The effect of magnetic stabilization on the thermal behaviour of fluidized beds

Chemical Engineering Science. Vol. 42, No. 6, pp. 1501-1506, Printed in Great Britain.

THE

1987. Q

EFFECT OF MAGNETIC THERMAL BEHAVIOUR

STABILIZATION OF FLUIDIZED

000%X09/87 1987 Pergamon

$3.00 + 0.00 Journals Ltd.

ON THE BEDS

JOSEP ARNALDOS, MANUEL LAZARO and JOAQUIM CASAL Chemical Engineering Department, Universitat Politkcnica de Catalunya, Diagonal 647, 08028-Barcelona, Spain (Received 24 June 1986; in revised

form

15 September

1986)

Abstract-The effect of a magnetic field on the thermal behaviour of a fluidized bed of magnetizable particles with an immersed heating surface has been studied. The temperature distribution inside the bed has been determined, both in the radial and axial directions. A model has been developed which allows calculation of data. the effective thermal conductivity of the bed from experimental

INTRODUCTION In the last decade a considerable number of communi-

cations have been published in the field of magnetic stabilization of fluidized beds. The hydrodynamical behaviour has been extensively studied, as well as some applications. Nevertheless, little attention has been paid to the heat transfer. Due to the influence of the bubbles on the agitation inside the bed, however, considerable changes in heat transfer coefficients and in bed temperature distribution should be expected in the stabilized beds; in them, bubbling does not exist or is reduced to a controlled degree, in the case of the semi-stabilized beds, due to the action of the magnetic field. These changes can be very important in applications in which heat transfer is involved. A few results on particle-to-fluid heat transfer were published by Lucchesi et al. (1979) and Rosensweig et al. (1981), while Neff and Rubinsky (1983) studied the influence of stabilization on the wall-to-bed heat transfer coefficient, Recently, Arnaldos et al. (1986) studied the influence of different operating variables on this coefficient, proposing some correlations to calculate it for both magnetic particles and mixtures of magnetic and non-magnetic particles. In this paper the effect of stabilization on the temperature distribution is studied for beds with an immersed heating surface under fixed bed, bubbling fluidization, semi-stabilization and stabilization conditions. A model is developed to allow calculation of the thermal conductivity of the bed.

Fig. 1. The radial profiles of temperature at different heights (30, 60, 90 and 120 mm from the distributor) were measured by moving a thermocouple (chromealumel) inside the bed, to eight positions situated respectively at 6.5, 13.5, 20.5, 27.5, 42.5, 49.5, 56.5 and 63.5 mm along a diametral chord in the bed (Fig. 1); these measurements were effectuated on a diameter perpendicular to the plane of the heating system, as well as on two diameters at 45” with respect to that plane. The gas was always air at atmospheric pressure, previously dried and filtered. In all the tests, the magnetic field was switched on before initiating the gas flow. The height of the bed was always such that (L/D) > 2. The characteristics of the particles are summarized in Table 1.

0 0 0

0 0 0 0

0 0 0

0

EXPERIMENTAL

0 0

ARRANGEMENT

Heat transfer measurements were conducted in a stainless steel (non-magnetic) column, 70 mm i.d.; good gas distribution was obtained with a fixed bed of glass particles and a perforated plate (1 mm dia. holes). The magnetic field was supplied by an external coil, coaxial with the column (Arnaldos et al., 1985; Arnaldos, 1986); all the measurements were achieved therefore with the magnetic field lines parallel to gas flow. DC current at constant intensity was used. The heating system consisted of four stainless steel (non-magnetic) tubes, 6 mm o.d., installed as shown in

0 0 : 0

g2 6

Fig. 1. Experimental arrangement. (1) Bed column, (2) electrical coil, (3) calming section, (4) manometer, (5) filter, (6) rotameter, (7) drying, (8) temperature measuring system and (9) heating system.

