INT. a3MM. HK~T MASS TRANSFE~ 0735-1933/87 $3.00 + .00 Vol. 14, pp. 437-446, 1987 @Pergamon Journals Ltd. Printed in the United States
FREEZING OF WATER AND WATER-SALT SOLUTIONS AROUND ALUMINUM SPHERES
S. Chellaiah and R. Viskanta Heat Transfer Laboratory School of Mechanical Engineering Purdue University W. Lafayette, IN 47907.
(Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT The freezing of water and salt (sodium chloride) solutions around aluminum spheres inside a tube kept in a pool of phase change material is experimentally investigated. Photographic observations reveal a faster rate of freezing inside the tube than outside the tube. In the case of water, ice formed around each sphere is in the form of an envelope of uniform thickness. With salt water solution no such envelope is observed.
Introduction
The study of solid-liquid phase change has received considerable research attention due to a wide range of engineering and geophysical applications [1]. ~ Yet, despite the numerous applications of solid-liquid phase change in !!quid saturated porous media, relatively few studies ha:ve been conducted [2-5]. When the thermal conductivities of the phase change material (PCM) and the porous medium differ considerably, the existence of directional solidificatioa , is speculated.
437
438
S. Chellaiah and R. Viskanta
The
Vol. 14, No. 4
freezing of pure wa~er with a l u m i n u m spheres c o n s t i t u t i n g the porous
m e d i u m in a r e c t a n g u l a r cavity was e x p e r i m e n t a l l y studied.
The ice formed was
p h o t o g r a p h e d a t different times during the freezing process. The p h o t o g r a p h s showed different s t r u c t u r e s along the thickness of the ice layer. Also, when only a p a r t of the PCM
inside the test
examined.
cell was frozen, the surface of the interface was visually
It was not p l a n a r as in the case of freezing of pure w a t e r b u t u n d u l a t e d as
shown in Fig.1. No directional solidification was observed, b u t for the u n d u l a t i o n , a n d the thickness of ice was the same a t all horizontal planes when the porous m e d i u m was s a t u r a t e d with the liquid P C M a t the fusion t e m p e r a t u r e .
Top
Surface
Ice7 LiquidPCM
0
Bottom of Test Cell Row of Aluminum Spheres Close 1o Interface
FIG.1 S c h e m a t i c r e p r e s e n t a t i o n of u n d u l a t e d interface between ice a n d w a t e r during freezing of w a t e r s a t u r a t e d porous medium. T e m p e r a t u r e m e a s u r e m e n t s revealed t h a t some supercooling of the l i q u i d t a k e s place, a n d the d e t e r m i n a t i o n of the interface location by the t h e r m o c o u p l e - r e a d - o u t m e t h o d is not possible.
Some thermocouples which were located in w a t e r i n d i c a t e d
Vol. 14, No. 4
FR~ZINGC~-~A~D~%TER-SALTSCLUTICNS
439
temperatures below 0 ' C , misleading the experimenter to conclude that ice layer has propagated upto this particular thermocouple junction.
Hence, to gain more complete
understanding of the freezing process, when the thermal conductivity of the solid differs by more than two orders of magnitude from that of the liquid, an experimental study of freezing around a single row of aluminum spheres surrounded by water and water-salt (NaCI) solutions was undertaken. Experimental Apparatus and Procedure
Solidification experiments were conducted in a rectangular test cell with inner dimensions, 131 mm in height, 163 ram in width and 40 mm in depth.
The two
vertical walls consisted of two copper heat exchangers that fitted snugly into the test cell. There was hardly any clearance between their surfaces and the front and back walls.
Glass plates, 6 mm thick covered the front and back of the test cell.
A
horizontal Plexiglass tube, 38.1 mm outside diameter and 3.2 ram wall thickness and 115 mm long spanned the width of the test cell bridging the two heat exchangers. As the length of the tube was just equal to the gap between the two heat exchangers, there was no need for any vertical support to keep the tube horizontal. A schematic of the test cell is shown in Fig.2. Copper-Constantan thermocouples placed at the center of the heat exchangers monitored their temperatures continuously.
