Gravity-assisted melting in a horizontal cylinder heated by external forced convection

Gravity-assisted melting in a horizontal cylinder heated by external forced convection

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 ...

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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).