1501

J~SEP ARNALD~S et aI.

1502

Table 1. Characteristics of the particles Material

(kg%‘)

Steel Sintered nickel

7500 5900

Shape factor

d

um/

CP,

(pm)

(m/s)

(J/kg K)

0.9 0.8

420-500 250-400

0.47 0.21

500 290

RESULTS AND DISCUSSION 1. Temperature distribution in the bed The radial and axial temperature distribution studied for a stabilized bed, semi-stabilized Auidized bed and fixed bed:

were bed, 360

(b) BubblingfIuidized bed. Figure 3 shows temperature profiles observed in the regime of typical bubbling fluidization. The isothermicity is good, as expected, except near the distributor where a fixed bed zone existed. (These results were obtained at velocities near incipient fluidization, in order to keep (u/u,,) similar to the value of (U/L+,)at which the semi-stabilized bed was operated.)

fixed bed sintcred nickel 250 < d < 400

:

H

500

-

=

0

fluidized bed sintercd nickel 250 t.irnmddC4OO~m

0000 __..Q._____.____ I 120 mm

H

:

(a) Fixed bed. The radial profile of temperature on a diameter perpendicular to the plane of the heating system, at different heights (Fig. 2) shows how, due to the lack of agitation, the air flowing near the heating surface is hotter, its temperature decreasing as the distance from this surface increases. The effect of the lack of bubbles can also be observed in the axial profile: the temperature of the gas increases as the fluid flows through the bed and the distance from the distributor increases, this effect being larger near the heating surface.

thermocouples Dosition

thermocouples position

j~rn

A/m

I = 120mm

360 360

r I-360 380

q

i

a--

1

=

------

q

mm

90

i

_,--

--_,

I -.-.-..-. --.... ._ ._.... _~_______ _._...___. _.._-. I = 60mm

I

-<--

----•\

360 _.._.___ _._..... ___._. _.__ ._

350

A/m

4 .._.._... _._.._. . . ..____ I

B-

370

0

1 y*

‘=y.P-

8

30

1

I

20

_ ___.__

I

I

10

I

0 r,mm

10

20

30

Fig. 3. Radial temperature profiles at different bed heights in a iluidized bed (U = 0.23 m/s; U/U,, = 1.1). Points indicate experimental data, and lines are drawn from the proposed model.

(c) Semi-stabilized bed. At a fluid velocity higher than that corresponding to the velocity of the gas at which the action of the magnetic field is partially overcome and bubbles appear, called the “transition velocity”, I+,, the bed is in a “semi-stabilized” regime. In this case, temperature profiles are similar to those for a fluidized bed (Fig. 4); the condition depends on (u/u,), this parameter playing a role similar to that of (u/u,/) in a typical fluidized bed.

400

_______. 400 Y

-

I = 90 mm

_._..____.L_

I~

i

-

400

-

300

-

400

-

300

-

_____ I=60mm

____

.

. .._.........

-._

I

-.--+

I-300

_ .

-2.,

_ _..._......._._

,.--

1

=.i._

.~.~~.~~~1~~.~~

..__

.-j I=30mm

i

._.----I 30

I 20

I Kl

0 r, mm

-•\ 1 10

1 20

I 30

Fig. 2. Radial temperature profiles at different bed heights in a fixed bed (U = 0.17 m/s). Points indicate experimental data; lines are drawn according to the proposed model.

bed. The behaviour of a stabilized (d) Stabilized bed is similar to that of a fixed bed, although the variation of temperature is smoother (Fig. 5); this is probably due to a certain degree of movement of particles inside the stabilized bed, as suggested by Zrunchev and Popova (1983), which improves the heat transfer and decreases the temperature difference, as well as to the effect of the higher gas velocity. The action of the magnetic field can be seen in Fig. 6. As the magnetic field intensity increases, the temperature profile becomes more abrupt; this effect should be attributed to the greater stabilization, with a higher restriction in the movement of particles and an increase in bed voidage. The comparison between the behaviour of the different regimes can be seen in Fig. 7, where the

Effect

1503

swrist&iGzed bed sintered nickel

thermocouples position

:

000

of magnetic stabilization on fluidized beds

0

Q

250 /.Wn <

d

H=

Aim

4000

<

400

)Im

~_~~~ Y

371 ):

e3% I-

,

371 iY t-351 3I

Fig. 6. Influence of the magnetic field intensity on the radial temperature profile in a stabilized bed.