The test cell was covered with 50 mm
thick Styrofoam insulation on all sides to minimize heat losses to the ambient.
Two
windows were provided on the front and back of this insulation to facilitate photographic and visual observations.
A mixture of ethyl-alcohol and water was
circulated through the heat exchangers, from two constant-temperature baths.
The
test cell was placed on an iron plate, fitted with levelling screws to eliminate the effect of inclination of the cell on the convection currents. Four solid aluminum spheres of 28 mm average diameter were placed inside the tube. These spheres were kept in contact with each other. As the tube inner diameter was 32 mm and the average sphere diameter was 28 mm, there was an average clearance of 4 mm at the top of the spheres.
But, it should be noted that this
clearance was not uniform around the outer surface of the spheres as the spheres were resting on the bottom of the tube.
Two small holes were drilled in the tube wall, to
facilitate entry of liquid into the surrounding pool.
440
S. Chellaiah and R. Viskanta
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FIG.2
Schematic of the test cell. Experiments were performed with both water and salt (research grade sodium chloride) solution of different concentrations. The spheres were placed inside the tube in contact with each other and the tube was kept horizontally inside the test cell. Distilled and degasified water was used. mixed
with
requisite
amount
In preparing salt solution, the water was
of sodium
chloride
to
obtaiu
the
desired
salt
concentration. This PCM was carefully siphoned into the test cell without introducing any air bubbles into the system. The test cell was placed on the levelled plate and covered with insulation. Alcohol-water mixture from two temperature controlled baths was circulated through each heat exchanger.
The temperature was controlled within :h 0.1°C. For
all the experiments the initial condition was 0 ° C. For salt solutions, the initial 0 ° C ,
Vol. 14, NO. 4
FREEZ~
OF ~
AND ~TER-SALT SOLUTIONS
d e n o t e d different a m o u n t s of s u p e r h e a t depending on the c o n c e n t r a t i o n .
441
Sumcient
t i m e was allowed to a t t a i n this desired initial condition before freezing was i n i t i t a t e d . A t h i r d c o n s t a n t t e m p e r a t u r e b a t h was m a i n t a i n e d a t a t e m p e r a t u r e close to the desired wall t e m p e r a t u r e for initiation of freezing. Once the initial condition has been achieved, the e x p e r i m e n t was s t a r t e d by switching the s u p p l y from the t h i r d b a t h to one of the h e a t exchangers, where the freezing is to be i n i t i a t e d . The o t h e r h e a t e x c h a n g e r was left u n d i s t u r b e d .
P h o t o g r a p h s were t a k e n a t different times using
Nikon c a m e r a equipped with a macrolens a n d K o d a k 400 A S A film.
W i t h the
macrolens the o b j e c t to be p h o t o g r a p h e d can be as much as 50 m m from the lens a n d focussing becomes very critical. A small m o v e m e n t of the c a m e r a d i s t o r t s the field of view or changes the magnification.
The insulation covering the window was r e m o v e d
j u s t for the time needed to m a k e observations. Results a n d Discussion Freezin~ of P u r e W a t e r Two different experiments, with different cold wall t e m p e r a t u r e s o f - 8 . 4 0 C - 1 3 . 1 ° C , respectively, are discussed.
and
Since a t the s t a r t of the experiment, the w a t e r
was a t the fusion t e m p e r a t u r e , n a t u r a l convection is a b s e n t in the s y s t e m a t a n y t i m e during the freezing process. The interface motion was always p l a n a r a n d a t very e a r l y times h a d the same thickness, b o t h inside a n d outside the tube.
A f t e r a b o u t 15
minutes, the ice was significantly thicker inside the tube t h a n outside it. The progress of the interface motion t r a c e d from the p h o t o g r a p h s is shown in Figs. 3a t h r o u g h 3d. A f t e r 35 minutes the ice inside the tube h a d covered p a r t of the first sphere a n d formed an envelope a r o u n d its circumference (Fig. 3a).
