight com-
of Reynolds
number
and free stream
temperature to obtain the desired average wall Stefan number.
A summary of
experimental parameters are given in Table i. Results for the variation of melt volume with time were lowed
three
slightly
different
patterns.
In general,
found to fol-
the v a r i a t i o n
temperature over the capsule wall was not large (< 5% in all cases), overall
melting process
uniform wall temperature. very
similar
Fig. 2.
is very similar
to that seen for the case with
For more than half the tests,
to that for the isothermal
in
and the
the melt rate was
wall temperature case as shown in
The deviation from the correlation of Bareiss and Beer [4] is quite
small and can be attributed to the non-uniform Stefan number at the wall. A second pattern is seen in all except Here
two of the remaining
tests.
the melt rate is distinctly slower during the initial stages of melting
as shown in Fig. 3. the location
The reason for this is obvious from Fig.
of the interface
4 which
melting process is seen to be distinctly asymmetric during the early of the melting process.
shows
at different times for a typical case.
As a consequence,
for the constant wall temperature case.
The
stages
the melt rate is slower than that
As the melting progresses,
the solid
core slowly repositions itself at the bottom of the capsule and the melt rate increases.
In an extreme case (Test i),
this repositioning
occured
after
C 0 Z
t
"0
E
~e C
c 0
1E
$
.+~
o>
IE :3
I
m >
6"
0
•
0/ 0 0 0
T
•
011+~
/
0O
N o n - d i m e n s iona~
I 0.5
•
°
•
70 7b 8
Analyti.cel
Test Test Test
lb 2a 2b 2c Test 4a
Test Test Test Test
(MtD2/u) FIG. 2
time
1 I
:
!
0
1.5
I
(Barelss
and Beer
(1984))
Comparison of experimental results with theoretical correlation for cylinders with uniform wall temperature: Cases with comparable melt rates
0.2
0.4
0.6
0.8
o [3
0
Z
n
< o
0
9
0
O~
I C 0 Z
E °-
0
41
.ao
0 >
qD E
!
0
//
o ,
o
°
0
D 0
~,_
÷
,,
,o
o
"
I 0.5
Non-cl~mensionol
I
FIG. 3
_
AnolytTcol
T e s t lo Teat lc T e s t 30 T e s t 3b Test 5
tTme (MtD2/~,)
1
_~
~ .:'o o -I-
o
13
1.5
I
(Barelss
o
and
o
Beer
(198¢))
Comparison of experimental results with theoretical correlation for cylinders with uniform wall temperature: Cases with slower initial melt rates
0
0.2
0.4
0.6
0.8
&
>
L~
Z P
642
J.J. Maldonado, S. Sengupta and S.K. Roy
Vol. 17, No. 5
TABLE I Experimental Parameters
No.
Re
Ste
Ar
Ste w
Pr
la.
4.6xi0 s
0.092
1.25xi0 ?
0.026
50.9
lb.
6.5xi0 s
0.065
1.25xi07
0.026
50.9
Ic.
1.5xlO s
0.096
1.26x10 T
0.026
50.9
2a.
4.1x10 s
0.096
1.70x107
0.035
50.9
2b.
4.6xi0 s
0.12
1.70x107
0.035
50.9
2c.
4.1x10 s
0.10
1.70x10 T
0.035
50.9
3a.
7.2xi0 s
0.089
5.96xi0 ?
0.039
50.9
3b.
2.9x10 s
0.087
5.88x10 ?
0.039
50.9
4a.
1.6x10 s
0.12
8.76xi0 e
0.039
50.9
4b.
3.5xi0 s
0.i0
9.01xlO s
0.040
50.9
5.
7.8xi0 s
0.091
6.08xi07
0.040
50.9
6.
3.5xi0 s
0.i0
9.68xi07
0.043
50.9
7a.
5.9xi0 s
0.13
3.93xi07
0.043
50.9
7b.
2.4xi0 s
0.i0
3.97xi0 ?
0.044
50.9
8.
l.lxlO 4
0.15
3.34xi08
0.053
50.9
U T
FIG. 4 Asymmetric melting:
Interface locations at different times (Test la)
Vol. 17, No. 5
GRAVITY-ASSISTED MELTING IN A CYLINDER
643
more than half the solid had melted, and the overall melt time was 50% more as shown in Fig. 3. The time after which the solid repositions itself was unpredictable, and is probably governed by a number of parameters which need further investigation.
These include surface properties such as roughness, the local
variation of wall Stefan number, end effects, the exact initial condition as well as possible vibrations of the capsule due to the air flowing past it. Finally, in two of the experiments (Fig. 5), the melt rate was found to be significantly higher than that predicted by the correlation of Bareiss and Beer [4].
No reason for this is readily apparent at this point.
Conclusions
Results from an experimental study of melting in a horizontal cylinder heated by external forced convection have been presented in this paper.
The
melt rate was found to be almost identical to that for the isothermally heated capsule in about half the tests.
In general however, the melt rate
seemed to be strongly affected by the dynamics of the melting process as two different patterns were seen in the remaining tests.
In most of these cases,
the melt rate during the initial stages of melting was significantly lower than expected.
An analysis of the experimental results suggested that this
was due to asymmetric melting during this period. tests,
In the two remaining
the melt rate was found to be significantly higher than expected.
This faster rate of melting could not be explained based on the experimental data.
Nomenclature
Ar
C P
Archimedes number (Ps-
9)gDS/V2Ps
Specific heat of liquid
D
Diameter of cylinder
Mt
Melt time parameter
Pr
Prandtl number
Re
Reynolds number UD/v a
((Step/PsPr)SAr)-*/4
v/a
Ste
Stefan number Cp(T - Tf)/hf
T
Temperature
U
Free stream velocity of air
V
Volume
g
Gravitational constant
hf
Latent heat of melting Thermal diffuslvity of liquid
E
O >
E
I
"10 t c 0 Z
E °-
¢-
tO 0-
v
0
O
Non-dimensional
I 0.5
n
4b
6 Analytical
Test Test
(MtD2/u) FIG. 5
time
l 1
O
o
..I 1,5
(Bareiss
and Beer ( 1 9 8 ¢ ) )
Comparison of experimental results with theoretical correlation for cylinders with uniform wall temperature: Cases with faster melt rates
0.2
0.¢
0.6
0.8
O
2
rJ~
O
Z
<
O
~O
P
O
O~ 4m 4~
Vol. 17, No. 5
GRAVITY-ASSISTED MELTING IN A CYLINDER
w
Kinematic viscosity of liquid
p
Density
645
Subscripts a
Air
s
Solid
w
Wall (average) Free stream
References i. R. Viskanta, Solar Heat Storaze: L a t e n t Heat Materials. Ed., p. 153, CRC Press, Inc., FL, (1983).
Vol.l,
G. Lane,
2. S. Sengupta and S.K. Roy, "Energy Storage Systems"._ NATO ASI Publ. Set. E., B. Kilkis and S. Kakac, Ed., p. 383, Kluwer Acad. Pub., Dordrecht, (1989). 3. J.J. Maldonado, Exverlmental Invest%ga~ion of the Melting Process Inside a Horizontal Cylinder, M.S. Thesis, University of Miami, FL, (1986). 4. M. Barelss and H. Beer, Int. J. Heat Mass Transfer, 2_/7, 739, (1984).