3% I-

331 IL __..._..._

_

.._.._..-..-..

_;________

.__.

_

.

.

.

..--...

341 3-

425

31 O-

1

Fig. 4. Radial temperature profiles at different bed heights in a semi-stabilized bed (u = 0.58 m/s; u/u, = 1.1). Points indicate experimental data, and lines are drawn from the proposed

H

0000 ._.___

120mm

q

351D-

=

LOOOAfm

//

.

I-37! j3251 321537 5*-

___________________________ ____.__..__.-.--..- -. I = 60mm

a_-----c

32 535 O-

-0

0

stabilized

.

swnistabhod

(uhmf

bed

(H bed

= 1.1)

-4000

A/ml

(H = 4000

A/m,%=l.l)

_..-. -7 ./

t 30

I m

1

10

0 r,mm

I

I

I

10

20

30

I

bed

u=

-=--a-._ L

I

30

fixed bed fluidized bed

Fig. 7. Radial temperature profiles under the different u = 0.29 m/s; 0, u = 0.52 m/s; 0 , conditions (0, 0.58 m/s; I, u = 0.93 m/s).

-*-

I =Xlmm _,*-

30 .o -

. o

:

u’ch, = 1.3 _ ___...--._....-....-.-

---a \

LO( I-

Y

d
=90mm

.

stabilized bed sintercd nickel 250 pm
:

I

t

model.

thermocouples position

a .____.._____________

steel ) 420pm<

20

10

I

0 r,mm

1

I

I

10

20

30

Fig. 5. Radial temperature profiles at different he-dheights in a stabilized bed (u = 0.27 m/s). Points indicate experimental data; lines are drawn from the proposed model.

temperature profiles have been represented for a given value of the distance to distributor, with the same scale. Although these temperature profiles are subject to the influence of gas velocity, which has different values for obvious reasons, this figure shows again the negative influence of the magnetic stabilization on the thermal behaviour of the bed, displaying how the magnetic field increases the lack of isothermicity as compared with a

fluidized bed. The temperature distribution of the stabilized bed shows an abrupt variation as compared with the fluidized bed. (In both situations the gas velocities were of the same order of magnitude.) The abrupt temperature profile shown by the fixed bed as compared with the stabilized bed can be attributed to the higher gas velocity. The behaviour of the semistabilized bed is similar to that of the fluidized bed, showing practically the same trend in their temperature profiles. This is due to the fact that in both cases the degree of bubbling was approximately the same, since u/ub = u/u,, = 1.1; as the gas velocity was higher in the semi-stabilized bed, however, the temperatures in it were lower than in the fluidized bed.

1504

JOSEP ARNALWS

2. Efjkctive thermal conductivity The temperature distribution inside the bed and the heat transfer rate are strongly influenced by the effective thermal conductivity of the bed. This coefficient is a function of the thermal conductivity of the particles, the thermal conductivity of the gas, the bed voidage and the gas flow. A mathematical model was developed to allow the prediction of k,. For the heat transfer inside the bed, the equation of energy takes the following form: k,

a=T a2T p+>y2+=

a+T

aT -. = UPCPaZ

>

(1)

The first term of this equation accounts for the variation of temperature due to the heat conduction in the bed, in three directions, while the second term corresponds to the change in temperature due to the convection originated by the fluid flow. Since this situation corresponds to a stationary state, these terms are not a function of time. The contribution of the vertical conduction, a*T/a.z’, can be neglected due to the superimposed effect of the convection. On the other hand, due to the geometrical structure of the system, the temperature profile in the X-Y plane is symmetrical with respect to the heating system (Fig. S), changing as a function of the radius and of the angle at which it is measured; the cyiindrical. symmetry is therefore appropriate Equation (1) can be expressed as:

aT

k

>

= WC,%.

heating

stabilized steel

at

T=

z = 0,

T,,.