This envelope o f ice h a d a
fairly uniform thickness a r o u n d the sphere. A f t e r 45 minutes (Fig.3b) the ice h a d fully covered the first sphere, a n d w a t e r a r o u n d the second sphere was p a r t i a l l y frozen forming an envelope of ice a r o u n d it. Thus, inside the t u b e the interface was no longer well defined. T h e r e were t h r e e regions : zone 1 of fully frozen ice, zone 2 a r o u n d the second sphere where b o t h w a t e r a n d ice were p r e s e n t a n d zone 3 containing pure w a t e r (Fig. 3b). In the second zone, t h e w a t e r a n d ice could be clearly seen a n d should not be confused with the m u s h y zone e n c o u n t e r e d during the freezing of some salt solutions, where b o t h solid a n d liquid phases coexist. Around each sphere, the w a t e r froze first Forming an envelope
442
S. Chellaiah and R. Viskanta
a)
b)
c}
d}
Vol. 14, No. 4
FIG.3 P r o p a g a t i o n of the ice-water interface with time T W = - 8 . 4 " C: a) t z 3 5
min,
b) t - ~ 4 5 min, c) t----60 min a n d d) t----100 min. a n d this envelope grew o u t w a r d s until it reached the inner surface of the tube. W h e r e a s , outside the tube, the freezing p r o p a g a t e d a t a slower, r a t e a n d the interface was always p l a n a r . Figure 3c shows the ice front at 60 minutes into the freezing process, a n d Fig. 3d a t 100 minutes into the process. In the e x p e r i m e n t with a lower wall t e m p e r a t u r e (T w = - 1 3 . 1 ° C ) , freezing was faster.
the r a t e of
T h e q u a l i t a t i v e observations were similar to those seen for the
e x p e r i m e n t with a lower wall t e m p e r a t u r e of T w = --8.4 " C. T h e s t r u c t u r e of ice v a r i e d with the r a t e of freezing. In the e x p e r i m e n t with T w ~-- - 8 . 4 ° C , the ice h a d a smooth, soft t e x t u r e devoid of a n y macroscopic s t r u c t u r e . T h e envelope of ice a r o u n d each sphere was clear a n d well defined, a n d its p e r i p h e r y was d i s t i n c t l y c o n t r a s t e d with the w a t e r surrounding it.
VOl. 14, NO. 4
FREEZING (~ ~ T E R
AND ~ T E R - S A L T SOIIEIONS
443
In the experiment with T w = -13.1° C, four different structures were observed across the width of the test cell from the cold to the hot wall. Outside the tube and near the cold wail, ice was translucent with no grains,
but near the ice-water
interface, some needle-like grains (resembling random scratches made on a glass plate) were noted. Inside the tube, random vein like structure was seen along the tube axis. But, as before, the partially frozen envelope surrounding the sphere was very clear (Fig. 4a).
FIG.4 a) Photograph of the partially frozen envelop of ice surrounding the sphere for freezing of water, T w -- - 1 3 ' C at t--~ 120 min. b) Photograph of ice-water interface for freezing of 5% salt solution, T w = - 1 0 . 3 ' C at t:5
min.
Freezing of Salt Solution
Two different experiments with salt
concentrations of 5~o and
10a/o and
respective cold wall temperatures o f - 1 0 . 3 ' C and -12.8°C, are discussed.
Since the
freezing point of salt solution is a function of its concentration, the 5% and 10% solution have freezing points o f - 2 . 9 7 ' C
a n d - 6 . 5 4 ' C, respectively [6]. The initial
temperature of salt solution was 0 ° C for both the experiments.
This translates to a
superheat of 2.97°C and 6.54°C for the lower and higher concentration solutions, respectively.
As the solution freezes, most of the dissolved salt is rejected at the
interface and only pure water freezes to form ice. There may be some entrapment of small packets of salt solution in the frozen region.
444
S. Chellaiah and R. Viskanta
Vol. 14, No. 4
The progression of the freezing process for the experiment with the lower wall temperature (T w = - - 1 0 . 3 ° C ) is shown in Figs. 5a-5d. time after the onset of freezing.
The ice was planar for a short
Even after five minutes into the experiment, the
influence of convection was seen on tile shape of the interface (Fig.4b). freezing inside the tube was higher than t h a t outside.