(3)

Figure 8 shows that there is symmetry with respect to the plane perpendicular to the heating system. The boundary conditions can be therefore defined for any quadrant in the bed (Fig. 9). The heat convection between the bed and the environment leads to the boundary condition: aT -= ar

r = R.

aT as’

at

0

0 = 90”.

The geometrical configuration of another boundary condition; coordinates, aT _= aY In cylindrical pressed as:

--

4 Sk,

coordinates, aT _= do

-~ 4r Sk,

at

(5)

the system gives in rectangular

y = 0.

(6)

this condition

at

can be ex-

8 = 0.

The last boundary condition is established for r = 0; in this case, assuming that the variation of Tas a function of 0 is negligible, the following expression is obtained:

system

aT _= dr

plm

A/m

-~

qsin8 Sk,

at

r = 0.

This model has been solved numerically, using finite differences, by an implicit procedure. The numerical solution was achieved by discretizing the system; the increments used, which keep the system stable, were AH = 5”, Ar = 4.375 mm and AZ = 0.5 mm. There

I=60mm

T.K

_q

Iheat

flow)

9=90*

T,K -RR

Fig. 8. Temperature profiles in a cross-section of a bed.

(4)

Assuming that there is no heat flow through the vertical plane perpendicular to the heating system, we may write

bed

, WOpm-500

Ii = 2000

situated; the flow of heat was therefore perpendicular to that plane, on its two surfaces. The initial and boundary conditions were next established. The inlet gas temperature is taken as room temperature; therefore

(2)

It was assumed that the heating surface was continuous over the X-Z plane in which the heating tube was

---.-

et al.

stabilized

Fig. 9. Heat flow in a bed quadrant.

y

Effect of magnetic stabilization on fluidized beds were 144 unknown

quantities

for each layer over the

An efficient method was used in order to get a short computer calculation time; the code system NAGLIB (Numerical computer Algorithm Group, 1983) was used, with a calculation time of approximately 1 s per cycle. To obtain the optimum values of k, an objective function was defined, which allowed minimization of the difference between the experimental value of temperature and the value calculated from this model. This objective function was expressed in terms of the relative error; as the absolute error usually increases with bed temperature as the distance to the distributor increases, it would not be adequate to be used in this function because of its unbalanced effect. The optimization was achieved through minimization of the parameter: whole

bed

1505

height.

1

P------.--------.

01

0

I

1000

2000

I

3000

I

4000

H.Alm

Fig. 11. Variation of the effective thermal conductivity as a function of the magnetic field intensity for different bed conditions.

Typical values can be seen in Fig. 10, where plotting of k, versus F allows an effective thermal conductivity to be obtained which gives the smallest error with the experimental data. The model agrees well with these data, as can be seen in Figs 2-5; in the worst case the standard deviation was 5.3 %_ The variation of k, with H can be seen in Fig. 11; from the value corresponding to a bubbling fluidized bed, k, decreases when H increases in the case of a stabilized bed. This change can be attributed to the increase in bed voidage due to the action of the

0.0030 l

d

fixed bed fluidized bed

nickel 25Opm - UY)pm

0.0025

F

0.0020

0.0015

0.0010

Fig.

10.

Plots showing best values of the effective thermal conductivity.

magnetic field, as well as to a probable diminution of movement of particles inside the bed, caused by increased stabilization. In the case of semi-stabilized bed, the decrease of kb is very low due to bubbling. CONCLUSIONS

The action of a magnetic field on a fluidized bed of magnetizable particles has an important influence on its thermal behaviour. The study of temperature distribution inside the bed has shown that a magnetically stabilized Ruidized bed with an immersed heating surface is not isothermal in both radial and axial directions; for the heating system used, the bed temperature decreases as the distance from the heating surface increases, this temperature profile becoming more abrupt as the distance from the distributor increases. This lack of isothermicity became also more significant as the magnetic field intensity increases. In the case of the semi-stabilized bed, the behaviour is similar to that of a fluidized bed. This behaviour is the result of the influence of a series of phenomena, the most important of which is the action of bubbles, and the corresponding lack of agitation in the stabilized bed. The effective thermal conductivity of the bed can be calculated from a mathematical model developed from the equation of energy. The numerical solution of this model has allowed the calculation of kb; the best values of this parameter have been obtained by optimizing an objective function. The temperature profiles calculated with these k, values agree very well with the experimental results. The effective thermal conductivity of the stabilized bed decreases as the magnetic field intensity increases, due to an increase in bed voidage and probably a diminution of particle movement. In the case of a semistabilized bed, the decrease of k, is very small due to the presence of bubbles. Acknowledgement-This paper is Part of the research project of the Institut d’estudis Catalans.

number 2214

1506

JOSEP ARNALDOS et al. REFERENCES

NOTATION

Amaldos, CP CPS

d F H h k, 4 R -; T TO U Ub I(mf x9

z P PP 0

Y

heat capacity of the gas, J/kg K heat capacity of the particles, J/kg! K diameter of the particles, pm parameter defined in eq. (9) magnetic field intensity, A/m heat transfer coefficient, W/m2 K effective thermal conductivity of the W/m K heat transfer velocity, W bed column radius, m radial (cylindrical) coordinate, m heat transfer surface area, m2 temperature, K room temperature, K fluid superficial velocity, m/s transition velocity, m/s minimum fiuidization velocity, m/s rectangular coordinates rectangular and cylindrical coordinate fluid density, kg/m3 particle density, kg/m’ angular (cylindrical) coordinate

J.,

1986,

Estudi

de

I’estabilitzaci6

dels

llits

flui’ditzats &lid-gas mitjanpnt I’aplicacibd’un camp mag-

bed,

nitic. Doctoral Thesis, Universitat Politt&nica de Catalunya, Barcelona. Arnaldos, J., Casal, J., Lucas, A. and Puigjaner, L., 1985, Magnetically stabilized fluidization: modelling and appliTechnni. 44, 57-62. cation to mixtures. Powder Arnaldos, J., Puigjaner, L. and Casal, J., 1986, Heat and mass transfer in magnetically stabilized fluid&d beds. In Fluidization V (Edited by K. Qstergaardand A. Sqkensen), pp. 425-432. EngineeringFoundation. New York. Licchesi, P. J., Hatch, W. H, Mayer, F. X.‘and Rosensweig, R. E., 1979, Magnetically stabilized bed-new eas solids contacting technology. Proc. of the 10th World Petroleum Congress. Bucarest, vol. 4, pp. l-7. Neff, J. J. and Rubinsky, B., 1983, The effect of a magnetic field on the heat transfer characteristics of an air fluid&d bed of ferromagneticparticles.Int. J. Heat Mass Transfer 26, i885-1889. Numerical Algorithm Group, 1983, NAG FORTRAN Library Manual. Oxford University. Rosensweig, R. E., Siegel& J. H., Lee, W. K. and Mikus, T., 1981, Magnetically stabilized fluidized solids. A.f.Ch.E. Symp. Ser. 77, 8-16. Zrunchev, I. and Popova, T., 1983, The effect of the field on TBE magnetically structured catalyst layer in ammonia synthesis under pressure. Commrrn. Dept. Chem. 16, 206-213.