The rate of
As water freezes, there is a
continuous rejection of salt
at the interface, thereby continuously increasing its
concentration
freezing
and
lowering
point
of the
solution.
The
difference
in
concentration between t h a t near the interface and t h a t near the hot wall causes solutal convection with the low concentration solution rising upwards along the hot wall and the higher concentration solution (also the heavier solution) descending downwards along the interface.
This results in the variation of both temperature and
concentration along the interface, with the temperature at each point being equal to the freezing point corresponding to the local salt concentration. As the cold wall temperature is maintained constant, with decrease in freezing point, the rate of freezing also drops. This explains the lower freezing rates evident at the b o t t o m of the test cell than at the top. This is in contrast with t h a t observed for pure liquids (except water), which freeze faster at the top than at the bottom. the thermal
Also,
convective flow is in the same direction as the solutal convection.
Comparison of the two experiments shows t h a t the curvature of the interface near the b o t t o m of the test cell is more prominent in the latter (with 10% salt solution) case. Inside the tube, the freezing rate was faster.
The water near the top of the
spheres froze faster than t h a t at the bottom, indicating the influence of convection inside the tube also. But, the difference in the rates of freezing outside and inside the tube was only moderate, compared with the corresponding difference for water. The effect of convection becomes weaker at later times.
The heavier (higher
concentration) salt solution settles down to the b o t t o m of the test cell, and the solution
becomes
stratified.
Furthermore,
with
the
wall temperature
remaining
constant, at later times the rate of heat conduction through the liquid is equal to t h a t in the solid.
The decrease in freezing point with increasing concentration promotes
earlier a t t a i n m e n t of steady state conditions than in the case of pure water for the same a m o u n t of superheat and imposed boundary temperatures.
Vol. 14, No. 4
FREEZING OFWATERA~Dg~%TER-SALTSfEL'I~ONS
a)
445
b)
~- Ice
•
Salt Solution---~
~-Aluminum Spheres
C)
d)
FIG.5 Solid-liquid interface motion during freezing of 5~o water-salt solution, T w = -10J3 °!C, a) t = 4 5 min, b) t = 5 0 min, c) t = 9 5 min and d) t = 2 1 5 min. Comparison of Freezing of Water and Salt Solution A number of differences were observed between the freezing of pure water and salt solution. Since water was at saturated conditions at the start of the experiment convection was absent in the system. Whereas, with salt solution both thermal and solutal convection influenced the shape of the iti~erface. The temperature of the interface along a vertical plane was not constant for the salt solution because of variation in salt concentration. During the freezing of water inside the tube, ice nucleated on tile surface of each sphere in the form of an envelope surrounding the sphere. This envelope waj uniformly thick around the circumference of the sphere. No envelope was evident the
446
S. Chellaiah and R. Viskanta
Vol. 14, No. 4
during freezing of salt solutions. For water the difference between the rates of freezing outside and inside the tube, increased with time at a much faster rate, and the structure of ice varied along the width of the cell. Freezing of salt solutions revealed no particular ice structure. Conclusions Freezing of pure
water
investigated experimentally. observed.
and
salt solution
around
aluminum spheres
was
In both the cases, no directional solidification was
In the case of water, ice formed around each sphere producing an ice
envelope of uniform thickness.
The rate of freezing was faster inside the tube than in
the pure PCM outside it.
References
1.
R. Viskanta, Solar Heat Storage : Latent Heat Materials, Vol.1 (Edited by G.A. Lane), p. 153. CRC Press, Boca Raton, Florida (1983).
2.
M.E. Goldstein and R.L. Reid, Proc. Roy.Soc. 364A~ 45 (1978).
3.
M. Okada and T. Fukumoto, Trans. J a p a n Soc. Mech. Engr. 48B~ 2041 (1982) (in Japanese).
4.
J.A. Weaver and R. Viskanta, J. Heat Transfer 104, 654 (1986).
5.
J.A. Weaver and R. Viskanta, Int. J. Heat Mass Transfer 29__~,1943 (1986).
6.
Dean, J.A., Lanse's Handbook of Chemistr~¢, p.10. McGraw Hill Book Co., New York (1979).